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The parable of the ant walking on the surface of a balloon tells us that as the balloon expands, more of surface is created, hence more place for the ant to walk.

Space-Time is also in the same manner and also it does not make sense to ask "What space-time is expanding into?". The expanding universe itself is the cause of creation of space time.

So,will I be safe if I were to say "space time is produced by magic?"

Or will any theory tell me that I am wrong? Of course the work in physics is to provide a good model for the working of the world and may not be to answer questions such as this.

This question is serious. Replace the word "magic" by any other nonsense you want.But will any theory tell me that I am wrong? Or do we know how spacetime is produced?

Qmechanic
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Sidarth
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3 Answers3

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Physicists have a tendency to talk about spacetime as if it were a thing, maybe something like the rubber sheet so beloved of popular science explanations of GR. However spacetime is not a thing - it is a mathematical construction. Specifically it is a manifold equipped with a metric. At the risk of over-simplifying, a manifold is a thing that has dimensionality (four dimensions for spacetime) and a metric is a function that defines distances between points in the spacetime.

The point of all this is that you don't have to create spacetime because it isn't an object.

However there is an energy associated with a spacetime geometry, and it seems reasonable to ask where this energy is coming from in an expanding universe. The answer is a bit surprising because energy is not conserved in an expanding universe so the energy doesn't have to come from anywhere, it can just appear. The law of conservation of energy is based on a symmetry called time shift symmetry, but this symmetry is broken in an expanding universe and as a result the law of conservation of energy doesn't apply.

In the interests of completeness I should mention that conservation of energy in an expanding universe is something that physicists argue about. Specifically it depends on what you count as energy. I won't say more here as the subject has already been discussed to death in existing questions.

Community
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John Rennie
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Spacetime expands into the future.

An example is taking a 4d spacetime such as: $$\{(a,b,c,d):a,b,c,d\in\mathbb R\}$$ and then set time as $t=\sqrt{a^2+b^2+c^2+d^2}$ then for each value of $t$ you get a whole 3d surface, just like for each altitude $r=\sqrt{x^2+y^2+z^2}$ above the earth you get a whole 2d surface.

Now clearly a later time is just a surface farther from the center. And a space at one moment within a spacetime expands into a space at a later moment. It expands into the future. One surface is the earlier time, a surface farther from the center literally is a later time.

It's hard to imagine you expect anything else other than it expands to the future. Worldlines advance to the future, spacetimes expand into the future. It's what happens.

Timaeus
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In regards to how the space-time is produced, I would say through the creation of the Universe from a singularity or possibly a destabilization of the quantum fluctuations on the verge of that singularity. Exact answer is subtle and under debate. I hope a more rigorous explanation is out there favoring a particular scenario. Would love to hear that.

Benjamin
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