"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!"

Henri Wilson wrote:
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.

Keep kicking and screaming and denying facts, Henri.
That way, you will force Nature to work as you think it should.

Paul

"Sorcerer" wrote in message
. uk...

"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!"

[Norman Bates]
Actully, its Henri who doesn't participate in the conversation, he doesn't
respond to many of the things people say, its like talking to a brick wall.
Anyway, I'm not qualified to argue about relativity, I know enough to know
that I know very little.

"Norman Bates" wrote in message ...
|
| "Sorcerer" wrote in message
| . uk...
|
| "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!"
|
| [Norman Bates]
| Actully, its Henri who doesn't participate in the conversation, he doesn't
| respond to many of the things people say, its like talking to a brick wall.
| Anyway, I'm not qualified to argue about relativity, I know enough to know
| that I know very little.
|

Henri's just an old guy that wanted to be a physicist and have his own
crackpot theories recognised. Tell him he's a crazy old abo, England
will win the ashes and he'll lick your hand like a bloodhound with
fleas. Henri will thrive on disagreement. Anyone is qualified to argue
with Henri, you only get disqualified if you agree with him. After
a couple of months go by he'll say that it was he that had your idea.
You are not going to learn or teach anything anyway, they are all
brick walls excepts Humpty Roberts who keeps falling off it.

Humpty Roberts sat on a wall,
Humpty Roberts had a great fall...

| SR is strictly valid only in a flat Lorentzian manifold with the
| topology of R^4. This of course is a very poor model of the world we
| inhabit. But physics is not math, and we often use approximations. SR is
| approximately valid when the curvature of the manifold is negligible
| over the region of interest compared to one's measurement accuracy. That
| is, if gravity is negligible (or compensated for), SR can probably be
| used. - Humpty Roberts.

"This is PHYSICS, not math or logic, and "proof" is completely irrelevant." - Humpty Roberts

Humpty Roberts in Wonderland:-
| Tom Roberts

Newsgroups: sci.physics.relativity
From: Tom Roberts - Find messages by this
author
Date: Sat, 17 Sep 2005 17:57:18 GMT
Local: Sat, Sep 17 2005 6:57 pm
Subject: Does the 'Curvature of Spacetime' cause gravity?


"Yes, tests of strong fields are few and far between, but there are
some:
the binary pulsars, and observations of accretion disks near black
holes

`I don't know what you mean by "observations",' Alice said.

Humpty Roberts smiled contemptuously. `Of course you don't -- till I tell
you.
I meant "there's a nice knock-down argument for you!"' shrug

`But "observations" doesn't mean "a nice knock-down argument",' Alice
objected.

`When I use a word,' Humpty Roberts said, in rather a scornful tone,
shrug,
`it means just what I choose it to mean -- neither more nor less.' shrug

`The question is,' said Alice, `whether you can make words mean so many
different things.'

`The question is,' said Humpty Roberts, `which is to be master -- that's
all.' shrug

Alice was too much puzzled to say anything; so after a minute Humpty Roberts
began again. `They've a temper, some of them -- particularly verbs: they're
the proudest -- adjectives you can do anything with, but not verbs --
however,
I can manage the whole lot of them! Impenetrability! That's what I say!'
shrug

"And you never responded to how a 2-d surface in a flat 4-d spacetime can
have nonzero curvature, and why that shows that the curvature of such
2-d surfaces is useless in "describing" the geometry of the 4-d
manifold...." he
droned on.

"If you say that the curvature of 2-d surfaces is useless in
"describing" the geometry of the 4-d manifold....I am willing to agree
with you. But I just wanted you people to help me visualize the
intrinsic curvature of 3-d Schw. space. I was told that the Gaussian
curvature of certain 2-d surfaces will represent the intrinsic
curvature of 3-d Schw. space. When I wanted these 2-d surfaces to be
identified, Jan PB had given some interesting suggestions. But now you
say it is *useless*....." said Alice.

"_SOME_ 2-d surfaces can be useful in describing the geometry of 4-d
spacetime, in particular those spanned by a 2-d vector space of
geodesics. But you were discussing 2-d surfaces defined by coordinates,
and _those_ are useless because coordinates are completely arbitrary,
and introducing that arbitrariness destroys their usefulness" replied Humpty
Roberts.

"That means the notion of intrinsic curvature of space is either too
complex that it cannot be visualized or it is just invalid." exclaimed
Alice.

"No. But in many cases using a ball of dust particles is a better
visualization tool than 2-d surfaces.", said Humpty Roberts, teetering
on his wall.

"Mathematically it is good enough to state that in Riemannian geometry
the Riemann tensor is non-zero. Where is the necessity of associating
it with a cooked up fictitious term 'curvature of space'? " asked Alice,
thinking of the cooked up egg she had for breakfast.

"Mathematicians and physicists are human. We share the common desire to
communicate with each other easily, accurately, and concisely -- that's
why technical vocabularies were invented." said Humpty Roberts scornfully
and pretending he is human by saying "we".

Alice pondered this for moment, then asked "Was it required to fool and
mislead the 'layman'?"

"Your problem, not mine", said Humpty Roberts, then realizing his
Freudian slip, he was pretending to be human, added "(ours).
But this technical vocabulary is not secret or unfathomable, it just
takes _STUDY_. shrug"

Alice then went back to say "The term *curvature* basically applies to
the bending of curves and 2-d surfaces."

Ho ho, thought Humpty Roberts, "Not in differential geometry or GR.
The term "curvature" was borrowed by analogy with 2-d surfaces, and
has come to mean the Riemann curvature tensor. That is, a manifold of
_any_ dimension with nonzero Riemann tensor is said to be curved."
and he shrugged like this :- "shrug"

Alice asked "Why *said* to be curved when it is actually not curved?"

Humpty Roberts let out a great sigh.
" sigh", he said.
"The nuances of English. I was discussing the usage of words and
not the concepts they represent."
-- Tom Humpty Roberts
om
The end.
With thanks to Lewis Carroll.

The reader should take careful note here.
Humpty Roberts is not discussing the concepts words represent, he is
discussing the meaning of words. The rest of us use a dictionary.

On Sat, 02 Dec 2006 17:14:49 +0100, "Paul B. Andersen"
wrote:

Henri Wilson wrote:
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.

Keep kicking and screaming and denying facts, Henri.
That way, you will force Nature to work as you think it should.

There could be a very small 'free fall' effect..but it is really very very
small.

The H&K had a 50% chance of coming up with the required GR answer, just on
clock drift alone.
So you run the experiment twice...... and don't tell anyone about the other
one...



Paul


HW.
www.users.bigpond.com/hewn/index.htm

Thank christ there is one genuine physicist on the NG.

Henri Wilson wrote:
The H&K had a 50% chance of coming up with the required GR answer, just on
clock drift alone.
So you run the experiment twice...... and don't tell anyone about the other
one...

Definitely one of your better, Henri. :-)

Paul

On Mon, 04 Dec 2006 14:32:08 +0100, "Paul B. Andersen"
wrote:

Henri Wilson wrote:
The H&K had a 50% chance of coming up with the required GR answer, just on
clock drift alone.
So you run the experiment twice...... and don't tell anyone about the other
one...

Definitely one of your better, Henri. :-)
..
This kiind of thing happens all the time.
Never trust a deluded relativist....


Paul


HW.
www.users.bigpond.com/hewn/index.htm

Thank christ there is one genuine physicist on the NG.