# Is space itself quantized?

kolkmvd
Hi,

Unfortunately I am not actively involved in physics anymore since high school, but still very interested in the matter. Something has been on my mind for a while and I could not find a answer to this on the internet. But maybe that's because I don't know the right way to look for it, or maybe it is just too complex for me. But my question is:

Has anyone theorized whether space itself is quantized?

I mean: if there would be something like a "minimum distance" of for instance the Planck length divided by some considerable constant, this would have funny consequences for the interactions of particles at quantum scale.

I think this idea might have other possible consequences:

- having a quantized space would mean particles cannot be at every position

- quantized space would also imply quantized time, because for a new state of the reality to exist, something has to change, otherwise it would go undetected.

- 'light speed' is just the effect we see of this quantisation, as it is the interaction of two (or more) nearby 'space points'.

I got triggered to this by http://www.nature.com/news/theoretical-physics-the-origins-of-space-and-time-1.13613 and I think the idea matches 'Causal dynamical triagulations' best, but that concept deals not with quantization.

I wish I'd started a carreer in physics to understand the matter better, but maybe someone on this forums is will to give some comments on this...

## Answers and Replies

kolkmvd
Yes, that looks quite similar!

mikeph
- having a quantized space would mean particles cannot be at every position
Why not?

Energy levels are quantised and there is no reason particles cannot exist in a superposition of more than one energy level! This browser window exists on my quantized computer screen and occupies more than one pixel.

- quantized space would also imply quantized time, because for a new state of the reality to exist, something has to change, otherwise it would go undetected.

You should be careful to distinguish between quantized space and a quantization of the field values at each point in space. I can give you an example of quantized space but continuous time:

Two points in space, x1 and x2. Let a particle's location in this quantized space be defined by f(x1,x2) = (1-t)*x1 + (t)*x2. As t evolves, continuously, from 0 to 1, the particle moves smoothly from x1 to x2. But it never occupies anywhere else but the two discrete points. Space is quantized but time is not!

Science Advisor
Two points in space, x1 and x2. Let a particle's location in this quantized space be defined by f(x1,x2) = (1-t)*x1 + (t)*x2. As t evolves, continuously, from 0 to 1, the particle moves smoothly from x1 to x2. But it never occupies anywhere else but the two discrete points. Space is quantized but time is not!

I think you're wading in deep water here. What happens to your example in the limit as t -> 0? In that case space is not quantized. If you say, well t can never be EXACTLY zero, then you're saying that time is quantized. I agree that quantized space implies quantized time based on your own example.

Science Advisor
Space and time are tied together in relativity, so if one if quantized, the other almost certainly is. But, as far as I know, there's no evidence currently of spacetime quantization, and in general relativity and quantum field theory, space and time are continuous.

Trenton
Energy levels are easy to determine and there are numerous rationales as to why particular energies are favoured and thus quantized. There is no equivent ease for measuring ultra small regions of space in order to detect (plank particle sized or worse) granules of vacuum. Doubtless if Zeno were alive today he would disagree.