Probably biased by the physicist I mostly listen to because they have a lot of lectures and talks online, Leonard Susskind and Nima Arkani-Hamed.
The idea that space is quantized is pretty unlikely to be true because of relativity, i.e. because of length contraction the size of those space quanta depends on the motion of the observer. So if you find those space quanta have a specific size in your reference frame I can just go to a reference frame moving relative to yours and I will see length contracted space quanta and we will therefore disagree on their size.
It is actually believed that neither space nor time are fundamental but that they emerge from something more fundamental because spacetime, relativity and quantum physics taken together are not really compatible, see for example "Space-time is doomed. What replaces it?" [1]. Susskind explores the idea that entanglement is what holds space together under the name "ER = EPR" [2].
So the lengths would seem contracted because you are actually traversing fewer pixels. Your information is "compressed" into fewer pixels, and pixels being the unit of length, your length contracts.
I'd be curious to know why the Planck length wouldn't be reference frame independent, though... (which may be explained in your links, but it will take some time to go through them).
Roughly because of Lorentz boost, aka length contraction. So if I take some distance, say 1m, and I look at it from relativistic speed it gets contracted. And if I do that from high enough speeds, it gets contracted below the Planck length, so a fundamental length constant would violate Lorentz symmetry.
Some people tried to construct such a theory, but as far as I understand, they are going nowhere. See
Well, if you have less length quanta then we could call them a unit of length, they would no longer be any kind of fundamental property. ( But actually the notion of a particle is a rather big problem of quantum field theory in curved backgrounds.)
This is essentially what I was asking - why wouldn't all inertial frames determine the size of length quanta to be the same, but disagree on the number of them between two events in spacetime.
Planck length, mass, time and so on are built from the most fundamental physical constants - the speed of light, the Planck constant and the gravitational constant - all of which are independent of the reference frame. But I don't think that is actually important.
It has more to do with units, i.e. the concrete value of the speed of light is determined by the way we defined the meter and the second and the same holds for the other constants. But that has no physical content, the value 299,792,458 m/s is a historical accident and we could as well have ended up with 42 foo/bar.
So what physicist do is just set those constants to one and get rid of those arbitrary numbers by choosing appropriatei units, e.g. the speed of light becomes one lightyear per year. Because nothing moves faster than the speed you can then also go further and measure velocities with a unitless value as a fraction of the speed of light, i.e. a number between zero and one, as it it appears in the equations of special relativity.
So if you throw those constants together in relatively simple expressions like hG/c³ you again get one as the numerical value and here for example something with units of area, the Planck area. But there is also no real physical content in the Planck units beyond that.
Because the laws of physics usually contain all the constants and values in small powers and with small factor like a Pi here and one half there those units define scales of length, time and so on where the quantities are all about one, nothing is ten to the twenty or minus thirty. So at that scales the laws of physics may show interesting behavior like (1 - v²/c²) becoming zero as v approaches c but that are also more like heuristics than hard truths.
So to make a long story short, Planck units are frame independent because they are built from constants and they are nice to think in because many things are of order one - a black hole of one Planck mass has probably a horizon of one Planck area or four Pi Planck areas or something small like that - but they are not that special.
But you seem to be claiming that spacetime is unlikely to be quantized because the Planck length or Planck time, i.e. the quanta of length in spacetime, would be contracted in different reference frames. Therefore Planck units of length/time wouldn't be frame invariant - they'd depend upon your inertial reference frame. So claiming Planck units are frame independent violates the idea that spacetime can't be quantized (at least for the reason you stated), since the quanta would experience relativistic contraction and dilation. The explanation seems to go against your original comment.
Edit: I may have given the wrong impression - when I said "Planck units" I meant quanta of space, time, area, etc. Not "natural units" where all relevant physical constants are taken to equal one. It appears the term "Planck units" refers to one of multiple sets of natural units, of which I was not aware: https://en.wikipedia.org/wiki/Natural_units#Planck_units
It depends if relativistic behaviour is emergent or fundamental. The whole point of the "spacetime is quantised" argument isn't just to suggest that spacetime comes in little lumps, but to investigate the possibility that the properties of spacetime - including curvature, relativistic effects, and all the weirdness in quantum theory - emerge from a common fundamental description.
Planck-scale invariance is a red herring - or rather, it's a naive assumption that may not be accurate. There isn't really much useful theory or experimental evidence in Planck-scale physics.
We have no reason to believe that the Planck length actually has any physical significance. It is just a way to get something of a certain order of magnitude from physical constants.
The quantization in quantum mechanics arises from constraints on the physical systems being studied. There are no constraints that would lead to length itself being quantized. You can get wavelength quantization for bound particles, but that's just for that particle, not for space in general.
