Sigh ... There is nothing easy to _understand_ about relativity.
The math of SR is relatively simple but the consequences are not.
Horace Heffner wrote:
On Jan 22, 2006, at 5:05 AM, Stephen A. Lawrence wrote:
Acceleration doesn't affect clocks. That's been verified (can't cite
references, sorry). A clock in a centrifuge slows only as a result
of the speed at which it's traveling, not as a result of the
centripetal force.
This can not be consistent with relativity,
But it is. It's built into GR from the get-go. In SR, where it's an
add-on, it's called the "Clocks hypothesis" and makes it possible to
extend SR to cover accelerated frames. Either way, it's been verified a
number of times because people weren't sure whether to believe it or
not, and there were competing theories which differed on this point.
Without the independence from acceleration, there would be no way to
construct a useful locally inertial frame for a given coordinate system
and a lot of the techniques (and proofs) used in GR would not work.
But I see the problem: there is a piece missing. Acceleration affects
_DISTANT_ clocks. This is weird. Please look here:
http://physicsinsights.org/revolving_astronaut.html
As you observe elsewhere, acceleration is equivalent to a uniform
G-field. When you accelerate away from something that's far, far away,
time on that object seems to run backwards. What happens if you replace
the "acceleration field" with a real, uniform, space-filling
gravitational field? How can time really run backwards? Answer: you
get something called a "Rindler horizon" which appears at the distance
from you where time stops, and it's just like the event horizon around a
black hole. The clocks which run backwards are on the wrong side of the
Rindler horizon and no information from those clocks can ever reach you
unless you stop accelerating (or turn off the space-filling G field).
I am not being intentionally obscure.
for the reasons I repeat
below. These issues demonstrate the usefulness of Jefimenko's work.
His physics is developed strictly on the basis of retardation - the
affects of photon travel delays upon the observer. He shows that the
effects of such delays depend on the type of clock being examined,
which leads to some potential conflicts with the type SR you are
applying.
If I understand you correctly, that is a flat violation of the principle
of relativity. If different types of clocks are affected differently by
ones velocity, then the laws of physics are not independent of velocity.
That may be true, but if so, then then theory of "relativity", both
general and special, must certainly be incorrect.
As of this moment, no experiment has shown different kinds of clocks to
show differing degrees of time dilation, which is what I believe you are
saying he claims here. If such an experiment ever shows a non-null
result, the consequences will depend critically on who did it and how
easy it is to replicate. If the experimenter is well known and
replication is straightforward it will stand a great deal of physics on
its head. If the experimenter is not well-known and the effect is hard
to replicate, it will be dismissed as obviously absurd because it
contradicts relativity.
I believe Jefimenko may have swung enough weight to pull down relativity
_if_ he had actually had the evidence to back him up, but I don't think
he did. Feel free to contradict me, of course!
He also derives the laws of electromagnetics, showing the
magnetic field is the result of retardation upon observations of the
Coulomb field.
I think this part of his work may now be incorporated into the standard
theory, if I understand you correctly.
The magnetic field can not both exist as an independent
entity and as an observational effect, otherwise magnetic field
intensities should be double that observed.
Say what?
It's not independent, it's part of the EM field...?
While effects based on retardation are of great interest for predicting
observational effects, like apparent clock rate changes and magnetic
field strength, they can not possibly explain the twins paradox
experiment. When the clocks return to be side by side in the same
reference frame, if there is any difference in their times, then those
differences have to be due to acceleration, or by Einstein's principle
of relativity, due to gravity. They can not be due to retardation
effects because there are none.
OK, I admit it, I'm lost here.
In Einstein's relativity, the twins "paradox" is resolved by the fact
that the moving twin's path deviated from a geodesic. The geodesic path
represents a (locally) maximal path; any deviation results in a shorter
path. Acceleration necessarily takes you off a geodesic, and results in
less time passing. HOWEVER the relationship is not simple, as in
"more acceleration => more dilation", and the effect is not direct.
Now, let me say this again, as clearly as possible:
The rate at which a clock is observed to tick does not depend on whether
the clock is _currently_ undergoing acceleration. That has been both
predicted and observed to be true, to the limits of the experiments
which have been done.
