Doesn't this "explanation" just shift the question to what is stiffness? Like it refactored the question but didn't actually explain it.
Previously, we had statement "the weak force is short range". In order to explain it, we had to invent a new concept "stiffness" that is treated as a primitive and not explained in terms of other easy primitives, and then we get to "accurately" say that the weak force is short due to stiffness.
I grant the OP that stiffness might be hard to explain, but then why not just say "the weak force is short range -- and just take that as an axiom for now".
I think it's a big improvement. Stiffness is something you can picture directly, so the data -> conclusions inference "stiffness" -> "mass and short range" follows directly from the facts you know and your model of what they mean. Whereas "particles have mass" -> "short range" requires someone also telling you how the inference step (the ->) works, and you just memorize this as a fact: "somebody told me that mass implies short range". You can't do anything with that (without unpacking it into the math), and it's much harder to pattern-match to other situations, especially non-physical ones.
It seems to me like the right criteria for a good model is:
* there are as few non-intuitable inferences as possible, so most conclusions can be derived from a small amount of knowledge
* and of course, inferences you make with your intuition should not be wrong
(I suppose any time you approximate a model with a simpler one---such as the underlying math with a series of atomic notions, as in this case---you have done some simplification and now you might make wrong inferences. But a lot of the wrongness can be "controlled" with just a few more atoms. For instance "you can divide two numbers, unless the denominator is zero" is such a control: division is intuitive, but there's one special case, so you memorize the general rule plus the case, and that's still a good foundation for doing inference with)
Intuition does not work in quantum mechanics. Intuition is based on observations at your scale, and this breaks dramatically at quantum levels. So this is not a good criterium.
That's false. Intuition does work in quantum mechanics, if you do the work to build up a good intuition for quantum mechanics. Which means exactly what I'm talking about: building your intuition on models that give true results in the situation, and which allow you to combine and remix atomic ideas in useful ways.
Unfortunately the version of QM that is taught in textbooks is not especially useful for figuring out what the intuition is. I have my own model that I've concocted that does a much better job, but there are still plenty of things I don't understand well (having not done, like, a graduate degree in it).
I have a PhD in physics, which does not say much apart from the fact that I had to think about this a lot. My PhD was in particle physics.
What I learned over the years is that, unfortunately, at some point you rely on maths. You solve equations, make predictions, and compare this to measurements. Uf they match your model (conveyed through equations) is "good for now"
The problem is that a lot of what you mathematically witness, then measure at macro scales (you do not get to measure quantum effects at their scale, only their effects on the apparatus) does not make sense at our scale.
A particle appearing for a shirt moment from nothing, interacting with another particle and vanishing, WTF?
A particle with energy X hitting a "wall" with energy Y > X and going through? WTF?
Single particles interacting with each other? Another WTF
QM is full of surprises that sound cool when presented with enthusiasm and simple words, or used in MARVEL movies but they are as intuitive for typical people as cosmic travel for Neanderthals . Sure you can handwave your way through them but how does that work with a cave and wall paintings - which is what they would witness on an everyday basis.
Well, I don't agree. Maybe you are talking about how people's intuition initially breaks on the double-split experiment, or spinors, or whatever else? But I'm not talking about broken macroscopic intuition failing on quantum systems. Of course that doesn't work. There is a separate "quantum" intuition that you get over time which lets you make true inferences. Surely you have a bunch of it if you've got a PhD in this stuff.
Things like: if you think of particles as blobs of mass and charge, you get the wrong answers; if you think of them as interfering waves then you start to get right answers. If you think of them as interfering light waves, you get the right answer for a while until you hit a situation where spin=1 gives the wrong answer, or m≠0 means the transverse component is nonzero, so you fix your intuition on that and get better answers. If you think of particle-waves as discrete atomic objects you can't intuit how different particles can be created in scattering; if you think of them as a label given to a particular vector which can be decomposed as a sum of other vectors which interact differently with different fields then you can see how particle creation/annihilation works.
Etc. There certainly are models you can construct in your mind that make this stuff start to make sense. I don't have them all, but I'm working on it. Mindlessly doing math might work for homework problems but it's not enough for actually explaining anything; you need some mental picture of what's going on as well. But the math is always there to make your intuitions concrete and keep them grounded in reality.
Look, physics is about discoveries and explanations. If your model explains everything we have measured then great -- publish it and you will get proper recognition.
I do not know your theory so I cannot comment on it, but when I was in academia I received quite a lot of these theories and they were breaking down rather quickly.
Physicists are always interested in new things but what you present must make sense and - most importantly - explain things and agree with measurements. If suddenly you end up with incorrect values it means the model is wrong. It may be completely wrong or maybe it needs adjustments.
The best way to send your message to the world is to publish.
Besides the fact that stiffness shows up as a term in the equations, stiffness is a concept that can be demonstrated via analogy with a rubber sheet, and so lends itself to a somewhat more intuitive understanding.
Also, the math section demonstrated how stiffness produces both the short-range effect and the massive particles, so instead of just handwaving "massive particles is somehow related to the short range" the stiffness provides a clear answer as to why that's the case.
If you read far enough into the math-y explanations, stiffness is a quantity in the equations. That makes it more than a hand waving explanation in my book.
In addition to what the sibling comments have said, the "axiom" is actually the term in the equations. That is, fundamentally, where this all comes from. "Stiffness" is just a word coined to help describe the behavior that arises from a term like this. Everything flows from having that piece in the math, so if you start there and with nothing else, you can reinvent everything else in the article. (Though it will take you a while.)
You might also ask where that term comes from. It really is "axiomatic": there is no a priori explanation for why anything like that should be in the equations. They just work out if you do that. Finding a good explanation for why things have to be this way and not that way is nothing more and nothing less than the search for the infamous Theory of Everything.
This is often I think a really unsatisfying thing about physics. Usually the qualitative descriptions don't quite make sense if you think very hard about them- and if you dig deeper it's often just "we found some math that fits our experimental data" - and ultimately that is as much as we know, and most attempts at explaining it conceptually are conjecture at best.
When I was a physics undergrad, most of my professors were fans of the "shut up and calculate" interpretation of quantum mechanics.
Ultimately, this is probably just a symptom of still not having yet discovered some really important stuff.
As a rule, I think physics should be expected to make less sense the further it gets from the human scale. It's not because it's inherently more complex, it's because we benefit from millions of years of brains evolving to understand what we can see and touch.
The universe does not owe us explainability in terms of everyday intuition.
You don't just "find some math that fits the data" the way you would mechanically tune the parameters of a given mathematical model to fit empirical data.
Indeed finding a mathematical formulation that seems to describe a corner of reality with any fidelity is such an extraordinary thing that physicists have always puzzled about why it is even possible!
Now it turns out that these mathematical inventions "work" even when our intuition (built on experiences around human scale) cannot quite grasp them. This is the case both in the realms of the very small (quantum) and very big (relativity).
This doesnt mean that at some point we might not find deeper mathematical abstractions that "work better" (e.g., this was the string theory ambition) but the practical result would still be every bit "shut up and calculate".
This is far from the truth in particle physics. The symmetries we've found there (together with the Lorentz symmetry from special relativity) guides and constrains the math very strongly, to the degree that it allows you to predict the photon and the other force-carrying particles, and it even allowed predicting the existence and mass of the weak force carriers (discussed in the article) along with the Higgs mechanism that gives masses to them and most of the other particles. This is certainly a triumph of the Standard Model.
There are limits to how much you can do though, I mean at some point it's going to be "just math that fits reality". If you try to enumerate the number of mechanisms and realities that could give a decent enough diversity of composition that life can arise in some form, there's going to be more than our universe possible.
> When I was a physics undergrad, most of my professors were fans of the "shut up and calculate" interpretation of quantum mechanics.
Well, you build "intuition" via "experience"--generally lots of experience to get small amounts of intuition.
> Usually the qualitative descriptions don't quite make sense if you think very hard about them- and if you dig deeper it's often just "we found some math that fits our experimental data"
Well, the math needs to fit the data and have predictive power. That "predictive" side is really important and is what sets "science" apart from everything else.
> Ultimately, this is probably just a symptom of still not having yet discovered some really important stuff.
Sure. But wouldn't the world be incredibly boring if we had it all figured out?
In my gravity simulations, on my YouTube, i found the short weak force distance was the same needed to avoid opposite charges from gaining so much speed that the next iteration's position wouldn't slow the electron down after passing the proton!
I think its more than "we just found some math that fits the data" in the sense that its not just a case of adding some terms to match an observed curve - for example like with Rayleigh-Jeans' law vs Wein's Approximation of blackbody radiation and eventually Max Planck's solution by quantizing energy to the curve match experiment, without actually having anything else to say about it.
Spiritually it feels more like what happened later, when people took the idea of quantized energy seriously and began finding ways to make it a theoretically consistent theory which also required a radical new approach of disregarding old intuitive assumptions about the way the most fundamental things worked solely to obey a new abstract, esoteric, purely theoretical framework (an approach which was sometimes controversial especially with experimentalists).
But of course this new theory of quantum mechanics turned out to be immensely successful in totally unprecedented ways, in a manner similar to Relativity and it's "theory first" origin with trying to ensure mathematical consistency of Maxwell's equations and disregarding anything else in the way (and eventually with Einstein's decade long quest to find a totally covariant general theory that folded gravity into the mix).
With physics the more I dug into "why" it was rarely the case that it was "just because", the justification was nearly always some abstract piece of math that I wasn't equipped to understand at the time but was richly rewarded later on when I spent the time studying in order to finally appreciate it.
The first time I solved Schrodinger Equation for a hydrogen atom, I couldn't see why anyone could've bothered to try discovering how to untangle such a mess of a differential equation with a thousand stubborn terms and strange substitutions (ylm??) and spherical coordinate transformations - all for a solution I had zero intuition or interest in. After I had a better grasp of the duality between those square integrable complex functions and abstract vector spaces I found classical QM elegant in an way I wasn't able to see before. When basic Lie theory and representations was drilled into my head and I had answered a hundred questions about different matrix representations of the SU(n) and S0(3) groups and their algebras and how they were related, it finally clicked how naturally those ylm angular momentum things I saw before actually arose. It was spooky how group theory had manifested in something as ubiquitous and tangible as the structure of the periodic table. After drudging through the derivation of QFT for the first time, when I finally understood what was meant by "all particles and fields that exist are nothing more than representations of the Poincare-Spacetime Algebra", I felt like Neo when everything turned into strings of code. And there's no point describing what it was like when Einstein's field equations clicked, before then I never really got what people meant by the beauty of mathematics or physics.
I guess its not really the answer "why" things are, but the way our current theories basically constrain nearly everything we see (at least from the bottom up) from a handful of axioms and cherry-picked coupling constants, the rest warped into shape and set in stone only by the self-consistency of mathematics, I feel like that's more of a "why" than I would've ever assumed answerable, and maybe more of one than I deserve.
I only got as far as "solved Schrodinger equation for a hydrogen atom" and never got to the next stage you describe with physics.
In a sense, I think your explanation is consistent with mine, but with the deeper context of math being a language itself, and the math itself being a more satisfactory explanation to someone with a greater intuition for what the equations actually mean. I can pump through all of the major equations in physics and explain almost anything I want with them, but it always just feels like rote application of algebra rules to completely arbitrary seeming formulas- nothing like what you describe. Frankly, I think I was more interested in girls than studying when I was a physics student decades ago, and I could probably get a lot more out of it revisiting this stuff now.
However, I do still think there is a real chance that we are missing something big that would fit all of these pieces together with qualitative explanations. Personally, I think Julian Barbour is likely on the right path with his timeless physics, but if so it will need a lot more research and development.
Not a physicist, but in classical mechanics stiffness is just the proportionality of some restorative force (ie the extent to which something tries to bounce back when you push it). It definitely would be overkill to make it an axiom.
So say you have a spring if you compress it, it pushes because it wants to go back to its natural length and likewise if you stretch it there is a restorative force in the opposite direction. The constant of proportionality of that force (in N/m) is the stiffness of the spring, and the force from the spring[1] is something like F=-k x with x being the position measured from the natural length of the spring and k being the stiffness. So not knowing anything about electromagnetism I read this and thought about fields having a similar property like when you have two magnets and you push like poles towards each other, the magnetic field creates a restorative force pushing them apart and the constant is presumably the stiffness of the field.
But obviously I’m missing a piece somewhere because as you can see the force of a spring is proportional to distance whereas here we’re talking about something which is short-range compared to gravity and gravity falls off with the square of distance so it has to decay more rapidly than that.
Edit to add: in TFA, the author defines stiffness as follows:
For a field, what I mean by “stiffness” is crudely this: if a field is stiff, then making its value non-zero requires more energy than if the field is not stiff.
So this coincides with the idea of restorative force of something like a spring and is presumably why he's using this word.
[1] Hooke’s law says the force is actually H = k (x-l)ŝ where k is stiffness, l is the natural length of the spring and ŝ is a unit vector that points from the end you’re talking about back towards the centre of the spring.
A simple, classical case where "stiff" fields arise is electrostatic plasma physics.
Electrons are tiny and nuclei are huge, so you have a bunch of mobile charge carriers which cost energy to displace to an equilibrium position away from their immobile "homes". A collection of test charges moving "slowly" through the plasma (not inducing B field, electrons have time to reach equilibrium positions) will produce exponentially decaying potentials like in the article. If you want to read more, this concept is called "Debye Screening"
Anyway, this might be a more helpful approach than trying to imagine a spring - a "stiff" field equation is an equation for a field in a medium that polarizes to oppose it, and you can think of space as polarizing to oppose the existence of a Z Boson in a way that it doesn't polarize to oppose the existence of a photon.
'Stiffness' is a better concept because it can be used to explain behavior of all forces of finite and infinite range and why force mediators can have mass or not.
If you need to assume some axiomatic concept it's better to assume one that can used to derive a lot of what is observed.
What makes me skeptical here is that the author claims that fields have a property that is necessary to explain this, and yet physicists have not given that property a name, so he has to invent one (“stiffness”). If the quantity appears in equations, I find it hard to believe that it was never given a name. Can anyone in the field of physics elucidate?
The author isn't inventing anything. He's just dumbing it down in an extreme way so that non-physicists could have the faintest hope of understanding it. Wich seems odd, because if you actually want to understand any of this you should prepare to spend two or three years in university level math classes first. The truth is that in reality all this is actually a lot more complex. In the Higgs field (or any simple scalar field for that matter) for example, there is a free parameter that we could immediately identify as "mass" in the way described in the article. But weirdly enough, this is not the mass of the Higgs boson (because of some complicated shenanigans). Even more counterintuitive, fermionic (aka matter) fields and massive bosonic fields (i.e. the W and Z bosons mentioned in the article) in the Standard Model don't have any mass term by themselves at all. They only get something that looks (and behaves) like a mass term from their coupling to the Higgs field. So it's the "stiffness" of the Higgs field (highly oversimplified) that gives rise to the "stiffness" of the other fields through complex interactions governed by symmetries. And to put it to the extreme, the physical mass you can measaure in a laboratory is something that depends on the energy scale at which you perform your experiments. So even if you did years of math and took an intro to QFT class and finally think you begin to understand all this, Renormalization Group Theory comes in kicks you back down. If you go really deep, you'll run into issues like Landau Poles and Quantum Triviality and the very nature of what perturbation theory can tell us about reality after all. In the end you will be two thirds through grad school by the time you can comfortably discuss any of this. The origin of mass is a really convoluted construct and these low-level discussions of it will always paint a tainted picture. If you want the truth, you can only trust the math.
I think perhaps the 'maths' at the bottom is a bit of a retelling of the Yukawa potential which you can get in a "relatively understandable" way from the Klein-Gordon equation. However, the KG equation is very very wrong!
Perhaps an approach trying to actually explain the Feynman propagators would be more helpful? Either way, I agree that if someone wanted to understand this all properly it requires a university education + years of postgrad exposure to the delights of QED / electroweak theory. If anyone here wants a relatively understandable deep dive, my favourite books are Quantum Field Theory for the Gifted Amateur [aka graduate student] by Stephen Blundell [who taught me] and Tom Lancester [his former graduate student], and also Quarks and Leptons by Halzel and Martin. It is not a short road.
