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Apr 7, 1997, 3:00:00 AM4/7/97

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I've written a small text on a calculation

of the time dilatation for satellites.

Now, I'm not a GR expert, so I can be werong.

If it is wrong, point it out please !

Here we go...

Time dilatations and satellites.

-------------------------------

1) The Schwarzschild metric:

An acceptable solution of the Einstein equations for a

spherically symmetric, non-rotating object, outside

the object itself, is given by the Schwarzschild metric,

(in god's unit system)

ds^2 = - (1 - 2M/r) dt^2 + dr^2/(1 - 2M/r)

+ r^2(d theta ^2 + sin^2 theta dphi ^2)

Moreover, one can show that for r --> inf. this

thing becomes flat Minkowskian, so an interpretation

is that very far from the mass, t can be seen as

a time coordinate, and r,theta, phi as spherical coordinates.

In the low gravity limit, those spherical coordinates remain

a very good approximation.

Hence, one has the relationship, for observers who are

"stationary" wrt eachother (dr/dt = d theta/dt = dphi/dt = 0)

that the clockrate (that is the rate of proper time wrt

to a clock very far from the object which has proper time

t) equals:

(d tau)^2 = - (ds)^2 for stationary observers -->

d tau / dt = sqrt(1 - 2M/r)

In SI units, this becomes:

d tau / dt = sqrt ( 1 - 2MG/(c^2.r))

So the closer you come to the object, the slower the

clocks appear to tick wrt a clock very far away.

Hence high clocks tick faster than low clocks.

The clockrate of a *stationary* observer at the orbit height

of a satellite at distance r2 from the center of the object,

wrt to a clock on the surface (so, at distance r1 from the

surface), using the low-gravity approximation so that r represents

a real radial coordinate, is:

clockrate up there = sqrt ( ( 1 - 2MG/(c^2.r2) / ( 1 - 2MG/(c^2.r1) )

*still stationary*

where clockrate means: wrt a clock on the surface.

2) Orbit, classical calculation:

We assume a circular orbit.

In order for the satellite to keep this orbit, it has

to have such a velocity that the gravity pull is

balanced by the centripetal force:

v^2/R = G.M/R^2

Hence, v^2 = GM/r2 if we use r2 as the orbit radius.

3) Special relativity time dilatation.

Wrt our stationary observer, the clocks in a satellite moving

at a velocity v are slowed down by a factor gamma:

clockrate moving satellite / clockrate stationary observer,

such as seen by the stationary observer = sqrt(1 - v^2/c^2)

Now, this is sqrt( 1 - GM/(c^2.r2))

4) everything together:

CR = clockrate in *moving* satellite, such as seen by an observer

on the ground:

CR = sqrt( 1 - GM/(c^2.r2)) . [...]

[...] sqrt ( ( 1 - 2MG/(c^2.r2) / ( 1 - 2MG/(c^2.r1) )

Numerically, for the earth, 2MG/c^2 = 0.0044 m

Let us call nu = 2MG/(c^2.r1), which is a small, dimensionless

number: it is (r1 = 6366000 m): 6.9e-10.

Let us call rho = r2/r1, it is a dimensionless number,

a bit larger than 1.

CR = sqrt( (1-2*nu/rho) * (1-nu/rho) / (1 - 2*nu) )

A series devellopment (using MuPAD) wrt nu gives:

clockrate := sqrt( (1-2*nu/rho) * (1-nu/rho) /(1 - 2*nu) );

/ / nu \ / 2 nu \ \1/2

| | - --- + 1 | | - ---- + 1 | |

| \ rho / \ rho / |

| ---------------------------- |

\ - 2 nu + 1 /

___________________________________________________________________________

simplify(series(clockrate,nu,3));

/ 3 \ 2 / 3 1 \ 3

1 + nu | - ----- + 1 | + nu | - ----- - ------ + 3/2 | + O(nu )

\ 2 rho / | 2 rho 2 |

\ 8 rho /

___________________________________________________________________________

So, for the MIR, we have, to first order:

rho is about 1.1

clockrate on MIR = 1 + 6.9e-10 * (1 - 3/(2*1.1)) = 1 - 6.9e-10*0.364

= 1 - 2.5e-10

meaning that a clock on the MIR looses about 22 microseconds per

day.

For the GPS satellites, we have (they are at an altitude of

20.200 km above the earth, so rho is 1+20200/6366 = 4.17

clockrate on GPS = 1 + 6.9e-10 * (1 - 3/(2*4.17)) = 1 + 6.9e-10*0.64

= 1 + 4.42e-10

* note the different sign ! *

meaning that a clock on GPS *gains* 38 microseconds per day.

disclaimer:

I've done this from scratch, the only thing I looked up

was the Schwarzschild metric. So if I'm wrong, please

explain me !

