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Mass and energy are interchangeable. Does that mean time and space are interchangeable too? Reason for question: The only difference I can comprehend between matter and energy is that energy has no duration; a photon does not age (even if the universe does). Matter has endurance, and travels through time. Close to a black hole (in regions of high gravitational fields), time slows, and the speed of light (as measured externally) would seem slower (would give doppler-like transformations); effectively time is converted into space; a photon may "appear" to take a year to travel a few yards (again, as seen from outside). But from the inside (the photon's-eye view) a light year is still a light year. So, can an area of space a few feet across (externally) be a light-year wide (internally) (TARDIS sort of thing)?

Famous Harley
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  • If it takes you 10 seconds to walk across a room, you exchange 10 seconds for the distance walked. If the room is 6 meters wide, this is expressed as 6/10 = 0.6 meters per second. You don't have to be near a black hole to exchange time for distance in the space-time manifold. – Ernie Aug 20 '15 at 20:21
  • Does that mean time and space are interchangeable too? you can go back and forwards, reverse your direction in other words, in space, but not in time. So in that way they are not interchangeable. –  Aug 20 '15 at 20:25
  • @AcidJazz: If I'm in the center of the room at time zero and on the left side at time one, then it's equally useful and equally accurate to say that my worldline goes from (center,zero) to (left, one) as to say that it goes from (left,one) to (center, zero). I can't see any meaningful sense in which "you can reverse your direction in space but not in time". (It's true of course that you can't go backward in time while going forward in time, but that has its exact analogue in the fact that you can't move left while moving right.) – WillO Aug 20 '15 at 21:12

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So, can an area of space a few feet across (externally) be a light-year wide (internally) (TARDIS sort of thing)?

Yes. It can and that's normal. If you made a region with less space inside than the surface area indicated that would require exotic matter. And with exotic matter you can make time machines. So ...

Ironically you need something smaller on the inside to make a time machine and being bigger on the inside is what normal matter does to space.

ln fact that is exactly what happens just outside a black hole the region that externally looks like has a little bit of space has a lot more and that contributes to it taking might longer to get outside. Its the balance between space and time that like has to get just right.

Timaeus
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