Re: [math-fun] dumb question about general relativity
My original question regarded "classical" GR, where interchanging "positive" and "negative" time doesn't change any laws. I.e., if you take a GR movie and simply run it backwards, it still agrees with all the GR laws. So, you don't need any notion of "white holes" -- I'm still talking about regular old "black" holes. So, nothing in these laws keeps such a black hole from burping an object out into space. We can ask what initial conditions would enable such a burp & may complain that they are highly unlikely, but they aren't ruled out by the laws themselves. Now I'm curious about what this implies for the "classical" energy, momentum, etc., of the object being burped. At 03:40 PM 7/24/2009, Dan Asimov wrote:
Re time reversal:
The fact that in our neighborhood in spacetime we see stars radiating only in positive time -- and all the entropic consequences of this -- is usually attributed to initial conditions, not to any actual "law" of physics.
(The Ehrenfest urn model is usually considered a good microcosm of thermodynamics, and shows time reversal symmetry.)
It's just a guess, but it seems likely to me that we are aware of only a small or infinitesimal fraction of the universe, and that some other time and place have stars radiating in negative time.
(Or is it possible that entropically opposite parts of the universe somehow always end up pinching off from each other by black holes?)
--Dan
Classical mechanics is invariant under translations in time - this results in conservation of energy via Noether's Theorem. Classical mechanics is *not* invariant under time reversal, as others have pointed out, since this violates the Second Law of Thermodynamics. I don't know what the implications of this are via Noether's Theorem, and I would be very interested in what others more knowledgeable than myself have to say. Note also that even Quantum Field Theory is not invariant under time reversal (T), but only under the combination of CPT (C = charge conjugation and P = parity). Rowan. Henry Baker wrote:
My original question regarded "classical" GR, where interchanging "positive" and "negative" time doesn't change any laws. I.e., if you take a GR movie and simply run it backwards, it still agrees with all the GR laws.
So, you don't need any notion of "white holes" -- I'm still talking about regular old "black" holes.
So, nothing in these laws keeps such a black hole from burping an object out into space.
We can ask what initial conditions would enable such a burp & may complain that they are highly unlikely, but they aren't ruled out by the laws themselves.
Now I'm curious about what this implies for the "classical" energy, momentum, etc., of the object being burped.
At 03:40 PM 7/24/2009, Dan Asimov wrote:
Re time reversal:
The fact that in our neighborhood in spacetime we see stars radiating only in positive time -- and all the entropic consequences of this -- is usually attributed to initial conditions, not to any actual "law" of physics.
(The Ehrenfest urn model is usually considered a good microcosm of thermodynamics, and shows time reversal symmetry.)
It's just a guess, but it seems likely to me that we are aware of only a small or infinitesimal fraction of the universe, and that some other time and place have stars radiating in negative time.
(Or is it possible that entropically opposite parts of the universe somehow always end up pinching off from each other by black holes?)
--Dan
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Quoting Rowan Hamilton <rowanham@gmail.com>:
Classical mechanics is *not* invariant under time reversal, as others have pointed out, since this violates the Second Law of Thermodynamics.
But that is not true, at least for a time independent or symmetric Hamiltonian. The Second Law is a statistical, or even empirical law, and is not part of Classical Mechanics; look at Poincare's recurrence theorem, for example. - hvm ------------------------------------------------- www.correo.unam.mx UNAMonos Comunicándonos
On Sat, Jul 25, 2009 at 10:21 PM, <mcintosh@servidor.unam.mx> wrote:
Quoting Rowan Hamilton <rowanham@gmail.com>:
Classical mechanics is *not* invariant under time reversal, as others have pointed out, since this violates the Second Law of Thermodynamics.
But that is not true, at least for a time independent or symmetric Hamiltonian. The Second Law is a statistical, or even empirical law, and is not part of Classical Mechanics; look at Poincare's recurrence theorem, for example.
From the perspective of an outside observer, the infalling matter never gets into the black hole. Time-reversing that gives a picture in which there's matter just outside the Schwarzschild radius that moves away from the star; that certainly happens all the time, so there's no contradiction with the second law. It's possible, though very difficult, to arrange things to end up in a low entropy state--for instance, Honda's Rube-Goldberg commercial used no computer graphics and required 606 takes.
http://video.google.com/videoplay?docid=-4187430023476942057 For an observer falling into the star, the light outside gets more and more blue-shifted, because from his perspective time outside is passing more quickly. Crossing over the Schwarzschild radius, the light is infinitely blue shifted and infinite time passes. (So if you want to solve the halting problem, leave your computer in orbit around a black hole and jump in! It will do infinitely many calculations in a finite time from your perspective.) -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com
On Fri, Jul 24, 2009 at 10:21 PM, Henry Baker <hbaker1@pipeline.com> wrote:
My original question regarded "classical" GR, where interchanging "positive" and "negative" time doesn't change any laws. I.e., if you take a GR movie and simply run it backwards, it still agrees with all the GR laws.
Yes, but the object in the center is not a black hole; it's the time-reversal of a black hole. A black hole is like an accelerating falling object. The time reversal of this, a decelerating rising object, is consistent with the laws of physics. That doesn't mean that a falling object can spontaneously start rising. In the same way, a black hole can't spontaneously become a time-reversed black hole and start emitting instead of absorbing.
So, you don't need any notion of "white holes" -- I'm still talking about regular old "black" holes.
You're talking about time-reversed black holes. To quote http://en.wikipedia.org/wiki/White_hole: In astrophysics <http://en.wikipedia.org/wiki/Astrophysics>, a *white hole*is the theoretical time reversal <http://en.wikipedia.org/wiki/T-symmetry> of a black hole<http://en.wikipedia.org/wiki/Black_hole>. While a black hole acts as a vacuum, drawing in any matter<http://en.wikipedia.org/wiki/Matter>that crosses the event horizon <http://en.wikipedia.org/wiki/Event_horizon>, a white hole acts as a source that ejects matter from its event horizon. The sign of the acceleration is invariant under time reversal, so both black and white holes attract matter. The only potential difference between them is in the behavior at the horizon. So the thing you're talking about is exactly what is called a white hole. Andy
So, nothing in these laws keeps such a black hole from burping an object out into space.
We can ask what initial conditions would enable such a burp & may complain that they are highly unlikely, but they aren't ruled out by the laws themselves.
Now I'm curious about what this implies for the "classical" energy, momentum, etc., of the object being burped.
At 03:40 PM 7/24/2009, Dan Asimov wrote:
Re time reversal:
The fact that in our neighborhood in spacetime we see stars radiating only in positive time -- and all the entropic consequences of this -- is usually attributed to initial conditions, not to any actual "law" of physics.
(The Ehrenfest urn model is usually considered a good microcosm of thermodynamics, and shows time reversal symmetry.)
It's just a guess, but it seems likely to me that we are aware of only a small or infinitesimal fraction of the universe, and that some other time and place have stars radiating in negative time.
(Or is it possible that entropically opposite parts of the universe somehow always end up pinching off from each other by black holes?)
--Dan
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participants (5)
-
Andy Latto -
Henry Baker -
mcintosh＠servidor.unam.mx -
Mike Stay -
Rowan Hamilton