The Yukawa potential is also just a more "classical" limit of an inherently quantum mechanical process. Sure you can explain things with it and even do some practical calculations, but if you plan on going to the bottom of it it'll always fail. If you want to explain Feynman propagators correctly you basically have to explain so many other things first, you might as well write a whole book. And even then you're trapped in the confines of perturbation theory, which is only a tiny window into a much bigger world. I really don't think it is possible to convey these things in a way that is both accurate (in the sense that it won't lead to misunderstandings) and simple enough so that people without some hefty prerequisites can truly understand it. I wish it were different. Because this is causing a growing rift between scientists and the normal population.
Ie: “I can’t explain it in terms of something else you’re more familiar with because I don’t understand it terms of anything else you’re more familiar with.”
Yet Einstein said something like "If you can't explain it simply, you don't understand it well enough". So maybe Feynman didn't understand it "well enough"
That was a pretty classical point of view. Quantum mechanics has gone so deep by now, there simply is nothing in a layperson's world that could accurately represent what is really going on. This was not a limit of Feynman, it's a limit of humans.
I sometimes listen to Jordan Peterson's podcasts (and have read the "12 rules..").
I understand the dude. Then I found on YT a speech/discussion he had with/for psychologists, and they were still speaking English, and I couldn't understand half of what they were saying.
Now, to my 'craft' (GRC). I lately catch myself speaking like Peter Thiel, taking 20-30 second 'silences', build in my mind what I want to say, 'translate it' to simple(r) English, and then slowly say it out loud to make sure I pave the path with mental & verbal stepping stones without using any jargon.
I very well understand what I want to say, but the gap between in the knowledge and the use of language puts the onus to the explainer.
The biggest glaring issue with it (eg in the form (square^2+m^2)\psi=0) is that it is a manifestly Lorentz invariant equation in which particle number is conserved (which is highly unlikely for any relativistic interaction). I know that you can extend it into a scalar field theory proper, quantize it, and sidestep around those issues (and use it as a model in cmp!), but the bigger problem I think is that you really need spin -- and ideally all other interactions...
EDIT: yes I tried pasting it in to Gemini, 4o, and Claude. Only Claude was able to zero-shot create the latex and an html wrapper that renders it, and open the html preview on iOS. It worked great.
At some point our understanding of fundamental reality will be limited not by how much the physicists have uncovered but by how many years of university it would take to explain it. In the end each of us only has one lifetime.
He addresses this in the comments. The term that corresponds to "stiffness" normally just gets called "mass", since that is how it shows up in experiments.
Roughly put:
- A particle is a "minimum stretching" of a field.
- The "stiffness" corresponds to the energy-per-stretch-amount of the field (analogous to the stiffness of a spring).
- So the particle's mass = (minimum stretch "distance") * stiffness ~ stiffness
The author's point is that you don't need to invoke virtual particles or any quantum weirdness to make this work. All you need is the notion of stiffness, and the mass of the associated particle and the limited range of the force both drop out of the math for the same reasons.
This is it. Typically in a QFT lecture, you'd include a "mass term" (in the article: stiffness term) in your field equations, and later show that it indeed gives mass to the excitations of this field (i.e. particles). So you temporarily have two definitions of "mass" and later show that they agree.
For this discussion it makes sense call the "mass" of a field "stiffness" instead, since it's not known a priori that it corresponds to particle mass.
I think mathematically "stiffness" is well-defined, but the interpretation varies substantially depending on the context. For example, in chemistry or plasma physics, one writes down Poisson's equation for a collection of positive and negatives charges in thermal equilibrium and linearise the Boltzmann factors. The result is called the Debye–Hückel equation and is identical to the one shown in the "with math" section.
Here the "stiffness" is interpreted as the effect of nearby charges "screening" a perturbing "bare" charge of the opposite sign. If you solve the equation you find the that effective electric field produced by the bare charge is like that of the usual point charge but with a factor exp(-r/λ). So, the effect of the "stiffness" term is reducing the range of the electric interactions to λ, which is called the Debye length. see this illustration [1].
Interestingly, if you look at EM waves propagating in this kind of system, you find some satifying the dispersion relation ω² = k²c² + ω_p² [2].
With the usual interpretation E=ℏω, p=ℏk you get E² = (pc)² + (mc²)², so in a sense the screening is resulting in "photons" gaining a mass.
> The term that corresponds to "stiffness" normally just gets called "mass", since that is how it shows up in experiments.
Then why not just call it "mass"? That's what it is. How is the notion of "stiffness" any better than the notion of "mass"? The author never explains this that I can see.
I think stiffness is an ok term if your aim is to maintain a field centric mode of thinking. Mass as a term is particle-centric.
It seems these minimum-stretching could also be thought of as a “wrinkle”. It’s a permanent deformation of the field itself that we give the name to, and thus “instantiate” the particle.
> I think stiffness is an ok term if your aim is to maintain a field centric mode of thinking.
"Stiffness" to me isn't a field term or a particle term; it's a condensed matter term. In other words, it's a name for a property of substances that is not fundamental; it's emergent from other underlying physics, which for convenience we don't always want to delve into in detail, so we package it all up into an emergent number and call it "stiffness".
On this view, "stiffness" is a worse term than "mass", which does have a fundamental meaning (see below).
> Mass as a term is particle-centric.
Not to a quantum field theorist. :-) "Mass" is a field term in that context; you will see explicit references to "massless fields" and "massive fields" all over the literature.
Do you also object quarks and gluons having "color" charge?
Mass is a bad term because it's loaded with so many meanings and equivalences already. But also in the kindest and most accurate reading here it still doesn't naturally lead to explaining why some forces have limited range the way that term "stiffness" does, which was the whole point of the article.
> Do you also object quarks and gluons having "color" charge?
No, because no physicist tries to argue that "color" is an appropriate term because of some physical interpretation that involves actual physical properties of colored objects.
This author, OTOH, appears to be arguing that "stiffness" is a better term than "mass" because of some physical interpretation that involves actual physical properties of stiff objects. An analogy with quarks would be to argue that "color charge" is an appropriate term because red, green, and blue quarks somehow have actual properties associated with those colors.
> it still doesn't naturally lead to explaining why some forces have limited range the way that term "stiffness" does
I'm not sure the explanation of that in terms of "stiffness" is any better, because in the setting where the term "stiffness" comes from, there is no such thing as what this author calls a "floppy" object. So his explanation only "explains" the behavior of forces associated with massive gauge bosons at the price of throwing away an explanation of the behavior of forces associated with massless gauge bosons.
> An analogy with quarks would be to argue that "color charge" is an appropriate term because red, green, and blue quarks somehow have actual properties associated with those colors.
They do, there are 3 and they add up like primary colors, so all 3 make stuff colorless. That's why those names were chosen. Because of similarities with color we know from color theory.
> there is no such thing as what this author calls a "floppy" object
It's easy enough to imagine as an unattached rope so pulling at one spot affects the whole rope because nothing holds remote parts of the rope in place. The only way for a wrinkle to exist in such rope is to travel at "rope speed". If there's stiffness then a wrinkle can travel at any speed or none at all, because it can oscilate without moving, which is rest energy (mass). So it explains all bosons.
What's great with this analogy is that it coveys that both mass and force range arise from a single term of the equation. There's really no causal connection between them. Neither limited range causes mass nor mass causes limited range. They both come from a single intrinsic field "quality".
There's also no anti-blue color in color theory but it's easy to imagine it so you can intuitively understand its behavior.
> It's easy enough to imagine as an unattached rope so pulling at one spot affects the whole rope
Not instantly; the force you apply at one point still has to be transmitted through the rope. And if the rope is unattached and not taut, it won't transmit force well at all, and you have very limited control over how the rest of the rope will move when you pull on one part.
I don't see how any of this is a useful analogy to how massless gauge bosons work in forces like electromagnetism.
It does have a name, it's called "coupling." A spring (to physicists all linkages are springs :-) ) couples a pair of train cars, and a coupling constant attaches massive fields to the higgs field.
as an electrical engineer I think any other form of coupling as a capacitance, i.e. electric field and rarely as inductive coupling (magbetic field). funny world.
The longer I read the article, the more "stiffness" feels like mass. In Lagrangians, the quantity saying how stiff it is is precisely the mass term, vide https://en.wikipedia.org/wiki/Scalar_field_theory.
At the same time, the author does not give any different definition; he says it's "stiffness". In the comment, he writes:
> The use of a notion of “stiffness” as a way to describe what’s going on is indeed my personal invention. Physicists usually just call the (S^2 phi) part of the equation a “mass term.” But that’s jargon, since this thing doesn’t give mass to the field; it just gives mass to its particles, which exist only in the context of quantum physics. The word “mass term” also doesn’t explain what’s going on physically. My view is that “stiffness” conveys the basic physical sense of what is happening to the field, an effect it has even without accounting for quantum physics.
So well, it is mass. Maybe not mass one may think about (in physics, especially Quantum Field Theory, there are a few notions of mass, which are not the same as what we set on a scale), but I feel the author is overzealous about not calling it "mass (term)".
So, I am not convinced unless the author shows a way to have massive particles carrying a long-term interaction (AFAIK, not possible) or massless particles giving rise to short-term interactions (here, I don't know QFT enough so that it might be possible). But the burden of proof is on the inventor of the new term.
> If the quantity appears in equations, I find it hard to believe that it was never given a name.
It does have a name: mass!
What I'm skeptical of is that this "stiffness" is somehow logically or conceptually prior to mass. Looking at the math, it just is mass. The term in the equation that this author calls the "stiffness" term is usually just called the "mass" term.
But it's not really just "mass", it's "characteristic mass of stationary minimal possible wrinkle in a given field". And it doesn't sound like it has anything to do with force range, and "stiffness" does.
> it's not really just "mass", it's "characteristic mass of stationary minimal possible wrinkle in a given field"
If you are referring to the claim in the article that goes along with the equation E = m c^2, that claim is the author's personal interpretation, which I don't buy. The mass appears in the dispersion relation whether the particle is at rest or not. "Rest mass" is an outdated term for it; a better term is "invariant mass", i.e., it's the invariant associated with the particle's 4-momentum. Or, in field terms, it's the invariant associated with the dispersion relation of the field and the waves it generates.
It's nonsense. The fact that the particle is massive is a direct cause of the fact that the interactions are short ranged.
The nuance is this: Naturally, in a field theory the word "particle" is ill-defined, thus the only true statement one can make is that: the propagator/green function of the field contains poles at +-m, which sort of hints at what he means by stiffness.
As a result of this pole, any perturbations of the field have an exponential decaying effect. But the pole is the mass, by definition.
The real interesting question is why Z and W bosons are massive, which have to do with the higgs mechanism. I.e., prior to symmetry breaking the fields are massless, but by interacting with the Higgs, the vacuum expectation value of the two point function of the field changes, thus granting it a mass.
In sum, whoever wrote this is a bit confused and just doesn't have a lot of exposure to QFT
Actually upon further reading I realize that the author actually goes deeper into what I thought, so it's not nonsense, it's actually a simplified version of what I tried to write.
But I don't particularly like the whole "mass vs not mass" discussion as it's pointless
One thing I'm not clear on when watching his videos is whether what he's describing is an established scientific interpretation, or his own thoughts as someone who has extensive knowledge on optical engineering (vs theory).
Very enjoyable and thought provoking stuff though!
That's great. Thanks. When you start watching it you think, it will be too long, but it gets better and better. Everything goes back to Einstein. YARH!
Yet another rabbit hole! It's amazing we have any time left to do anything after reading HN.
>NOTICE THERE IS NO QUANTUM PHYSICS IN THIS DISCUSSION! The short range of the field is a “classical” effect; i.e., it can be understood without any knowledge of the underlying role of quantum physics in our universe. It arises straightforwardly from ordinary field concepts and an ordinary differential equation. Nothing uncertain about it.
It's interesting to me how fuzzy the definition of quantum physics is. For example, I've seen the description of particles as described by a wave function (e.g. electron position and momentum in an atom) labeled as a quantum phenomenon, but have also heard it, as in this quote, as classical, since it's defined by a differential equation; a "classical" wave. In that view, quantum only enters the model when modelling exchange effects, spin, fermion states etc.
With the former definition, as in the article, you see descriptions of the wave nature of matter, replete with Planck's constant, complex wave function representations etc described as classical.
If we wanted to model the universe as a set of equations or a cellular automaton, how complex would that program be?
Could a competent software engineer, even without knowing the fundamental origins of things like particle masses or the fine-structure constant, capture all known fundamental interactions in code?
I guess I'm trying to figure out the complexity of the task of universe creation, assuming the necessary computational power exists. For example, could it be a computer science high school project for the folks in the parent universe (simulation hypothesis). I know that's a tough question :)
I'm surprised that more sibling comments aren't covering the lack of a unified theory here. Currently, our best understanding of gravity (general relativity) and our best understanding of everything else (electromagnetism, quantum mechanics, strong/weak force via the standard model) aren't consistent. They have assumptions and conclusions that contradict each other. It is very difficult to investigate these contradictions closely because the interesting parts of GR show up only in very massive objects (stars, black holes) and the interesting parts of everything else show up in the tiniest things (subatomic particles, photons).
So we don't have a set of equations that we could expect to model the whole universe in any meaningful way.
They definitely wouldn’t work because we have strong evidence that relativity is a more accurate theory and significant evidence that either gravity does not obey an inverse square law or our estimation of the distribution or nature of dark matter is incorrect.
Our present best guess is that cellular automatons would be an explosively difficult way to simulate the universe because BQP (the class of problems that can be related to simulating a quantum system for polynomial time) is probably not contained in P (the class of problems Turing machines can solve in polynomial time).
You can expand that Lagrangian out to look more complex, but that's just a matter of notation rather than a real illustration of its complexity. There's no need to treat all of the quarks as different terms when you can compress them into a single matrix.
General relativity adds one more equation, in a matrix notation.
And that's almost everything. That's the whole model of the universe. It just so happens that there are a few domains where the two parts cause conflicts, but they occur only under insanely extreme circumstances (points within black holes, the universe at less than 10^-43 seconds, etc.)
These all rely on real numbers, so there's no computational complexity to talk about. Anything you represent in a computer is an approximation.
It's conceivable that there is some version out there that doesn't rely on real numbers, and could be computed with integers in a Turing machine. It need not have high computational complexity; there's no need for it to be anything other than linear. But it would be linear in an insane number of terms, and computationally intractable.
Yes, and it's exactly those "smart definitions" that are the Standard Model. The whole goal is to produce even smarter definitions, including showing that as much as possible of it couldn't be any other way, preferably.
Nah it really is simpler than that, that picture has exploded the summations to make it look complicated. Although it is strangely hard to find the compressed version written down anywhere...
the thing about Lagrangians is that they compose systems by adding terms together: L_AB = L_A + L_B if A and B don't interact. Each field acts like an independent system, plus some interaction terms if the fields interact. So most of the time, e.g. on Wikipedia[0], people write down the terms in little groups. But still, note on the Wikipedia page that there are not that many terms in the Lagrangian section, due to the internal summations.
I can't help but wonder if, under extreme conditions, the universe has some sort of naturally occurring floating-point error conditions, where precision is naturally eroded and weird things can occur.
That would occur if a naked singularity could exist. If black holes have a singularity then you could remove the event horizon. In general relativity, the mathematical condition for the existence of a black hole with an event horizon is simple. It is given by the following inequality: M^2 > (J/M)^2 + Q^2, where M is the mass of the black hole, J is its angular momentum and Q is its charge.
Getting rid of the event horizon is simply a question of increasing the angular momentum and/or charge of this object until the inequality is reversed. When that happens the event horizon disappears and the exotic object beneath emerges.
I doubt it. Even the simplest physical system requires a truly insane number of basic operations. Practically everything is integrals-over-infinity. If there were implemented in a floating-point system, you'd need umpteen gazillion bits to avoid flagrant errors from happening all the time.
It's not impossible that the universe is somehow implemented in an "umpteen gazillion bits, but not more" system, but it strikes me as a lot more likely that it really is just a real-number calculation.
That could very well be what the quantum uncertainty principal is, floating point non deterministic errors. It also could just be drawing comparisons among different problem domains.
