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Does quantum physics apply to other dimensions? Common sense seems to dictate that in a universe with two dimensions, quantum physics wouldn't apply, because particles would be vastly different from what we have in our universe, same for universes with four dimensions or more, but I was wondering if mathematically speaking quantum physics would be impossible.

In other words, does the mathematics of quantum physics imply that the universe must be of a certain dimension? I am at least guessing that it wouldn't work in a universe with 0 or 1 dimension.

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    $\begingroup$ Never use the words “common sense suggests” and “quantum mechanics” in the same sentence. Your guesses are wrong. Quantum mechanics is a framework that works in any dimension. $\endgroup$
    – Prahar
    Aug 21 at 6:51
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Our current leading theory of quantum physics is quantum field theory. For example this is what we use to describe the collisions at particle accelerators like the large hadron collider. Quantum field theory is experimentally tested to a very high precision.

But curiously we find that quantum field theory works in any number of dimensions. It's true that the physical behaviour it predicts is very different in different numbers of dimensions, but the theory itself works just fine. Indeed physicists often use quantum field theories in two space and one time dimension, or indeed just one space and one time dimension as models to help investigate various aspects of how the theory works. Alternatively, eleven dimensional supergravity is a quantum field theory that has been suggested as a way of including gravity in a quantum field theory.

The exception to this is string theory, where the theory requires that there be nine space and one time dimensions, though it remains to be seen whether this is physically relevant.

However in classical physics rather than quantum physics that we find arguments suggesting three space and on time dimensions are special. See for example Is 3+1 spacetime as privileged as is claimed?

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Simple quantum mechanical models such as the particle in a box model and the particle in a one-dimensional lattice model are one-dimensional, so we know quantum mechanics can be applied to a one-dimensional universe.

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As far as I know, there's no impediment to having a quantum-mechanical theory in different numbers of dimensions, and I'm not sure how you reach your "common sense" conclusion. You could describe something like a two-level quantum system as being zero-dimensional, since it has no notion of space.

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