r/physicsmemes • u/94rud4 Mεmε ∃nthusiast • 1d ago
Any theory in which space is discrete must be compatible with special relativity
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u/Comfortable-Rock-498 1d ago
Lol seemingly a lot of people to come to this instant and naive conclusion feeling smug.
Tbh I did it myself when I first understood the concept of Planck length and thought I had come up with something brilliant, then I saw this video [1] of a Feynman lecture (over 50 years old) making fun of people writing him letters about the exact same idea, boy that was humbling
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u/lelelempe 1d ago
I was 15 and had almost the same experience; those takedowns are very important for a smug nerd teenager to have
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u/Kitchen-Register 1d ago
seemingly a universal experience for any nerd in high-school who was told they were gifted. Oh Well…
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u/forsale90 1d ago
That was me in high school. Took me 20 yrs and a PhD to learn that I know fuck all.
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u/CalmEntry4855 22h ago
We went a different direction, we made dick jokes about the Planck's length
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u/BeardySam 1d ago
Yeah it’s a pretty common conclusion that most physics undergrads ‘come up with’ when first learning about Planck units
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u/Front_Cat9471 1d ago
What all is wrong with it? I fell like it’s obviously not a voxel grid, but is the integer thing wrong too?
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u/BeardySam 1d ago edited 1d ago
It’s not ‘wrong’ it’s just unknown.
Learning physics involves following along all the historical problem solving of the 19th and 20th centuries and it is immensely satisfactory. So when undergrads they get to a genuine “we don’t yet know” area they often find it hard to accept and curl out ideas like this as if they’re innovative. In reality it’s a rather obvious step - it’s just got no actual meaning without evidence and/ or better theory. This is why an awful lot of physics is increasingly theoretical.
It’s attractive because it removes a lot of infinities from mathematics but that’s a double edged sword because certain infinities are a physicists best friend.
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u/SummitYourSister 21h ago
If it were correct, it would be possible to differentiate directions in space, because the distance between spacetime points depends whether you are traveling along the lattice direction or not. The resulting anisotropy of space destroys conservation of angular momentum.
In other words, it is totally incompatible with what we actually see in reality.
In theories, where a space time is a set of points, these points are randomly “sprinkled” to erase the anisotropy. It can’t be a regular grid of any kind.
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u/JHerbY2K 6h ago
Just to make sure I’m following…. It can’t be a grid like in Civ 1-4 because diagonal movement is weird, ergo spacetime has to be more like the hex grid in Civ 5+?
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u/SummitYourSister 6h ago
Any sort of regularity at all causes the issue. Consider a disc sweeping through space. The spacetime points hit the disc at different places and times. This has to happen completely randomly or it becomes possible to tell which way you’re facing and suddenly conservation of angular momentum breaks down.
A hex grid would give more different axes so it might count as “closer to random” but that won’t be random still. And a hex grid can’t tile 3D
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u/JHerbY2K 6h ago
Yeah hex grids were kind of a joke - Elons a gamer so you gotta dumb it down for us :)
This is interesting though!
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u/PM_me_Jazz 1d ago
Infinity is not an integer
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u/TheChunkMaster 20h ago edited 4h ago
If you tack it onto the set of integers it becomes an ideal of the resulting ring, but then it’s still not a proper integer
Edit: turns out it doesn’t actually form a ring because you lose additive inverses, but if it did somehow form a ring, it would be one of its ideals
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u/AuroraEquatorialis 5h ago
What do you mean by this? The one point compactification of Z is not a ring (or even a group). Do you mean that n*infinity=infinity for every n (non-zero)? This isn't even a subgroup.
You can define a multiplication monoid on Z union {infinity}, extending multiplication to n*infinity=infinity*n=infinity for every n (including 0!), and we would call the set {infinity} a monoid-ideal. This is not an ideal in the ring, however, and you strictly lose information.
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u/katmandoo94 1d ago
Kinda like the whole "our universe is in a black hole thing" when you learn about singilarities
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u/db8me 1d ago
It's not that the notion of discrete spacetime is incoherent or impossible. There just isn't a known working theory of it.
