 Quote by Grimble
Then you deny Einstein's notion of simultaneity, two events occurring 'at the same time' as set out here? |
This part of my comment was clearly assuming Einstein's definition: "Each observer synchronizes their own clocks using the assumption that light signals travel at the same speed in all directions relative to themselves, and the result is that according to each observer's definition of simultaneity, the clocks of the other observer are out-of-sync."
Do you not understand that Einstein's definition is based on the assumption that each frame defines "simultaneity" using light signals, making the assumption that all light signals travel at the same speed relative to
that frame? He says this in the section you quote:
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After thinking the matter over for some time you then offer the following suggestion with which to test simultaneity. By measuring along the rails, the connecting line AB should be measured up and an observer placed at the mid-point M of the distance AB. This observer should be supplied with an arrangement (e.g. two mirrors inclined at 90°) which allows him visually to observe both places A and B at the same time. If the observer perceives the two flashes of lightning at the same time, then they are simultaneous.
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Obviously if we assumed the light from A did
not travel at the same speed as the light from B in the observer's frame, then the fact that the light reached him at the same time would not mean the flashes were simultaneous.
But the in the
very next section Einstein makes clear that if observers in different frames all assume light travels at a constant speed
relative to themselves, then they will
disagree about whether a given pair of events (like the lightning strikes in his example) are simultaneous, which is equivalent to my comment that if each frame synchronizes their own clocks using light-signals, each frame will say the other frame's clocks are out-of-sync. Did you read this part of Einstein's text?
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Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.
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Do you understand that Einstein's definition of "same time" is frame-dependent, i.e. a pair of events that occur at the "same time" in one frame occurred at "different times" in other frames?
If you have trouble following Einstein's example, you might also consider this one. According to Einstein's definition, two clocks in my frame are "synchronized" in my frame (i.e. they always show a given reading, say 3:00, simultaneously) if, whenever I set off a flash of light at the exact midpoint between the two clocks, both clocks are showing the same reading at the moment the light from the flash reaches them. But now suppose I am on a rocket (with the clocks at the front and back of the rocket) being observed by someone in a different frame who defines simultaneity by assuming light travels at the same speed in all directions relative to
himself. If he sees the rocket traveling forward, then after the flash is set off at the middle of the rocket he will see the clock at the back moving
towards the position (in his frame) where the flash was set off, while the clock at the front is moving
away from that position, so if he assumes the light travels at the same speed in both directions, he must conclude the light reaches the back clock before it reaches the front clock. But I have set my clocks to both show the same reading (say, 3:00) at the instant the light from the flash hits them, so in the observer's frame the clock at the back shows a reading of 3:00 before the clock at the front shows a reading of 3:00, and thus in his frame my two clocks are out-of-sync. Of course as I said, the effect is totally symmetrical, since if he synchronizes his own clocks under the assumption that light travels at a constant speed relative to himself, then in my frame (using my definition of simultaneity)
his clocks will be out-of-sync.
So do you understand that according to Einstein's definition, each frame has their
own definition of simultaneity and clock synchronization which different frames disagree about, and there is no physical basis to judge one frame's opinion as more "correct" than any other's? If so please read my comment again more carefully and tell me if you disagree with any specific part of it:
How are you going to define "same time"? Each observer synchronizes their own clocks using the assumption that light signals travel at the same speed in all directions relative to themselves, and the result is that according to each observer's definition of simultaneity, the clocks of the other observer are out-of-sync. If I think my clocks are synchronized and I use my clocks to determine that your clocks are out-of-sync, but you think your clocks are synchronized and you use your clocks to determine that my clocks are out-of-sync, how do you propose to settle the matter? Remember that if we construct our own coordinate systems using clocks synchronized this way, the laws of physics will obey exactly the same equations in both coordinate systems, which means any experiment I do with an apparatus at rest in my frame will give the same result if you do the same experiment with the same apparatus at rest in your frame.
Relativity doesn't rule out the notion that there is some metaphysical truth about simultaneity, so that only one observer's clocks are "really" synchronized. But only God could no that truth--according to relativity, there is no experimental way to show that the laws of physics "prefer" one frame, they are all exactly equivalent as far as empirical experiments go so there can be no experimental basis for judging one frame's definition of simultaneity to be "correct" and another's to be "incorrect".
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