That just means it can't be quantized in a lattice-like structure, it can still be 'foam'-like with some characteristic length.
Also I'm not entirely convinced that space-time and quantum field theory are completely incompatible. General relativity and Yang-Mills (in the classical limit) fit beautifully together, it would be extremely odd if this becomes impossible when you add quantum physics.
I don't see how the exact structure could be important. No matter what it exactly looks like you would probably introduce a preferred reference frame, the frame in which the space quanta are at rest. Or looking at it the other way round, you would observe different lengths when you measure those space quanta from different reference frames no matter what the exact structure is but that contradicts the assumption that they are fundamental and have observer independent properties.
Relativity does not allow for fundamental lengths because you can mix space and time by going to a different reference frame. You could maybe say that you have quanta of spacetime with some proper length, quanta that look like separation in space to some observers and like separation in time to others, but no idea if that makes any sense and it probably has not less problems than quanta of space.
Quantum physics and special relativity fit nicely together, the standard model and its parts are relativistic quantum field theories. The problems arise when one tries to combine general relativity and quantum physics. When someone says quantum physics and relativity are incompatible he pretty surly means general relativity not special relativity.
>I don't see how the exact structure could be important. No matter what it exactly looks like you would probably introduce a preferred reference frame, the frame in which the space quanta are at rest. Or looking at it the other way round, you would observe different lengths when you measure those space quanta from different reference frames no matter what the exact structure is but that contradicts the assumption that they are fundamental and have observer independent properties.
Well, you can make a Lorentz invariant theory of an ideal gas, this gives you what's called a relativistic fluid. This can be formulated in a completely Lorentz invariant way, meaning that things like the temperature and the average speed of the particles will be the same for every observer. This also implies that the average distance between particles will be the same for all observers. Which combined with the average speed, will give you a characteristic time.
So supposing you simply freeze a relativistic fluid in place you'll get an amorphous solid with a characteristic length scale and characteristic time scale. Which are both Lorentz invariant.
>Quantum physics and special relativity fit nicely together, the standard model and its parts are relativistic quantum field theories. The problems arise when one tries to combine general relativity and quantum physics. When someone says quantum physics and relativity are incompatible he pretty surly means general relativity not special relativity.
I was talking about general relativity; quantum field theories almost always use special relativity, it's trivial to combine those two. But it is even possible to extend (classical) Yang-Mills field theory from special to general relativity in a very natural way. But for some reason it's very difficult to 'quantize' the resulting field theory.
So supposing you simply freeze a relativistic fluid in place you'll get an amorphous solid with a characteristic length scale and characteristic time scale. Which are both Lorentz invariant.
Doesn't that work because the fluid has no particles in that description, because it is a continuous and smooth average about some ignored micro structure? It seems to me like you would easily loose that nice description if you replaced, for example, the smooth scalar mass density with a collection of discrete particles scattered throughout space. And that seems to be what you really want if you want to quantize space, discrete things, not smooth functions. But you seem to know physics way better than I, so I am probably missing the point, have some serious misunderstanding or something like that.
A relativistic fluid consists of actual discrete particles, although the quantities you can calculate will be be continuous approximations (very accurate ones). So, basically it is possible to make something discrete, with some associated length scale, but which looks the 'same' for all observers.
Even I am not entirely sure how to imagine such an object though, Lorentz boosts are difficult to wrap your head around.
By the way, I just realised it's a bit unclear what 'freezing it in place' means. Basically I meant that you just fix all trajectories of all particles, since there are no interactions you'll basically end up with some random straight lines. The distribution of these lines (i.e. their direction / position) will be the same for all observers.
I now see how that could work. I imagine creating two particle trajectories so that the distance between the particles is Lorentz invariant, i.e. it looks the same for all observers. Once you managed that you can kind of fill space with many copies making sure that the relation holds for all possible pairs.
I never thought about that and it I would probably naively have dismissed the idea that you can even have two trajectories that are Lorentz invariant let alone fill space that way. And it is even more unintuitive to me that you end up with something as well behaved as a fluid and not some totally unphysical mess.
Now I would really like to see a visualization of two or three such trajectories, assuming I am picturing that at least somewhat right.
You may also enjoy "The theoretical minimum" [1], a set of courses by Susskind covering physics from classical physics over relativity and quantum physics to string theory and cosmology. It's quite a bit beyond popular science and comes with math included but is still quite accessible if one is interested in some serious physics.
> If the universe were similarly segmented, then there would be a limit to the amount of information space-time could contain.
I thought there is a limit to the amount of information spacetime can contain: the Bekenstein bound[1], and its variations[2]. Though it's related to the surface area bounding the region, and not the volume enclosed itself. For a spherical cubic cm, about 10^66 bits, iirc.