--

Patrick Van Esch

mail: van...@dice2.desy.de

for PGP public key: finger van...@dice2.desy.de

Apr 7, 1997, 3:00:00 AM4/7/97

to

I can't believe it ! Keith, actually involved in some *physics* ???

Ok, I'll switch off my "bashing Keith" mode for a moment :-)

keith stein wrote:

>

> CLS

> PRINT " TIME-DILATIONS IN ORBIT"

> PRINT

> PRINT "This program gives the SR and GR predicted time-dilations for"

> PRINT "an Earth Satelite in a circular orbit, at any given altitude."

> PRINT

> REM VALUES OF THE PHYSICAL CONSTANTS USED

> c = 2.99792E+08

> G = 6.67259E-11

> m = 5.976E+24

> R = 6378000

> DO: REM prompt user for 'ALTITUDE OF SATALITE'

> PRINT

> PRINT "Enter M (or m) to simulate the 'MIR Space Station at 300 km'"

> PRINT

> PRINT "OR Enter G (or g) to simulate the 'GPS Satelites at 20,000 km'"

> PRINT

> INPUT "OR Enter the altitude of the satelite in 'km' "; h$: PRINT

> h = VAL(h$) * 1000

> IF h$ = "M" OR h$ = "m" THEN h = 300000!: PRINT "MIR SPACE STATION"

> IF h$ = "G" OR h$ = "g" THEN h = 2E+07: PRINT "GPS SATELITES"

>

> LOOP UNTIL h > 0

>

> velocity = SQR(G * m / (R + h))

> gamma# = (1 - velocity ^ 2 / c ^ 2) ^ -.5

> SRtd = (gamma# - 1) * 24 * 60 * 60

This is correct, I think.

> GRtd = G * m * (1 / (R + h) - 1 / R) / c ^ 2 * 24 * 60 * 60

This is not 100 % correct but I think it is a very good approximation,

actually, let's see if I can find your thing back as a series

devellopment...

my symbols:

mu = G.M/c^2, r1 = R, r2 = R + h, I find for the GR part:

dilatgr := sqrt((1-2*mu/r2)/(1-2*mu/r1));

/ 2 mu \1/2

| - ---- + 1 |

| r2 |

| ---------- |

| 2 mu |

| - ---- + 1 |

\ r1 /

___________________________________________________________________________

series(dilatgr,mu,2);

/ 1 1 \ 2

1 + mu | -- - -- | + O(mu )

\ r1 r2 /

___________________________________________________________________________

Which is your factor, except for the sign...

But that's ok, because you also changed the sign of the 1 - gamma.

> NETtd = INT((GRtd + SRtd) * 10 ^ 7) / 10

>

> PRINT "Altitude = "; h; "m"

> PRINT "Velocity = "; INT(velocity); " m / s "

> PRINT "gamma = "; gamma#

> PRINT "Time lost per day due to SR time dilation = "; SRtd; "sec"

> PRINT "Time lost per day due to GR time dilation = "; GRtd; "sec"

> PRINT

> PRINT "Net time lost per day in satelite = "; NETtd; "micro sec"

>

> PRINT

> PRINT

> PRINT

> PRINT "N.B. These are Einstein predictions, not mine! - K.Stein "

>

> Well done Patrick! You did the sums! ,even if you failed to get the

> answers quite right:-(

> I notice that our predictions are similar,but not identical. If on

> reflection you think that you are correct,and that i am therefore

> a little less than correct,i would be gratefull to see your suggested

> modification to my little BASIC program.

about getting the answer right for the MIR,

I took very roughly rho = 1.1 = (R + h) / R for I thought that MIR

was hovering at about 600 km. But you say it is at only 300 km.

Just modify the rho in my formula to the right value (for example,

if you say that MIR is at only 300 km, then my rho should be 1.05.

That brings my prediction to:

clockrate on MIR = 1 + 6.9e-10 * (1 - 3/(2*1.05)) = 1 - 6.9e-10 * 0.428

= 1 - 2.96e-10

and this comes to about 25.5 microseconds per day...

Close enough ?

CONGRATULATIONS KEITH !! ONE DAY YOU WILL BE A TRUE RELATIVIST

:-))))))

cheers,

Patrick.

> Thank you Patrick.

