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What confuses me about black holes is that they appear to break time symmetry. Most equations in physics can be run forwards or backwards and the equations wor

What confuses me about black holes is that they appear to break time symmetry. Most equations in physics can be run forwards or backwards and the equations work the same. But if you imagine taking an object just after crossing the event horizon of a black hole, and then you were to flip the sign of its velocity vector so it was going backwards the way it came, you might expect the math to predict it to fly back out of the black hole. But, this can’t be right if nothing can escape the gravity of a black hole. Running the simulation backwards must not retrace the path it took when it went in. Doesn’t that break time symmetry?

r0uv3n 3y ago
No, classical general relativity is entirely time symmetric: time symmetry means here that if you have a solution for the equations that describe nature, then you still have a solution after you make the coordinate transformation t -> -t. This follows directly from the fact that the Einstein field equations involve only tensors and are thus diffeomorphism invariant. For the case of a black hole, the solution you get by reversing time describes a white hole., which is again an entirely valid solution to the Einstein field equations.
- fallingfrog 3y ago
  Ah I see! Time reversed, every path eventually exits the black hole. So it’s a different thing. Thank you
Ygg2 3y ago
Time symmetry can be broken. Just not Charge Parity Time symmetry. Also if you invert time, black hole behaves differently.
evanb 3y ago
Time reversal symmetry is probably the most subtle of the discrete symmetries. Suppose you have a video that follows the moon and the Earth from some distance but that no other celestial bodies are visible, for simplicity. If you reversed the orbit of the moon but didn't change the rotational sense of the Earth (sun rises in the east) then you could distinguish a video of that system from the original true-to-life video played backwards. Only if you ALSO reverse the rotational sense of the Earth (sun rises in the west) do you have a system that you can't distinguish from a backward true-to-life video. The same thing is happening in your scenario; if you want to apply time reversal, you'd better time reverse EVERYTHING relevant. Here, what you're missing is that you also need to time-reverse the black hole, which produces something called a white hole [0]. We have never observed any white-hole like object. But the point is, if you take your time-reversed object at the just-inside-the-bh-event-horizon radius away from the white hole's center, you'd get the correct reverse simulation. [0] https://en.wikipedia.org/wiki/White_hole https://en.wikipedia.org/wiki/White_hole
- fallingfrog 3y ago
  This makes sense! Thank you

r0uv3n 3y ago

No, classical general relativity is entirely time symmetric: time symmetry means here that if you have a solution for the equations that describe nature, then you still have a solution after you make the coordinate transformation t -> -t. This follows directly from the fact that the Einstein field equations involve only tensors and are thus diffeomorphism invariant. For the case of a black hole, the solution you get by reversing time describes a white hole., which is again an entirely valid solution to the Einstein field equations.

fallingfrog 3y ago
Ah I see! Time reversed, every path eventually exits the black hole. So it’s a different thing. Thank you

Ygg2 3y ago

Time symmetry can be broken. Just not Charge Parity Time symmetry. Also if you invert time, black hole behaves differently.

evanb 3y ago

Time reversal symmetry is probably the most subtle of the discrete symmetries. Suppose you have a video that follows the moon and the Earth from some distance but that no other celestial bodies are visible, for simplicity. If you reversed the orbit of the moon but didn't change the rotational sense of the Earth (sun rises in the east) then you could distinguish a video of that system from the original true-to-life video played backwards. Only if you ALSO reverse the rotational sense of the Earth (sun rises in the west) do you have a system that you can't distinguish from a backward true-to-life video. The same thing is happening in your scenario; if you want to apply time reversal, you'd better time reverse EVERYTHING relevant. Here, what you're missing is that you also need to time-reverse the black hole, which produces something called a white hole [0]. We have never observed any white-hole like object. But the point is, if you take your time-reversed object at the just-inside-the-bh-event-horizon radius away from the white hole's center, you'd get the correct reverse simulation. [0] https://en.wikipedia.org/wiki/White_hole https://en.wikipedia.org/wiki/White_hole

fallingfrog 3y ago
This makes sense! Thank you