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fckm · 02-20-2005, 09:41 AM

I believe you are wrong. Because the two events occur simultaneously in the frame of M, by the tenets of special relativity, there can be no causal relationship between them. In other words, you can't say that A caused B, or B caused A (Since the two events occur simultateously in frame M, it's impossible that one caused the other).
Causal relationships are preserved under transformation (this is a tautology, causation is defined that way), so that if A caused B, then A must occur before B in ALL reference frames. In order for this to occur, special relatvity tells us that (if A caused B), B must occur at least t=d/c seconds after A occurs (where d is the distance between the two and c is the speed of light). Since this problem states that A and B occur simultaneously in the M frame, then we can see that A and B do not have a causal relationship.
The causal relationship (t>=d/c) is the only time in special relativity where the order of the events is preserved under transformation. In all other cases, it is possible to find a frame M' where A occurs before B, or B occurs before A.
So in this case with the lightning, since in the M frame, A and B occur simultaneously, they do not have a causal relationship. Thus it is possible that in M', A occurs before B, or B occurs before A.

It's been a while since I've taken SR. Hopefully someone else will chime in and correct any mistakes I've made.

edit:spelling

02-20-2005, 09:41 AM	#14 (permalink)
fckm Insane Location: Ithaca, New York	I believe you are wrong. Because the two events occur simultaneously in the frame of M, by the tenets of special relativity, there can be no causal relationship between them. In other words, you can't say that A caused B, or B caused A (Since the two events occur simultateously in frame M, it's impossible that one caused the other). Causal relationships are preserved under transformation (this is a tautology, causation is defined that way), so that if A caused B, then A must occur before B in ALL reference frames. In order for this to occur, special relatvity tells us that (if A caused B), B must occur at least t=d/c seconds after A occurs (where d is the distance between the two and c is the speed of light). Since this problem states that A and B occur simultaneously in the M frame, then we can see that A and B do not have a causal relationship. The causal relationship (t>=d/c) is the only time in special relativity where the order of the events is preserved under transformation. In all other cases, it is possible to find a frame M' where A occurs before B, or B occurs before A. So in this case with the lightning, since in the M frame, A and B occur simultaneously, they do not have a causal relationship. Thus it is possible that in M', A occurs before B, or B occurs before A. It's been a while since I've taken SR. Hopefully someone else will chime in and correct any mistakes I've made. edit:spelling __________________ And if you say to me tomorrow, oh what fun it all would be. Then what's to stop us, pretty baby. But What Is And What Should Never Be.