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Registered Member #175
Joined: Tue Feb 14 2006, 09:32PM
Location: Sudbury, ON
Posts: 111
Okay, so I'm trying to get my head wrapped around all this Einsteinian stuff and I hit an interesting/tricky question on simultaneity. We've got 2 inertial reference frames, K (Alice) and K' (Bob); K' is moving at sine appreciable %of c in the x direction. At t=0, t'=0 -- the two reference frames synchronize their clocks. The origins of the two reference frames also coincide at t=t'=0. Now, knowing that the synchronizing event, the one they decided was simultaneous occurred at (x', y', z') in the K' reference frame, where does it occur in K? Since motion is only in x, y'=y and z'=z, but what about x? My personal thinking was that we could consider this a length-contraction problem: Alice in K is going to see Bob in K' 's x' as length contracted, and thus x=x'/lambda But of course, Bob's reference frame is valid too, and then the length contraction would go the other way, right? Though we are only concerned with Alice's perception in this problem... It should be symmetrical, I thought. I thought I understood this stuff in context of fixed-position, differing times, but apparently not since I'm so flabbergasted at the reverse. Anyone have any ideas? If not I'll amend this when/if I get it figured out.
Registered Member #32
Joined: Sat Feb 04 2006, 08:58AM
Location: Australia
Posts: 549
Your post is a little much for me to wade through right now but I'll have a go clarifying SR.
With any pair of SR events, there is some reference frame where they occur in the same place. (For example, if I fly from here to the moon my departure and arrival occur in one place - me - in my own reference frame.) Observers in this frame measure the proper time for the event. All other observers measure a longer time, the dilated time, which is calculated from the relative gamma.
The observer who measures the proper time won't measure the proper length but a contracted length. The observer who is at rest relative to the length being measured measures the proper length.
(Note that terms like "proper" are just labels. There isn't nothing more valid about one SR measurement over another.)
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Special Relativity Problem (Simultinaity)