Let me say this, even more clearly:
Any attempt to boil the math of relativity down to a few simple English
sentences which "explain" it will fail. Any attempt to explain time
dilation as a simple ratio will also fail.
We can state things like the principle of relativity in English. But
trying to explain "why" one twin ages by a particular amount using
English is doomed to failure. "The twin ages less because of the
acceleration" is a simple English sentence and necessarily gives an
incomplete picture.
As I mentioned in an earlier post [and earlier in this post -- I think
I'm repeating myself], in this case acceleration is only HALF of the
picture, because acceleration doesn't affect clocks directly. What
acceleration _DOES_ do is affect _DISTANT_ clocks. When YOU accelerate,
clocks that are far, far away and toward which you are accelerating seem
to you to run _faster_. Clocks that are far, far away from you but
"behind" you, so you're accelerating _away_ from them, seem to run
slower, or even run _backwards_. If the moving twin accelerates toward
Earth when far away from Earth, it appears to him that, during the
acceleration, clocks on Earth whizz ahead very rapidly. If he does the
same thing when adjacent to Earth, nothing much happens. The distance
makes the difference, and the distance depends on how long the
"coasting" phase of the trip lasted.
But really, the fundamental problem is that the "rate" of a clock in
relativity theory is NOT A NUMBER. The time "coordinate" for a
particular frame of reference is a scalar field on a 4-dimensinoal
manifold, and the "rate at which it passes" is the gradient 1-form
associated with that scalar field. The rate at which you see a clock
associated with a particular reference frame tick depends on the angle
your worldline makes with the time coordinate gradient of that FoR.
THE ONE DIMENSIONAL MODEL
The issues are simplified by looking at things one dimensionally, and
such a simplified system is sufficient to examine the critical issues.
The difficult math seems to me to disappear in a flash! 8^) No longer
are fancy transforms and distance functions required. Further, we can
look at each flash from earth as a single photon.
As the traveler departs in a straight line away from the earth
transmission point, and distance from earth gets greater, the photons
arrive further apart in time, and red shifted for the same reason, the
wave peaks arrive slower, thus time back on earth appears to the
traveler to slow down. However, no matter what kinds of accelerations
the traveler has experienced or is experiencing, he keeps receiving his
regular periodic set of photons from earth. The only thing that
changes are the time increments sensed by the traveler between photons,
and their colors. No matter where he is or how far he goes or how he
accelerates, assuming a fast rate of photon transmission from earth,
there are always photons in route from earth to the traveler. As the
traveler turns about, and returns, the rate he absorbs those photons
increases, and he sees a blue shift as well, for the same reason, i.e.
the wave peaks arrive faster. The earth increments its clock each time
a photon is transmitted. The traveler can increment his on board
"earth clock" each time he receives a photon. He can use a similar
clock to the earth clock to keep track of his local time.
As the traveler closes the distance to earth on the return trip, fewer
photons are in flight with passing time. Assuming the traveler's on
board clock was not affected by his acceleration, his "earth time"
clock and local clock will come back in synchronization. Further, his
earth time clock and earth's clock will be in perfect synchronization
upon arrival. If not, the number of photons sent and the number
received can not match, which is nonsense. The only other way for the
traveler's clock to not agree with the earth clock, or his own "earth
time" clock for that matter, is for the traveler's clock to have been
affected by the acceleration.
Yes, it is "affected" by the acceleration -- the acceleration changed
the worldline of the traveler, and moved him onto a shorter path.
No, the acceleration was not directly responsible for the dilation.
If the traveler accelerates in a blazing flash lasting a few
microseconds, and then IMMEDIATELY decelerates again, he'll experience
negligible time skew. On the other hand, if he accelerates, coasts a
long time, and then decelerates, he'll experience a lot of time skew.
If this makes any sense, then faster than light travel can make sense
as well, assuming the traveler has an infinite Isp drive, like a ZPE
drive. As the traveler exceeds the speed of light, he simply does not
see any photons from earth. This does not mean he is traveling
backwards in time. It only means his communication with earth is cut
off (unless of course he has some spooky action at a distance
communication device.) When he the traveler turns around, he
eventually starts receiving the photons again, but very much blue
shifted. When traveling faster than light relative to earth, his earth
clock merely stops, it doesn't run backwards. His own local clock,
however, keeps on ticking. Again, without some change in the
traveler's clock due to acceleration, all the clocks must be in
synchronization upon his return.