The QUP is indeed what allows to quantize continuous equations with h, and once they have been turned into integers like this we can then meaningfully calculate our lack of information (aka 'entropy').
The trick is (as the sibling comments explain) that it involves an exponential number of calculations, so it's extremely slow unless you are interested only in very small systems.
Going more technical, the problem with systems with the strong force is that they are too difficult to calculate, so the only method to get results is to add a fake lattice and try solving the system there. It works better than expected and it includes all the forces we know, well except gravity , and it includes the fake grid. So it's only an approximation.
> Could a competent software engineer, even without knowing the fundamental origins of things like particle masses or the fine-structure constant, capture all known fundamental interactions in code?
Nobody know where that numbers come from, so they are just like 20 or 30 numbers in the header of the file. There is some research to try to reduce the number, but I nobody knows if it's possible.
Stephen Wolfram has been taking a stab at it. Researching fundamental physics via computational exploration is how I'd put it. https://www.wolframphysics.org/
He is basically a crackpot. Any attempt at fundamental physics that doesn't take quantum mechanics into account is.... uhm.... how to put this.... 'questionable'.
I'm not even able to hold a candle to Wolfram intellectually- the guy is a universe away from me in that regard. But: Given a cursory look at his wiki page and Cosma Shalizi's review of his 2002 book on cellular automata [1], I feel fairly comfortable saying that it seems like he fell in the logician's trap of assuming that everything is computable [2]:
>There’s a whole way of thinking about the world using the idea of computation. And it’s very powerful, and fundamental. Maybe even more fundamental than physics can ever be.
>Yes, there is undecidability in mathematics, as we’ve known since Gödel’s theorem. But the mathematics that mathematicians usually work on is basically set up not to run into it. But just being “plucked from the computational universe”, my cellular automata don’t get to avoid it.
I definitely wouldn't call him a crackpot, but he does seem to be spinning in a philosophical rut.
I like his way of thinking (and I would, because I write code for a living), but I can't shake the feeling that his physics hypotheses are flawed and are destined to bear no fruit.
Someone seems to say something demeaning like that about him whenever he comes up, and I don't really know why. Which is fine, maybe it's a subjective thing. For what it's worth, the few times I read something of his, I loved it.
It's a complex issue. He is obviously extremely intelligent and at least a decent business man. If you've never used Wolfram Mathematica before, I implore you to pick up a raspberry pi and play with the educational version. It's nothing short of magical in many ways. I still prefer Python in a lot of ways (least of all with Python being free/open), but Mathematica notebooks are nuts. You can do anything from calculus to charts, geographic visualizations, neural networks, NLP, audio processing, optimization, text processing, time series analysis, matrices, and a bazillion other things with a single command or by chaining them together. It has its warts, but is very polished.
He also did some important early work on cellular automata if iirc.
Then he wrote "A New Kind of Science", which reads like an ego trip and was not received well by the community (it is a massive tome that could have been summarized with a much smaller book). He also tried to claim discoveries from one of his workers due to some NDA shenanigans (or something along these lines iirc). The latter doesn't make him a crank, just a massive egotist, which is a trait nearly all cranks have. Sabine Hossenfelder did a video on him and how he only publishes in his own made up journals and generally doesn't use the process used by all other scientists. I think a lot believe where there is smoke, there is fire. To his credit, she also mentioned that some physicists gave him some critical feedback and he did then go and spend a bunch of time addressing the flaws they found.
Well, one can love playing chess and that is all fine and good and so on but if someone says that chess is the fundamental theory of the universe, how much sense does that make? There might even even be truth in that statement, who could possibly know? All we can be quite certain about is that to actually demonstrate the hypothetical truth of the statement 'chess is the fundamental theory of the universe' some number, presumably larger than 5, of nobel price level of physics discoveries need to take place.
Wolfram's claim is that Cellukar Automata can provide as good or better mathematical model of the universe than current current theories, by commonly appreciated metrics such as "pasimony of theory" (Occam's Razor). He's not making claims about metaphysical truth.
I think Wolfram might be one of the 1000 smartest people alive and he has accomplished many great things and is very good at math. But it really seems he wants to be thought of in the same was as Newton and Einstein. So he tries to find some new ultra fundamental theory to achieve this. His book A New Kind of Science failed so now he is trying with the Wolfram Physics Project.
I sympathize with your opinion of him being a crackpot but he is also a genius and the idea is that the graphs in his theory are more fundamental than quantum mechanics and it would emerge from them.
The universe is already modeled that way. Differential equations are a kind of continuous time and space version of cellular automata, where the next state at a point is determined by the infinitesimally neighboring states.
I do wonder if you'd want to implement a sort of 3D game engine that simulates the entire universe, if somehow the weird stuff quantum physics and general relativity do (like the planck limit, the lightspeed limit, discretization, the 2D holographic bound on amount of stuff in 3D volumes, the not having an actual value til measured, the not being able to know momentum and speed at the same time, the edge of observable universe, ...) will turn out to be essential optimizations of this engine that make this possible.
Many of the quantum and general relativity behaviors seem to be some kind of limits (compared to a newtonian universe where you can go arbitrarily small/big/fast/far). Except quantum computing, that one's unlocking even more computation instead so is the opposite of a limit and making it harder rather than easier to simulate...
Ugh, I just listed things from the top of my head, no rigorous correct physics!
I'd be interested to know where those so many other people who feel that would be an optimization are, because I don't often see opinions like this at all, only either rigorous physicists posting equations and papers, or people not knowing anything about it at all to even philosophize about it.
How complex? I'm no physicist nor an expert at this, but AFAIK we aren't really capable of simulating even a single electron at the quantum scale right now? Correct me if I'm wrong.
We can simulate much more than that, even at the quantum scale. What we cannot do is calculate things analytically, so we only have approximations, but for simulation that’s more than enough.
Less ambitiously, how small and clear could you make a program for QED calculations? Where you're going for code that can be clear to someone educated with only undergrad physics, with effort, to help explain what the theory even is -- not for usefulness to career physicists.
Maybe still too ambitious, because I haven't heard of such a program.
To be fair, his universe was much simpler than ours. He didn't need a nuclear reactor or particle accelerator to transmute lead into gold in his theory.
Rephrasing what some of the other answers have said, with a decent knowledge of math you could write the program, but you wouldn’t be able to run it in a reasonable time for anything but the most trivial scenarios.
(1) quantum mechanics means that there is not just one state/evolution of the universe. Every possible state/evolution has to be taken into account. Your model is not three-dimensional. It is (NF * NP)-dimensional. NF is the number of fields. NP is the the number of points in space time. So, you want 10 space-time points in a length direction. The universe is four-dimensional so you actually have 10000 space-time points. Now your state space is (10000 * NF)-dimensional. Good luck with that. In fact people try to do such things. I.e., lattice quantum field theory but it is tough.
(2) I am not really sure what the state of the art is but there are problems even with something simple like putting a spin 1/2 particle on a lattice. https://en.wikipedia.org/wiki/Fermion_doubling
(3) Renormalization. If you fancy getting more accuracy by making your lattice spacing smaller, various constants tend to infinity. The physically interesting stuff is the finite part of that. Calculations get progressively less accurate.
To go down this rabbit hole, the deeper question is about the vector in Hilbert space that represents the state of the universe. Is it infinite dimensional?
Yes, but that is not saying very much. Just one single harmonic oscillator already has a state space that is an infinitely dimensional Hilbert space. It is L^2. Now make a tensor product of NF * NP of these already infinitely dimensional Hilbert spaces defined above to get quite a bit more infinite.
> Could a competent software engineer, even without knowing the fundamental origins of things like particle masses or the fine-structure constant, capture all known fundamental interactions in code?
I don't think so.
In classical physics, "all" you have to do is tot up the forces on every particle and you get a differential equation that is pretty easy to numerically work with. Scale is a challenge all of its own, and of course you'd ideally need to learn about all the numerical issues you can run into. But the math behind Runge-Kutta methods isn't that advanced (really, you just need some calculus to even explain what you're doing in the first place), so that's pretty approachable to a smart high schooler.
But when you get to quantum mechanics, it's different. The forces aren't described in a way that's amenable to tot-up-all-the-forces-on-every-particle, which is why you get stuff like https://xkcd.com/1489/ (where the explainer is unable to really explain anything about the strong or weak force). As an arguably competent software engineer, my own attempts to do something like this have always resulted in my just bouncing off the math entirely. And my understanding of the math--as limited as it is--is that some things like gravity just don't work at all with the methods we have at hand to us, despite us working at it for 50 years.
By way of comparison, my understanding is that our best computational models of fundamental forces struggle to model something as complicated as an atom.
The problem is it's upfront that "X thing you learned is wrong" but is then freely introducing a lot of new ideas without grounding why they should be accepted - i.e. from sitting here knowing a little physics, what's the intuition which gets us to field "stiffness"? Stiff fields limit range, okay, but...why do we think those exist?
The article just ends the explanation section and jumps to the maths, but fails to give any indication at all as to why field stiffness is a sensible idea to accept? Where does it come from? Why are non-stiff fields just travelling around a "c", except that we observe "c" to be the speed of light that they travel around?
When we teach people about quantum mechanics and the uncertainty principle even at a pop-sci level, we do do it by pointing to the actual experiments which build the base of evidence, and the logical conflicts which necessitate deeper theory (i.e. you can take that idea, and build a predictive model which works and here's where they did that experiment).
This just...gives no sense at all as to what this stiffness parameter actually is, why it turned up, or why there's what feels like a very coincidental overlap with the Uncertainty principle (i.e. is that intuition wrong because actually the math doesn't work out, is this just a different way of looking at it and there's no absolute source of truth or origin, what's happening?)
In all honesty, this gives a delightful if frightening look into how physicists are thinking amongst themselves. As a (former) particle physicist myself, I can’t remember the number of times an incredulous engineer has confronted me with “the truth” about physics. But you see, for practicing physicists, the models and theories are fluid and actually up for discussion and interpretation, that’s our job after all. The problem is that the official output is declared to be immutable laws of nature, set in formulae and dogmatic conventions.
That said, I agree that he is trading one possible fallacy for another here, but the beauty of the thing is that the “stiffness” explanation is invoking less assumptions than the quantum one - which physicists agree is a “good thing” (Occam’s razor).
There definitely seems to be a modern trend of over complication in physics along with the voodoo-like worship of math. Humbly enough, people have only come to understand the equations for an apple falling out of a tree within the last 500 years, and that necessitated the invention of Calculus.
What's more distressing than the insular knowledge cults of modern physics is the bizarre fixation on unfalsifiable philosophical interpretation.
That just makes it incomprehensible to outsiders when they quibble over the metaphors used to explain the equations that are used to guess what may happen experimentally. (Rather than admitting that any definition is an abstraction and any analogies or metaphors are merely pedagogical tools.)
My kneejerk reaction: Give me the equations. If they are too complicated give me a computer simulation that runs the equations. Now tell me what your experiment is and show me how to plug the numbers so that I may validate the theory.
If I wanted to have people wage war over my mind concerning what I should believe without evidence, I would turn back to religion rather than science.
Anyway, I hope this situation improves in the future. Maybe some virtual particle will appear that better mediates this field (physics).
Having studied undergraduate physics, I think this viewpoint is inverted from the realities of the matter. It is less that the math is complicated and more so these are the relevant tools invented for us to model the experimental results we obtain post discovery/formalization of SR/GR/Quantum experiences. There are computers that can run these simulations but they are infeasible to model large scale processes. That is the reason people are looking for more than numerical solutions to problems, but laws and tools that can simplify modeling large scale emergent behavior that it would be infeasible or unnecessarily complicated to do with numerical simulation. These tools are the more straightforward approach
It's evident and obvious in any of these explanations that the equations and properties of math are taken as true a priori, not grounded on observation (in their invocation).
If I write a partial differential equation that I came up with randomly and ask you to find all the potential solutions that really doesn't tell you anything about the natural world.
I think that's more your interpretation/experience rather than the intention of the tools. Those constants and coefficients are there because the math is describing the shape of the solution based on logic, mathematical object rules, and symmetry/conservation laws and needs to be "grounded" to make them physical.
The Lagrangian is just "conservation of energy" (L = T[kinetic] - V[potential]). There isn't some magic, it's a statement that the energy needs to go somewhere.
Your straw-man belies the underlying issue you are experiencing, you don't just come up with a PDE, you see nature and then you describe ways to conserve counts of things, "energy", "population", whatever. The PDEs describe the exchange between these counts. The accuracy and additional terms are about more accurately representing the counts and conservation of things.
Voodoo worship of math? I am getting a bit tired of that sentiment, especially around string theory.
Math is all you've got to work with, we wouldn't have modern day physics without math.
The issue is that people think they can find some kind of magic shortcut by playing around with abstractions without reference to or grounding in physical observables. That's not a math problem, that's a psychology problem.
I don't think that's what I would say, but if that's what you are anticipating, then I don't think you have a very good take, either. I don't even think we'd resolve our problems with physics if everyone were a mathematician first. However, it will always take many years of training to understand some of the major equations to a sufficient degree.
Once again, my point is that people are trying to take shortcuts with abstractions that are not grounded in reality. That is a matter of self-discipline, of priorities, of putting the cart before the horse. Consider string theories: we have worked out so many ways in which strings can behave, etc. with so many possibilities and permutations. However, we never proved the ground reality for strings, we just ran with a bunch of assumptions and then parameterized them, went meta a bunch of times, and called that a research program.
All of that mathematical sophistication and model-building could have went to, e.g. perfecting QCD, or even in other directions.
Yeah, the whole 'immutability' thing is just a front for the layperson, and that's honestly fine. However it does generate a weird set of expectations and culture shock when you cross that barrier into proper physics and you see people don't consider these things immutable, the best you've got is instrumentalism and functionalist treatment of observables. These worldviews have been a source of too many red herrings for the unprepared.
I agree this doesn't gel well with the pop-science approach.
However, it is actually a similar approach to how De Broglie, Schrodinger, and others originally came up with their equations for quantum behavior - we start with special relativity and consider how a wave _must_ behave if its properties are going to be frame-independent, and follow the math from there. That part is equation (*), and the article leads with a bit of an analogy of how we might build a fully classical implemenation of it in an experiment (strings, possibly attached to a stiff rubber sheet) so we get some everyday intuition into the equation's behavior. So from my point of view, I found it very interesting.
(What the article doesn't really get into is why certain fields might have S=0 and others not, what the intuition for the cause of that is, etc. It also presupposes you have bought into quantum field theory in the first place, and wish to consider the fundamental "wavicles" that would emerge from certain field equations, and that you aren't looking closely at the EM force or spin or any other number of things normally encountered before learning about the weak force).
I had very much the same feeling. Honestly this might be all true, but it's got a vibe I don't like. I did QFT in my PhD and have read plenty of good and bad science exposition, and it doesn't feel right.
I can't point at any outright mistakes, but for example I think the dismissal of the common interpretation of virtual particles in Feynman diagrams is not persuasive. If you think the prevailing view among experts is wrong then the burden of proof is high, perhaps right than you can reach in am article pitched so low, but I don't feel like reading his book.
> This just...gives no sense at all as to what this stiffness parameter actually is, why it turned up, or why there's what feels like a very coincidental overlap with the Uncertainty principle
Because not everyone has the prerequisite math or time/attention to go into quantum field theory for a rather intuitive point about mass and fields.
This reminds me a bit of how high school physics classes are sometimes taught when it comes to thermodynamics and optics. You learn these "formulas" and properties (like harmonics or ideal gas law) because deriving where they come from require 2-3 years of actual undergraduate physics with additional lessons in differential equations and analysis.
> Because not everyone has the prerequisite math or time/attention to go into quantum field theory for a rather intuitive point about mass and fields.
This gets into the problem though: the article is framed as "the Heisenberg explanation is wrong". Okay...then if thats your goal, to explain that without math, you need to do better then "actually it's this other parameter, trust me bro".
As read, I cannot tell if there's something new or different here, or if "stiffness" just wraps up the Heisenberg uncertainty principle neatly so you can approach the problem classically.
