Here is one fact that seems, to me, pretty convincing that there is another layer underneath what we know.
The charge of electrons is -1 and protons +1. It has been experimentally measured out to 12 digits or so to be the same magnitude, just opposite charge. However, there are no theories why this is -- they are simply measured and that is it.
It beggars belief that these just happen to be exactly (as far as we can measure) the same magnitude. There almost certainly is a lower level mechanism which explains why they are exactly the same but opposite.
That's some interesting/wacky stuff, but there has been more research to improve those calculations - like deriving the electron charge and magnetic moment.
Personally I like the idea that a proton is somehow literally an electron and 3 up quarks (a neutron gets 2 electrons and 3 up quarks). I am not a physicist though, so I'm sure there are reasons they "know" this is not the case.
I find it fascinating that some physicists say wave functions are somehow "real" and then we've got Jacob Barandes saying you don't even need wave functions to do the computations of QM:
https://www.youtube.com/watch?v=7oWip00iXbo
IMHO there is a lot of exploration to be done without particle accelerators.
The hint from quantum field theory (and things like lattice gauge theory) is that charge emerges from interesting topological states/defects of the underlying field (by "interesting topological shapes" I mean - imagine a vortex in the shape of a ring/doughnut). It's kind of a topological property of a state of the photonic field, if you will - something like a winding number (which has to be an integer). Electric charge is a kind of "defect" or "kink" in the photonic field, while color charge (quarks) are defects in the strong-force field, etc.
When an electron-positron pair is formed from a vacuum, we get all sorts of interesting geometry which I struggle to grasp or picture clearly. I understand the fact that these are fermions with spin-1/2 can similarly be explained as localized defects in a field of particles with integer spin (possibly a feature of the exact same "defect" as the charge itself, in the photonic field, which is what defines an electron as an electron).
EDIT:
> However, there are no theories why this is -- they are simply measured and that is it.
My take is that there _are_ accepted hypotheses for this, but solving the equations (of e.g. the standard model, in full 3D space) to a precision suitable to compare to experimental data is currently entirely impractical (at least for some things like absolute masses - though I think there are predictions of ratios etc that work out between theory and measurement - sorry not a specialist in high-energy physics, had more exposure to low-energy quantum topological defects).
> something like a winding number (which has to be an integer). Electric charge is a kind of "defect" or "kink" in the photonic field, while color charge (quarks) are defects in the strong-force field, etc.
Technically, the charge of a proton can be derived from its constituent 2 up quarks and 1 down quark, which have charges 2/3 and -1/3 respectively. I'm not aware of any deeper reason why these should be simple fractional ratios of the charge of the electron, however, I'm not sure there needs to be one. If you believe the stack of turtles ends somewhere, you have to accept there will eventually be (hopefully simple) coincidences between certain fundamental values, no?
There does appear to be a deeper reason, but it's really not well understood.
Consistent quantum field theories involving chiral fermions (such as the Standard Model) are relatively rare: the charges have to satisfy a set of polynomial relationships with the inspiring name "gauge anomaly cancellation conditions". If these conditions aren't satisfied, the mathematical model will fail pretty spectacularly. It won't be unitary, can't couple consistently to gravity, won't allow high and low energy behavior to decouple,..
For the Standard Model, the anomaly cancellation conditions imply that the sum of electric charges within a generation must vanish, which they do:
3 colors of quark * ( up charge 2/3 - down charge 1/3) + electron charge -1 + neutrino charge 0 = 0.
So, there's something quite special about the charge assignments in the Standard Model. They're nowhere near as arbitrary as they could be a priori.
Historically, this has been taken as a hint that the standard model should come from a simpler "grand unified" model. Particle accelerators and cosmology hace turned up at best circumstantial evidence for these so far. To me, it's one of the great mysteries.
Well yes, but the coincidence that Quarks have charges of multiples of another particle, that is not made up of quarks, should rise your brow, shouldn't it?
