Athena's blog

Bigger on the inside

Athena Lilith Martin

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The TARDIS is meant to be a pocket dimension. But, if it weren't, if it were actually physically a larger space on the inside... What does general relativity tell us?

I'm not a physicist so this is based on my fuzzy intuition.

Well, spacetime has a constant density. You can't distort space without distorting time, and in order to add space (to make lines within an area longer) you have to take away time (making durations shorter). Essentially, you bend all the worldlines (paths through spacetime) from the time dimension into the space dimensions. Which means the inside of the TARDIS should run at an increased rate compared to the world beyond; you go inside for a few moments and when you emerge, much more time has passed. This is called time contraction, sibling to the more familiar time dilation experienced by fast-moving objects, and inseparably bonded to the length dilation that was our whole goal.

Now, this bending of time into space has other consequences. That is, after all, what acceleration is; you bend your worldline through spacetime away from one direction and towards another, trading off some of your constant speed-of-light motion (yes, you are currently moving at the speed of light, just mostly through time) from time to space or vice versa or between spatial directions. Bending all the worldlines in a region, well, that's what we call gravity. But normally, the gravity of massive/energetic objects shrinks space, expanding time. Because we're expanding space, that means the gravitational acceleration is actually negative. Away from the altered region.

And you can't shear spacetime; it has to bend smoothly, so the effect radiates outwards (diminishing the further it gets).

So the TARDIS is a powerful negative-gravity bomb that sends everything around it flying apart. Probably including itself. You could try to contain the negative gravity with a surrounding field of positive gravity, but that would only change the sign of the problem without affecting its magnitude. Now you have a black hole (or at least a very intense gravity well).

Probably best to say it's a pocket dimension.