The core question coming into the article which I was looking for an answer for is "is the Heisenberg uncertainty principle explanation wrong?" and...it doesn't answer that. Showing that you can model the system a different way without reference to it, but by just introducing a parameter which neatly gives the right result, doesn't grant any additional explanatory power. It's just another opaque parameter: so, is "stiffness" wrapping up a quantum truth in a way which interacts with the real world? Is the uncertainty principle explanation unable to actually model these fields at all? I have no idea!
But the Uncertainty principle is something you can demonstrate in a first year lab with a laser and a diffraction grating, and turns up all the time in all sorts of basic physics (i.e. tunneling). Where does "stiffness" turn up and how does it relate? Again, I have no idea! The article purports to explain, but rather just declares.
> quantum physics plays no role in why the weak nuclear force is weak and short-range. (It plays a big role in why the strong nuclear force is strong and short-range, but that’s a tale for another day.)
It seems to me that there is a 1:1 correlation between mass of virtual particle and field stiffness. Given that fact, why isn't it equally correct to say "The field stiffness is caused by the mass of the virtual particle" and "The virtual particle necessarily has mas because the field is stiff"
The author states that "it is short range because the particles that “mediate” the force, the W and Z bosons, have mass;" is misleading as to causality, but I missed the part where they showed how/why it was misleading.
This arises from a parameter in the elementary field equation. If that parameter is non-zero than it is both true that the field is stiff and it must be mediated by a particle with non-zero rest mass. This says nothing about causality.
Correct. The author explains how both limited range and particles ability to have energy even at rest comes from "stiffness" (which is how he decided to call this parameter you talk about, in order to convey physics to laymen).
How I learned it, as a mere undergrad, was that the mass of the virtual particle for the field in question determined exactly how long it could exist, just by the uncertainty principle -- much like the way the virtual particles drive Hawking radiation.
In short, a massive virtual particle can exist only briefly before The Accountant comes looking to balance the books. And if you give it a speed of c, it can travel only so far during its brief existence before the books get balanced. And therefore the range of the force is determined by the mass of the force carrier virtual particle.
There's probably some secondary and tertiary "loops" as the virtual particle possibly decays during its brief existence, influencing the math a little further, but that is beyond me.
The effect of stiffness can also be represented by stretchability of the string. Picking up a string with a free end will result in the same shape described by adding stiffness. A fanciful analogy might be a chain of springs with constant k2 where each spring junction is anchored to the ground with a spring with constant k1. If k2>>k1 the entire spring chain lifts in a gentle arc when a spring is lifted. If k1>>k2, only the springs near the pulling point really stretch and displace. It’s these kinds of simple analogies that engage our intuition. I still however cannot envision a mechanical analogy to demonstrate wavicles.
"In a quantum world such as ours, the field’s waves are made from indivisible tiny waves, which for historical reasons we call “particles.” Despite their name, these objects aren’t little dots; see Fig. 8."
Does anyone know when physicists realized that the world is not made of indivisible units called "particles" but waves? Is there a specific experiment or are we talking about the results of many experiments?
But he is not talking about wave particle duality. He explicitly states that it is not helpful "to imagine them as both wave and particle." He calls waves with very small amplitude "particles" (for historical reasons). So, according to this picture the building blocks of the universe are waves. It makes no difference if physicists choose to call a wave "particle". Calling a wave particle does not make the wave a particle.
> He explicitly states that it is not helpful "to imagine them as both wave and particle."
Where? I can't find that quote in the article.
> He calls waves with very small amplitude "particles" (for historical reasons).
The closest thing I see is
In a quantum world such as ours, the field’s waves are made from indivisible tiny waves, which for historical reasons we call “particles.”
Note the "indivisible" part. That's not how waves work in your everyday experience. The common understanding of "wave" is based on classical physics, where waves can be scaled up or down arbitrarily. But here you have "waves" which can only get so small, but no smaller, which he then goes on to parenthetically suggest calling "wavicles".
Is coining a new word which is literally a combination of "wave" and "particle" not a way "to imagine them as both wave and particle"?
I copied the quote you couldn’t find from his figure 8: “Figure 8: There’s no perfect intuition for quantum physics. But it’s not helpful to imagine photons and electrons as particles (top right), meaning a “tiny speck”. Nor is it helpful to imagine them as both wave (top left) and particle (top right).”
He seems to gloss over the connection to experiment though. Let's say you shoot an electron through slits in a screen and want to find out where it ends up using a photographic plate; you'll get a single dot somewhere on your plate, not an extended pattern. You can repeat the experiment with a new electron and get another dot, and keep repeating the experiment until all the dots form a pattern, in well known fashion:
The top of fig 3 doesn't accurately represent a string pulled down in the middle. A string pulled down in the middle would have no curve to it in the legs unless some force is acting on it, it would look like a V.
To me it seems like it's depicting a situation where the string hasn't been pulled fully, so some of its slack hasn't straightened out into the otherwise resulting triangle yet.
> Only stiff fields can have standing waves in empty space, which in turn are made from “particles” that are stationary and vibrating. And so, the very existence of a “particle” with non-zero mass is a consequence of the field’s stiffness.
It's really difficult to reconcile "standing waves in empty space" with "stiff fields". If the space is truly empty, then the field seems to be an illusion?
If we think about fields as the very old concept of aether, then it actually makes more intuitive sense. Stiffness then becomes simply the viscosity of the aether.
But I don't think this is where this article is trying to get us!!
And if you can hop from each standing wave node to the next, you can teleport, or move ridiculously fast by moving discretely instead of continuously. What if you could tune the wavelength of these standing waves with particles stationary and vibrating?
I like the speaker on water / styrofoam particle demonstration of standing waves.
The real answer is we don't know or otherwise some kind of anthropic argument, i.e. the weak force has the range it does becuase otherwise we wouldn't have this kind of universe with people in it pondering why the weak force is the way it is.
Seems generally unhelpful to say 'the weak force is short range because it's field is stiffer!' When you can then immediately say 'well why is the weak force's field stiffer?'
In reality, little of what we understand in physics was predicted, because there are no underlying reasons to predict the universe works the way it does.
In reality, almost all of our math was retrodicted (the result of taking observation and creating math to fit it).
So, as you said, we're left with anthropic arguments or religious arguments.
For me, I've ended this song and dance by realizing the crazy math works because it was part of a plan.
The more you look at the math, the more you realize that:
1. We can only work from observation back to the math. There is no consistency to the math, except "these are the rules needed to make a stable, habitable universe."
2. Our current mathematical understanding is mostly approximations and idealizations. Every time we look at the universe at a deeper level, we find exceptions that we are fortunate exist, because they allow for a richer universe than our math suggested should exist. (Quantum mechanics is a good example. Things like quantum tunneling were not imagined 150 years ago, but it allows fusion to take place in the sun at far lower densities than should seem possible.)
So, I agree with you. I'm convinced the real answer will never be found in the math of physics, only in the realm of philosophy and religion.
Edit: I love science and I believe we should keep studying and asking how this all works. But, I feel we can make plenty of progress simply asking "how" it works and realize that at this point, "why" it works seems to be fully unanswerable by science.
Not sure I get this because we have no deeper understanding using the example I gave.
I.e. The weak force is short range because it's field is stiffer -> the weak force's field is stiffer because it is more oblong -> the weak force's field is more oblong because it has more sparkles -> it has more sparkles because it ha slower mushiness -> it has more mushiness because ...etc.
We haven't gained anything in that sequence.
I don't think we can answer fundamental questions like this. The fine structure constant is the value it is because without that value we can't have a universe like this. Maybe in some multiverse system the physical laws and constants we know are fluid and can take different values in different universes but in our universe simply because of observation selection effects they can only be what they are.
Thw piano string produces a higer torque because it is shorter does not answer you why it is shorter or how waves travel exactly within it, but it sure as hell would be required knowledge to start researching beyond that first observation.
> The weak force is short range because it's field is stiffer.
May seem like a simple redirection that could go on forever, but we learned that fields can be stiffer, which probably wasn't all that clear. Now we can observe all other forces and look how their fields vary in terms of stiffness — a parameter we might not have thought about before. And by looking in those other places we might find a clue on how to shape an experiment that allows us to vary the stiffness. That could already have useful applications, but also lead to answering the question why some forces have stiffer fields than others.
This article goes to great contortions to avoid talking about electroweak theory or spontaneous symmetry breaking, both of which have decent Wikipedia articles, and are crucial to understanding what's going on here. Spontaneous symmetry breaking of the electroweak interaction and the Higgs mechanism is the reason _why_ the W and Z have mass. The article throws up a "who knows?" at this. When you write down the field equations for a massive boson field, you get an additional m^2 term in the denominator of the propagator, which contributes a e^(-r/m) term to the interaction force at low energy, such as the decay of a neutron or a weak-mediated nuclear decay.
Is there an ELI5 version of this? I think the article tries, and it's always cool to see physics described from a different vantage point.
My ELI5 version would be: fields with a massive gauge boson are "dragged down" in energy by the mass of the boson, so interactions propagate as if they have negative energy. What does a negative energy wave propagation look like? Similar negative energy wave propagations in physics are evanescent waves and electron tunneling, both of which have exponential drop-off terms, so it makes sense to see an exponential factor in massive boson interactions.
This is a lot of words to say that the field oscillations (i.e., particles) require very high energy. This shows up as the mass-(energy) of the particle, or stiffness of the field; take your pick.
Whether you call that stiffness or mass is a little beside the point IMO -- it shows up in the Yukawa force as an exponential dependence on that parameter which means the force quickly decays to zero unless the parameter is 0.
The reason is because of the anthropic principle. If it wasn't short range, we probably wouldn't exist and there would be no consciousness to observe it.
Stiffness just seems to be rewriting mass as a different term. Only things with mass have stiffness, stiffness is exactly proportional to mass, light isn’t stiff…
One thing that confused me at the very beginning is, the author says the weak force is weak because it is short range. But the strong force is also short range.
The strong force is short range for a different reason. It's called [confinement][1]. The strong force gets stronger as you pull color charges apart. At some point the energy is so high that it's very likely that corresponding matching-color particles will exist, and so now there two pairs of close charges, instead of one pair of far charges.
TLDR; It is short range primarily because the underlying fields (those of the W and Z bosons) are “stiff,” causing any disturbance to die off exponentially at distances much smaller than an atom’s diameter. In quantum language, that same stiffness manifests as the nonzero masses of the W and Z bosons, so their corresponding force does not effectively propagate over long distances—hence it appears “weak” and short-range.
No one answered my question, but I figured out a point on a tightly stretched rubber sheet or drumhead is better analogy than a spring, because the tighter the material, the more force required and the less propagation
As an aside, is there conclusive evidence to say that no aether exists, or are we just saying it doesn't exist because a handful of tests were conducted to match what we thought this aether would behave like and the tests came back negative?
Lorentz formulated his ideas in terms of a motionless aether. But his aether theory yielded predictions identical to special relativity, so later physicists ditched his interpretation in favor of Einstein's theory that didn't need an undetectable global reference frame.
Overall, we can't really have 'conclusive evidence' against any mechanism, as long as our observations might possibly be simulated on top of that mechanism. So as far as evidence goes, 'what really exists' might be higher-dimensional strings, or cellular automata, or turtles all the way down, or whatever.
Instead, physics has some number of models (either complementary or competing) that people find compelling, and mechanisms on top of those models to explain our observations. If you did come up with a modern aether theory, you'd have to come up with a mechanism on top of it to explain all the relativistic effects we've observed.
We say the "aether" as it was originally conceptualized in the 19th century doesn't exist for the same reason we say that Russell's teapot or Carl Sagan's invisible dragon in the garage doesn't exist: we have a model of the world that makes all the same predictions without it, so it gets scraped right off by Occam's Razor.
If electromagnetic radiation is propagating through some medium, then that medium is at rest with respect to all inertial reference frames simultaneously.
It's simpler not to have a medium. The field components transform a certain way under coordinate transformations, and that's all you need.
Doesn't this "explanation" just shift the question to what is stiffness? Like it refactored the question but didn't actually explain it.
Previously, we had statement "the weak force is short range". In order to explain it, we had to invent a new concept "stiffness" that is treated as a primitive and not explained in terms of other easy primitives, and then we get to "accurately" say that the weak force is short due to stiffness.
I grant the OP that stiffness might be hard to explain, but then why not just say "the weak force is short range -- and just take that as an axiom for now".
I think it's a big improvement. Stiffness is something you can picture directly, so the data -> conclusions inference "stiffness" -> "mass and short range" follows directly from the facts you know and your model of what they mean. Whereas "particles have mass" -> "short range" requires someone also telling you how the inference step (the ->) works, and you just memorize this as a fact: "somebody told me that mass implies short range". You can't do anything with that (without unpacking it into the math), and it's much harder to pattern-match to other situations, especially non-physical ones.
It seems to me like the right criteria for a good model is:
* there are as few non-intuitable inferences as possible, so most conclusions can be derived from a small amount of knowledge
* and of course, inferences you make with your intuition should not be wrong
(I suppose any time you approximate a model with a simpler one---such as the underlying math with a series of atomic notions, as in this case---you have done some simplification and now you might make wrong inferences. But a lot of the wrongness can be "controlled" with just a few more atoms. For instance "you can divide two numbers, unless the denominator is zero" is such a control: division is intuitive, but there's one special case, so you memorize the general rule plus the case, and that's still a good foundation for doing inference with)
Intuition does not work in quantum mechanics. Intuition is based on observations at your scale, and this breaks dramatically at quantum levels. So this is not a good criterium.
That's false. Intuition does work in quantum mechanics, if you do the work to build up a good intuition for quantum mechanics. Which means exactly what I'm talking about: building your intuition on models that give true results in the situation, and which allow you to combine and remix atomic ideas in useful ways.
Unfortunately the version of QM that is taught in textbooks is not especially useful for figuring out what the intuition is. I have my own model that I've concocted that does a much better job, but there are still plenty of things I don't understand well (having not done, like, a graduate degree in it).
I have a PhD in physics, which does not say much apart from the fact that I had to think about this a lot. My PhD was in particle physics.
What I learned over the years is that, unfortunately, at some point you rely on maths. You solve equations, make predictions, and compare this to measurements. Uf they match your model (conveyed through equations) is "good for now"
The problem is that a lot of what you mathematically witness, then measure at macro scales (you do not get to measure quantum effects at their scale, only their effects on the apparatus) does not make sense at our scale.
A particle appearing for a shirt moment from nothing, interacting with another particle and vanishing, WTF?
A particle with energy X hitting a "wall" with energy Y > X and going through? WTF?
Single particles interacting with each other? Another WTF
QM is full of surprises that sound cool when presented with enthusiasm and simple words, or used in MARVEL movies but they are as intuitive for typical people as cosmic travel for Neanderthals . Sure you can handwave your way through them but how does that work with a cave and wall paintings - which is what they would witness on an everyday basis.
Well, I don't agree. Maybe you are talking about how people's intuition initially breaks on the double-split experiment, or spinors, or whatever else? But I'm not talking about broken macroscopic intuition failing on quantum systems. Of course that doesn't work. There is a separate "quantum" intuition that you get over time which lets you make true inferences. Surely you have a bunch of it if you've got a PhD in this stuff.
Things like: if you think of particles as blobs of mass and charge, you get the wrong answers; if you think of them as interfering waves then you start to get right answers. If you think of them as interfering light waves, you get the right answer for a while until you hit a situation where spin=1 gives the wrong answer, or m≠0 means the transverse component is nonzero, so you fix your intuition on that and get better answers. If you think of particle-waves as discrete atomic objects you can't intuit how different particles can be created in scattering; if you think of them as a label given to a particular vector which can be decomposed as a sum of other vectors which interact differently with different fields then you can see how particle creation/annihilation works.
Etc. There certainly are models you can construct in your mind that make this stuff start to make sense. I don't have them all, but I'm working on it. Mindlessly doing math might work for homework problems but it's not enough for actually explaining anything; you need some mental picture of what's going on as well. But the math is always there to make your intuitions concrete and keep them grounded in reality.
Look, physics is about discoveries and explanations. If your model explains everything we have measured then great -- publish it and you will get proper recognition.
