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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)

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.

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:

   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.

[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.

'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.

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.

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.

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.

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.

I will go one deeper. Are fields (quantum fields) even 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

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

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.

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.

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).

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.

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/

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...

http://oyhus.no/QuantumMechanicsForProgrammers.html gives a flavor of one possible shape of things. It's pretty intractable to actually compute anything this way.

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.

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.

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.

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.

> 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.

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).

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 in a classical theory, where there are no particles, there is still the same short range potential.

And the article we are discussing explains why this is incorrect.

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.

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.

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.

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.

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".

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?

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...

https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality

No, his use is intentional. It's a portmanteau for "physics fib".