[Phys-L] Re: "moving clock runs slower" (yes)

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 22:23  -0400 9/12/05, Bob Sciamanda wrote:
> Consider the simple "bouncing photon" clock.  In its proper frame, a photon
> bounces back and forth, in one dimension, between two parallel mirrors -
> registering one tick per round trip.  As viewed from a moving frame this
> photon travels a longer, "triangular" path through space.  Since the photon
> speed is numerically the same (c) as measured in both frames, the clock must
> tick at a slower rate when viewed from the second frame (when compared to an
> identical clock at rest in the second frame).
>
> What is it about this effect that is not real, and only an appearance - must
> we say that the invariance of vacuum light speed is not real, and only an
> appearance?
I'm not sure what the issue is here. What do we mean by "real"? If we
look at two observers, in different RFs, each with a clock as you
describe, *each* will see the other's clock running slow, when
compared to their own. It is this apparent dichotomy that confuses my
high-school students--they are not ready for three-vectors yet, so
four-vectors are well beyond the realm of consideration (they may be
mathematically skilled, but most are not yet mathematically
sophisticated). They have to reconcile themselves with the fact that
"reality" is what you see happening in your own RF, and what you see
happening is another RF can only be appearance. since each will see
the other's clock running slow.

I think the key to understanding this is the requirement that events
that are simultaneous in one RF will not be simultaneous in any other
RF (unless they happen to be located at the same point in both
RFs-which with the photon clock in the example we are pursuing here
is not the case).

For my students, the vast majority of whom are still in the concrete
thinking phase, they find the fairly concrete examples one comes up
with to illustrate these phenomena sufficiently mind-bending. Some of
them never get it, but eventually most do to some extent. But the
abstraction of rotations of 4-vectors in 4-space is going to be well
beyond their ability to absorb this time around. When they get it
again in college, things will probably be different, but they need to
concrete examples at this stage.

So while I agree with the physics and with the philosophy of JD's
presentation, I think my students are not yet ready for that level of
sophistication (I've tried some of the ideas JD talks about on them
and managed to lose *every* one of the students in the process--maybe
I didn't do it well enough, but it seemed to me that this was way too
abstract for them).

But back to "real." This is the question students ask (usually in the
context of "since they two observers get different answers, one of
them must be 'wrong,' which one?"). It appears to me that the answer
is that what is real are proper lengths and proper times, and
contracted lengths and dilated times, are appearances--well described
as rotations of a 4-vector. The fact that, if observers in RF#1 and
RF#2 each hold up a meter stick oriented parallel to the relative
velocity, for *both* observers, the meter stick in the other RF will
appear shorter. What is real are the proper lengths, that is the
lengths of the meter sticks that are at rest relative to the
observer. Every time I measure one of them, I will get the same
result. But the ones I measure in other RFs will all have different
lengths. I don't have any trouble with not calling that "real."

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

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