Like we could accept coincidences if at the bottom is all turtles, but here we see a stack of turtles and a stack of crocodiles and we are asking why they have similar characteristics even if they are so different.
I'm aware of the charge coming from quarks, but my point remains.
> you have to accept there will eventually be (hopefully simple) coincidences between certain fundamental values, no?
When the probability of coincidence is epsilon, then, no. Right now they are the same to 12 digits, but that undersells it, because that is just the trailing digits. There is nothing which says the leading digits must be the same, eg, one could be 10^30 times bigger than the other. Are you still going to just shrug and say "coincidence?"
That there are 26 fundamental constants and this one is just exactly the same is untenable.
I think I agree with you. It could be just a matter of static bias or some other fairly simple mechanism to explain why these numbers are the same.
Imagine an object made of only red marbles as the 'base state'. Now you somehow manage to remove one red marble: you're at -1. You add a red marble and you're at +1. It doesn't require any other marbles. Then you go and measure the charge of a marble and you and up at some 12 digit number. The one state will show negative that 12 digit number the other will show positive that 12 digit number.
Assigning charge as being the property of a proton or an electron rather than one of their equivalent constituent components is probably a mistake.
If you imagine the universe is made of random real fundamental constants rather than random integer fundamental constants, then indeed there's no reason to expect such collisions. But if our universe starts from discrete foundations, then there may be no more satisfying explanation to this than there is to the question of, say, why the survival threshold and the reproduction threshold in Conway's Game of Life both involve the number 3. That's just how that universe is defined.
Why do you assume the two have to be small integers? There is nothing currently in physics which would disallow the electron to be -1 and the proton to be +1234567891011213141516171819. The fact they are both of magnitude 1 is a huge coincidence.
I'm not assuming they have to be small integers—I'm saying that if the universe is built on discrete rather than continuous foundations, then small integers and coincidences at the bottom-turtle theory-of-everything become much less surprising. You're treating the space of possible charge values as if it's the reals, or at least some enormous range, but I consider that unlikely.
Consider: in every known case where we have found a deeper layer of explanation for a "coincidence" in physics, the explanation involved some symmetry or conservation law that constrained the values to a small discrete set. The quark model took seemingly arbitrary coincidences and revealed them as consequences of a restrictive structure. auntienomen's point about anomaly cancellation is also exactly this kind of thing. The smallness of the set in question isn't forced, but it is plausible.
But I actually think we're agreeing more than you realize. You're saying "this can't be a coincidence, there must be a deeper reason." I'm saying the deeper reason might bottom out at "the consistent discrete structures are sparse and this is one of them," which is a real explanation, but it might not have the form of yet another dynamical layer underneath.
It's simple to say "Ah well, it's sparse" that doesn't mean anything and doesn't explain anything.
Symmetries are equivalent to a conserved quantity. They exist because something else is invariant with respect to some transformation and vice versa. We didn't discover arbitrary constraints we found a conserved quantity & the implied symmetry.
"There are integers", "the numbers should be small" all of these are nothing like what works normally. They aren't symmetries. At most they're from some anthropic argument about collections of universes being more or less likely, which is its own rabbit hole that most people stay away from.
Perhaps only visible matter is made up of particles with these exactly matching charges? If they did not match, they would not stay in equilibrium, and would not be so easily found.
Whence your confidence? As they say in math, "There aren't enough small numbers to meet the many demands made of them." If we assume the turtle stack ends, and it ends simply (i.e. with small numbers), some of those numbers may wind up looking alike. Even more so if you find anthropic arguments convincing, or if you consider sampling bias (which may be what you mean by, "in stable particles that like to hang out together").
Which makes every constant fair game. Currently, we don’t have a good process for explaining multiple universes beyond divine preference. Hence the notion that a random number settled on mirror whole sums.
