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It is believed among people working on Quantum Gravity, that space-time must be quantised at the Planck scale. Although it is very hard to verify such proposition, it is interesting from a philosophical and epistemological point of view.

According to this view, no spatial or time interval shorter than the Planck values exist:

For length: $l_p=\sqrt{\frac{\hbar G}{c^3}}\sim 10^{-35}$m

For time: $t_p=\sqrt{\frac{\hbar G}{c^5}}\sim 10^{-43}$s.

Let us assume there is no structure smaller than $l_p$, and let us imagine some kind of cube of side $l_p$. This cube must be distinct and “distinguishable” from other similar cubes around it. For this to be possible, and for the cubes to be able to display some dynamics, something in the form of continuous space must stand in between these cubes.


If the above reasoning is correct, then, what is the meaning or need for space-time quantisation?

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Most of the people I know who think about quantum gravity study string theory, and they aren't assuming that spacetime is "quantized". They have a slightly more subtle picture in mind, in which space and time are continuous (in so far as they make sense at all) but physical effects prevent you from seeing features which are smaller than (roughly) the Planck scale. The idea is that we are not looking at something discrete, but rather that we are always seeing the world through blurry glasses.

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On the other hand, in loop quantum gravity, spacetime really is thought to be a discrete spin foam, or rather a quantum superposition of many spin foams. –  Nathan Reed Feb 23 '13 at 3:41
@user1504 Thank you for your answer. You are right; string theorists don’t think of space-time as a discrete “object.” Instead, they rather think of a physical length as being discrete (quantised so to speak) in the length of the string? On the other hand as mentioned by Nathan Reed, Loop QG theorists perceive space itself as being quantised. –  JKL Feb 23 '13 at 13:27
@John: Nope, string theorists don't think length is quantized either. Like I said, it's subtle; the physics of strings prevents experiments from resolving features smaller than the Planck scale, but there is no discreteness of the sort you seem to be imagining. –  user1504 Feb 23 '13 at 13:48
User1504 It is very subtle indeed! I meant it from the point of view of continuously dividing the length of a fundamental string to get strings arbitrarily shorter than the fundamental string length (Planck length.) –  JKL Feb 23 '13 at 14:18
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