zanket
02-27-07, 02:13 PM
(The “Alpha” in the title indicates that the Alpha rules (http://www.sciforums.com/showthread.php?t=62837) apply to this thread.)
In another thread (http://www.sciforums.com/showthread.php?p=1304481#post1304481) I proved that general relativity (GR) is self-inconsistent. Here I will prove that the inconsistency leads to a violation of the equivalence principle. First see the supporting info in the other thread (http://www.sciforums.com/showthread.php?p=1304481#post1304481), which includes the equivalence principle as stated by Einstein. (For the record, this is my second attempt. The first (http://www.sciforums.com/showthread.php?t=61902) was refuted by Pete here (http://www.sciforums.com/showpost.php?p=1269096&postcount=44).)
Now the proof:
Let X be an inertial frame falling through the horizon of a black hole. Since the spacetime throughout an inertial frame is flat, it must be possible to set up an inertial frame Y that extends throughout X and in which a free test particle, that is above the horizon and moves away from the black hole indefinitely, stays at rest. But GR predicts that nothing may pass outward through a horizon. Then Y cannot extend below the horizon (if only because otherwise a latticework of synchronized clocks, that is spread throughout Y and stays at rest with respect to Y, would be passing outward through the horizon), and so the spacetime cannot be flat throughout X. The equivalence principle says that X is equivalent to an inertial frame J in an idealized, gravity-free universe. Yet the spacetime throughout J is flat. Then X and J are nonequivalent, and so GR violates the equivalence principle.
Note that:
The definitions of flat spacetime and inertial frame in the supporting info (http://www.sciforums.com/showthread.php?p=1304481#post1304481) account for the tidal force. The tidal force in X need not be nonexistent.
X can be arbitrarily small and its duration can be arbitrarily short. Then the tidal force in X can be nonexistent in the limit.
In another thread (http://www.sciforums.com/showthread.php?p=1304481#post1304481) I proved that general relativity (GR) is self-inconsistent. Here I will prove that the inconsistency leads to a violation of the equivalence principle. First see the supporting info in the other thread (http://www.sciforums.com/showthread.php?p=1304481#post1304481), which includes the equivalence principle as stated by Einstein. (For the record, this is my second attempt. The first (http://www.sciforums.com/showthread.php?t=61902) was refuted by Pete here (http://www.sciforums.com/showpost.php?p=1269096&postcount=44).)
Now the proof:
Let X be an inertial frame falling through the horizon of a black hole. Since the spacetime throughout an inertial frame is flat, it must be possible to set up an inertial frame Y that extends throughout X and in which a free test particle, that is above the horizon and moves away from the black hole indefinitely, stays at rest. But GR predicts that nothing may pass outward through a horizon. Then Y cannot extend below the horizon (if only because otherwise a latticework of synchronized clocks, that is spread throughout Y and stays at rest with respect to Y, would be passing outward through the horizon), and so the spacetime cannot be flat throughout X. The equivalence principle says that X is equivalent to an inertial frame J in an idealized, gravity-free universe. Yet the spacetime throughout J is flat. Then X and J are nonequivalent, and so GR violates the equivalence principle.
Note that:
The definitions of flat spacetime and inertial frame in the supporting info (http://www.sciforums.com/showthread.php?p=1304481#post1304481) account for the tidal force. The tidal force in X need not be nonexistent.
X can be arbitrarily small and its duration can be arbitrarily short. Then the tidal force in X can be nonexistent in the limit.