As soon as charge is quantized, this will happen. In any quantization scheme you will have some smallest charge. There are particles with charge +2 (the Delta++, for example), but ... anything that can decay while preserving quantum numbers will decay, so you end up with protons in the end. (ok, the quarks have fractional charge but that's not really relevant at scales we care about QED)
If the question is, why is quantum mechanics the correct theory? Well, I guess that's how our universe works...
One argument (while unsatisfying) is there are trillions of possible configurations, but ours is the one that happened to work which is why we're here to observe it. Changing any of them even a little bit would result in an empty universe.
There’s a name for that: the Anthropic principle. And it is deeply unsatisfying as an explanation.
And does it even apply here? If the charge on the electron differed from the charge on the proton at just the 12th decimal place, would that actually prevent complex life from forming. Citation needed for that one.
I agree with OP. The unexplained symmetry points to a deeper level.
I was born to this world at a certain point in time. I look around, and I see environment compatible with me: air, water, food, gravity, time, space. How deep does this go? Why I am not an ant or bacteria?
Agreed (well, assuming the delta is more than a small fraction of a percent or whatever). But this is begging the question. If they are really independent then the vast, overwhelming fraction of all possible universes simply wouldn't have matter. Ours does have matter, so it makes our universe exceedingly unlikely. I find it far more parsimonious to assume they are connected by an undiscovered (and perhaps never to be discovered) mechanism.
Some lean on the multiverse and the anthropic principle to explain it, but that is far less parsimonious.
Also note that the proton is not an elementary particle so it is really a question of "are the various quarks really 1/3, 2/3 of an electron charge".
Crackpots have found thousands of formula that try to explain the ratio of the proton to electron mass but there is no expectation that there is a simple relationship between those masses since the proton mass is the sum of all sorts of terms.
Crackpots are downstream of the "physics community" awarding cultural cachet to certain types of questions -- those with affordances they don't necessarily "deserve"-- but not others.
(I use quotes because those are emergent concepts)
Same as "hacker community" deciding that AI is worth FOMO'ing about
An interesting early theory of gravity was: "What if opposite charges attract slight more strongly than identical charges repel each other?"
If you tally up the forces, the difference is a residual attraction that can model gravity. It was rejected on various experimental and theoretical grounds, but it goes to show that if things don't cancel out exactly then the result can still leave a universe that would appear normal to us.
For a given calculation on given hardware, the 100th digit of a floating point decimal can be replicated every time. But that digit is basically just noise, and has no influence on the 1st digit.
In other words: There can be multiple "layers" of linked states, but that doesn't necessarily mean the lower layers "create" the higher layers, or vice versa.
Or why the quarks that make up protons and neutrons have fractional charges, with +1 protons mixing two +2/3 up quarks and one -1/3 down quark, and the neutral neutron is one up quark and two down quarks. And where are all the other Quarks in all of this, busy tending bar?
They have fractional charges because that is how we happen to measure charge. If our unit of charge had been set when we knew about quarks, we would have chosen those as fundamental, and the charge of the electron would instead be -3.
Now, the ratios between these charges appear to be fundamental. But the presence of fractions is arbitrary.
> If our unit of charge had been set when we knew about quarks, we would have chosen those as fundamental, and the charge of the electron would instead be -3.
Actually, I doubt it. Because of their color charge, quarks can never be found in an unbound state but instead in various kinds of hadrons. The ways that quarks combine cause all hadrons to end up with an integer charge, with the ⅔ and -⅓ charges on various quarks merely being ways to make them come out to resulting integer charges.
Isn’t charge quantized? Observable isolated charges are quantized in units of e. You can call it -3 and +3 but that just changes the relative value for the quanta. The interesting question is still why the positive and neutral particles are nonelementary particles made up of quarks with a fraction of e, the math made possible only by including negatively charged ones (and yet electrons are elementary particles).
This is "expected" from theory, because all particles seem to be just various aspects of the "same things" that obey a fairly simple algebra.
