Just a couple brief comments.
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.
[HH]
This can not be consistent with relativity,
[SAL]
But it is. It's built into GR from the get-go.
[HH]
I thought Einstein's equivalence principle was built into relativity.
The equivalence principle is built in. So is the principle of
relativity, and, as a consequence of the assumption that you can change
to any arbitrary coordinate system without affecting the results, the
lack of any local effect due to acceleration is built in, too.
[snip enormous amounts, after reading -- thanks for the additional
explanation of the retardation comments]
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.
No, I haven't, because, as stated elsewhere, clocks in GR are apparently
affected by gravitational _potential_ but not by the local intensity of
the gravitational _field_.
When you accelerate, in SR, you find that distant clocks are apparently
affected by _your_ acceleration. _THAT_ is equivalent to the GR clocks
being affected by the gravitational potential. The effects are identical.
You cannot separate the observations from the observer, and the concept
of observable properties of external things being affected by changes
within yourself (such as your acceleration) is a consequence of that.
[ ... ]
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.
Whether an effect is "real" or not is so slippery that I don't think
there's any definitive answer.
IMHO the Sagnac effect proves that time dilation is "real". In the
opinion of lots of other people it does not. If you spin a rigid disk
it will crack due to Fitzgerald contraction. I think that proves the
contraction is "real". Many other people think it does not.
The trouble with m0*gamma is it's the total energy of the object, and
that's frame-dependent. Your point of view determines how big it is.
But does that mean it isn't "real"? I don't think so -- that's like
saying kinetic energy isn't "real" because it's frame dependent.
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.
Retardation explains what you see as you watch the other party, right?
By using a powerful telescope, you can actually watch the other party's
clock throughout the whole trip. By looking at the _size_ of the image,
and the rate at which it's changing, you can see how fast the other
party is moving (relative to you) and how far away the other party is.
That picture-show which you can watch _MUST_ agree with the physical
effects observed when you get home again and put the clocks next to each
other. If you can explain how that happens you're probably as close to
"understanding" this as you can get.
The weird thing is that all the "effects of retardation" do _not_ cancel
when you get home, and it's very hard to draw a line between what was
"real" and what was an illusion.
The weirdness you apparently see comes directly from the (assumed) fact
that the light signal travels at C relative to _both_ the stationary and
the moving parties.
* * *
In the "stationary" frame you can explain it all by using time dilation
-- you can, with the help of extra (stationary) observers spaced out
along the route, actually observe the traveler's clock running _slow_.
(Just assume time dilation is real and you're done!)
In the "moving" frame you've got a much bigger problem; just exactly
when does the stationary clock run _fast_? The answer is: while you are
accelerating.
[ ... ]
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.
Relativistic Doppler shift includes a term for gamma. The emitter's
motion changes the apparent frequency, _and_ the emitter's different
time base changes the apparent frequency, and the two effects must be
combined to obtain the total observed effect.
The "extra" mass of a moving body is (gama-1)*m0. At relativistic
speeds that's where most of the body's energy is. If that's not "real",
then most of the energy isn't "real", either.
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.
That would make sense. The redshift "happens" in regions where the
field is non-zero, of course, which is exactly where the photons would
be interacting with it.
If the field is the gradient of the potential, then the places where the
field is strongest are also the places where the potential, and degree
of redshift, are changing most rapidly.
But I'm just talking about where and when you would "observe" a
red-shift. The "observed" redshift is a function of the gravitational
potential, but that's not the same as saying it's "caused" by it -- I
should be more careful about how I say things...
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.
It seems that way but it's not.
In relativity, the E field and the G "field" produce totally different
kinds of "forces". Let's see if I can dredge this out of my memory....
The E field contains a heat-like component (heat is a force, too -- a
candle increases the momentum of an object placed above it, so dP/dt is
nonzero in that case). Gravity is not a heat-like force, and I'm
failing completely to recall just what difference that makes in this case.
More mundanely, charge is conserved; you drop a charged rock down the
hole, at the bottom of the hole it still has the same charge as it had
at the top of the hole. If you turn it into a beam of light you need to
figure out what to do with the charge -- you can't just throw it away.
Gravitational mass is apparently _not_ conserved, not the same way; in
particular, when you drop the rock down the hole, it gains gravitational
mass.
Oh well I'm just babbling at this point I should drop this line of
reasoning until and unless I look it up again...
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.
If you work it out, it's a completely uniform field. Very strange.
(Easiest way to analyze it is to pretend the chamber is a separate
sphere of "negative mass" and just sum its "negative" field with the
field of an intact planet.)
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.
I don't know if I understand you. Light should be redshifted as it
crosses the chamber, in proportion to the intensity of the field in the
chamber, right?
If that's what you're saying, I agree. Note again that since the field
strength is the gradient of the potential, that's equivalent to saying
the degree of redshift varies with the 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.
Only if there's a gravitational field filling the universe, pointing to
the center. That's the only way you'll get a lower gravitional
potential at the center of the universe.
And if there is such a field, then there must be a redshift associated
with it, too.
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.
Hmmm ... Consider again the laser-ring gyro. What causes the fringe
shift when you rotate it?
Signal velocity relative to the rim of the disk can be measured and is
constant.
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.
But would such effects not be swamped by the local influence of the Earth?
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.
Hmmm ... Interesting.
