# What really is Spacetime?

What is a good definition on Space, Time and the most specific topic "Spacetime"? Because someone told me that spacetime is the foundation of the entire universe?

And also, Is it possible to create spacetime?

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I'm hopign ti doesn't get close and thanks for the help. – Nick1o2 Oct 22 '12 at 6:43
+1 good question :) – user10001 Oct 22 '12 at 13:21
Most physicists believe that i) Spacetime was created at big bang. ii) Energy controls its "shape" and "size" iii) If in some region of space you can create a high energy density then you can even create a hole in space time. iv) however nobody knows what spacetime would look like at such high energies, or even if it would exist or not. In particular, there is no agreement among physicists as to what should be a quantum theory of spacetime. – user10001 Oct 22 '12 at 13:44
Thanks everyone who helped! – Nick1o2 Oct 23 '12 at 6:50

Position and time are the parameters by means of which we identify where and when an event happens. Space is the collection of all possible positions, and spacetime the collection of all possible (time,position) pairs. Spacetime can therefore not be created by processes within our universe, it is the movie-like arena where everything happens.

Empirically, one finds that spacetime can be described mathematically by the structure of a 4-dimensional Lorentzian manifold without boundary. This is why we have 3 position coordinates and one time coordinate, no matter how we set up the coordinate system.

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In the picture of some quantum gravity approaches, space "atoms" can be dynamically created and destroyed by invoking creation and annhihilation operators, and time elapses in (very small) discrete steps ... – Dilaton Oct 22 '12 at 11:22
@Nemo: Yes, but quantum gravity is so far not established physics, only conjecture, and many scenarios are tried out. I was talking about established physics. – Arnold Neumaier Oct 22 '12 at 12:28
Yeah, it is not established but it is not excluded either I think ... ? Anyway, I like your answer. – Dilaton Oct 22 '12 at 12:54
@Nemo Please make a mental note of the following statement in the LQG article you reference, "Presently, no semiclassical limit recovering general relativity has been shown to exist." Meaning that LQG is yet to be shown to recover General Relativity in any limit. This would normally be the death of any theory of quantum gravity. – user11547 Oct 22 '12 at 19:26

The notion of dimension is related to the idea of distance. To say that time is like another dimension typically implies that we can measure some sort of "spacetime distance" between two events separated by space and time. Let's see how this is different from the old picture of space and time.

In the Galilean/Euclidean/Newtonian picture, we live in a universe with three dimensions, and the distance $\Delta s = \sqrt{\Delta x^2+\Delta y^2+\Delta z^2}.$ This quantity is invariant under rotations of the coordinate system or shifts $x\rightarrow x+\epsilon$. Notice that the separation between two events separated not only by a distance but a time cannot be captured by a single number.

In special relativity, time is like the another dimension. We have an invariant "spacetime distance" $\Delta s = \sqrt{\Delta x^2+\Delta y^2+\Delta z^2 - \Delta t^2},$ which is invariant under spatial rotations, shifts, and also boosts. In other words, two observers traveling at different speeds will agree on the "spacetime distance" between two events. This is not true in the Galilean picture.

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but note that this ''distance'' does not satisfy the triangle inequality, and becomes imaginary when one of the events is in the past or future of the other. – Arnold Neumaier Oct 22 '12 at 19:32