For example, pair production is:
photon + photon = electron + (-)electron
You can take that diagram, rotate it in spacetime, and you have the direct equivalent, which is electrons changing paths by exchanging a photon:
electron + photon = electron - photon
There are similar formulas for beta decay, which is:
proton = neutron + electron + (-)neutrino
You can also "rotate" this diagram, or any other Feyman diagram. This very, very strongly hints that the fundamental particles aren't actually fundamental in some sense.
The precise why of this algebra is the big question! People are chipping away at it, and there's been slow but steady progress.
One of the "best" approaches I've seen is "The Harari-Shupe preon model and nonrelativistic quantum phase space"[1] by Piotr Zenczykowski which makes the claim that just like how Schrodinger "solved" the quantum wave equation in 3D space by using complex numbers, it's possible to solve a slightly extended version of the same equation in 6D phase space, yielding matrices that have properties that match the Harari-Shupe preon model. The preon model claims that fundamental particles are further subdivided into preons, the "charges" of which neatly add up to the observed zoo of particle charges, and a simple additive algebra over these charges match Feyman diagrams. The preon model has issues with particle masses and binding energies, but Piotr's work neatly sidesteps that issue by claiming that the preons aren't "particles" as such, but just mathematical properties of these matrices.
I put "best" in quotes above because there isn't anything remotely like a widely accepted theory for this yet, just a few clever people throwing ideas at the wall to see what sticks.
> This is "expected" from theory, because all particles seem to be just various aspects of the "same things" that obey a fairly simple algebra.
But again, this is just observation, and it is consistent with the charges we measure (again, just observation). It doesn't explain why these rules must behave as they do.
> This very, very strongly hints that the fundamental particles aren't actually fundamental in some sense.
This is exactly what I am suggesting in my original comment: this "coincidence" is not a coincidence but falls out from some deeper, shared mechanism.
Sure, but that's fundamental to observing the universe from the inside. We can't ever be sure of anything other than our observations because we can't step outside our universe to look at its source code.
> It doesn't explain why these rules must behave as they do.
Not yet! Once we have a a theory of everything (TOE), or just a better model of fundamental particles, we may have a satisfactory explanation.
For example, if the theory ends up being something vaguely like Wolfram's "Ruliad", then we may be able to point at some aspect of very trivial mathematical rules and say: that "the electron and proton charges pop out of that naturally, it's the only way it can be, nothing else makes sense".
We can of course never be totally certain, but that type of answer may be both good enough and the best we can do.
Well OK then! Let's tell all the physicists they can close up shop now. They might not have realized it, but they're done. All their little "theories" and "experiments" and what not have taken them as far as they can go.
> Let's tell all the physicists they can close up shop now.
Yes, that's part of the plan. I mean, not to all the physicists, just to those whose work doesn't bring in results anymore, and it hasn't for 30 to 40 years now. At some point they (said physicists) have to stop their work and ask themselves what it is that they're doing, because judging by their results it doesn't seem like they're doing much, while consuming a lot of resources (which could have been better spent elsewhere).
We're already in the realm of virtual particles, instantaneous collapse, fields with abstract geometric shape and no material reality, wave particle duality, quantized energy etc. The project of physics was to discover what the universe was made of. None of these things can answer that. If intelligibility was the goal, we lost that. So in an important sense, they might as well have closed up shop. If you're interested in the specific value of a certain property to the nth decimal place, there is work to do, but if you're interested in the workings of the universe in a fundamentally intelligible sense, that project is over with. What they're doing now is making doodles around mathematical abstractions that fit the data and presenting those as discoveries.
By observing the discrepancies between theories we are accessing those layers. Whether we can access them with instruments is a different matter but with our minds we apparently can.
The charge of electrons is -1 and protons +1. It has been experimentally measured out to 12 digits or so to be the same magnitude, just opposite charge. However, there are no theories why this is -- they are simply measured and that is it.
It beggars belief that these just happen to be exactly (as far as we can measure) the same magnitude. There almost certainly is a lower level mechanism which explains why they are exactly the same but opposite.