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I realize this question is going to come off as extremely physical (as in physics) and might even be subjected to being closed but I think it is better for me to voice it here because I realize there are a lot of smart people that are in both stacks and well-versed in both.

So my question, is actually how small could space and time be? Are space and time continuous or discrete or even quantized?

To answer this question myself, I did some research and there are cosmological models like the Loop Quantum Gravity that say that space-time is not a background but actually emerge from the evolution of quantum states and are themselves quantized and discrete at the Plank volume and therefore the plank length.

Now one of my main questions stems from this answer, so is being discrete and being quantized the same thing? Apparently not necessarily, I saw a definition that said that to be quantized doesn't necessarily mean to be discrete but I don't understand how that could be. Would anyone care to explain?

Another question of mine that reside more on the philosophical side is whether we could ever know if space continues just like the number line infinitely smaller and bigger or if it is actually discretized? When Plank wrote the plank length I am pretty sure that He wasn't trying to say that that was the smallest length there could possibly be but that classical definition of the laws of physics change and so can we possibly know how small we can go to know realty?

I am partially aware of that this argument has been going for generation like Zeno and his teacher Parmenides claiming continuity where as people like Democritus trying to maintain a discrete nature of reality that is limited at the atom, but what makes it even more captivating is that right now we know that we can have particles that occupy spaces far smaller than the atom like the electrons and neutrinos and so maybe Zeno is right and space could be divided into smaller continuous segments i.e., space is continuous and not discrete.

Regardless, say, we know that space is discrete in some way would that make time discrete because it seems like time according to relativity is a dimension that is dependent on space and therefore would also be discrete making space-time discrete, but what does that say about the arrow of time, I understand that time and the arrow of time are different concepts and that arrow of time is more tied to thermodynamics and energy arrangement and entropy but it seems that even if time is slow or fast depending on the region of space the observer is in, the only thing that helps us separate the past from the future regardless is this arrow of time so now can we say the arrow of time is discretized in any way, can it be or is it necessarily continuous regardless of the theory or model we use?

Is Plank length a limit in reality or a limit of our knowledge? Is there no smaller scale than the Plank length or is the problem the fact that we are just not capable of measuring and comprehending such length?

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    Planck found energy is discrete. That limits how time can be measured but not whatever time actually is.
    – Chris Degnen
    Commented Jun 14 at 20:59
  • @ChrisDegnen Thank you, this is also what i think but do we know what time actually is, do we know what space-time is or is it just an incomplete model that can't be casted unto reality yet
    – How why e
    Commented Jun 14 at 21:01
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    I don't think you will find a comprehensive enough answer here. But, I could be surprised.
    – Scott Rowe
    Commented Jun 14 at 23:13
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    Quantized does not mean discrete. For energy it means that certain systems can only have it in increments of some value (quantum). This value is different for different systems, and some have continuous spectrum, so their energy is not quantized. Planck length is not the shortest length either. There is a heuristic argument based on uncertainty principle that no shorter length can be measured, but length is not an operator of quantum mechanics, like energy, so nothing precise can be said. Most likely, below some threshold space-time description breaks down and "how small" does not make sense.
    – Conifold
    Commented Jun 14 at 23:34
  • @Conifold So you are basically saying that one can infinitely go smaller the only problem is a matter of it making sense to us, not that it doesn't actually exist.
    – How why e
    Commented Jun 14 at 23:53

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We don't know whether spacetime is continuous or discrete. You might suspect it is discrete, on the grounds that almost everything else seems to be. As you know, there are various efforts underway to reconcile general relativity with quantum theory, from which all kinds of ideas have emerged but little certainty about any of them. One of the fundamental challenges to developing an improved theoretical framework is that the Planck scale- at which quantised effects are expected to be apparent- is utterly beyond the scope of our current experimental technology. Another is that the mathematics involved is hugely complicated. Given those challenges, you can expect progress to be slow.

The Planck length itself is just a unit of length, like the metre- you shouldn't make the mistake of assuming it is something more fundamental, like a quantum of length. If there is a quantum of length, it could be much bigger or much smaller than the Planck length.

The thermodynamic arrow of time is not especially relevant to the question of whether spacetime is quantised. It refers to the fact that many processes which are totally commonplace are vanishingly rare in reverse. For example, if you strike a cue ball to make a break at snooker, the balls scatter and as a result of countless collisions between the molecules forming the balls and those forming the cloth and the atmosphere, the energy of the balls is dispersed and they come to rest. In principle that process could reverse spontaneously if bazillions of air molecules just happened to strike all the balls in exactly the right way, but the probability of that occurring at random is effectively zero.

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  • +1 Well written, concise answer that I actually agree with. Although I must mention that there are some people and some communities of Scientists that are convinced enough that spacetime is actually both discrete and quantized, see wikiwand.com/en/Loop_quantum_gravity. And currently this model seems to be one of the well accepted models alongside string theory. One other thing, if the arrow of time is just probabilistic definition of reversibility, I feel like we need a clear cut definition that can separate the past from the future, not some thermodynamic concept that could fail.
    – How why e
    Commented Jun 15 at 19:28
  • I find the Planck density to be a useful quantity for exploding the notion that "Planck" means "minimum".
    – g s
    Commented Jun 16 at 0:39
  • @gs What exactly do you mean by minimum, minimum as in the minimum space there is in reality entirely, or minimum as in we can't explore such spaces because our limited knowledge and energy and access.
    – How why e
    Commented Jun 16 at 18:00
  • @Howwhye I mean that the Planck density is roughly a hundred million billion billion times bigger than the density that you would get if you took every single atomic nucleus of every single atom in the entire observable universe and put it in the same place. It's a pretty good candidate for the most uselessly large unit in all of physics.
    – g s
    Commented Jun 16 at 19:40
  • @gs I must disagree with your personal understanding of Plank to be "minimum" take Planck mass for instance there are particles and subatomic particles far smaller and bigger than this measurement so either your personal definition is wrong or your definition is inconsistent or Planck's scale and related measurements are not good enough.
    – How why e
    Commented Jun 17 at 0:46

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