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JesseM
JesseM is offline
#48
Feb13-08, 11:39 AM
Sci Advisor
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Quote Quote by neopolitan View Post
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?
I don't think the statement about the nose clock being further in the future can make sense except as a comparison of simultaneity in two frames, the outside observer's frame and the rocket's rest frame. The idea as I understood it is to take two readings on the nose and tail clock which are simultaneous in the rocket's frame, then look at when these same two readings occur in the outside observer's frame, and note that the nose reading happens further in the future than the tail reading in the observer's frame. Do you think it is possible to explain your idea of the nose being further in the future without referring to simultaneity in the rocket's rest frame, and also without necessarily assuming the clocks themselves have been properly synchronized in the rocket's rest frame?
Quote Quote by neopolitan
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.
Well, if you talk about which clock "reaches the observer's now first", this sounds more like viewing the outside observer's plane of simultaneity (his 'now') from the perspective of the rocket rest frame--as illustrated in DaleSpam's second diagram, the observer's planes of simultaneity are tilted in the rocket's frame so that the the nose will hit a given plane before the tail (here the 'before' refers to time in the rocket's own frame). So again, considering both the outside observer's frame and the rocket's frame seems critical here, which you seemed to at leas partially acknowledge when you said above "IF the clocks are synchonised relative to their rest frame..."
Quote Quote by neopolitan
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.
That's right, it'd be 6s. If two clocks are synchronized in their own frame, then in a frame where they're moving at speed v they'll be out-of-sync by vx/c^2, where x is the distance between them in their own rest frame. The clock in the middle is the same distance from the clock on the nose as it is from the clock on the tail, so it must be out-of-sync with each by the same amount (ahead of one and behind the other).
Quote Quote by neopolitan
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.
OK, if he takes the midpoint clock as a reference for what he "should" see (though I hope you agree he could equally well take another clock for his reference) then he'll only see the nose clock give the same reading in the future, and he's already seen the tail clock show this reading in the past. I understand, and this is equivalent to the interpretation of you're comments that I've been talking about since post #26 (again, my interpretation is just that you pick simultaneous readings in the rocket's rest frame--in this case each of the three clocks reading 6 s--and then look at the order of these same readings in the observer's frame, noting that the nose reaches its reading at a time more 'in the future' for the observer than the tail reaches its own reading, and likewise the middle clock reaches its reading at a time midway between the other two in the observer's frame).
Quote Quote by JesseM
DaleSpam is most probably right, we are probably arguing over semantics.
If you're just talking about the best way to conceptualize the relation between simultaneity in the observer's frame and the rocket's frame, then I'm not really arguing with you at all, I've said since post #26 that I think "the nose clock is further in the future" can be interpreted in a reasonable way. My issues were the ones I mentioned in post #40--that sometimes you seemed to suggest we didn't have to think about the rocket frame at all, and also that you wrote this paragraph which suggested you might be hinting at something more than just a way of conceptualizing simultaneity in relativity:
Just try to apply the same logic to the rocket and the two clocks. Relative to an observer not at rest relative to the rocket, the clock on the nose travels into the observer's future faster than the clock on the tail. The clock on the tail travels into the observer's future faster than the observer.

The observer also moves into the clocks' future faster than the clocks do.

This is where it gets less like semantics and more like something interesting ... can you model that? Not just wave it away, not just say "that's just relativity", not just show the mathematics on what must happen, but describe a model in which that is possible.
If you didn't mean to suggest here that what you were talking about was anything more than a way of conceptualizing simultaneity in SR, then just say so and my mind will be put at ease that you're not making any claims I would need to argue with.