Holometer rules out first theory of space-time correlations
symmetrymagazine.org
symmetrymagazine.org
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-...
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.
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
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.
For an overview, see
http://newt.phys.unsw.edu.au/einsteinlight/jw/module6_Planck...
Some people tried to construct such a theory, but as far as I understand, they are going nowhere. See
I mean if spacetime is emergent why limit ourselves to an intuitive sense of what distance is.
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.
Hmm
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.
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.
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.
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.
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 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.
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.
There was a good HN discussion on the theoretical limits of information density a few years ago: https://news.ycombinator.com/item?id=6466430
1. A quantum foam space-time.
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.
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 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 ;)
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.
Maybe you have in mind countable dense?
https://news.ycombinator.com/item?id=10664272
Published acoincidentally on the 100th anniversary of Einstein's original General Relativity Paper.
EDIT: It was probably not this exact article [1] but it matches my memories pretty well. They also mention some of the countermeasures.
[1] http://www.nature.com/news/physics-wave-of-the-future-1.1556...