I do not know your theory so I cannot comment on it, but when I was in academia I received quite a lot of these theories and they were breaking down rather quickly.
Physicists are always interested in new things but what you present must make sense and - most importantly - explain things and agree with measurements. If suddenly you end up with incorrect values it means the model is wrong. It may be completely wrong or maybe it needs adjustments.
The best way to send your message to the world is to publish.
Besides the fact that stiffness shows up as a term in the equations, stiffness is a concept that can be demonstrated via analogy with a rubber sheet, and so lends itself to a somewhat more intuitive understanding.
Also, the math section demonstrated how stiffness produces both the short-range effect and the massive particles, so instead of just handwaving "massive particles is somehow related to the short range" the stiffness provides a clear answer as to why that's the case.
If you read far enough into the math-y explanations, stiffness is a quantity in the equations. That makes it more than a hand waving explanation in my book.
In addition to what the sibling comments have said, the "axiom" is actually the term in the equations. That is, fundamentally, where this all comes from. "Stiffness" is just a word coined to help describe the behavior that arises from a term like this. Everything flows from having that piece in the math, so if you start there and with nothing else, you can reinvent everything else in the article. (Though it will take you a while.)
You might also ask where that term comes from. It really is "axiomatic": there is no a priori explanation for why anything like that should be in the equations. They just work out if you do that. Finding a good explanation for why things have to be this way and not that way is nothing more and nothing less than the search for the infamous Theory of Everything.
This is often I think a really unsatisfying thing about physics. Usually the qualitative descriptions don't quite make sense if you think very hard about them- and if you dig deeper it's often just "we found some math that fits our experimental data" - and ultimately that is as much as we know, and most attempts at explaining it conceptually are conjecture at best.
When I was a physics undergrad, most of my professors were fans of the "shut up and calculate" interpretation of quantum mechanics.
Ultimately, this is probably just a symptom of still not having yet discovered some really important stuff.
As a rule, I think physics should be expected to make less sense the further it gets from the human scale. It's not because it's inherently more complex, it's because we benefit from millions of years of brains evolving to understand what we can see and touch.
The universe does not owe us explainability in terms of everyday intuition.
You don't just "find some math that fits the data" the way you would mechanically tune the parameters of a given mathematical model to fit empirical data.
Indeed finding a mathematical formulation that seems to describe a corner of reality with any fidelity is such an extraordinary thing that physicists have always puzzled about why it is even possible!
Now it turns out that these mathematical inventions "work" even when our intuition (built on experiences around human scale) cannot quite grasp them. This is the case both in the realms of the very small (quantum) and very big (relativity).
This doesnt mean that at some point we might not find deeper mathematical abstractions that "work better" (e.g., this was the string theory ambition) but the practical result would still be every bit "shut up and calculate".
This is far from the truth in particle physics. The symmetries we've found there (together with the Lorentz symmetry from special relativity) guides and constrains the math very strongly, to the degree that it allows you to predict the photon and the other force-carrying particles, and it even allowed predicting the existence and mass of the weak force carriers (discussed in the article) along with the Higgs mechanism that gives masses to them and most of the other particles. This is certainly a triumph of the Standard Model.
There are limits to how much you can do though, I mean at some point it's going to be "just math that fits reality". If you try to enumerate the number of mechanisms and realities that could give a decent enough diversity of composition that life can arise in some form, there's going to be more than our universe possible.
> When I was a physics undergrad, most of my professors were fans of the "shut up and calculate" interpretation of quantum mechanics.
Well, you build "intuition" via "experience"--generally lots of experience to get small amounts of intuition.
> Usually the qualitative descriptions don't quite make sense if you think very hard about them- and if you dig deeper it's often just "we found some math that fits our experimental data"
Well, the math needs to fit the data and have predictive power. That "predictive" side is really important and is what sets "science" apart from everything else.
> Ultimately, this is probably just a symptom of still not having yet discovered some really important stuff.
Sure. But wouldn't the world be incredibly boring if we had it all figured out?
In my gravity simulations, on my YouTube, i found the short weak force distance was the same needed to avoid opposite charges from gaining so much speed that the next iteration's position wouldn't slow the electron down after passing the proton!
Imagine my surprise!!
We might live in a simulation!
care to link to your YT videos?
I think its more than "we just found some math that fits the data" in the sense that its not just a case of adding some terms to match an observed curve - for example like with Rayleigh-Jeans' law vs Wein's Approximation of blackbody radiation and eventually Max Planck's solution by quantizing energy to the curve match experiment, without actually having anything else to say about it.
Spiritually it feels more like what happened later, when people took the idea of quantized energy seriously and began finding ways to make it a theoretically consistent theory which also required a radical new approach of disregarding old intuitive assumptions about the way the most fundamental things worked solely to obey a new abstract, esoteric, purely theoretical framework (an approach which was sometimes controversial especially with experimentalists).
But of course this new theory of quantum mechanics turned out to be immensely successful in totally unprecedented ways, in a manner similar to Relativity and it's "theory first" origin with trying to ensure mathematical consistency of Maxwell's equations and disregarding anything else in the way (and eventually with Einstein's decade long quest to find a totally covariant general theory that folded gravity into the mix).
With physics the more I dug into "why" it was rarely the case that it was "just because", the justification was nearly always some abstract piece of math that I wasn't equipped to understand at the time but was richly rewarded later on when I spent the time studying in order to finally appreciate it.
The first time I solved Schrodinger Equation for a hydrogen atom, I couldn't see why anyone could've bothered to try discovering how to untangle such a mess of a differential equation with a thousand stubborn terms and strange substitutions (ylm??) and spherical coordinate transformations - all for a solution I had zero intuition or interest in. After I had a better grasp of the duality between those square integrable complex functions and abstract vector spaces I found classical QM elegant in an way I wasn't able to see before. When basic Lie theory and representations was drilled into my head and I had answered a hundred questions about different matrix representations of the SU(n) and S0(3) groups and their algebras and how they were related, it finally clicked how naturally those ylm angular momentum things I saw before actually arose. It was spooky how group theory had manifested in something as ubiquitous and tangible as the structure of the periodic table. After drudging through the derivation of QFT for the first time, when I finally understood what was meant by "all particles and fields that exist are nothing more than representations of the Poincare-Spacetime Algebra", I felt like Neo when everything turned into strings of code. And there's no point describing what it was like when Einstein's field equations clicked, before then I never really got what people meant by the beauty of mathematics or physics.
I guess its not really the answer "why" things are, but the way our current theories basically constrain nearly everything we see (at least from the bottom up) from a handful of axioms and cherry-picked coupling constants, the rest warped into shape and set in stone only by the self-consistency of mathematics, I feel like that's more of a "why" than I would've ever assumed answerable, and maybe more of one than I deserve.
I only got as far as "solved Schrodinger equation for a hydrogen atom" and never got to the next stage you describe with physics.
In a sense, I think your explanation is consistent with mine, but with the deeper context of math being a language itself, and the math itself being a more satisfactory explanation to someone with a greater intuition for what the equations actually mean. I can pump through all of the major equations in physics and explain almost anything I want with them, but it always just feels like rote application of algebra rules to completely arbitrary seeming formulas- nothing like what you describe. Frankly, I think I was more interested in girls than studying when I was a physics student decades ago, and I could probably get a lot more out of it revisiting this stuff now.
However, I do still think there is a real chance that we are missing something big that would fit all of these pieces together with qualitative explanations. Personally, I think Julian Barbour is likely on the right path with his timeless physics, but if so it will need a lot more research and development.
I don't think electric force is necessarily shorter distance than gravity.
But electric charges cancel out each other over big regions, while gravity never cancels.
Not a physicist, but in classical mechanics stiffness is just the proportionality of some restorative force (ie the extent to which something tries to bounce back when you push it). It definitely would be overkill to make it an axiom.
So say you have a spring if you compress it, it pushes because it wants to go back to its natural length and likewise if you stretch it there is a restorative force in the opposite direction. The constant of proportionality of that force (in N/m) is the stiffness of the spring, and the force from the spring[1] is something like F=-k x with x being the position measured from the natural length of the spring and k being the stiffness. So not knowing anything about electromagnetism I read this and thought about fields having a similar property like when you have two magnets and you push like poles towards each other, the magnetic field creates a restorative force pushing them apart and the constant is presumably the stiffness of the field.
But obviously I’m missing a piece somewhere because as you can see the force of a spring is proportional to distance whereas here we’re talking about something which is short-range compared to gravity and gravity falls off with the square of distance so it has to decay more rapidly than that.
Edit to add: in TFA, the author defines stiffness as follows:
So this coincides with the idea of restorative force of something like a spring and is presumably why he's using this word.[1] Hooke’s law says the force is actually H = k (x-l)ŝ where k is stiffness, l is the natural length of the spring and ŝ is a unit vector that points from the end you’re talking about back towards the centre of the spring.
A simple, classical case where "stiff" fields arise is electrostatic plasma physics.
Electrons are tiny and nuclei are huge, so you have a bunch of mobile charge carriers which cost energy to displace to an equilibrium position away from their immobile "homes". A collection of test charges moving "slowly" through the plasma (not inducing B field, electrons have time to reach equilibrium positions) will produce exponentially decaying potentials like in the article. If you want to read more, this concept is called "Debye Screening"
Anyway, this might be a more helpful approach than trying to imagine a spring - a "stiff" field equation is an equation for a field in a medium that polarizes to oppose it, and you can think of space as polarizing to oppose the existence of a Z Boson in a way that it doesn't polarize to oppose the existence of a photon.
'Stiffness' is a better concept because it can be used to explain behavior of all forces of finite and infinite range and why force mediators can have mass or not.
If you need to assume some axiomatic concept it's better to assume one that can used to derive a lot of what is observed.
Because you may get something else out of stiffness besides this explanation? Usually that's how a level deeper explanation works.
What makes me skeptical here is that the author claims that fields have a property that is necessary to explain this, and yet physicists have not given that property a name, so he has to invent one (“stiffness”). If the quantity appears in equations, I find it hard to believe that it was never given a name. Can anyone in the field of physics elucidate?
The author isn't inventing anything. He's just dumbing it down in an extreme way so that non-physicists could have the faintest hope of understanding it. Wich seems odd, because if you actually want to understand any of this you should prepare to spend two or three years in university level math classes first. The truth is that in reality all this is actually a lot more complex. In the Higgs field (or any simple scalar field for that matter) for example, there is a free parameter that we could immediately identify as "mass" in the way described in the article. But weirdly enough, this is not the mass of the Higgs boson (because of some complicated shenanigans). Even more counterintuitive, fermionic (aka matter) fields and massive bosonic fields (i.e. the W and Z bosons mentioned in the article) in the Standard Model don't have any mass term by themselves at all. They only get something that looks (and behaves) like a mass term from their coupling to the Higgs field. So it's the "stiffness" of the Higgs field (highly oversimplified) that gives rise to the "stiffness" of the other fields through complex interactions governed by symmetries. And to put it to the extreme, the physical mass you can measaure in a laboratory is something that depends on the energy scale at which you perform your experiments. So even if you did years of math and took an intro to QFT class and finally think you begin to understand all this, Renormalization Group Theory comes in kicks you back down. If you go really deep, you'll run into issues like Landau Poles and Quantum Triviality and the very nature of what perturbation theory can tell us about reality after all. In the end you will be two thirds through grad school by the time you can comfortably discuss any of this. The origin of mass is a really convoluted construct and these low-level discussions of it will always paint a tainted picture. If you want the truth, you can only trust the math.
I think perhaps the 'maths' at the bottom is a bit of a retelling of the Yukawa potential which you can get in a "relatively understandable" way from the Klein-Gordon equation. However, the KG equation is very very wrong!
Perhaps an approach trying to actually explain the Feynman propagators would be more helpful? Either way, I agree that if someone wanted to understand this all properly it requires a university education + years of postgrad exposure to the delights of QED / electroweak theory. If anyone here wants a relatively understandable deep dive, my favourite books are Quantum Field Theory for the Gifted Amateur [aka graduate student] by Stephen Blundell [who taught me] and Tom Lancester [his former graduate student], and also Quarks and Leptons by Halzel and Martin. It is not a short road.
The Yukawa potential is also just a more "classical" limit of an inherently quantum mechanical process. Sure you can explain things with it and even do some practical calculations, but if you plan on going to the bottom of it it'll always fail. If you want to explain Feynman propagators correctly you basically have to explain so many other things first, you might as well write a whole book. And even then you're trapped in the confines of perturbation theory, which is only a tiny window into a much bigger world. I really don't think it is possible to convey these things in a way that is both accurate (in the sense that it won't lead to misunderstandings) and simple enough so that people without some hefty prerequisites can truly understand it. I wish it were different. Because this is causing a growing rift between scientists and the normal population.
IIRC, Feynman said something like "I can't explain magnetism to a layperson in terms they can understand."
> ...causing a growing rift between scientists and the normal population.
True.
The full quote is better.
Ie: “I can’t explain it in terms of something else you’re more familiar with because I don’t understand it terms of anything else you’re more familiar with.”
Yet Einstein said something like "If you can't explain it simply, you don't understand it well enough". So maybe Feynman didn't understand it "well enough"
That was a pretty classical point of view. Quantum mechanics has gone so deep by now, there simply is nothing in a layperson's world that could accurately represent what is really going on. This was not a limit of Feynman, it's a limit of humans.
Einstein was giving a rule of thumb, not a law of nature.
I sometimes listen to Jordan Peterson's podcasts (and have read the "12 rules.."). I understand the dude. Then I found on YT a speech/discussion he had with/for psychologists, and they were still speaking English, and I couldn't understand half of what they were saying.
Now, to my 'craft' (GRC). I lately catch myself speaking like Peter Thiel, taking 20-30 second 'silences', build in my mind what I want to say, 'translate it' to simple(r) English, and then slowly say it out loud to make sure I pave the path with mental & verbal stepping stones without using any jargon.
I very well understand what I want to say, but the gap between in the knowledge and the use of language puts the onus to the explainer.
I haven't read the other two, but I'll second 'Quarks and Leptons'. I do believe it's Halzen though, rather than Halzel...
> the KG equation is very very wrong!
How so? It's the standard equation for a scalar (spin zero) field.
The biggest glaring issue with it (eg in the form (square^2+m^2)\psi=0) is that it is a manifestly Lorentz invariant equation in which particle number is conserved (which is highly unlikely for any relativistic interaction). I know that you can extend it into a scalar field theory proper, quantize it, and sidestep around those issues (and use it as a model in cmp!), but the bigger problem I think is that you really need spin -- and ideally all other interactions...
Fortuitously the author of the posted article also has a series on the Higgs mechanism (with the math, but still including some simplifications): https://profmattstrassler.com/articles-and-posts/particle-ph...
Those posts would really benefit from some math typesetting in latex.
I wholeheartedly agree.
Can an LLM reliably re-format it for us?
EDIT: yes I tried pasting it in to Gemini, 4o, and Claude. Only Claude was able to zero-shot create the latex and an html wrapper that renders it, and open the html preview on iOS. It worked great.
I love Claude Sonnet 3.5 so much. DeepSeekv3 is also very good.
Did you check whether it got all equations right though?
At some point our understanding of fundamental reality will be limited not by how much the physicists have uncovered but by how many years of university it would take to explain it. In the end each of us only has one lifetime.
He addresses this in the comments. The term that corresponds to "stiffness" normally just gets called "mass", since that is how it shows up in experiments.
Roughly put:
- A particle is a "minimum stretching" of a field.
- The "stiffness" corresponds to the energy-per-stretch-amount of the field (analogous to the stiffness of a spring).
- So the particle's mass = (minimum stretch "distance") * stiffness ~ stiffness
The author's point is that you don't need to invoke virtual particles or any quantum weirdness to make this work. All you need is the notion of stiffness, and the mass of the associated particle and the limited range of the force both drop out of the math for the same reasons.
This is it. Typically in a QFT lecture, you'd include a "mass term" (in the article: stiffness term) in your field equations, and later show that it indeed gives mass to the excitations of this field (i.e. particles). So you temporarily have two definitions of "mass" and later show that they agree.
For this discussion it makes sense call the "mass" of a field "stiffness" instead, since it's not known a priori that it corresponds to particle mass.
