"Norman Bates" wrote in message ...
|
| "Henri Wilson" HW@.. wrote in message
| ...
| On Fri, 1 Dec 2006 12:38:07 +0200, "Norman Bates"
| wrote:
|
|
| "Henri Wilson" HW@.. wrote in message
| . ..
| On Thu, 30 Nov 2006 12:57:21 +0100, "Paul B. Andersen"
| wrote:
|
| Henri Wilson wrote:
| On Wed, 29 Nov 2006 10:47:37 +0100, "Paul B. Andersen"
|
| The clocks in the planes will measure different proper times between
| the same two events because their paths through space and time are
| different,
| and the gyros in the planes will measure different rotations of the very
| same reason.
|
| Hahaha! This is becoming quite funny.
|
| Tell me how the clocks will somehow be affected by the fact that the
| Earth
| stops rotating midway through the experiment?
|
| This is what GR predicts for a K&H like experiment:
|
| Let's do a similar exeriment with satellites.
|
|
| Let's start with the Schwarzschild Solution:
|
| ds^2 = (1 - 2m/r)dt^2 - 1/(1 - 2m/r)dr^2 - r2 (dp^2 + (sin p)^2 dq^2)
|
| where t is the temporal coordinate,
| r is the radial coordinate,
| p is latitude, and q is longitude.
|
| m = G*M/c2 where G is the gravitational constant
| and M is the mass of the Earth.
|
| If the speed in the Earth centred non rotating frame
| (Schwarzschild frame, hereafter called ECI-frame) is v,
| we have v*dt = r*dp.
| Constant height (dr=0) around equator (dq=0)
| and the equation above becomes:
|
| ds^2 = (1 - 2*m/r - v^2/c^2)*dt^2 (v in conventional units - thus c^2)
| or
| ds = sqrt(1 -2*m/r - v^2/c^2)*dt
| or a first order approximation (m/r 1, v c):
| T' = (1 - m/r - 0.5*v^2/c^2)*T
| where T' is the proper time of the clock, and T is the travelling
| time in the ECI-frame.
| Since we are interested in finding the difference between two
| clocks at different height and speed (Earth clock and plane clock),
| we get:
| (T1 - T2)/T = -(m/r1) + (m/r2) + (0.5*v2^2/c^2 - 0.5*v1^2/c^2)
|
| So where is the proof that this is true.
|
| Inserting m = G*M/c^2 and G*M/r1^2 = g, acceleration at Earth's surface,
| we get:
| (T1 - T2)/T = -(g/c^2)*r1*(1-r1/r2) + (0.5*v2^2/c^2 - 0.5*v1^2/c^2)
| if we set: r2 = r1 + h, and approximate (r1+h)/r1 = ca. 1 since h r1,
| we can write this:
| (T1 - T2)/T = -g*h/c^2 + (0.5*v2^2/c^2 - 0.5*v1^2/c^2)
|
| Let's use the equation above on our idealized case with
| two planes flying in opposite direction around equator, same ground
| speed
| and height. We will use "reasonable values" for commercial planes.
| (They will have to fly non stop, though.)
|
| Let's suppose the ground speeds of the aircrafts are 232.5 m/s,
| and that they are flying at a height 9000m. The aircrafts
| will use two sideral days on the journey.
| The speeds of the clocks in the ECI-frame will be:
| Earth clock A: va = 465 m/s
| West bound B: vb = va - 232.5 m/s = 232.5 m/s
| East bound C: vc = va + 232.5 m/s = 697.5 m/s
|
| Observer speed makes no difference to time flow anywhere else..
|
| West bound:
| TA - TB = 2*sideral_day*(-g*h/c^2 + 0.5*vb^2/c^2 - 0.5*va^2/c^2) sec
| TA - TB = 2*86160*(-1 + 0.3 - 1.2)*10^-12 sec = - 327 ns
| West bound clock gains 327 ns (H&K 273 ns)
|
| According to your stupid theory.
|
| East bound:
| TA - TC = 2*sideral_day*(-g*h/c^2 + 0.5*vc^2/c^2 - 0.5*va^2/c^2) sec
| TA - TC = 2*86160*(-1 + 2.7 - 1.2)*10-12 sec = + 86 ns
| East bound clock loses 86 ns (H&K 59 ns)
|
| According to your stupid theory.
|
| A gyro in the west going plane would measure one rotation,
| a gyro in the east going plane would measure 3 rotations,
| and a gyro on the ground would measure 2 rotations.
|
| Now tell me, Henry:
| Where in the above do you see the rotation speed of the Earth?
| The only speeds that appear are the speeds of the CLOCKS.
| Since these are different, the three clocks and gyros will all
| measure different values because their paths through space and
| time are different.
|
| Their 'paths through time' are identical.
|
|
| GR's predictions for what clocks will show are tested in
| a number of experiments, and have in all cases proven to
| be correct within the precision of the measurements.
| H&K is the least precise of these experiments.
|
| You know this, Henri, and you have accepted the results
| of these experiments (except the H&K) before.
|
| The results have been officially withdrawn.
|
| You will of course keep insisting that the predictions
| of GR are stupid even if they invariably are "accidentally"
| correct. :-)
|
| There is absolutely no evidence that any of Einstein's version of
| relativity is
| correct.
| There is insurmounable evidence that it is nonsense from start to
| finish.
|
| If Henri accepts this, he wouldn't have anything to rave about.
|
| When the clocks are initially in the air, they are supposed to run at
| differet
| rates, according to you. If the Earth stops spinning, both clocks
| experience
| exactly the same acceleration for the same time. They have identical
| forces on
| them.
| From a purely physical point of view, there is no reason why this should
| cause
| one to change more than the other.
|
|
| HW.
| www.users.bigpond.com/hewn/index.htm
|
| Thank christ there is one genuine physicist on the NG.
|
| Henri, I'm not in the mood for this discussion anymore, take it to the nobel
| science committee, see what they think, maybe you are right then you can go
| buy a suit.
|
You lost, huh?

A hungry fox noticed a juicy bunch of grapes growing high on a grapevine. He leaped. He snapped. Drooling, he jumped to reach them, but try as he might, he could not obtain the tasty prize.

Disappointed by the fruitless efforts he'd made to get the grapes that day, he said, with a shrug, to comfort himself, "Oh, they were probably sour anyway!"