On Jan 22, 2006, at 6:25 PM, Stephen A. Lawrence wrote:
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.
I thought Einstein's equivalence principle was built into
relativity. If a clock does not change with acceleration then the
equivalence, by definition, is broken. A clock in a centrifuge must
slow down in part because it is accelerating ... or there is no time
dilation due to gravity.
[snip]
As you observe elsewhere, acceleration is equivalent to a uniform G-
field.
This seems to contradict what you just said above.
When you accelerate away from something that's far, far away, time
on that object seems to run backwards.
Hopefully we are not going to get sidetracked talking about how
things *appear* in motion. I am trying to focus on what happens when
clocks can be brought back together.
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.
I think the above above only makes the simple complex. My
proposition is simple: if clocks go away and then come back together,
any difference in time can not be due to any effect caused by
retardation. If velocity can not affect the clocks then a difference
in final time must be due to acceleration along the path.
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.
Clocks of some kinds are affected by velocity as well as
acceleration. Those clocks which involve mass, like muon decay
rates, atomic fine structure, etc. are affected by the fact m =
m0*gamma. Clocks not involving mass, like photons bouncing between
mirrors, behave differently, and their behavior is a result of
retardation, if I understand Jefimenko. Jefimenko shows us how far
relativity can go on just retardation. Jefimenko does use m=m0*gamma
in his clock calculations for clocks involving mass. I think I
neglected to mention that.
That may be true, but if so, then then theory of "relativity", both
general and special, must certainly be incorrect.
The problem I think is distinguishing between types of clocks. There
is a big issue as to whether m = m0*gamma is talking about a real
effect. This relation was discovered before relativity. It was
originally considered a real effect, and if so there was no problem
accepting that clocks actually slowed down for moving objects.
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.
Yes, I think he does.
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 don;t know of any experiments involving (a) mass free clocks and
(clocks returning to the point of origin.
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!
It would be tough to design the experiment I think.
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...?
The point is there is no magnetic field. There are no special
messenger particles for the magnetic field. The momentum exchange is
purely by virtual photons. The only field is the Coulomb field. The
magnetic effects are mere artifacts of retardation.
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.
Retardation only explains what is *observed* between the clock
separation and clock rejoining. Any effect based purely on
retardation disappears upon clock rejoining. In other words it is
completely undone in the process of return. Any time difference
remaining is a result of actual effects upon the clock. Effects due
to m=m0*gamma can not be reversed, so I would consider these actual
effects as opposed to retardation effects, because they are not
undone upon return. This seems to me to be a really simple concept.
Some effects due to acceleration or gravity may also fall into this
"real" category because they are not undone by simply leaving a
gravitational field or stopping or reversing the acceleration.
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.
Then you have conclusively proved GR is based upon a false assumption.
Let me say this, even more clearly:
Any attempt to boil the math of relativity
That is the last thing I would want to do! I just want to
distinguish between retardation effects and other effects.
down to a few simple English sentences which "explain" it will fail.
I am not explaining anything, merely pointing out some inconsistencies.
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.
Agreed - but only if you agree that clocks involving mass actually
change due to velocity alone. In other words, if m = m0*gamma is
purely due to appearances, i.e. due to retardation, then the only
effect left to cause a time difference upon rejoining the clocks is
acceleration. I don't think it is generally accepted an more that
m=m0*gamma is a real effect. I definitely read that in some text.
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.
If acceleration does not affect clocks directly then neither does
gravity.
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_.
Irrelevant. Who cares how the clocks appear during the journey. I
only care what happens when they come back together in the same
location in the same reference frame. Then all retardation effects
have cancelled because there is no retardation remaining.
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.
OK, but then this implies the clock is mass related, and m=m0*gamma
is a real, not a retardation effect.
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.
I wish I had time for the discussion.
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.
I think this is not the only possible explanation. An alternative
explanation is the red shift is due to the effect of gravity on the
photon. Gravitons exchange momentum with photons, but not virtual
photons. If this were not true black holes would not exist. In the
case of a spherical shell object with a hole in it, I think the red
shift would occur at the surface as light goes through the hole.
It sounds like you are attributing a "real" effect to static
gravitational potential that should be matched by an equivalent
"real" effect from a static electromagnetic potential A. No such
effect exists to my knowledge. AFAIK, The only effects that manifest
as real are the result of changes in A, i.e in @a/@t.
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.
It should have a g field due to the sphere having the radius from the
hole to the center. I think any object held in that chamber would
experience a gravitational red shift proportional to the g at its
location, not to the gravitational potential. If what you were
saying were true then objects in the center of the universe (assuming
here a big bang) should all be massively red shifted, instead of vice
versa.
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.
I didn't mention synchronization.
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.
Here again you are talking about how things appear in motion. I just
want to figure out in an intuitive way what accounts for differences
when clocks are brought back together. If there is no velocity
effect which does this, then what remains except acceleration?
Retardation is out of the picture.
Now that I can see some real data it would be good to look at the
effects of gravimagnetism, because these should modify the expected
values. It is probably going to take an FEA program to do this
right, and I just do not have the time right now.
What I *can* see from the airplane data is it can not be fully
analysed using only the earth's gravimagnetic field. It requires
quantifying the solar and/or galactic gravimagnetic field.
Gravimagnetics, given the presence of the significant ambient
gravimagentic field, should enhance the time difference on the
*airplane* clocks. In other words it agrees qualitatively with the
time differences, but may be too small to make any difference. It
does mean the two east-west opposed orbit satellites would have their
orbital parameters affected, thus their velocities, and thus their
clocks.
It is interesting that polar satellites should veer left going over
the North pole and right going over the South pole, from the point of
view of a person in the satellite oriented feet down and facing the
direction of motion. Satellites going west-to-east should experience
a lower g value than those going east-to-west, and the higher the
velocity the lower the g value. This means the g value at the
surface should be, due to gravimagnetism, slightly less at the
equator than at the pole, and should cycle in value over a 24 hour
period, due to the earth's axis not aligning with the ambient
gravimagnetic field.
Horace Heffner
