Re: Grandfather Clocks and Relativity

On Mon, 05 Feb 2007 09:06:29 -0500, jem <xxx@xxxxxxx> wrote:

David wrote:
On Sun, 04 Feb 2007 08:55:55 -0500, jem <xxx@xxxxxxx> wrote:


David wrote:

On Sat, 03 Feb 2007 09:30:24 -0500, jem <xxx@xxxxxxx> wrote:



David wrote:


Please explain why the accelerating twin is not allowed to use the
following logic.

Instead of twins, lets use triplets. Two of them are always in the
same inertial frame and never have a relative velocity. They are on
the x-axis separated by a distance L, they are the same age, their
clocks are synchronized in their inertial frame, and their clocks run
at the same rate. Now apply my original post that a triplet (or long
lost twin) is traveling along the x-axis with velocity V. I'll call
this twin Ta because he will be accelerating later. Right now he has
a constant velocity V. At the point in time and space where the two
twins meet, they discover that they are the same age. Everything is
identical about them at that point in time and space. Twin Ta learns
that they have a triplet. While traveling along the x-axis toward the
other triplet, he makes measures regarding the two triplets who are
always in the same inertial frame. He finds that the two triplets in
the same inertial frame age at the same rate as each other, and their
clocks tick at the same rate as each other. He doesn't compare his
tick rate to theirs. He simply measures that the two triplets with
zero relative velocity have clocks and aging that always run at the
same rate. Twin Ta has done other experiments and has learned that
these clocks in this inertial frame always run at the same rate unless
acted upon by some external force. As long as accelerometers at each
clock always read zero, as long as electromagnetic sensors at each
clock always read zero, as long as gravitometers at each clock always
read zero, as long as thermometers at each clock always have constant
readings, etc., both clocks of the two inertial triplets always run at
the same rate.
Now when triplet Ta travels the distance L to the other inertial
triplet, he decides to accelerate into that frame and visit there. We
can make the acceleration instantaneous, or the distance L between the
two inertial triplets very large. We find that the time difference
shown on the nearby inertial clock before and after the acceleration,
and time difference shown on the accelerating twins clock before and
after the acceleration are identical (or negligibly small).
The accelerating twin knows that the nearby clock always runs at
the same rate of the other inertial triplets clock unless some
external force acts on the two clocks. The accelerating twin also
measures that his clock did not change substantially during the
acceleration with respect to the nearby inertial clock. Why can't he
continue to conclude that both inertial clocks always ran at the same
rate unless acted upon by some external force? There was no force
acting on either of those clocks.
Why must the accelerating twin abandon this simple logic?
Thanks,
David

Relativity would never require the accelerating twin to abandon that
simple logic.

OTOH, it does have severe criticism for his use of the "clocks running
slow" terminology.

Before the acceleration, the acclerating twin says clock A and clock B
(the two inertial clocks) are running at the same rate, but do not
show the same time. Before the acceleration, the accelerating twin
says, the distant clock has ticked fewer times than his own clock
since the time when he and the distant clock were at the same point in
space.

Since the time the two clocks were together, the distant clock has /been
measured to have/ ticked fewer times than Ta's own clock (based on the
use of a /particular/ measurement procedure).

Now the twin accelerates into the inertial frame of both the

nearby and distance twin. The accelerated twin's clock did not change
noticeably with respect to the nearby clocks during the acceleration.

During the instantaneous acceleration, the *time* shown on Ta's clock
didn't change noticeably relative to the time shown on the nearby clocks.


The distant clock and nearby inertial clock always run at the same
rate.

As do all (standard) clocks at all times.

The distant clock now shows more ticks (instead of less as it

did before the acceleration) than the accelerated twin's clock.

The number of ticks on the distant clock post-acceleration is more than
the number of ticks that were /inferred/ to show on that clock
pre-acceleration (where the inference is based on the results of a
particular measurement procedure).


When in this process does the accelerated twin say the extra ticks
in the distant clock relative to his own clock occurred?

Clearly, during the acceleration.

However, there's nothing absolute about this - the measured tick count
increase during the acceleration is a direct result of the particular
procedure chosen to measure the tick count prior to the acceleration.
Other measurement procedures could have been used which would have
resulted (e.g.) in no change at all in the tick count during acceleration.


No.

Yes.

