Horace Heffner wrote:
> This has not made it back to me for over 4 hours so here goes again:
>
> On Jan 19, 2006, at 8:11 AM, Stephen A. Lawrence wrote:
>
>> The speed of the flights is not a factor, either -- the same time
>> lag will be observed no matter how fast they go. However, in order
>> to keep the precision with which one needs to keep time down to
>> something manageable, it's important to go quickly. If you used a
>> ship and retraced Magellan's route instead of using an airplane,
>> for instance, the tiny difference in the readings would be totally
>> lost in the accumulated inaccuracy of the clocks over a period of
>> several months.
>>
>
> Interesting about the speed independence.
>
> Reminds me of the old Jefimenko's clocks issues discussed here some
> years back. There is something I have not understood about the twin
> paradox...
Ding, ding! I think I just heard my cue! :-)
> , and relativity in general. SR appears to be based solely on
> observational differences, i.e. retardation. This is true of
> Jefimenko's view also, except possibly for relativistic mass
> changes. However, in the case of the returned twin, the two twins
> stand next to each other at the end. They are in the same reference
> frame. If there is a difference in age between them then that
> difference can not be simply a result of retardation. If the
> "permanent" clock difference effect is due to acceleration
That's a useful way to think of it, at least in the sense that it's
the acceleration which breaks the symmetry and resolves the apparent
logical paradox: the twins are _not_ identical, and the one whose path
diverged from a geodesic is the older twin.
But it's not the whole story, as you also observed.
> (GR effects),
No GR needed! One can get more than adequately confused just using SR
here.
GR is only necessary when there's gravity. Otherwise you can do it
all using flat-space concepts, maybe with a little bit of tensor
calculus thrown in. But the real hair of GR is the curvature tensor
and everything related to it and we absolutely don't need that stuff
in this case.
Furthermore in GR you can never ask how old someone is unless they're
standing right next to you, which takes all the fun out of it.
> and the journey consisted of only brief acceleration phases,
> followed by long segments of uniform motion, then it seems that the
> final clock difference from a long journey would be the same as that
> of a short journey with the same accelerations and no coasting.
OK, let's go with that for a moment. If the period of acceleration is
negligibly short, then all we really have to worry about is the period
when the moving twin is coasting. So what happens then?
A simple answer is that the acceleration jumps the moving twin into a
different frame of reference. During the outbound trip, before
turnaround, each twin sees the other growing older more slowly. It's
exactly symmetric.
But even that is a misleading statement, because they're not standing
next to each other; they each actually only _compute_ the other to be
aging more slowly. And when the traveling twin turns around, suddenly
his frame of reference changes radically. Once he's finished turning
around, if he redoes his calculation, he now computes that the
stay-at-home twin is much older than he previously computed. During
the trip home, the stay-at-home twin seems to the traveler to be aging
slowly again, but it's not enough to make up for what (seems to have)
happened during turnaround.
(Before continuing, I should mention that I have a web page on the
"linear twins" problem which _might_ be of some slight interest. If
nothing else it is unusual in that I didn't use any Lorentz transforms
in working it out:)
http://www.physicsinsights.org/linear_twins.html
But wait ... before you say anything about the irrelevance of the
coast phase in the picture I'm presenting here, let's recall a vitally
important truism in relativity: Acceleration does _NOT_ affect time!
If the twins are next to each other and one is accelerating rapidly,
that makes no difference. BUT when the distant twin turns around,
they're _not_ next to each other. Strangely, your OWN acceleration
causes distant clocks to be _computed_ to run FAST if you accelerate
toward them, or SLOW (... or backward ...) if you accelerate away from
them. And the farther away the other party is, the bigger the impact
your acceleration has on how rapidly they seem to age. So that's the
missing piece: It's acceleration COMBINED with distance that makes the
magic, and the distance at which the traveler accelerates is
determined by how long he coasted for. Less coasting => acceleration
takes place closer to home => it has less effect.
By no small coincidence, I happen to have a little page on this too;
if you've never seen the calculation showing time running backwards
it's worth a peek:
http://www.physicsinsights.org/revolving_astronaut.html
But wait ... wait ... what if you look at those distant clocks in a
telescope while you're accelerating? What will you see? Surely the
hands on the clocks won't be seen whizzing around frentically in one
direction or the other?
No, they won't, but something equally strange will appear to happen.
