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



Bob Sciamanda wrote:

If c were a much smaller number, these effects would be commonplace and
accepted as real, prima facie.

The real ones would be accepted as real, and the unreal ones
would be dismissed as illusions. Apparently there is still some
difference of opinion as to what is real and what is not.

Prima facie evidence should not be mistaken for conclusive evidence.

Presently our Galilean experiences prejudice
us toward expecting and seeking observer independent absolutes.

Yes. That's true and important.

It is also important to recognize that some of "us" have different
prejudices and different intuitions about relativity.

Kip Thorne is fond of saying that "education is the process of
cultivating your intuition". In particular, I heard him say it
in precisely this context, i.e. in connection with the twins
"paradox" or something very similar. This is related to the idea
(which I endorse) that physics is not paradoxical. Things only
seem paradoxical when there is a collision between good physics
and bad intuition, bad prejudices, bad formalism, bad notation,
et cetera.

Teaching in general and teaching relativity in particular consists
in large measure of providing a framework of ideas, notation, and
other formalism so that people can think about the topic without
risk of getting confused.

Thanks for the quick response John! But you speak only of projections, etc
in a graphical representation of the Lorentz transformation.

No I do not! I feel I am being whipsawed here. When I describe
things in formal terms, I am upbraided for giving arguments that
are too formal and too sophisticated for high-school students to
grasp. Meanwhile, when I show how to make the same point graphically,
I am upbraided for being not 100% general and not 100% rigorously
convincing. Phooey!

I have presented the key ideas in analogical terms, i.e. comparing clocks
to odometers. I have given the graphical representation, i.e. spacetime
diagrams. I have also given the matrix representation. I have also
given the bivector / quaternion / Clifford algebra representation. If
this doesn't meet your standards, please tell me what *would* be good
enough for you.

Also please set a good example by upholding high standards yourself.

I'll let you in on a little secret about how I work. It is something
of a spiral approach:
-- First using analogies or whatever, I develop an intuition
about what might be true.
-- Then I draw myself a diagram.
-- Then based on the diagram, I upgrade my analogies and intuitions
if necessary.
-- Then I do the math, using bivectors or whatever.
-- Then I redraw the diagram, or, more likely, I *compute* the
diagram. Most of my recent spacetime diagrams were computed with
part-per-million accuracy, not drawn freehand.
-- Then I check again to see if my analogies and intuitions are
accurate.

After a few trips around this spiral, my analogies, intuitions,
diagrams, and formulas are pretty reliable.

Usually when I present my results, I just present the summary, e.g.
the diagram ... especially when presenting to an introductory-level
audience. However, if somebody challenges my conclusions, I can
back them up eleventeen ways.

If you want to persuade me that my analogy is wrong, you can't do
it by presenting an opposing analogy backed up by nothing more than
an appeal to authority ("Einstein said blah-blah") or PbBA (Proof
by Bold Assertion). I've explained how I did my calculations; if
you think they are wrong, you are cordially invited to redo the
calculations and show in what way mine are wrong. Please be specific.

If you can't do the calculation, or can't be bothered to do it, you
should prepare for the possibility that you will never persuade me.
In a contest between a calculation and an unsubstantiated opinion,
the calculation always wins.

Please address
the physical reality. What is it in the physical reality that is not real,
and only appearance.

Is it not *real* that if two photon clocks are synchronized while both are
at rest, when they are set in relative motion their ticks ( as viewed from
either frame) will no longer be simultaneous and that the moving clock will
*really* run slower. What is not real in this *physical* situation?

If c were a much smaller number, these effects would be commonplace and
accepted as real, prima facie.

Except they wouldn't. For thousands of years, people have considered
the length of a ruler to be invariant with respect to rotations. The
projection of a ruler on the wall of the cave has been recognized as
not "really" a ruler, just a projection. As Joel R. says, it is "really"
a projection ... but it is not "really" a ruler.

It seems overwhelmingly probable that if people were more familiar with
rotations in the (t, x) plane -- i.e. boosts -- they would consider
the relevant property of a clock to be the invariant interval between
clock-ticks. Anybody in his right mind would want it this way, so why
not let it be this way?

To say the same thing in other words: considering just plain Euclidean
rotations, let the (x', y') frame be rotated relative to the (x, y) frame.
The tick-marks of either frame "(as viewed from the other frame)" will
appear foreshortened, but I haven't heard anybody arguing that either
frame "really" becomes shorter.

"If c were a much smaller number" then everybody would be aware of the
analogy between rotations and boosts. Although the ticks of a moving
clock might appear foreshortened, nobody would argue that they were
"really" shorter.
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