I think mathematically "stiffness" is well-defined, but the interpretation varies substantially depending on the context. For example, in chemistry or plasma physics, one writes down Poisson's equation for a collection of positive and negatives charges in thermal equilibrium and linearise the Boltzmann factors. The result is called the Debye–Hückel equation and is identical to the one shown in the "with math" section.
Here the "stiffness" is interpreted as the effect of nearby charges "screening" a perturbing "bare" charge of the opposite sign. If you solve the equation you find the that effective electric field produced by the bare charge is like that of the usual point charge but with a factor exp(-r/λ). So, the effect of the "stiffness" term is reducing the range of the electric interactions to λ, which is called the Debye length. see this illustration [1].
Interestingly, if you look at EM waves propagating in this kind of system, you find some satifying the dispersion relation ω² = k²c² + ω_p² [2]. With the usual interpretation E=ℏω, p=ℏk you get E² = (pc)² + (mc²)², so in a sense the screening is resulting in "photons" gaining a mass.
[1]: https://en.wikipedia.org/wiki/File:Debye_screening.svg
[2]: https://en.wikipedia.org/wiki/Electromagnetic_electron_wave#...
> The term that corresponds to "stiffness" normally just gets called "mass", since that is how it shows up in experiments.
Then why not just call it "mass"? That's what it is. How is the notion of "stiffness" any better than the notion of "mass"? The author never explains this that I can see.
Undergrad-only level physics person here:
I think stiffness is an ok term if your aim is to maintain a field centric mode of thinking. Mass as a term is particle-centric.
It seems these minimum-stretching could also be thought of as a “wrinkle”. It’s a permanent deformation of the field itself that we give the name to, and thus “instantiate” the particle.
Eye opening.
> I think stiffness is an ok term if your aim is to maintain a field centric mode of thinking.
"Stiffness" to me isn't a field term or a particle term; it's a condensed matter term. In other words, it's a name for a property of substances that is not fundamental; it's emergent from other underlying physics, which for convenience we don't always want to delve into in detail, so we package it all up into an emergent number and call it "stiffness".
On this view, "stiffness" is a worse term than "mass", which does have a fundamental meaning (see below).
> Mass as a term is particle-centric.
Not to a quantum field theorist. :-) "Mass" is a field term in that context; you will see explicit references to "massless fields" and "massive fields" all over the literature.
Do you also object quarks and gluons having "color" charge?
Mass is a bad term because it's loaded with so many meanings and equivalences already. But also in the kindest and most accurate reading here it still doesn't naturally lead to explaining why some forces have limited range the way that term "stiffness" does, which was the whole point of the article.
> Do you also object quarks and gluons having "color" charge?
No, because no physicist tries to argue that "color" is an appropriate term because of some physical interpretation that involves actual physical properties of colored objects.
This author, OTOH, appears to be arguing that "stiffness" is a better term than "mass" because of some physical interpretation that involves actual physical properties of stiff objects. An analogy with quarks would be to argue that "color charge" is an appropriate term because red, green, and blue quarks somehow have actual properties associated with those colors.
> it still doesn't naturally lead to explaining why some forces have limited range the way that term "stiffness" does
I'm not sure the explanation of that in terms of "stiffness" is any better, because in the setting where the term "stiffness" comes from, there is no such thing as what this author calls a "floppy" object. So his explanation only "explains" the behavior of forces associated with massive gauge bosons at the price of throwing away an explanation of the behavior of forces associated with massless gauge bosons.
> An analogy with quarks would be to argue that "color charge" is an appropriate term because red, green, and blue quarks somehow have actual properties associated with those colors.
They do, there are 3 and they add up like primary colors, so all 3 make stuff colorless. That's why those names were chosen. Because of similarities with color we know from color theory.
> there is no such thing as what this author calls a "floppy" object
It's easy enough to imagine as an unattached rope so pulling at one spot affects the whole rope because nothing holds remote parts of the rope in place. The only way for a wrinkle to exist in such rope is to travel at "rope speed". If there's stiffness then a wrinkle can travel at any speed or none at all, because it can oscilate without moving, which is rest energy (mass). So it explains all bosons.
What's great with this analogy is that it coveys that both mass and force range arise from a single term of the equation. There's really no causal connection between them. Neither limited range causes mass nor mass causes limited range. They both come from a single intrinsic field "quality".
There's also no anti-blue color in color theory but it's easy to imagine it so you can intuitively understand its behavior.
> It's easy enough to imagine as an unattached rope so pulling at one spot affects the whole rope
Not instantly; the force you apply at one point still has to be transmitted through the rope. And if the rope is unattached and not taut, it won't transmit force well at all, and you have very limited control over how the rest of the rope will move when you pull on one part.
I don't see how any of this is a useful analogy to how massless gauge bosons work in forces like electromagnetism.
> I don't see how any of this is a useful analogy to how massless gauge bosons work in forces like electromagnetism.
That's fine. No analogy works for everybody.
In the unit analysis it appears as if it's just kinematic viscosity.
Kinematic viscosity, though, is an emergent property just as stiffness is. See my response to kridsdale1 upthread.
In the unit analysis that is most natural to quantum field theory, it's mass.
It does have a name, it's called "coupling." A spring (to physicists all linkages are springs :-) ) couples a pair of train cars, and a coupling constant attaches massive fields to the higgs field.
Even capacitors and thermal models in solids are springs.
as an electrical engineer I think any other form of coupling as a capacitance, i.e. electric field and rarely as inductive coupling (magbetic field). funny world.
The longer I read the article, the more "stiffness" feels like mass. In Lagrangians, the quantity saying how stiff it is is precisely the mass term, vide https://en.wikipedia.org/wiki/Scalar_field_theory.
At the same time, the author does not give any different definition; he says it's "stiffness". In the comment, he writes:
> The use of a notion of “stiffness” as a way to describe what’s going on is indeed my personal invention. Physicists usually just call the (S^2 phi) part of the equation a “mass term.” But that’s jargon, since this thing doesn’t give mass to the field; it just gives mass to its particles, which exist only in the context of quantum physics. The word “mass term” also doesn’t explain what’s going on physically. My view is that “stiffness” conveys the basic physical sense of what is happening to the field, an effect it has even without accounting for quantum physics.
So well, it is mass. Maybe not mass one may think about (in physics, especially Quantum Field Theory, there are a few notions of mass, which are not the same as what we set on a scale), but I feel the author is overzealous about not calling it "mass (term)".
So, I am not convinced unless the author shows a way to have massive particles carrying a long-term interaction (AFAIK, not possible) or massless particles giving rise to short-term interactions (here, I don't know QFT enough so that it might be possible). But the burden of proof is on the inventor of the new term.
> If the quantity appears in equations, I find it hard to believe that it was never given a name.
It does have a name: mass!
What I'm skeptical of is that this "stiffness" is somehow logically or conceptually prior to mass. Looking at the math, it just is mass. The term in the equation that this author calls the "stiffness" term is usually just called the "mass" term.
But it's not really just "mass", it's "characteristic mass of stationary minimal possible wrinkle in a given field". And it doesn't sound like it has anything to do with force range, and "stiffness" does.
> it's not really just "mass", it's "characteristic mass of stationary minimal possible wrinkle in a given field"
If you are referring to the claim in the article that goes along with the equation E = m c^2, that claim is the author's personal interpretation, which I don't buy. The mass appears in the dispersion relation whether the particle is at rest or not. "Rest mass" is an outdated term for it; a better term is "invariant mass", i.e., it's the invariant associated with the particle's 4-momentum. Or, in field terms, it's the invariant associated with the dispersion relation of the field and the waves it generates.
I will go one deeper. Are fields (quantum fields) even real, or just a model ?
You can go even deeper and ask what the difference between "real" and "model" even is.
Are forces real or just a model?
It's nonsense. The fact that the particle is massive is a direct cause of the fact that the interactions are short ranged.
The nuance is this: Naturally, in a field theory the word "particle" is ill-defined, thus the only true statement one can make is that: the propagator/green function of the field contains poles at +-m, which sort of hints at what he means by stiffness.
As a result of this pole, any perturbations of the field have an exponential decaying effect. But the pole is the mass, by definition.
The real interesting question is why Z and W bosons are massive, which have to do with the higgs mechanism. I.e., prior to symmetry breaking the fields are massless, but by interacting with the Higgs, the vacuum expectation value of the two point function of the field changes, thus granting it a mass.
In sum, whoever wrote this is a bit confused and just doesn't have a lot of exposure to QFT
> whoever wrote this ... just doesn't have a lot of exposure to QFT
Incredible.
https://scholar.google.com/citations?user=19WGkFsAAAAJ&hl=en
be sure to check past the first 20 papers or so, like, oh, say his 1990 paper with Michael Peskin (438 citations), a copy of which can be found at <https://www.slac.stanford.edu/pubs/slacpubs/5250/slac-pub-53...>.
Actually upon further reading I realize that the author actually goes deeper into what I thought, so it's not nonsense, it's actually a simplified version of what I tried to write.
But I don't particularly like the whole "mass vs not mass" discussion as it's pointless
Well, the author did superbly better job of explaining anything to people that haven't graduated quantum mechanics than you did. That's something.
Recognizing correct analogies is not easy and it's insanely powerful educational tool.
that & pointless is an amazing pun intentional or otherwise; well-done, just absolutely
There is an interesting video essay by the Huygens Optics channel where some simulations of these field effects are considered.
Turning Waves Into Particles https://www.youtube.com/watch?v=tMP5Pbx8I4s
And if unfamiliar, that channel constantly delivers high quality thought provoking content on the nature of light.
One thing I'm not clear on when watching his videos is whether what he's describing is an established scientific interpretation, or his own thoughts as someone who has extensive knowledge on optical engineering (vs theory).
Very enjoyable and thought provoking stuff though!
Edit: spelling
When he provides sources, then it's the first one, otherwise the second.
Nature of light? You May really like this:
https://youtu.be/A-2XQQDD6QQ
That's great. Thanks. When you start watching it you think, it will be too long, but it gets better and better. Everything goes back to Einstein. YARH! Yet another rabbit hole! It's amazing we have any time left to do anything after reading HN.
>NOTICE THERE IS NO QUANTUM PHYSICS IN THIS DISCUSSION! The short range of the field is a “classical” effect; i.e., it can be understood without any knowledge of the underlying role of quantum physics in our universe. It arises straightforwardly from ordinary field concepts and an ordinary differential equation. Nothing uncertain about it.
It's interesting to me how fuzzy the definition of quantum physics is. For example, I've seen the description of particles as described by a wave function (e.g. electron position and momentum in an atom) labeled as a quantum phenomenon, but have also heard it, as in this quote, as classical, since it's defined by a differential equation; a "classical" wave. In that view, quantum only enters the model when modelling exchange effects, spin, fermion states etc.
With the former definition, as in the article, you see descriptions of the wave nature of matter, replete with Planck's constant, complex wave function representations etc described as classical.
If we wanted to model the universe as a set of equations or a cellular automaton, how complex would that program be?
Could a competent software engineer, even without knowing the fundamental origins of things like particle masses or the fine-structure constant, capture all known fundamental interactions in code?
I guess I'm trying to figure out the complexity of the task of universe creation, assuming the necessary computational power exists. For example, could it be a computer science high school project for the folks in the parent universe (simulation hypothesis). I know that's a tough question :)
I'm surprised that more sibling comments aren't covering the lack of a unified theory here. Currently, our best understanding of gravity (general relativity) and our best understanding of everything else (electromagnetism, quantum mechanics, strong/weak force via the standard model) aren't consistent. They have assumptions and conclusions that contradict each other. It is very difficult to investigate these contradictions closely because the interesting parts of GR show up only in very massive objects (stars, black holes) and the interesting parts of everything else show up in the tiniest things (subatomic particles, photons).
So we don't have a set of equations that we could expect to model the whole universe in any meaningful way.
At the level of writing a program to simulate the universe as we see it, ideas like classical gravity (see Penrose) would probably work.
They definitely wouldn’t work because we have strong evidence that relativity is a more accurate theory and significant evidence that either gravity does not obey an inverse square law or our estimation of the distribution or nature of dark matter is incorrect.
https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gr...
Our present best guess is that cellular automatons would be an explosively difficult way to simulate the universe because BQP (the class of problems that can be related to simulating a quantum system for polynomial time) is probably not contained in P (the class of problems Turing machines can solve in polynomial time).
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The formulas are really not very complex. The Standard Model is a single Lagrangian with a couple of dozen constants.
https://visit.cern/node/612
You can expand that Lagrangian out to look more complex, but that's just a matter of notation rather than a real illustration of its complexity. There's no need to treat all of the quarks as different terms when you can compress them into a single matrix.
General relativity adds one more equation, in a matrix notation.
And that's almost everything. That's the whole model of the universe. It just so happens that there are a few domains where the two parts cause conflicts, but they occur only under insanely extreme circumstances (points within black holes, the universe at less than 10^-43 seconds, etc.)
These all rely on real numbers, so there's no computational complexity to talk about. Anything you represent in a computer is an approximation.
It's conceivable that there is some version out there that doesn't rely on real numbers, and could be computed with integers in a Turing machine. It need not have high computational complexity; there's no need for it to be anything other than linear. But it would be linear in an insane number of terms, and computationally intractable.
>The Standard Model is a single Lagrangian with a couple of dozen constants.
I hear it's a bit more complex than that!
https://www.sciencealert.com/this-is-what-the-standard-model...
It's a single lagrangian with a couple of dozen constants, in their pics there as well. It's just expanded out to different degrees.
Through smart definitions I can contract any longer term as much as I want.
Yes and that's precisely why you're writing high-level code instead of ASM. It's your job.
Yes, and it's exactly those "smart definitions" that are the Standard Model. The whole goal is to produce even smarter definitions, including showing that as much as possible of it couldn't be any other way, preferably.
Nah it really is simpler than that, that picture has exploded the summations to make it look complicated. Although it is strangely hard to find the compressed version written down anywhere...
the thing about Lagrangians is that they compose systems by adding terms together: L_AB = L_A + L_B if A and B don't interact. Each field acts like an independent system, plus some interaction terms if the fields interact. So most of the time, e.g. on Wikipedia[0], people write down the terms in little groups. But still, note on the Wikipedia page that there are not that many terms in the Lagrangian section, due to the internal summations.
[0]: https://en.wikipedia.org/wiki/Mathematical_formulation_of_th...
I can't help but wonder if, under extreme conditions, the universe has some sort of naturally occurring floating-point error conditions, where precision is naturally eroded and weird things can occur.
That would occur if a naked singularity could exist. If black holes have a singularity then you could remove the event horizon. In general relativity, the mathematical condition for the existence of a black hole with an event horizon is simple. It is given by the following inequality: M^2 > (J/M)^2 + Q^2, where M is the mass of the black hole, J is its angular momentum and Q is its charge.
Getting rid of the event horizon is simply a question of increasing the angular momentum and/or charge of this object until the inequality is reversed. When that happens the event horizon disappears and the exotic object beneath emerges.
I doubt it. Even the simplest physical system requires a truly insane number of basic operations. Practically everything is integrals-over-infinity. If there were implemented in a floating-point system, you'd need umpteen gazillion bits to avoid flagrant errors from happening all the time.
It's not impossible that the universe is somehow implemented in an "umpteen gazillion bits, but not more" system, but it strikes me as a lot more likely that it really is just a real-number calculation.
Right, I don't mean literally floating-point errors, but something similar.
That could very well be what the quantum uncertainty principal is, floating point non deterministic errors. It also could just be drawing comparisons among different problem domains.
The QUP is indeed what allows to quantize continuous equations with h, and once they have been turned into integers like this we can then meaningfully calculate our lack of information (aka 'entropy').
>These all rely on real numbers, so there's no computational complexity to talk about.
There's a pretty decent argument real numbers are not enough:
https://www.nature.com/articles/s41586-021-04160-4/
https://physics.aps.org/articles/v15/7
You (sorta) can! https://en.wikipedia.org/wiki/Lattice_QCD
The trick is (as the sibling comments explain) that it involves an exponential number of calculations, so it's extremely slow unless you are interested only in very small systems.