If you watch a clock as you accelerate toward it, you'll see it
continue to tick normally ... as it zooms _away_ from you at very high
velocity! (And this is a _classical_ effect!! It's' _NOT_ unique to
special relativity!) And _that_ is the final piece that lets us fit
the computed solution to the paradox into the picture which is
actually seen by the traveling astronaut: when he's finished
accelerating he _observes_ that the stay-at-home twin is now coming
toward him going very fast, but coming from much farther away than he
previously thought; when he adds the time the light signal must have
taken to traverse the apparent distance of the new image to the time
he sees on the face of the clock in the telescope, he gets a much
later date than what he found before accelerating.
And by golly I've got a few words on a web page on this aspect, too:
http://www.physicsinsights.org/porthole_view_1.html
The pieces of the picture all do end up fitting together, but they
never, as far as I know, can be made to make "intuitive sense".
Finally, if you are a glutton for punishment, I've got a page on the
computed solution to the twins problem taking full account of
acceleration. It's got some nice graphs down at the bottom, after all
the equations.
http://www.physicsinsights.org/accelerating_twins.html
Ironically, after all that work on the accelerating twins page, I
stopped short of doing the traveler's porthole view and hence missed
the bizarre behavior of the image in the telescope; the
porthole_view_1 page came much, much later.
I had some ideas for some additional spacetime graphs which would have
pulled together the porthole and computed views on a full round-trip
but I never got around to doing them.
> You might find it interesting that in his book *Retardation and
> Relativity*, Jefimenko takes a different but interesting view of the
> relativistic clock paradox. He says the clock speed is a function
> of what kind of clock is being obeserved in motion.
Perhaps, but doesn't this make rather nasty hash of the principle of
relativity? I.e., it suggests that physical laws change rather
dramatically as a result of a change in speed, which seems peculiar.
In other words, if I'm carrying two different kinds of clocks, and I
take off in a spaceship, I would then see the two clocks running at
different rates. This would be disturbing, particularly if the two
clocks happened to be represented by two different enzyme reaction
paths in my body...
> He calculates the
> speed of various natural clocks.
>
> His calculations for the twelve clocks were based on "the
> fundamental laws of electromagnetism and mechanics with no input
> from relativity theory (although we shall use the longitudinal and
> transverse masses, which may be regarded as either experimentally
> obtained masses, or as relativistic concepts)" (p. 237)
Erk. Yeah, I'd say that's a relativistic concept. As to being
"experimentally derived" you could say just about all of SR falls into
that category at this point, anyway.
By the way, either the transverse or longitudinal mass calculation
(forget which off hand) is the site of the only error I know of in
Einstein's 1905 electrodynamics paper; he botched the derivation and
got a formula wrong. It's close to the end, and I've got a reference
to it buried someplace in old email if anyone's interested. Nobody
cares these days because nobody uses longitudinal and transverse mass
values for anything anyway AFAIK.
> However, his EM equations, based on retardation, are similar to SR
> based equations.
Well they should be -- the E&M equations are the foundations Einstein
built relativity on, after all! And the retarded integrals are
very fundamental to E&M.
> His view is interesting. In the twin paradox, as viewed by
> Jefimenko, perhaps the "young" twin may have varied aging effects,
> depending on the mechanics of some specific chemical interactions.
>
>
> Jefimenko's clocks consisted of:
>
> 1. A charged particle oscillating in the x axis, the central axis,
> of an oppositely charged ring. Relative direction of motion of the
> clock is in the x axis.
>
> 2. Two (outer) particles A and B of the same charge located on the
> y axis at points +-a, an inner particle C, oppositely charged,
> oscillates in the x axis between the two particles and near the
> midpoint. Relative direction of motion of the clock is in the x
> axis.
>
> 3. Same as 2, but the motion of C is in the y axis, the two like
> particles A and B are located in the z axis. Relative direction of
> motion of the clock is in the x axis.
>
> 4. The time delta t it takes for two charges to separate (in the y
> axis) a small fixed distance d when initially separated by distance
> R. The ratio d/r ~ 0. Relative direction of motion of the clock is
> in the x axis. If t_y is the time it takes for the same separation
> to occur in the y axis, then t/t_y = gamma.