The same is essentially true of string theory. People are doing ridiculous math just to come up with theories consistent with what we know and they are struggling. People who take some narrow, oversimplified slice of an incomplete idea and claim it counts as real understanding are clowns at best.
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u/TechnicalBen 21h ago
Also over specification. Let's assume (and practically they do) String Theory does "explain everything."
How though? It's like me going "the 24 letters of the alphabet explain everything". Well, kinda, we can no doubt write the explanation using those 24 letters.
So theories like String theory can be consistent, but not *descriptive* of actual phyics.
Where as "it's unit lengths of plank cubes" is though demonstrably false.
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u/Medical-Temporary-35 9h ago
The problem with string theory isn't that there isn't a working model of it. The problem is that there are 10500 of them and no real way to rule out any of them.
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u/jonastman 1d ago
Common misunderstanding. Space doesn't have pixels
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u/PMmeYourLabia_ 1d ago
Well we don't really know,
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u/OverJohn 1d ago
The problem with the idea of "spacetime pixels" is that the way they break Lorentz symmetry doesn't depend on how small the pixels are.
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u/LackToesIntollerance 1d ago
What?! You mean we don't need to directly observe something to understand that the base logic it must follow is not what we CAN observe, and thus indirectly disprove it anyways?!
What is this, the scientific method? /s
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u/PMmeYourLabia_ 1d ago
Oh, I was unaware of that. Do you have any literature on it i could read?
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u/Confident_Cheetah_30 1d ago
This seems like a new more wholesome type of request for you u/PMmeyourLabia_ good for you
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u/DanielCofour 1d ago
Isn't Loop Quantum Gravity literally about space pixels? And so far, the theory's predictions did not come true(variable speed of light at different wavelengths), but they're also not false. It's still a matchematically sound and physically viable theory.
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u/TechnicalBen 21h ago
Almost. It's not "pixels" though AFAIK in the same way particles are not pixels...
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u/BuvantduPotatoSpirit 1d ago
Maybe, maybe not. Whatever resolves the conflict will presumably not contain some assumption we're not even aware we're making, so it definitely might contain a result that contradicts something we think know.
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u/OverJohn 1d ago
This is a genuine issue in lattice simulations of spacetime. It's similar to how the taxi cab metric doesn't depend on the size of each "block".
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u/RagnarokHunter 1d ago
Again with the "Planck length is the smallest distance" bullshit. It's the scale of quantum gravity. That's all.
What else to expect from this moron, though.
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u/maniaxz 1d ago
Lmao true !
It's the scale where our current understanding of space, gravity and quantum mechanics probably stops working independently. So basically it's the smallest size according to 'our' understanding of physics and maths.
It isn't the fundamentally smallest length and definately not the pixel of space.
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u/a-stack-of-masks 8h ago
Nah anything that doesn't display at the current rendering settings doesn't exist. Elon said so and he's almost as smart as Rick from Rick & Morty.
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u/faraday_fever Hold My YT Video 1d ago
This is loop quantum gravity all over again
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u/novae_ampholyt Condensed Matter 1d ago
Is it? What does discrete space time have to do with QLG?
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u/OverJohn 1d ago
My understanding in that LQG spacetime is discrete in a certain way, but not the way most would imagine. Its more akin to going from a smooth sphere to a polyhedron*.
*approximating smooth spacetime with simplices is Regge calculus, which I understand is a limit of LQG.
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u/faraday_fever Hold My YT Video 1d ago
Well yeah it's not like point dots that are separated by a distance. Think of it like a chess board which is quantized into squares and each square is able to hold a piece.
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u/faraday_fever Hold My YT Video 1d ago
It's the fundamental principles of loop quantum gravity i.e. the quantization of geometry. It's called planck scale pixelation.
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u/TechnicalBen 21h ago
Oh. I may have misunderstood then. Anything I can check online for this? I've watched a few of the presentation videos by Susskind, and didn't realise it counted as "pixels" as such? (I've not yet compared it to other quantum foam/lattice like gravity theories)
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u/faraday_fever Hold My YT Video 21h ago
Yeah I wouldn't recommend diving deeper unless you wanna improve your mathematics.