EN-GAUGING
Clock rates in a gravitational field are affected by the
gravitational potential, not the local gravitational field strength.
The gravitational potential cannot change without the gravitational
strength changing.
Ho ho, I'm glad you asked me that! :-) This is a fun subject.
First, there's no deep GR math here. We throw that all away, and just
go back to the original Gedanken experiment which led to the conclusion
that there had to be a gravitational redshift. It goes like this:
Einstein stands on a ladder. Poincare is seated on the floor. Einstein
drops a rock on Poincare. As the rock falls, it gains energy. Poincare
catches the rock, and turns it ... all if it, _including_ the energy it
gained during the fall ... into a beam of light, which he shoots back up
at Einstein. Einstein catches the lightray, and turns it back into a rock.
But the energy of the lightray included all the energy of the original
rock _plus_ the energy gained during the fall. So, the final rock
weighs more than the original rock. OOPS -- First law violation --
we've just extracted energy from a conservative field.
To fix this, we must assume the light was redshifted during its trip up
the ladder.
To make the gravitational redshift work with the principle of relativity
(which says, basically, physical laws are the same everywhere) we find
that time must run more slowly for Poincare, sitting on the floor.
Einstein, standing on a ladder, has a clock which ticks faster, so
Poincare's light beam _looks_ redshifted to Einstein.
Let me reiterate: The problem was the difference in _potential_ energy,
which had to be compensated for _somehow_.
Now, let's go down, down, to the very center of the Earth, and carve a
spherical chamber out of the rock. Inside a hollow planet, there's NO
APPARENT GRAVITY, as we all know, Edgar Rice Burroughs' book
"Pellucidar" aside. Now, drill a skinny hole all the way from the
surface of the earth to the chamber in the center of the earth. Put an
astronaut carrying a watch into the chamber down inside, and put another
one on the surface of the Earth. Whose clock runs faster? The one on
the surface is experiencing 1G of acceleration, the one inside is
experiencing zero g.
To answer this, let the one on the surface drop a rock down the hole.
It gains energy. At the bottom of the hole, turn the rock, and the
energy it gained during the fall, into a light ray, and send it back to
the surface. It _must_ be redshifted, else we'd have another first-law
violation. And the redshift means the clocks down inside must run _slower_.
The gravitational time dilation is due to the gravitational potential,
_not_ the local acceleration of the field.
One dimensionally speaking, anything which is a
function of the gravitational potential is a function of the
gravitational field plus an arbitrary constant of integration.
Again, I can construct a situation where the potential increases while
the field strength is constant or even drops.
Here's another cute example: A spherical chamber cut out of a uniformly
dense planet which was _offset_ from the center would have a _uniform_
(but non-zero) G-field inside it.
No
matter how you cut it, clock rate is a function of gravitational
field. If the effects of the gravitational field differ from the
effects of acceleration (this difference at any point) then Einstein's
fundamental assumption for GR is violated and GR disappears in a
flash! 8^)
I also have to question the validity of the tangential straight rod
approach you use. I could be missing something, but it doesn't seem to
account for how we would see the clock advance as it passes behind the
earth in the opposite direction.
You can't synchronize all the clocks on a rotating disk. You can't
synchronize all the clocks on the Equator. If you try, you find there
is a "date line" where two adjacent clocks are out of sync. It's
crossing the "date line" which causes the hiccup.
The "date line" is the point where we cut the ring and straighten it out.
Note that the usual way to "synchronize" the clocks on the Earth
involves using an external standard, like sidereal time; in reality,
when "synchronized" this way, no two clocks at separate longitudes are
exactly in sync in the "Earth frame".
What does that mean? It means that if you take a single clock and carry
it _very_ slowly to a neighboring clock which was nominally in sync with
it you'll find that they don't agree. The one you moved will seem to
have gone off-sync, no matter how slowly you moved it. Alternatively,
if you try to radio-sync them, you'll find that the result doesn't agree
with the "sidereal time synchronization", and if you try to radio-sync
all of them all the way around the Earth you're back to the first
situation with a "date line" someplace.
Horace Heffner