Going more technical, the problem with systems with the strong force is that they are too difficult to calculate, so the only method to get results is to add a fake lattice and try solving the system there. It works better than expected and it includes all the forces we know, well except gravity , and it includes the fake grid. So it's only an approximation.
> Could a competent software engineer, even without knowing the fundamental origins of things like particle masses or the fine-structure constant, capture all known fundamental interactions in code?
Nobody know where that numbers come from, so they are just like 20 or 30 numbers in the header of the file. There is some research to try to reduce the number, but I nobody knows if it's possible.
The scales get you:
You can’t simulate a molecule at accurate quark/gluon resolution.
The equations aren’t all that complex, but in practice you have to approximate to model the different levels, eg https://www.youtube.com/playlist?list=PLMoTR49uj6ld32zLVWmcG...
Stephen Wolfram has been taking a stab at it. Researching fundamental physics via computational exploration is how I'd put it. https://www.wolframphysics.org/
He is basically a crackpot. Any attempt at fundamental physics that doesn't take quantum mechanics into account is.... uhm.... how to put this.... 'questionable'.
I'm not even able to hold a candle to Wolfram intellectually- the guy is a universe away from me in that regard. But: Given a cursory look at his wiki page and Cosma Shalizi's review of his 2002 book on cellular automata [1], I feel fairly comfortable saying that it seems like he fell in the logician's trap of assuming that everything is computable [2]:
>There’s a whole way of thinking about the world using the idea of computation. And it’s very powerful, and fundamental. Maybe even more fundamental than physics can ever be.
>Yes, there is undecidability in mathematics, as we’ve known since Gödel’s theorem. But the mathematics that mathematicians usually work on is basically set up not to run into it. But just being “plucked from the computational universe”, my cellular automata don’t get to avoid it.
I definitely wouldn't call him a crackpot, but he does seem to be spinning in a philosophical rut.
I like his way of thinking (and I would, because I write code for a living), but I can't shake the feeling that his physics hypotheses are flawed and are destined to bear no fruit.
But I guess we'll see, won't we?
[1] http://bactra.org/reviews/wolfram/ [2] https://writings.stephenwolfram.com/2020/04/how-we-got-here-...
Wolfram really loves to talk about computational irreducibility.[1]
But I think his articles about Machine Learning are excellent. [2]
[1]https://www.google.com/search?client=firefox-b-1-d&q=%22comp...
[2]https://writings.stephenwolfram.com/category/artificial-inte...
That really seems to be mischaracterizing his work. The idea is that the quantum effects we see will eventually emerge.
Most people in the field don't think his research will be fruitful, but that doesn't make him a crack pot
most people in the field believe his research isn't even capable of being wrong
Someone seems to say something demeaning like that about him whenever he comes up, and I don't really know why. Which is fine, maybe it's a subjective thing. For what it's worth, the few times I read something of his, I loved it.
It's a complex issue. He is obviously extremely intelligent and at least a decent business man. If you've never used Wolfram Mathematica before, I implore you to pick up a raspberry pi and play with the educational version. It's nothing short of magical in many ways. I still prefer Python in a lot of ways (least of all with Python being free/open), but Mathematica notebooks are nuts. You can do anything from calculus to charts, geographic visualizations, neural networks, NLP, audio processing, optimization, text processing, time series analysis, matrices, and a bazillion other things with a single command or by chaining them together. It has its warts, but is very polished.
He also did some important early work on cellular automata if iirc.
Then he wrote "A New Kind of Science", which reads like an ego trip and was not received well by the community (it is a massive tome that could have been summarized with a much smaller book). He also tried to claim discoveries from one of his workers due to some NDA shenanigans (or something along these lines iirc). The latter doesn't make him a crank, just a massive egotist, which is a trait nearly all cranks have. Sabine Hossenfelder did a video on him and how he only publishes in his own made up journals and generally doesn't use the process used by all other scientists. I think a lot believe where there is smoke, there is fire. To his credit, she also mentioned that some physicists gave him some critical feedback and he did then go and spend a bunch of time addressing the flaws they found.
Well, one can love playing chess and that is all fine and good and so on but if someone says that chess is the fundamental theory of the universe, how much sense does that make? There might even even be truth in that statement, who could possibly know? All we can be quite certain about is that to actually demonstrate the hypothetical truth of the statement 'chess is the fundamental theory of the universe' some number, presumably larger than 5, of nobel price level of physics discoveries need to take place.
You are making an unscientific criticism.
Wolfram's claim is that Cellukar Automata can provide as good or better mathematical model of the universe than current current theories, by commonly appreciated metrics such as "pasimony of theory" (Occam's Razor). He's not making claims about metaphysical truth.
Well, the question 'is this Wolfram guy doing science' is as such not a scientific question. And the answer is a resounding 'no'.
I think Wolfram might be one of the 1000 smartest people alive and he has accomplished many great things and is very good at math. But it really seems he wants to be thought of in the same was as Newton and Einstein. So he tries to find some new ultra fundamental theory to achieve this. His book A New Kind of Science failed so now he is trying with the Wolfram Physics Project.
I sympathize with your opinion of him being a crackpot but he is also a genius and the idea is that the graphs in his theory are more fundamental than quantum mechanics and it would emerge from them.
The universe is already modeled that way. Differential equations are a kind of continuous time and space version of cellular automata, where the next state at a point is determined by the infinitesimally neighboring states.
My first thought was 'ah, yes.' My second thought was 'but what about nonlocality?'
I do wonder if you'd want to implement a sort of 3D game engine that simulates the entire universe, if somehow the weird stuff quantum physics and general relativity do (like the planck limit, the lightspeed limit, discretization, the 2D holographic bound on amount of stuff in 3D volumes, the not having an actual value til measured, the not being able to know momentum and speed at the same time, the edge of observable universe, ...) will turn out to be essential optimizations of this engine that make this possible.
Many of the quantum and general relativity behaviors seem to be some kind of limits (compared to a newtonian universe where you can go arbitrarily small/big/fast/far). Except quantum computing, that one's unlocking even more computation instead so is the opposite of a limit and making it harder rather than easier to simulate...
I don’t think the “not having an actual value until measured”, properly understood, would seem like an optimization.
I don’t know why so many people feel like it would be an optimization?
Storing a position is a lot cheaper than storing an amplitude for each possible position.
One-hot vectors are much more compressible than general vectors, as you can just store the index.
Also, it is momentum and position that are conjugate, not momentum and speed.
Ugh, I just listed things from the top of my head, no rigorous correct physics!
I'd be interested to know where those so many other people who feel that would be an optimization are, because I don't often see opinions like this at all, only either rigorous physicists posting equations and papers, or people not knowing anything about it at all to even philosophize about it.
http://oyhus.no/QuantumMechanicsForProgrammers.html gives a flavor of one possible shape of things. It's pretty intractable to actually compute anything this way.
One of the real promises of Quantum Computers is being able to simulate quantum systems better.
Stephen Wolfram is trying to model physics as a hypergraph
https://www.wolframphysics.org/universes/
How complex? I'm no physicist nor an expert at this, but AFAIK we aren't really capable of simulating even a single electron at the quantum scale right now? Correct me if I'm wrong.
We can simulate much more than that, even at the quantum scale. What we cannot do is calculate things analytically, so we only have approximations, but for simulation that’s more than enough.
Less ambitiously, how small and clear could you make a program for QED calculations? Where you're going for code that can be clear to someone educated with only undergrad physics, with effort, to help explain what the theory even is -- not for usefulness to career physicists.
Maybe still too ambitious, because I haven't heard of such a program.
Wolfram actually got his start writing these.
I've always thought that gravity exists because without it, matter doesn't get close enough for interesting things to happen.
Well, Newton thought he could do it with just 3 lines, and we've all been playing code golf ever since.
To be fair, his universe was much simpler than ours. He didn't need a nuclear reactor or particle accelerator to transmute lead into gold in his theory.
Rephrasing what some of the other answers have said, with a decent knowledge of math you could write the program, but you wouldn’t be able to run it in a reasonable time for anything but the most trivial scenarios.
Horribly complex and/or impossible.
(1) quantum mechanics means that there is not just one state/evolution of the universe. Every possible state/evolution has to be taken into account. Your model is not three-dimensional. It is (NF * NP)-dimensional. NF is the number of fields. NP is the the number of points in space time. So, you want 10 space-time points in a length direction. The universe is four-dimensional so you actually have 10000 space-time points. Now your state space is (10000 * NF)-dimensional. Good luck with that. In fact people try to do such things. I.e., lattice quantum field theory but it is tough.
(2) I am not really sure what the state of the art is but there are problems even with something simple like putting a spin 1/2 particle on a lattice. https://en.wikipedia.org/wiki/Fermion_doubling
(3) Renormalization. If you fancy getting more accuracy by making your lattice spacing smaller, various constants tend to infinity. The physically interesting stuff is the finite part of that. Calculations get progressively less accurate.
To go down this rabbit hole, the deeper question is about the vector in Hilbert space that represents the state of the universe. Is it infinite dimensional?
Yes, but that is not saying very much. Just one single harmonic oscillator already has a state space that is an infinitely dimensional Hilbert space. It is L^2. Now make a tensor product of NF * NP of these already infinitely dimensional Hilbert spaces defined above to get quite a bit more infinite.
> Could a competent software engineer, even without knowing the fundamental origins of things like particle masses or the fine-structure constant, capture all known fundamental interactions in code?
I don't think so.
In classical physics, "all" you have to do is tot up the forces on every particle and you get a differential equation that is pretty easy to numerically work with. Scale is a challenge all of its own, and of course you'd ideally need to learn about all the numerical issues you can run into. But the math behind Runge-Kutta methods isn't that advanced (really, you just need some calculus to even explain what you're doing in the first place), so that's pretty approachable to a smart high schooler.
But when you get to quantum mechanics, it's different. The forces aren't described in a way that's amenable to tot-up-all-the-forces-on-every-particle, which is why you get stuff like https://xkcd.com/1489/ (where the explainer is unable to really explain anything about the strong or weak force). As an arguably competent software engineer, my own attempts to do something like this have always resulted in my just bouncing off the math entirely. And my understanding of the math--as limited as it is--is that some things like gravity just don't work at all with the methods we have at hand to us, despite us working at it for 50 years.
By way of comparison, my understanding is that our best computational models of fundamental forces struggle to model something as complicated as an atom.
Urgh, I'm half way through this and I hate it.
The problem is it's upfront that "X thing you learned is wrong" but is then freely introducing a lot of new ideas without grounding why they should be accepted - i.e. from sitting here knowing a little physics, what's the intuition which gets us to field "stiffness"? Stiff fields limit range, okay, but...why do we think those exist?
The article just ends the explanation section and jumps to the maths, but fails to give any indication at all as to why field stiffness is a sensible idea to accept? Where does it come from? Why are non-stiff fields just travelling around a "c", except that we observe "c" to be the speed of light that they travel around?
When we teach people about quantum mechanics and the uncertainty principle even at a pop-sci level, we do do it by pointing to the actual experiments which build the base of evidence, and the logical conflicts which necessitate deeper theory (i.e. you can take that idea, and build a predictive model which works and here's where they did that experiment).
This just...gives no sense at all as to what this stiffness parameter actually is, why it turned up, or why there's what feels like a very coincidental overlap with the Uncertainty principle (i.e. is that intuition wrong because actually the math doesn't work out, is this just a different way of looking at it and there's no absolute source of truth or origin, what's happening?)
In all honesty, this gives a delightful if frightening look into how physicists are thinking amongst themselves. As a (former) particle physicist myself, I can’t remember the number of times an incredulous engineer has confronted me with “the truth” about physics. But you see, for practicing physicists, the models and theories are fluid and actually up for discussion and interpretation, that’s our job after all. The problem is that the official output is declared to be immutable laws of nature, set in formulae and dogmatic conventions. That said, I agree that he is trading one possible fallacy for another here, but the beauty of the thing is that the “stiffness” explanation is invoking less assumptions than the quantum one - which physicists agree is a “good thing” (Occam’s razor).
There definitely seems to be a modern trend of over complication in physics along with the voodoo-like worship of math. Humbly enough, people have only come to understand the equations for an apple falling out of a tree within the last 500 years, and that necessitated the invention of Calculus.
What's more distressing than the insular knowledge cults of modern physics is the bizarre fixation on unfalsifiable philosophical interpretation.
That just makes it incomprehensible to outsiders when they quibble over the metaphors used to explain the equations that are used to guess what may happen experimentally. (Rather than admitting that any definition is an abstraction and any analogies or metaphors are merely pedagogical tools.)
My kneejerk reaction: Give me the equations. If they are too complicated give me a computer simulation that runs the equations. Now tell me what your experiment is and show me how to plug the numbers so that I may validate the theory.
If I wanted to have people wage war over my mind concerning what I should believe without evidence, I would turn back to religion rather than science.
Anyway, I hope this situation improves in the future. Maybe some virtual particle will appear that better mediates this field (physics).
Having studied undergraduate physics, I think this viewpoint is inverted from the realities of the matter. It is less that the math is complicated and more so these are the relevant tools invented for us to model the experimental results we obtain post discovery/formalization of SR/GR/Quantum experiences. There are computers that can run these simulations but they are infeasible to model large scale processes. That is the reason people are looking for more than numerical solutions to problems, but laws and tools that can simplify modeling large scale emergent behavior that it would be infeasible or unnecessarily complicated to do with numerical simulation. These tools are the more straightforward approach
It's evident and obvious in any of these explanations that the equations and properties of math are taken as true a priori, not grounded on observation (in their invocation).
If I write a partial differential equation that I came up with randomly and ask you to find all the potential solutions that really doesn't tell you anything about the natural world.
I think that's more your interpretation/experience rather than the intention of the tools. Those constants and coefficients are there because the math is describing the shape of the solution based on logic, mathematical object rules, and symmetry/conservation laws and needs to be "grounded" to make them physical.
The Lagrangian is just "conservation of energy" (L = T[kinetic] - V[potential]). There isn't some magic, it's a statement that the energy needs to go somewhere.
Your straw-man belies the underlying issue you are experiencing, you don't just come up with a PDE, you see nature and then you describe ways to conserve counts of things, "energy", "population", whatever. The PDEs describe the exchange between these counts. The accuracy and additional terms are about more accurately representing the counts and conservation of things.
Voodoo worship of math? I am getting a bit tired of that sentiment, especially around string theory.
Math is all you've got to work with, we wouldn't have modern day physics without math.
The issue is that people think they can find some kind of magic shortcut by playing around with abstractions without reference to or grounding in physical observables. That's not a math problem, that's a psychology problem.
If you're going to say that you need to study math exclusively for many years to understand your formulas then you are not using abstraction well.
I don't think that's what I would say, but if that's what you are anticipating, then I don't think you have a very good take, either. I don't even think we'd resolve our problems with physics if everyone were a mathematician first. However, it will always take many years of training to understand some of the major equations to a sufficient degree.
Once again, my point is that people are trying to take shortcuts with abstractions that are not grounded in reality. That is a matter of self-discipline, of priorities, of putting the cart before the horse. Consider string theories: we have worked out so many ways in which strings can behave, etc. with so many possibilities and permutations. However, we never proved the ground reality for strings, we just ran with a bunch of assumptions and then parameterized them, went meta a bunch of times, and called that a research program.
All of that mathematical sophistication and model-building could have went to, e.g. perfecting QCD, or even in other directions.
Yeah, the whole 'immutability' thing is just a front for the layperson, and that's honestly fine. However it does generate a weird set of expectations and culture shock when you cross that barrier into proper physics and you see people don't consider these things immutable, the best you've got is instrumentalism and functionalist treatment of observables. These worldviews have been a source of too many red herrings for the unprepared.
I agree this doesn't gel well with the pop-science approach.
However, it is actually a similar approach to how De Broglie, Schrodinger, and others originally came up with their equations for quantum behavior - we start with special relativity and consider how a wave _must_ behave if its properties are going to be frame-independent, and follow the math from there. That part is equation (*), and the article leads with a bit of an analogy of how we might build a fully classical implemenation of it in an experiment (strings, possibly attached to a stiff rubber sheet) so we get some everyday intuition into the equation's behavior. So from my point of view, I found it very interesting.
