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Feb13-08, 06:31 AM
P: 645
Quote Quote by JesseM View Post
Did you mean to write "C" rather than "B" here? B was the rocket's frame, in that frame the nose doesn't read less than the tail, assuming the two clocks are synchronized in their own rest frame. But in the C frame, yes, the tail clock could read 10 s simultaneously with the nose clock reading 2 seconds, so if we go back to the observer's frame A where the tail clock reads 8 s simultaneously with the nose clock reading 2 seconds (using the numbers from my example near the end of post #28), then the tail reading 10 s is still in the future.
Looking over it again, yes, I meant C rather than B. It think it is reasonably clear that I was referring to another frame which was not at rest relative to the rocket. I am not 100% sure that we are there yet with what I meant about "the nose being more in the future as compared to the tail" - noting that I was only referring to a frame where two synchonised clocks were at rest and one observer who was not at rest relative to the clocks such that one "nose" clock is ahead of the other "tail" clock in terms of their relative motion according to the observer. In that limited scenario, do you agree?

To try to clarify again, in a now moment in the observer's frame (all now moments are relative, since "now" changes all the time), the observer may observe the tail clock reading 10s and the nose clock reading 2s. IF the clocks are synchonised relative to their rest frame - noting that the observer can work this out from the relative velocity of the clocks and their apparent separation from each other - THEN the observer can further deduce that the nose clock he sees "now" is a younger version of the nose clock and an older version of the tail clock (the observed nose clock manifests earlier in the clocks's rest frame than the observed tail clock - in our example 8s earlier). The nose clock, if you like, has reached the observer's "now" before the tail clock has.

I am sorry to have to do this, but I hope I can justify it. Let's introduce a third clock - on the rocket, in the midpoint between the nose and the tail. That clock will read a midpoint value. Without thinking too deeply about the specifics, I suspect it is 6s (midway between 10s and 2s) but the acutal reading is immaterial - what is important is that it is more than 2s and less than 10s.

If the observer not at rest relative to the clocks observes a reading of 6s on the midpoint clock, 2s on the nose clock and 10s on the tail clock - and knows from his deductions that in their own rest frame the clocks are synchonised then he can say, taking the midpoint clock as his reference, that the nose clock he "should" (see since the clocks are synchronised) is in the future and the tail clock he "should" see is in the past. Whose past and whose future? the past and future of the observer.

What that observer sees, as you point out (I think), is a past version of the nose clock, relative to the midpoint clock, and a future version of the tail clock, relative to the midpoint clock.

You don't really need the third clock, since the same logic applies with only two points, but hopefully the temporary introduction of a third clock makes it easier to understand.

DaleSpam is most probably right, we are probably arguing over semantics.

More later, I must attend a meeting.