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Re: [Phys-l] how to prove relativity



I don't understand the difference between "longer in the timelike direction" (longer time interval) and "slower".
Regards,
Jack

"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley




On Thu, 3 Jun 2010, John Denker wrote:

On 06/02/2010 09:29 PM, Bernard Cleyet wrote:

Satellite clocks are slowed by their orbital speed

Really? I wouldn't have said that.

but sped up by
their distance out of the Earth's gravitational well.

Really?

If we send two identical cars on different trips, and
their odometers come back with very different elapsed
distance readings, do you assume that the odometers must
have been miscalibrated, or do you consider it more likely
that one of them simply followed a longer path?

If the clocks in the cars come back with very different
elapsed time readings, do you assume that one of the
clocks was "slowed" in some spooky way, or do you consider
it more likely that one of them simply followed a longer
path, longer in the timelike direction?

===============

The following must be one of the most profound sentences
in human history:

Von Stund′an sollen Raum für sich und Zeit für sich
völlig zu Schatten herabsinken
und nur noch eine Art Union der beiden
soll Selbständigkeit bewahren.

Hermann Minkowski (1908)

From now on, space of itself and time of itself
are to sink into mere shadows
and only a kind of union of the two
is to maintain its independence.


As humans, not to mention scientists, we ought not turn
our backs on this. We ought not feign ignorance of
spacetime.

I assume you agree that when a ruler has been rotated,
"the" length of the ruler (i.e. the proper length) is
not changed. If this is a false assumption, please
explain.

By the same token, when a ruler has been boosted, "the"
length of the ruler (i.e. the proper length) is not changed.
Right?

And when a clock has been boosted, "the" time between
ticks (i.e. the proper time) is not changed. Right?

It may be that the /projection/ of the length onto this-
or-that reference frame is changed. It may be that the
/projection/ of the time onto this-or-that reference
frame is changed. But the shadow of a thing does not
behave the same as the thing itself.

Suppose you are trying to explain or "prove" relativity
to some non-experts who are predisposed to believe that
"the" timing of a clock is unchanged by its state of motion.
Why not simply agree with them?!! The professionals who
do relativity for a living agree with them, and have for
more than 100 years; why not join the party?

You can then go on to say that when the clock is moving,
the /projection/ of its timing onto our reference system
is foreshortened -- just as when a ruler has been rotated,
the /projection/ of its length is foreshortened.

Relativity is not mysterious or paradoxical. It is just
the geometry and trigonometry of spacetime. A boost is
a rotation in the xt plane. Just as a rotation in the
xy plane mixes the x and y coordinates, a boost i.e.
rotation in the xt plane mixes the x and t coordinates.
The fourth dimension is not /exactly/ the same as the
other three, but it is more same than different.

You can explain this to 12-year-olds. You can even
explain it to adults, which is harder. They won't get
all the details, but they will accept the overall
picture as plausible and sensible. You need not (and
should not) talk about spooky rulers that can't be
trusted and spooky clocks that can't be trusted.


Sometimes bad ideas hide behind bad terminology. Sometimes
it is suggested that when one physicist says to another
physicist that the length is changed, "everybody" knows
we are talking about the projective length, not the
proper length. But that way of speaking is a misleading
misnomer at best ... and is grossly misleading and grossly
inappropriate to this thread, since we are discussing how
to explain and/or "prove" relativity to an audience of
non-physicists. Such an audience certainly does not know
how to decode the misnomer. A big part of the game is to
explain the difference between the proper length and the
projective length, and wallowing in misnomers is not a
winning strategy.

The winning terminology is simple:
-- "the" length == proper length
(invariant with respect to rotations in spacetime)
-- "the" time == proper time
(invariant with respect to rotations in spacetime)
-- "the" mass == proper mass
(invariant with respect to rotations in spacetime)

And of course the set of rotations in spacetime includes
boosts as well as old-style spatial rotations.
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