I personally do not see anything misleading in the statement "moving clock runs slower" so far as we carefuly emphasize the corresponding experimental conditions. I would even emphasize that a clock moving with respect to me DOES tick slower in my reference frame rather than only appears to me to be ticking slower. After all, my reference frame is as good as the rest-frame of the clock, and the whole Relativity is about equivalent descriptions of the world from the viewpoint of different inertial frames. In this respect, the time dilation is damn real experimental fact, manifest, for instance, when the atmospheric muons, having the average proper lifetime of about 2x10^6 s, (apparently not enough for them to travel more than 100 km down to the sea level!), are nevertheless observed at this level and underwater. The same can be said about the length contraction: it is real (although relative) physical effect, - a longitudinally moving rod IS shorter in my reference frame, w
hich can be experimentally verif
The analogy John makes with the projection of a pencil as opposed to its true length is totally legitimate and is used in many presentations of the subject (my own included, and I also use it in the class). But again, analogies have their limitations, and we must be careful to show them as well. Even though switching to another RF can be formally described as the corresponding rotation in spacetime, physically to change the angle of observation of the pencil (say, by rotating it within the same RF) is something different from changing the RF itself (say, by jumping into another train). I would even challenge anyone who disagrees with this to experimentally demonstrate the opposite. Mathematically, the difference is manifest in the fact that the pure spatial rotations within the same RF conserve the angle between the basis axes (say, x and y in rotation about the z-direction), whereas the rotation describing Lorentz transformation between different RF does not have this prop
erty, and the primed x' and y' a
Emphasizing the rest frame of an object is important for finding its proper characteristics; but upholding it as something preferrable does not appeal to me when it is used to deny the objective nature of the properties of this object for other observers moving with respect to it. Moreover, such logics could even take us back to Aristotle, with the distinction that there would be as many aristotles as there are different RF! Using the same logics, a driver could legitimately sue a cop for an attempt of arresting him for speed limit violation, - by saying that he was at rest in his car, and he, just as John's clock, does not care if the cop was moving outrageously fast with respect to him. That should be the cop's problem, not his. Ironically, the mere expression "moving clock" would in this case become contradiction in terms. It would only mean an illusion of all who dare to move with respect to this clock. Other than this, it would have no objective meaning at all.
Actually, the whole discussion may be just an academic question of terminology, if we define clearly what we
mean.
Moses Fayngold,
NJIT
-----Original Message-----
From: Forum for Physics Educators [mailto:PHYS-L@list1.ucc.nau.edu]On
Behalf Of John Denker
Sent: Friday, September 09, 2005 2:00 AM
To: PHYS-L@LISTS.NAU.EDU
Subject: "moving clock runs slower" (not)
Hi --
There are a lot of references that try to explain relativity on an
elementary level by saying "a moving clock runs slower".
Some authors seem to take that as one of the axioms -- or at least one
of the theorems -- of relativity. It's not. It describes only part
of what's happening, and doesn't even do a very good job at that.
I reckon most people on this list already know this, but it seems
worth mentioning anyway. I confess I recently caught myself having
used the "moving clock runs slower" notion. I mentioned it only in
passing, not as an important part of any argument, but still I was
embarrassed.
To make amends, I cooked up the following analogy:
It would be unwise to say that a pencil gets shorter if we look at
it nearly end-on. ItâEUR(tm)s OK to say that the projection of the pencil
on our field of view is shorter, or perhaps that the appearance of
the pencil is foreshortened -- but there has been no real change
in what the pencil *is*.
By the same token it would be unwise to say that a clock runs slowly
if we are moving relative to it. The clock doesnâEUR(tm)t know or care whether
we are moving. ItâEUR(tm)s OK to say that the projection of the clockâEUR(tm)s world
line onto our field of view projects tick marks that are more widely
spaced, but there has been no real change in what the clock *is* or
what it *does*.
This issue came up in an off-list discussion of the infamous travelling
twins. It caused me to expand, revise, and re-organize my web page on
the subject: http://www.av8n.com/physics/twins.htm