On 1/3/2014 8:10 AM, Edgar L. Owen wrote:
Jason,
Thanks for your several posts and charts. You really made me think and I like
that!
I'm combining my responses to your multiple recent posts here.
First though there are two ways to analyze it, GR acceleration, as opposed to SR world
lines, is the most useful because it makes the following argument re present time easier
to understand.
Imagine a new experiment in which Pam is completely still relative to Sam but somewhere
way off in the universe and in a gravitational field of exactly the same strength. In
this case both Pam's and Sam's clock times run at exactly the same rates and both agree
to this. Therefore it is clear they inhabit the exact same present moment even by your
arguments, and their identical clock times correlate to this.
No, that doesn't follow at all. Running at the same rate doesn't mean at the same time.
My watch runs at the same rate as my grandfathers - but not at the same time. All you can
conclude is that, by exchanging signals Pam and Sam can set their clocks to *the same time
in their frame* and by symmetry they will run at the same rate.
Now assume Pam's gravitational field increases to the point where her clock time runs
half as fast as Sam's. Again there is no relative motion so again both agree that Pam's
clock time is running half as fast as Sam's. And again both exist in the exact same
present moment, it's just that Sam's clock time is running twice as fast through that
common present moment. Again clock time correlates with present moment time...
First, they are in relative motion in spacetime. Second, there is no "present moment".
Pam and Sam are at different locations, so even aside from gravitational effects, their
agreement on how to set their clocks is arbitrary, it holds only in their frame, and
another observer moving relative to them will see their clocks as NOT reading the same
time even when their gravity fields were the same.
This gravitational time slowing is a GR, not SR effect,
They are actually the same effect, except in GR the path lengths are measured over a
non-flat geometry. See Epstein's book "Relativity Visualized".
and GR effects are absolute in the sense that they are permanent real effects that all
observers agree upon. They must be distinguished from SR effects which make the
situation more difficult to understand in terms of a present moment.
An acceleration equivalent to the gravitational field would produce the exact same GR
effect, but also introduces an SR relative velocity effect.
Now consider an pure SR effect in which Pam and Sam are traveling past each other at
relativistic speeds but there is no acceleration. Velocity is relative, as opposed to
acceleration which is absolute, therefore both observers think the other is moving
relative to them, and both views are equally true. Now because of this relativity of
velocity both observers see the clock of the other observer slow and by equal amounts.
But the absolutely crucial thing to understand here is that this SR form of time
dilation is not permanent and absolute like GR time dilation is. It vanishes as soon as
the relative motion stops, whereas GR time differences are absolute and persist even
after the acceleration stops.
The effect on *rate* stops, but the integrated effect of the rate having been different
over some duration is real. That's why the twins are different ages when they re-unite.
This is why the SR versus GR model is more useful in understanding what is going on
particularly with respect to the common present moment.
You "common present moment" is just an arbitrary inertial frame choice which you use to
label events with a t-value. It's just coordinate time.
So during relative motion between Pam and Sam there most certainly is a common present
moment,
There is a whole range of moments which will be at the same coordinate time depending on
what inertial frame is chosen to define coordinates.
but trying to figure out what clock times of Pam and Sam correspond to that present
moment leads to a contradiction (as you quite rightly pointed out with your diagrams)
because Pam and Sam see clock time differently and do not agree on it. They did agree on
their GR relativistic time differences
There was no gravity in my diagrams.
and thus knowing which of their clock times corresponded to the same present moment was
easy.
No, there is the same arbitrariness of "now" in your GR example. You just chose to
privilege the frame in which both are at rest (in space). In any other inertial frame
their clocks will still be seen to run at the same rate, but they will no longer be set to
the same time.
With SR, equal and opposite, time dilation it is impossible to correlate both observers'
clock times to the same present moment.
Sure it is, when they are at the same event.
Nevertheless that's just an artifact of SR clock time which doesn't falsify a common
present moment. A common present moment exists, it just isn't correlated with clock
times the same way by both observers.
It isn't correlated because clock's measure real physical intervals while present moments
are artifacts of coordinate choices and are arbitrary.
All the nice chart examples you took the time to produce demonstrate this. They are
trying to assign an agreed upon clock time to the common present moment time during SR
relative velocities and thus they correctly lead to the contradiction you pointed out.
They are showing that different coordinate choices change what you count as "present
moments".
However once you understand how this works you understand that fact doesn't falsify a
common present moment as you implied.
You can't falsify an arbitrary choice.
Now consider the twins from the original example. In this case there is both lots of
relative velocity SR effects between both twins, and there is the absolute GR
acceleration effect on Pam only.
Now the SR effects persist only during relative motion and when the twins meet up again
that leaves ONLY the GR acceleration effect which is the only cause of the twins' clock
time difference.
Nonsense. There is no gravity in by diagram, but a twin who traveled the white/blue world
line comesback 2.67 ticks younger than the stay-at-home twin.
All SR relative velocity effects must vanish when the relative velocities cease.
Only effects on rate vanish. The effect of different path length are measured by clocks
and biological processes and they are not arbitrary.
Otherwise we would have Pam and Sam meeting up again with each claiming the other's
clock time was going slower than theirs. That is impossible. At rest in the same present
moment all observers must be able to agree on their clock time differences. Both agree
Pam's clock time passed more slowly than Sam's and both agree as to the amount, based
ONLY on GR (acceleration) effects.
They will also agree that there is a difference if one simply traveled a shorter path
through spacetime to the comparison event - whether it was shorter because the space
wasn't flat or because they just took a non-straight path.
Assume again the twins passing each other at a constant (no acceleration) velocity. Both
see the other's time passing slower than theirs and thus both see each other at an
earlier clock time date than themselves. This is contradictory and cannot last when they
meet. It is the acceleration that brings the relative velocities to zero that produces
the only absolute persistent time effect
No, it is the difference in path length. That's the point of my diagram. The clocks of
White and Blue never experience any accelerations, but they measure a shorter world line
between two events than does Black's clock. Acceleration has nothing to do with it except
that it can be integrated to get distances - given a couple of constants of integration.
and when, and only when, that happens will the twins agree as to their time differences,
as always in a shared universal present moment.
This is why is is possible to correlated clock times to present moment time for GR
acceleration time dilation, but NOT for SR relative velocity time dilation.
Hope this is clear. It may be a little difficult...
It's clear to me. What's difficult is getting you to see it. Introducing GR is just
obfuscation.
Brent
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