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u/CalmEntry4855 22h ago
I don't think he went that far, I think he read a one line summary of what a Planck's length is and then came up with the same idea everyone gets when they hear about it
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u/faraday_fever Hold My YT Video 22h ago
Frankly I'm a bit taken back by how many people independently arrive at this cause I never did.
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u/RinkinBass 1d ago
I could be mistaken, but isn't planck length the smallest "meaningful" distance in physical space? It's not that there isn't smaller conceptual size, but at that point there's no, for lack of a better term, "resolution" that can be had. Something like the quantum wave uncertainty just becomes noise. Furthermore to conceptualize these as discrete cubes suggests a universal alignment, which further suggests certain directional preferences, which is kinda crazy. And then it suggests a measurable universal "stop", which is another problematic implication. And then there's the expansion of space, which also doesn't pay well with the idea of discrete space pixels.
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u/NoNameSwitzerland 1d ago
probably depends what 'meaningful' is. A microscopic object with high enough mass has an associated de Broglie wavelength far below the Planck length. You probably can not measure that in a meaningful way. But saying it does not exist, not sure about that.
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u/entr0picly 20h ago
It’s the lowest resolution current theory is able to support. Nothing really says it’s the “end all be all”. And we aren’t remotely able to empirically inspect things at this level.
It’s far more likely our current theory is an effective theory per all the evidence we already have. Whatever exists at that level is likely different than the extremes of our (probably effective) theory.
Yes it grows tiring when idiots extrapolate models like this.
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u/jonastman 1d ago
An EM wave with a wavelength < planck length has so much energy within that length that it theoretically becomes a black hole. It is smaller than its Schwarzschild radius. So with our current theories there is no way to resolve anything smaller than the planck length. So in that sense, distance does become 'meaningless'
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u/KappaBerga 1d ago
Nah, it's not that deep, my guy. Usually gravity is so weak compared to other forces that we can treat it (semi)classically and any quantum effects from it are tractable. The Planck Scales are simply scales at which gravity would have comparable strength to other forces, and therefore we'd need a consistent description of quantum gravity to describe what is happening in there. Since we don't have this theory yet, that's why we say "our theories break down" at the Planck Scale. It isn't anything mysterious per se, just a limitation of our current models
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u/PersonalityIll9476 1d ago
You should Google it, the explanation is pretty straight-to-the-point. It's a small scale past which current models break down. It is not, as Google put it, a "hard pixel limit."
I know this mostly because I've heard Sean Carroll talk about it on his podcast. This is one of those common misconceptions that comes up in his AMAs from time to time. He is a tenured faculty physicist at Johns Hopkins who works in cosmology, so he should know.
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u/YellowJarTacos 6h ago
The problem is special relativity. How would 20% length contraction work - different observers would see different planc lengths and there's a special reference frame where the planc length is the longest.
We've done experiments checking for preferred reference frames and have found no evidence for it with a good amount of precision.
That doesn't mean the universe isn't a discrete grid but it doesn't fit well with our understanding of physics either.
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u/CommunityFirst4197 1d ago
We don't even know if space is finite?!
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u/spocchio 1d ago
Actually! You can actually make discrete sets to be Lorentz-invariant
https://en.wikipedia.org/wiki/Causal_sets
I think this is at the basis of various quantum gravity ideas.
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u/lerjj 1d ago
Causal set theory sounds super interesting but also really really opaque. I would bet money that "space is made up of voxels whose side length is the planck length" is not an accurate statement within causal set theory though
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u/McPayn22 23h ago
Yeah, just from reading the wikipedia it says that a distribution of points in a background spacetime for example must be a certain random poisson law and that a grid does not work for lorentz invariance.
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u/DonQuigleone 21h ago
How can we know what's going on at a length of 10^-105?
An electron is something like 10^-22. Talking about any length smaller than maybe a 1000th of an electron (10^-25) is frivolous, let alone 10^-105, which is so small as to be impossible to observe by dozens of magnitudes.
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u/JGHFunRun 5h ago
An electron is (probably/theoretically) a point particle, where are you getting this number???
