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Re: [Phys-l] Relativity Question

I'm also unclear on what John Denker means, but many introductory relativity books delineate a procedure for synchronizing clocks _within_ a given reference frame.

One such scheme is to send a light ray from the origin of the reference frame to the location of the clock we want to synchronize with the origin clock and back, say by having the ray bounce off a mirror and return. The time for the round-trip is noted and then half of this time is used as an offset to apply whenever a synchronizing time mark is sent out from the origin clock.

More practical might be to have any local clock A in the reference frame to send a time-stamped sender-identified message to the origin. The origin clock responds to these queries by immediately returning a copy to the sender with the origin's time-stamp attached. Suppose that the clock A showed times tA1 when the query was sent and tA2 when the response was received. Suppose the origin's time-stamp reads tO. Then when clock A showed tA2, the origin clock was showing t0 + (tA2-TA1)/2, and clock A should be set forwarded by t0 + (tA2-tA1)/2 - tA2 = t0 - (tA1+tA2)/2.

Ah, I see John has sent a further replay, and mentions that synchronizing pulses can be sent by sound or electric signals, etc. (But don't use email, we can't count on equal travel time out and back. :-)

Alright, the whole set of clocks in any reference frame can be synchronized. But in addition, most thought SR experiments ask that the origin clocks of two different coordinate systems be synchronized to both read 0 at the moment they pass each other: t = t' = 0 when x = x' = 0. (Only possible if the origins ever actually do coincide, but that is guaranteed for the 1-dimensional case, as has been pointed out recently in this thread.)

So we have synchronizing all the clocks within each reference frame, and we have the origin clocks of two different reference frames synchronized. Pre-relativity thinking would indicate that all the clocks are in sync, and we could take their common time reading and rate as "universal" time. But the fun thing in special relativity is that according to each observer, the clocks of the other reference frame are not synchronized with each other, in fact their readings are position-dependent, offset by (v x / c^2), and of course they are all "running slow" by a factor of 1/sqrt(1-v^2/c^2). Incidentally, if acceleration effects are added in, clock rates in an accelerating frame are position dependent and vary by a factor of (a x / c^2), where a is the proper acceleration and x the position within the accelerating system.

John is trying to convince us to just use the 4-vector formalism from the get-go, and there's a great deal to be said for that. But I'd still like to know what he meant by the "swindle".

Ken Caviness
Physics @ Southern

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Philip Keller
Sent: Friday, May 15, 2009 9:18 AM
To: 'Forum for Physics Educators'
Subject: Re: [Phys-l] Relativity Question

I believe that the point is that the scientists on the train have NOT
been lied to. In their reference frame, their clocks ARE synchronized.
When you first introduce the setup to students, they don't realize that
when we say that both sets of scientists don't really have synchronized
clocks, we are reporting the facts from another reference frame, a
third reference frame no more valid or less valid than that of the
scientists on the two trains.

To take things further, you can consider a procedure that the
scientists could use to ensure that the clocks on their own train were
synchronized. Suppose that there is a star that is known to
occasionally emit a burst of light at a specific frequency. And
suppose you could design clocks that start running when exposed to that
frequency. You could preset your clocks but with each clock set
further ahead than the one before it. Then when the light from the
star reached the individual clock, it would start the clock. The
preset time differences would be to allow for the additional time it
takes for the light to reach that train car.

If both sets of train scientists performed this procedure, they could
each argue that their own clocks were in fact synchronized. And they
would each argue that the other train performed the procedure
incorrectly because that other train was in motion relative to the
light source -- but we weren't. So in the final analysis, it is
simultaneity that is relative and it leads to the other weird things
about clocks and lengths.

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of chuck britton
Sent: Friday, May 15, 2009 8:45 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Relativity Question

Please elaborate a bit on this point.

Are you implying that the folks on the train can't 'really' have a
set of synchronized clocks?
or what is the swindle to which you refer?



On May 14, 2009, at May 14(Thu) 5:38 , John Denker wrote:

they involve some sort of swindle, such as lying to the
trainmen about their clocks.

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_______________________________________________
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Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l