In this process, prior to the acceleration, both twins had equal
and opposite motion. After the acceleration, they can have equal and
opposite motion and meet again. But if they do they are not the same
age.

and that in no way contradicts what I said.

Something happened during the acceleration of the one twin -
that was the only thing that was done differently.

Well, it certainly isn't the *only* thing that was different (e.g.
consider the speeds of each twin relative to the reference frame in
which the age comparison was done), but (and this should be sounding
pretty familiar by now) the aging of the distant twin, that was measured
to occur during the acceleration, is due to a shift in perspective.
I don't know what you are saying when you say consider the speeds of
each twin relative to the reference frame in which the age comparison
was done. The first age comparison was done when the twins were at
the same point in space and time and had a relative velocity V. Their
ages were identical. Every frame inertial frame, and every
non-inertial frame observes this. The twins meet a second time, but
have an equal an opposite motion. When they meet the second time the
twin that has undergone the initial acceleration is younger when they
meet. Now the various frames disagree on why the one twin is younger
when they meet the second time. But from either twin's point of view,
the only thing done differently by the one twin was to undergo a brief
acceleration.
David


David

If he says the extra ticks occurred during the acceleration, then
he must conclude that the nearby inertial clock and the distant clock
ran at different rates eventhough they have zero relative velocity.

That's a non sequitur. All the clocks *always* ran at the same rate.
The rate differentials being discussed are between clock rates and
received signal rates.


But he knows this is false, so this is not a logical choice.
If he says the extra ticks occurred after the acceleration,
then again he must conclude that the nearby inertial clock and the
distant clock ran at different rates eventhough they have zero
relative velocity and his clock and the nearby clock ran at the
identical rate. Again he must reject this answer.
What other explanation does the accelerating twin have other
than concluding that his measurement of the distant clock relative to
his own clock is in error?
I don't see a fourth possibility that logically works.
David

You're unable to see because you have too many misconceptions blocking
your view. And now it looks like you're going to have to contend with
conflicting instruction which promotes at least one of those
misconceptions, as well. C'est la vie.

Consider this analogy - as you walk away from an object, the object can
be measured to get smaller (e.g. by measuring the angle its image
subtends at your eye), but clearly it makes no sense to deem those
measurements an indication that the object is shrinking, because the
effect is unique to your view of the object.

That's the sense in which the tick rates of moving clocks change in
Relativity, and once you're able to appreciate the dichotomy between a
clock's tick rate and measurements of a clock's tick rate, those logical
dilemmas won't arise.
.

Relevant Pages

  • Re: Grandfather Clocks and Relativity
    ... this twin Ta because he will be accelerating later. ... clock always read zero, as long as gravitometers at each clock always ... can make the acceleration instantaneous, or the distance L between the ... That's the sense in which the tick rates of moving clocks change in Relativity, and once you're able to appreciate the dichotomy between a clock's tick rate and measurements of a clock's tick rate, those logical dilemmas won't arise. ...
    (sci.physics.relativity)
  • Re: Proper Time v. Absolute Motion.
    ... Twin A shows 200 days less elapsed ... >> absolute comparative motion. ... hide all traces of the engine that was powering the acceleration which would ... > inertial frame, the Origin. ...
    (sci.physics.relativity)
  • Re: Grandfather Clocks and Relativity
    ... Instead of twins, lets use triplets. ... this twin Ta because he will be accelerating later. ... clock always read zero, as long as gravitometers at each clock always ... can make the acceleration instantaneous, or the distance L between the ...
    (sci.physics.relativity)
  • Re: Proper Time v. Absolute Motion.
    ... After a snack they start wondering as to which twin had traveled the ... Call the point they leave from, in that shared inertial frame, the Origin. ... of an inertial coordinate system in which two travelers leave, move around, and return to the same spatial point at a later moment in time. ... He can also find his way back to his starting point in the inertial frame he began in by dead reckoning, and he can tell, from the record of his acceleration, how much "life-line time" he's "saved" by comparison with how much time would have passed for him if he'd never started his engine and had simply waited until he got to this event in the original inertial frame. ...
    (sci.physics.relativity)
  • Re: Proper Time v. Absolute Motion.
    ... Twin A shows 200 days less elapsed ... > absolute comparative motion. ... Acceleration does not affect the rate at which a clock runs. ... inertial frame, the Origin. ...
    (sci.physics.relativity)