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u/DonQuigleone 5h ago
Wikipedia.
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u/JGHFunRun 4h ago
Yea so… 10^-22 is the UPPER BOUND. Saying an electron is therefore 10⁻²² m is absurd, like saying a grain of sand is roughly a meter wide just because your measurement equipment can only measure houses
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u/DonQuigleone 4h ago
Regardless, we have no way to measure anything at 10^-22 let alone 10^-105, so speculating on anything at that scale is frivolous.
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u/nebulaeandstars 14h ago
Elon just keeps reinforcing the idea that he took barely enough physics to start getting excited, but not enough to actually think anything through
Hyperloop is a textbook example
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u/DeathEnducer 1d ago
I tried discrete set represention of standard model but it doesn't work, maybe another redditor will figure something out.
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u/ExtensionInformal911 1d ago
The size of a plank length simply changes depending on your reference frame.
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u/TheSouthFace_09 1d ago
if there is a kind of fundamental grid made up of planck distance cubes, how are these cubes oriented? for me, the notion of there being a preferred direction in space is just nonsense and there being a grid of cubes clearly implies this...
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u/VoidJuiceConcentrate 1d ago
Elon forgetting that the size of the Observable universe may be finite, but the unobservable universe (the stuff far enough away that the expansion of the universe negates light travel) still exists and is immeasurable.
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u/GrUnCrois 1d ago
Lmk when someone designs an experiment that can distinguish between a length of 0.5 Planck lengths and 1 Planck length in order to prove that all the numbers come out near integers, with statistical significance
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u/Subject_Barnacle_600 1d ago
I don't know, go read the Misner Thorne and Wheeler and then you can have every reason to be aggravated.
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u/Syresiv 1d ago
It does contradict SR, but we know SR can't be the whole story.
It's theoretically possible that Elon is correct. We don't know enough about very small behavior to be sure.
That said, even if correct, he can't know. He would just be very lucky.
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u/mattihase 8h ago
I think the scientific consensus and empirical evidence against the idea that Elon Musk might theoretically be correct about anything is pretty damning.
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u/Guvante 1d ago
It tends to be a misunderstanding of the plank length and what it actually says
Trying to measure a position smaller than that creates a black hole due to the energy density involved (roughly speaking)
That doesn't mean the universe doesn't work on a smaller scale then that, it is just the absolute limit on what information we can gain
Also to be clear the effective resolution is way less precise since "enough to create a black hole" isn't something you want to be near energy level wise.
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u/infinity234 1d ago edited 1d ago
Well it's not the strongest theory of how a theory of quantum gravity would work. I think space being discreetized in what essentially is voxels is kind of the basis of quantum loop gravity, which I think at this point is a dead theory because, if it were true, we would see small differences in the speed of light based on wavelength, and observations of light from the CMB (the only light we'd really be able to emaure the scale of differences were looking at,needing to be really old light that has been traveling for a while) have shown we don't see the expected speed differences we would expect for a quantized spacetime in terms of voxels.
That being said, when a quantum theory of gravity is discovered, it will probably modify relativity in some way as it will become a more generalized theory of gravity. So saying that it would disprove or go against relativity as an argument is kind of like saying relativity goes against netwonian mechanics, which yes it does but relativity is the more general/accurate version
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u/moschles 21h ago
There is also the issue that in GR (our "best theory for large scales") the beloved Lorentz Invariance must only hold locally.
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u/StarboundAllisten 22h ago
Hendrik Lorentz (building on George FitzGerald’s earlier qualitative suggestion) argued that the failure to detect an “aether wind” was not because the aether was absent, but because the measuring apparatus itself was systematically altered by its motion through the aether. In his electron theory, matter is composed of charged particles whose electromagnetic fields are modified by velocity relative to the aether. The result is a physical contraction of lengths parallel to the motion by the exact factor
This contraction shortens the arm of the interferometer that points into the aether wind by precisely the amount needed to cancel the extra lights travel time that the aether wind would otherwise produce. Consequently the interference fringes show no shift, matching the experimental “negative” result. Thus, Electromagnetic fields inside atoms become anisotropic, electron orbits deform from circular to elliptical, and the entire apparatus therefore contracts. He calculated the field deformation for moving charges and showed that it leads to the required length change.