I'm wondering about that as well. The closely related covariant entropy bound is predicated on both the holographic principle and our current understanding of quantum gravity, so I'm not sure if this finding calls that into question or not.
2. A networked/graphed space-time in which the nodes can have plank-scale (or larger) movements and re-arrangements.
But I'm not sure if this experiment disproves a space-time of fixed-position nodes which have additional properties (such as a field of scalars / vectors / spinors / etc).
To test the above I think measuring the smallest possible change-of-angle that a laser can make off a reflective surface (compounded X times) would do well. If the arrangement is as above, rotating the reflective surface by the smallest amount will affect the produced angle in a non-linear way (compared to larger amounts).
You don't have to describe infinite (or very many) ever smaller layers at all times -- as with the fractal example, you can just render them when someone looks at them (which is almost always never below some point) and only at those areas and levels in which they look (make measurements) at a particular moment.
Besides, we assume a simulation that's uniformly behaving at all points. They designer of the simulation could very well hard-code the result of that experiment to be what it is.
As always, observer-dependent effects are actually information-dependent effects.
In this case, the Universe is simulated as a single entity. Since the behaviour of the Universe depends on its contents (i.e. we can gain information about the contents by observing the overall entity), this coarse-grained simulation is forced to sub-divide into smaller regions. The simulation keeps subdividing (some regions more than others) until it reaches a level where some hard-coded criterion is reached that further subdivision will have no effect on the outcome. For example, if an entire planet is getting swallowed by a star, it is not useful to simulate each atom of the planet; just treat the whole thing as one entity.
Unfortunately, the simulation has to spend a lot of resources simulating part of the Milky Way galaxy, because it contains a chaotic mechanism of "life", which may cause an observable effect on the Universe as a whole, e.g. by seeding galaxies with star-engulfing, self-replicating megastructures. In the region around Earth, the simulation was forced to sub-divide to a level we might call "classical mechanics", in order to calculate outcomes with enough precision.
Unfortunately, during the 20th Century, more subdivision has become necessary, as "life" has begun performing "experiments" with a precision beyond that of the "classical mechanics" level. These experiments act as amplifiers, turning very small effects (such as the discrete nature of space) into large ones (such as the publication of scientific papers, development of technology, colonisation of intergalactic space, etc.).
It turns out that the Universe is written in Haskell, and a "print" statement caused a thunk to be forced ;)
Anyone outside the simulation for starters. If you run a simulation and zoom to a certain area, you want to see it properly "rendered".
And people inside the simulation too, I guess. If they make measurements at some specific area and zoom level, you want them to get results for that level consistent with their model of the world -- not to have them see the "seams" of the simulation engine so to speak.
In addition to the other points, the thing simulating us need not run on our physics, or even resemble our physics. They may have infinite computational power. We don't, but that doesn't mean anything about them.
From a purely scientific perspective the rational response would be to assume it's a yet-to-be-accounted-for experimental artifact, but no one in the reporting chain has an economic incentive to approach it that way.
> If the universe were similarly segmented, then there would be a limit to the amount of information space-time could contain.
Not really, if those "pixels" are a countable set. Is still wouldn't be continuous, but it could hold any information. Symbolic elements ("pixels", letters etc.) actually are basis of information, so it kind of implies a discrete space when information is involved.
The first time I learned about this project was from the BBC Documentary on Reality (excellent BTW) ... here is the holometer segment ... https://youtu.be/DbqB0--Td28?t=2346
Reading how sensitive this equipment can measure short duration displacements, and the distance the laser beams travel.. I wonder if - and how - they would adjust this for the drift due to the earth rotating. (and its speed is not even constant)
It's probably even way worse. I think it was one of the gravity wave experiments and they talked about how they picked up signals from people walking in neighboring building, cars driving on the highway and even the ocean waves hitting the beach while the beach was fifty or a hundred or so kilometers away. Maybe it's as simple as a high pass filter but I'd also like to know more about the details.
EDIT: It was probably not this exact article [1] but it matches my memories pretty well. They also mention some of the countermeasures.
The idea that space is quantized is pretty unlikely to be true because of relativity, i.e. because of length contraction the size of those space quanta depends on the motion of the observer. So if you find those space quanta have a specific size in your reference frame I can just go to a reference frame moving relative to yours and I will see length contracted space quanta and we will therefore disagree on their size.
It is actually believed that neither space nor time are fundamental but that they emerge from something more fundamental because spacetime, relativity and quantum physics taken together are not really compatible, see for example "Space-time is doomed. What replaces it?" [1]. Susskind explores the idea that entanglement is what holds space together under the name "ER = EPR" [2].
[1] http://www.cornell.edu/video/nima-arkani-hamed-spacetime-is-...
[2] https://youtube.com/watch?v=OBPpRqxY8Uw