(What the article doesn't really get into is why certain fields might have S=0 and others not, what the intuition for the cause of that is, etc. It also presupposes you have bought into quantum field theory in the first place, and wish to consider the fundamental "wavicles" that would emerge from certain field equations, and that you aren't looking closely at the EM force or spin or any other number of things normally encountered before learning about the weak force).
I had very much the same feeling. Honestly this might be all true, but it's got a vibe I don't like. I did QFT in my PhD and have read plenty of good and bad science exposition, and it doesn't feel right.
I can't point at any outright mistakes, but for example I think the dismissal of the common interpretation of virtual particles in Feynman diagrams is not persuasive. If you think the prevailing view among experts is wrong then the burden of proof is high, perhaps right than you can reach in am article pitched so low, but I don't feel like reading his book.
> introducing a lot of new ideas without grounding
The grounding is 3 years of advanced math.
> This just...gives no sense at all as to what this stiffness parameter actually is, why it turned up, or why there's what feels like a very coincidental overlap with the Uncertainty principle
Because not everyone has the prerequisite math or time/attention to go into quantum field theory for a rather intuitive point about mass and fields.
This reminds me a bit of how high school physics classes are sometimes taught when it comes to thermodynamics and optics. You learn these "formulas" and properties (like harmonics or ideal gas law) because deriving where they come from require 2-3 years of actual undergraduate physics with additional lessons in differential equations and analysis.
> Because not everyone has the prerequisite math or time/attention to go into quantum field theory for a rather intuitive point about mass and fields.
This gets into the problem though: the article is framed as "the Heisenberg explanation is wrong". Okay...then if thats your goal, to explain that without math, you need to do better then "actually it's this other parameter, trust me bro".
As read, I cannot tell if there's something new or different here, or if "stiffness" just wraps up the Heisenberg uncertainty principle neatly so you can approach the problem classically.
The core question coming into the article which I was looking for an answer for is "is the Heisenberg uncertainty principle explanation wrong?" and...it doesn't answer that. Showing that you can model the system a different way without reference to it, but by just introducing a parameter which neatly gives the right result, doesn't grant any additional explanatory power. It's just another opaque parameter: so, is "stiffness" wrapping up a quantum truth in a way which interacts with the real world? Is the uncertainty principle explanation unable to actually model these fields at all? I have no idea!
But the Uncertainty principle is something you can demonstrate in a first year lab with a laser and a diffraction grating, and turns up all the time in all sorts of basic physics (i.e. tunneling). Where does "stiffness" turn up and how does it relate? Again, I have no idea! The article purports to explain, but rather just declares.
It says that it's not necessary for this specific question :
https://profmattstrassler.com/2025/01/10/no-the-short-range-...
> quantum physics plays no role in why the weak nuclear force is weak and short-range. (It plays a big role in why the strong nuclear force is strong and short-range, but that’s a tale for another day.)
It seems to me that there is a 1:1 correlation between mass of virtual particle and field stiffness. Given that fact, why isn't it equally correct to say "The field stiffness is caused by the mass of the virtual particle" and "The virtual particle necessarily has mas because the field is stiff"
The author states that "it is short range because the particles that “mediate” the force, the W and Z bosons, have mass;" is misleading as to causality, but I missed the part where they showed how/why it was misleading.
Because in a classical theory, where there are no particles, there is still the same short range potential.
This arises from a parameter in the elementary field equation. If that parameter is non-zero than it is both true that the field is stiff and it must be mediated by a particle with non-zero rest mass. This says nothing about causality.
Correct. The author explains how both limited range and particles ability to have energy even at rest comes from "stiffness" (which is how he decided to call this parameter you talk about, in order to convey physics to laymen).
How I learned it, as a mere undergrad, was that the mass of the virtual particle for the field in question determined exactly how long it could exist, just by the uncertainty principle -- much like the way the virtual particles drive Hawking radiation.
In short, a massive virtual particle can exist only briefly before The Accountant comes looking to balance the books. And if you give it a speed of c, it can travel only so far during its brief existence before the books get balanced. And therefore the range of the force is determined by the mass of the force carrier virtual particle.
There's probably some secondary and tertiary "loops" as the virtual particle possibly decays during its brief existence, influencing the math a little further, but that is beyond me.
And the article we are discussing explains why this is incorrect.
The effect of stiffness can also be represented by stretchability of the string. Picking up a string with a free end will result in the same shape described by adding stiffness. A fanciful analogy might be a chain of springs with constant k2 where each spring junction is anchored to the ground with a spring with constant k1. If k2>>k1 the entire spring chain lifts in a gentle arc when a spring is lifted. If k1>>k2, only the springs near the pulling point really stretch and displace. It’s these kinds of simple analogies that engage our intuition. I still however cannot envision a mechanical analogy to demonstrate wavicles.
"In a quantum world such as ours, the field’s waves are made from indivisible tiny waves, which for historical reasons we call “particles.” Despite their name, these objects aren’t little dots; see Fig. 8."
Does anyone know when physicists realized that the world is not made of indivisible units called "particles" but waves? Is there a specific experiment or are we talking about the results of many experiments?
https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality
But he is not talking about wave particle duality. He explicitly states that it is not helpful "to imagine them as both wave and particle." He calls waves with very small amplitude "particles" (for historical reasons). So, according to this picture the building blocks of the universe are waves. It makes no difference if physicists choose to call a wave "particle". Calling a wave particle does not make the wave a particle.
> He explicitly states that it is not helpful "to imagine them as both wave and particle."
Where? I can't find that quote in the article.
> He calls waves with very small amplitude "particles" (for historical reasons).
The closest thing I see is
In a quantum world such as ours, the field’s waves are made from indivisible tiny waves, which for historical reasons we call “particles.”
Note the "indivisible" part. That's not how waves work in your everyday experience. The common understanding of "wave" is based on classical physics, where waves can be scaled up or down arbitrarily. But here you have "waves" which can only get so small, but no smaller, which he then goes on to parenthetically suggest calling "wavicles".
Is coining a new word which is literally a combination of "wave" and "particle" not a way "to imagine them as both wave and particle"?
I copied the quote you couldn’t find from his figure 8: “Figure 8: There’s no perfect intuition for quantum physics. But it’s not helpful to imagine photons and electrons as particles (top right), meaning a “tiny speck”. Nor is it helpful to imagine them as both wave (top left) and particle (top right).”
Thanks. I didn't find it because of the redacted parentheses.
What he's trying to explain without math is essentially the canonical quantization formalism due to Dirac, circa 1927:
https://en.wikipedia.org/wiki/Second_quantization
It's still the first approach to quantum field theory which physics students are likely to encounter.
His "wavicle" is essentially the field expectation value for a free particle. There is a nice animation (in the non-relativistic limit) here:
https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation
He seems to gloss over the connection to experiment though. Let's say you shoot an electron through slits in a screen and want to find out where it ends up using a photographic plate; you'll get a single dot somewhere on your plate, not an extended pattern. You can repeat the experiment with a new electron and get another dot, and keep repeating the experiment until all the dots form a pattern, in well known fashion:
https://en.wikipedia.org/wiki/Double-slit_experiment
The "wavicle" explains the pattern, but the pattern is made of dots...
The top of fig 3 doesn't accurately represent a string pulled down in the middle. A string pulled down in the middle would have no curve to it in the legs unless some force is acting on it, it would look like a V.
To me it seems like it's depicting a situation where the string hasn't been pulled fully, so some of its slack hasn't straightened out into the otherwise resulting triangle yet.
> Only stiff fields can have standing waves in empty space, which in turn are made from “particles” that are stationary and vibrating. And so, the very existence of a “particle” with non-zero mass is a consequence of the field’s stiffness.
It's really difficult to reconcile "standing waves in empty space" with "stiff fields". If the space is truly empty, then the field seems to be an illusion?
If we think about fields as the very old concept of aether, then it actually makes more intuitive sense. Stiffness then becomes simply the viscosity of the aether.
But I don't think this is where this article is trying to get us!!
fields are a non-mechanical aether, more precisely they are lorentz invarient (ie., their motion is the same for all observers)
And if you can hop from each standing wave node to the next, you can teleport, or move ridiculously fast by moving discretely instead of continuously. What if you could tune the wavelength of these standing waves with particles stationary and vibrating?
I like the speaker on water / styrofoam particle demonstration of standing waves.
Or change the frequency of the wave you are standing on (or those around you, I’m not sure which) and move forward like an inchworm
I believe this is not dissimilar to the mechanics suggested by the ZPE/antigravity people like Ashton Forbes
The real answer is we don't know or otherwise some kind of anthropic argument, i.e. the weak force has the range it does becuase otherwise we wouldn't have this kind of universe with people in it pondering why the weak force is the way it is.
Seems generally unhelpful to say 'the weak force is short range because it's field is stiffer!' When you can then immediately say 'well why is the weak force's field stiffer?'
In reality, little of what we understand in physics was predicted, because there are no underlying reasons to predict the universe works the way it does.
In reality, almost all of our math was retrodicted (the result of taking observation and creating math to fit it).
So, as you said, we're left with anthropic arguments or religious arguments.
For me, I've ended this song and dance by realizing the crazy math works because it was part of a plan.
The more you look at the math, the more you realize that:
1. We can only work from observation back to the math. There is no consistency to the math, except "these are the rules needed to make a stable, habitable universe."
2. Our current mathematical understanding is mostly approximations and idealizations. Every time we look at the universe at a deeper level, we find exceptions that we are fortunate exist, because they allow for a richer universe than our math suggested should exist. (Quantum mechanics is a good example. Things like quantum tunneling were not imagined 150 years ago, but it allows fusion to take place in the sun at far lower densities than should seem possible.)
So, I agree with you. I'm convinced the real answer will never be found in the math of physics, only in the realm of philosophy and religion.
Edit: I love science and I believe we should keep studying and asking how this all works. But, I feel we can make plenty of progress simply asking "how" it works and realize that at this point, "why" it works seems to be fully unanswerable by science.
Fundamentally, no matter how far we deep, there's always going to be that final "just because".
Got you, but I am unsure if moving to the next question isn't a success as well. You understood a thing and move on, rinse and repeat.
Or: consider where science would be had it operated under your proposed maxime for the past 3 centuries.
Not sure I get this because we have no deeper understanding using the example I gave.
I.e. The weak force is short range because it's field is stiffer -> the weak force's field is stiffer because it is more oblong -> the weak force's field is more oblong because it has more sparkles -> it has more sparkles because it ha slower mushiness -> it has more mushiness because ...etc.
We haven't gained anything in that sequence.
I don't think we can answer fundamental questions like this. The fine structure constant is the value it is because without that value we can't have a universe like this. Maybe in some multiverse system the physical laws and constants we know are fluid and can take different values in different universes but in our universe simply because of observation selection effects they can only be what they are.
Thw piano string produces a higer torque because it is shorter does not answer you why it is shorter or how waves travel exactly within it, but it sure as hell would be required knowledge to start researching beyond that first observation.
> The weak force is short range because it's field is stiffer.
May seem like a simple redirection that could go on forever, but we learned that fields can be stiffer, which probably wasn't all that clear. Now we can observe all other forces and look how their fields vary in terms of stiffness — a parameter we might not have thought about before. And by looking in those other places we might find a clue on how to shape an experiment that allows us to vary the stiffness. That could already have useful applications, but also lead to answering the question why some forces have stiffer fields than others.
This article goes to great contortions to avoid talking about electroweak theory or spontaneous symmetry breaking, both of which have decent Wikipedia articles, and are crucial to understanding what's going on here. Spontaneous symmetry breaking of the electroweak interaction and the Higgs mechanism is the reason _why_ the W and Z have mass. The article throws up a "who knows?" at this. When you write down the field equations for a massive boson field, you get an additional m^2 term in the denominator of the propagator, which contributes a e^(-r/m) term to the interaction force at low energy, such as the decay of a neutron or a weak-mediated nuclear decay.
Is there an ELI5 version of this? I think the article tries, and it's always cool to see physics described from a different vantage point.
My ELI5 version would be: fields with a massive gauge boson are "dragged down" in energy by the mass of the boson, so interactions propagate as if they have negative energy. What does a negative energy wave propagation look like? Similar negative energy wave propagations in physics are evanescent waves and electron tunneling, both of which have exponential drop-off terms, so it makes sense to see an exponential factor in massive boson interactions.
This is a lot of words to say that the field oscillations (i.e., particles) require very high energy. This shows up as the mass-(energy) of the particle, or stiffness of the field; take your pick.
Whether you call that stiffness or mass is a little beside the point IMO -- it shows up in the Yukawa force as an exponential dependence on that parameter which means the force quickly decays to zero unless the parameter is 0.
The reason is because of the anthropic principle. If it wasn't short range, we probably wouldn't exist and there would be no consciousness to observe it.
This particular article has a prelude on the same website
https://profmattstrassler.com/2025/01/10/no-the-short-range-...
Stiffness just seems to be rewriting mass as a different term. Only things with mass have stiffness, stiffness is exactly proportional to mass, light isn’t stiff…
One thing that confused me at the very beginning is, the author says the weak force is weak because it is short range. But the strong force is also short range.
The strong force is short range for a different reason. It's called [confinement][1]. The strong force gets stronger as you pull color charges apart. At some point the energy is so high that it's very likely that corresponding matching-color particles will exist, and so now there two pairs of close charges, instead of one pair of far charges.
[1]: https://en.wikipedia.org/wiki/Color_confinement
The weak force is weak not because it has "short range" but because its range "dies off at distances ten million times smaller than an atom".
> Google’s AI, for instance, and also here — that the virtual particles with mass actually “decay“
Do virtual particles decay?
"For the subtleties of different meanings of “mass”, see chapters 5-8 of my book.]"
Isn't this called "equivocation" in logic?
TLDR; It is short range primarily because the underlying fields (those of the W and Z bosons) are “stiff,” causing any disturbance to die off exponentially at distances much smaller than an atom’s diameter. In quantum language, that same stiffness manifests as the nonzero masses of the W and Z bosons, so their corresponding force does not effectively propagate over long distances—hence it appears “weak” and short-range.
No one answered my question, but I figured out a point on a tightly stretched rubber sheet or drumhead is better analogy than a spring, because the tighter the material, the more force required and the less propagation
So it’s like a stiff spring /strut vs a loose one? Doesn’t a loose suspension dampen and stiff propagate quicker though?
As an aside, is there conclusive evidence to say that no aether exists, or are we just saying it doesn't exist because a handful of tests were conducted to match what we thought this aether would behave like and the tests came back negative?
Lorentz formulated his ideas in terms of a motionless aether. But his aether theory yielded predictions identical to special relativity, so later physicists ditched his interpretation in favor of Einstein's theory that didn't need an undetectable global reference frame.
Overall, we can't really have 'conclusive evidence' against any mechanism, as long as our observations might possibly be simulated on top of that mechanism. So as far as evidence goes, 'what really exists' might be higher-dimensional strings, or cellular automata, or turtles all the way down, or whatever.
Instead, physics has some number of models (either complementary or competing) that people find compelling, and mechanisms on top of those models to explain our observations. If you did come up with a modern aether theory, you'd have to come up with a mechanism on top of it to explain all the relativistic effects we've observed.
We say the "aether" as it was originally conceptualized in the 19th century doesn't exist for the same reason we say that Russell's teapot or Carl Sagan's invisible dragon in the garage doesn't exist: we have a model of the world that makes all the same predictions without it, so it gets scraped right off by Occam's Razor.
For a strict enough definition of "conclusive," there is never conclusive evidence that something doesn't exist.
On top of that, if we find something that behaves nothing like what people meant when they said aether, then is it really aether?
You can call spacetime "aether" if you prefer - Einstein himself did. It's just that it becomes redundant at that point.
If electromagnetic radiation is propagating through some medium, then that medium is at rest with respect to all inertial reference frames simultaneously.
It's simpler not to have a medium. The field components transform a certain way under coordinate transformations, and that's all you need.
Magnetic field is that aether.
https://samzdat.com/2018/05/31/science-cannot-count-to-red-t...
PSA: it's "fib," not "phib"
No, his use is intentional. It's a portmanteau for "physics fib".
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