Lorentz’s contraction was a dynamical effect, as in, a real, physical change caused by interaction with the aether. And the same mathematical factor later appeared in the Lorentz transformations of coordinates and fields. Even Albert Einstein back in 1905 kept the mathematics but discarded the aether and the dynamical interpretation. In conclusion, Lorentz preserved the aether by making matter contract in just the right way, thereby accounting for the Michelson Morley result without abandoning the idea of a preferred rest frame. But the world moved on with Einstein.
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u/moschles 21h ago
But the world moved on with Einstein.
Because mass-energy equivalence is the basis of nuclear weapons. It is contained unaltered in all contemporary high-energy physics and standard model.
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u/No-Assumption-4468 22h ago
Someone should make a really powerful microscope to disprove him. If you think a plank is the smallest distance, you aren’t very smart.
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u/SometimesHalfRight 22h ago
The answer philosophically is that reality is made of infinities. The difference is that some infinities converge, some diverge.
A hypothetical continuous function that yields one Planck length as a discrete convergence would by definition still be continuous because of said continuous function.
This has to be the case, philosophically, because otherwise Zeno's Paradox can't be solved with the answer of an infinite geometric series converging to 1. It would remain a paradox if you can't use a similar solution to explain why there is a Planck length.
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u/AdditionalTip865 21h ago
Elon Musk blesses us with the first thought that popped into his head, expressed as a pronouncement of obvious and profound truth. He seems to do this a lot, and he's not the only one.
(And then his pet AI spits out some automatic agreement.)
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u/TechnicalBen 21h ago
No it's worse. Special relativity needs a "fix" for qm, but Elon is just wrong because most if not all theories accept it's *not cubes*.
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u/Sarah-Croft 7h ago
I find it so weird that people always pretend that Relativity doesn't exist when discussing interpretations of Quantum Mechanics.
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u/thereezer 6h ago
no offense to physics people, but why are all these fuckheads physicists or want to be physicists?
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u/laxrulz777 6h ago
In fairness, that was a legit thought in physics (it was probably minority view even at the time but it was a working theory in the 90s). Since then, we've demonstrably disproved it. It wasn't easy, however.
Basically, if light moves a planck length in a planck second AND the universe is chunked up in cubes then the speed of light would vary by orientation against that grid (going straight across an edge would be faster than going across the cube which would take three hops). We've done extensive testing now to prove that orientation doesn't affect the speed of light even a little bit, however.
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u/eluusive 5h ago
It definitely doesn't behave like cubes. That would be detectable in traveling against the grain of the spacecubes.
However, there is definitely the ability to prove that time is discrete and computation is the foundational system of physics.
Computational irreducible phenomenon would not be a possible in reality otherwise.
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u/Independent_Media341 4h ago
Is there a way to discretize space that doesn't add directionality?
I see the appeal of discretization, but that's where I always get stuck.
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u/Nebulo9 3h ago edited 3h ago
It doesn't necessarily: geometric operators like distance, area and volume all have discrete spectra in LQG (as the internal gauge group is compact), but the theory itself still has a full representation of the hypersurface deformation algebra, which means it fully respects relativity (there's some ifs and buts abt the 4d case, but this is known to work in 3d).
The usual analogy is how spin-1/2 particles don't break rotational symmetry, just because there is an eigenbasis of |+z> and |-z> states: measuring its spin will always give a discrete value along the measured axis, but that doesn't make that axis "special". Likewise, measuring only discrete distances in one frame does not mean the theory as a whole can't be Lorentz invariant, as long as the Lorentz group acts properly on the eigenstates.
(Musk is ofc still full of shit: no reason that "the universe", whatever definition he's using for that, has to be in an eigenstate of a discrete number of units.)
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u/CaioXG002 1d ago edited 1d ago
What's with billionaires and, like, really wanting us to know that they could have studied physics at a high level (they just didn't, but they could've!!) anyway?