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I know that on the smallest scales, general relativity predicts that space-time is flat. But I've also read that space-time can be described as a sort of "quantum foam" for distances smaller than the Planck length. Isn't this something of a contradiction (one more way in which quantum mechanics and general relativity disagree)? To make matters worse, theories about quantized space-time means that space-time could be "discrete", and not smooth at all.

So which principle does the physics community think is right? The idea of smooth, locally flat space-time, or the idea of "block-like", discrete space-time?

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    $\begingroup$ At any scales describable by modern physics, we go with smooth and locally flat. Works okay thus far (he said ignorantly) $\endgroup$ – Jim Aug 30 '14 at 18:29
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I know that on the smallest scales, general relativity predicts that space-time is flat

It's part of the Einstein Equivalence Principle that on a small scale spacetime is approximately described by the Minkowski metric, but you need to be clear that this is an assumption used to construct general relativity and it is not a prediction of general relativity.

As far as I know John Wheeler kicked off this debate with his ideas on spacetime foam. However this was based on the idea that the gravitational field was a fundamental field and could be quantised like all the other fields. Whether you are a string theorist, a loop quantum gravity fan or a supporter of the more speculative ideas like causal dynamical triangulation I would guess you'd agree that it doesn't make sense to describe spacetime as a smooth surface at the very smallest scales.

But the choice you offer between The idea of smooth, locally flat space-time or the idea of "block-like", discrete space-time is too restrictive. All the physicists I've discussed this with, and all the physicists I've seen interviewed on the subject, would agree something weird and currently not understood happens at the Planch scale, but no-one knows what it is.

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"Quantum foam" is a physical phantasy, for which no evidence exists, so far.

Having said that, contradictions between actual theories are normal and nothing to be upset about. Every theory has a range of applications, which is partly defined inside the theory and partly by its experimental limits. It is well understood, that Newtonian mechanics has nothing to say about electricity and that classical electromagnetism can not explain the stability of atoms. Nevertheless, it's much easier to navigate a spacecraft to Mars using classical mechanics than quantum field theory (even though that may be possible if somebody put their mind to it).

The main takeaway is, that physics is not only tolerant to having multiple descriptions of the same phenomena, it actually embraces them, as long as these theories are useful for the level of description of the universe that they were originally made for. The most interesting "stuff" in science always happens where things don't work. In case of physics that's at the limits of theories.

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  • $\begingroup$ This is a great statement and I hope all scientists take this very much to heart. Humans, I believe, have an inherent tendency to take things as either/or, or as a so-called "zero-sum" game. You see this a lot with QM vs. hidden-variable theories like SED. QM is the most accurate theory of all time, but it's got limits, and there may be a different approach that's compatible with QM but also with general relativity, etc. I think the work of Joy Christian and John Bush et al. is showing us that another paradigm shift may be coming. But as always more chickens need to hatch before it counts :D $\endgroup$ – CommaToast Mar 31 '15 at 17:41
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I know that on the smallest scales, general relativity predicts that space-time is flat.

This is not the case. First of all, General Relativity assumes that the spacetime on the smallest scales is flat. This is a pre-condition for GR mathematical apparatus to start to work. So, this cannot be the prediction of the theory.

Second, if we try to predict something with General Relativity, then we use its Einstein equation, saying that the curvature is proportional to the mass density. So if the mass density is uniform, then the curvature is uniform too, and the smaller the scale, the flatter is the spacetime. But this is not the case, when the mass density is not uniform. For example, for a point-like mass the curvature grows on the smaller scales. And as far as the modern particle physics knows, the fundamental particles are point-like.

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