>
> 5. This clock is similar to clock 4, except one charge is replaced
> by a long line of charge of uniform line density lambda, lying in
> the z axis and having its midpoint at the origin. The point charge
> of opposite sign is placed on the y axis at initial distance R from
> the origin. Relative direction of motion of the clock is in the x
> axis.
>
> 6. This clock is similar to to Clock 2, except charges A and B are
> replaced with line charges in the yz plane parallel to the z axis.
>
> All of the above clocks appear to run gamma times slower than the
> identical stationary clock, so t_moving = gamma * t_observer. All
> the following clocks run at a different rate.
I'm sorry, I got rather lost at this point and did not try to dig
through the derivations of the last six clock rates. But unless he's
found a contradiction in SR or E&M I don't see how any valid clock
could be _computed_ to tick at a rate different from 1/gamma.
So do I understand this? He is suggesting that there is an absolute
stationary frame, the principle of relativity is false, and one can
determine ones absolute velocity by observing various kinds of clocks?
But we still need to deal with Maxwell's equations, we need to figure
out what happens when a moving observer applies Maxwell's equations,
and we need to come to terms with the Michelson-Morley and Sagnac
experiments, and that doesn't leave a lot of wiggle room if we also
want mechanics to be described by reasonably simple and consistent
laws...
> 7. This clock is the same as Clock 3, but A and B are placed at
> points +-a on the x axis. Charge C oscillates in the y axis.
> Relative direction of motion of the clock is in the x axis. Here
> t_moving = 1/(1-v^2/c^2)^(5/4) * t_observer, or gamma^(5/2) times
> the rate for the same stationary clock.
>
> 8. This clock is similar to Clock 5, except the line charge is now
> placed on the x axis with the midpoint at the origin. Again, the
> point charge of opposite sign is placed on the y axis at initial
> distance R from the origin. Relative direction of motion of the
> clock is in the x axis. Here t_moving = 1/(1-v^2/c^2)^(3/4) *
> t_observer, or gamma^(3/2) times the rate for the same stationary
> clock.
>
> 9. This clock is similar to Clock 3, except the two point charges A
> and B are replaced with line charges that are parallel to the x axis
> and are at distance +-a from the origin in the xz plane. The point
> charge C of opposite sign oscillates about the origin in the y axis.
> Relative direction of motion of the clock is in the x axis. Here
> t_moving = 1/(1-v^2/c^2)^(3/4) * t_observer, or gamma^(3/2) times
> the rate for the same stationary clock.
>
> 10. The time delta t it takes for a charge to separate from a plate
> of surface charge density lambda, of the same polarity, lying in the
> xy plane to separate (in the y axis) a small fixed distance d when
> initially separated by distance R. The ratio d/r ~ 0. Relative
> irection of motion is in the x axis. If t_y is the time it takes
> for the same separation to occur in the y axis, then t/t_y =
> gamma. The point charge C of opposite sign oscillates about the
> origin in the y axis. Relative direction of motion of the clock is
> in the x axis. Here t_moving = 1/(1-v^2/c^2)^(3/4) * t_observer, or
> gamma^(3/2) times the rate for the same stationary clock.
>
> 11. The time delta t it takes for a charge to separate from a plate
> of surface charge density lambda, of the same polarity, lying in the
> yz plane to separate (in the x axis) a small fixed distance d when
> initially separated by distance R. The ratio d/r ~ 0. (This is
> similar to Clock 10, but rotated so the particle moves in the x
> axis.) Relative direction of motion of the clock is in the x axis.
> If t_y is the time it takes for the same separation to occur in the
> y axis, then t/t_y = gamma. The point charge C of opposite sign
> oscillates about the origin in the y axis. Relative direction of
> motion is in the x axis. Here t_moving = 1/(1-v^2/c^2)^(3/4) *
> t_observer, or gamma^(3/2) times the rate for the same stationary
> clock.
>
> 12. This clock is similar to Clock 4, except rotated into the x
> axis. The time delta t it takes for two charges to separate (in the
> x axis) a small fixed distance d when initially separated by
> distance R. The ratio d/r ~ 0. Motion of the charges is in the x
> axis. Relative direction of motion of the clock is in the x axis.
> This clock is similar to Clock 4, except rotated into the x
> axis. Here t_moving = 1/(1-v^2/c^2)^(5/4) * t_observer, or
> gamma^(5/2) times the rate for the same stationary clock.
>
>
> Horace Heffner
>
>