> --

> keith stein

Apr 7, 1997, 3:00:00 AM4/7/97

to

GRtd = G * m * (1 / (R + h) - 1 / R) / c ^ 2 * 24 * 60 * 60

NETtd = INT((GRtd + SRtd) * 10 ^ 7) / 10

PRINT "Altitude = "; h; "m"

PRINT "Velocity = "; INT(velocity); " m / s "

PRINT "gamma = "; gamma#

PRINT "Time lost per day due to SR time dilation = "; SRtd; "sec"

PRINT "Time lost per day due to GR time dilation = "; GRtd; "sec"

PRINT

PRINT "Net time lost per day in satelite = "; NETtd; "micro sec"

PRINT

PRINT

PRINT

PRINT "N.B. These are Einstein predictions, not mine! - K.Stein "

Well done Patrick! You did the sums! ,even if you failed to get the

answers quite right:-(

I notice that our predictions are similar,but not identical. If on

reflection you think that you are correct,and that i am therefore

a little less than correct,i would be gratefull to see your suggested

modification to my little BASIC program.

Apr 8, 1997, 3:00:00 AM4/8/97

to

van...@jamaica.desy.de (Patrick van Esch) wrote:

>I've written a small text on a calculation of the time dilatation

>If it is wrong, point it out please !

I think your derivation is valid (although I believe the MIR's orbit

is actually about 360 miles up), but I'm always a little uneasy about

splitting up a problem into separate SR and GR components. I suppose

your reason for doing that was to highlight the effects that would be

induced with just the relative velocities in the absence of a

gravitational field. However, as your results show, the velocity

effect is about the same size as the gravitational effect - with the

net result actually changing sign in the range of interest - so I

think it's fair to say that measuring proper time lapses in orbit is

not really a very robust way of testing SR (as opposed to GR)

specifically, for the simple reason that the results won't come

anywhere close to what SR predicts unless we agree to apply the GR

corrections, but if we agree that GR is correct then the status of

SR is moot (because GR totally subsumes SR).

All of which you already know. Anyway, just for fun here's a pure

GR derivation of orbital proper time. It's actually simpler (in my

opinion) than trying to split up the problem into gravitational

and non-gravitational effects. As you said, in the vicinity of an

isolated non-rotating spherical body whose Scwartzchild radius is

2M the metric has the form

ds^2 = A dt^2 - B dr^2 - C d theta^2 - D d phi^2

where A = (1 - 2M/r), B = 1/A, C = r^2, D = r^2 sin^2(theta),

phi = latitude and theta = longitude (e.g., theta=0 at the North

Pole and theta=PI/2 at the equator). Let's say our radial position

r and our latitude phi are constant for each path in question

(treating r as the "radius" in the weak field approximation).

Then A and D are both constants, and the metric reduces to

ds^2 = A dt^2 - D d phi^2

If I'm sitting on the Earth's surface at the North Pole, I have

D=0, so it follows that ds = sqr(1-2M/r) dt where r is the

radius of the Earth.

On the other hand, if I'm in an equatorial orbit with radius R then we

have theta=PI/2, sin^2(theta)=1, and so D is simply R^2. Now, recall

Kepler's law w^2 R^3 = M, which also happens to hold exactly in GR

(where w, M, and R have their GR meanings). Since w = d phi/dt we

have D = R^2 = M/(w^2 R) = (dt/d phi)^2 (M/R). Thus the path of the

orbiting particle satisfies

ds^2 = (1 - 2M/R) dt^2 - (M/R) dt^2

= (1 - 3M/R) dt^2

Now for each test particle, one sitting at the North Pole and one

in a circular orbit of radius R, the path parameter s is the local

proper time, so the ratio of the orbital proper time to the North

Pole's proper time is

_______________

d s_orbit / 1 - 3M/R

------------- = / --------------

d s_earth \/ 1 - 2M/r

To isolate the *difference* in the two proper times, we can

expand the above function into a power series in M/r to give

d s_orbit

----------- = 1 + (1 - 3r/(2R)) (M/r) + ...

d s_earth

The mass of the earth, represented in geometrical units by half the

Scwartzchild radius, is about 0.00443 meters, and the radius of the

earth is about 6.38(10)^6 meters, so this gives

ds_orbit = ds_earth + (6.9E-10) (1 - 3k/2) ds_earth

which shows that the discrepancy in the orbit's lapse of proper time

during a given lapse delta_T of proper time measured on Earth is

/ 3r \

(delta_T) (6.9E-10) ( 1 - ---- )

\ 2R /

Consequently, for an orbit at the radius R=3r/2 (about 2000 miles

up) there is no difference in the lapses of proper time. Thus, if

someone wants to get a null result, that would be their best choice.

(Perhaps this should be named the "sci.physics radius".) As you

noted, for orbits lower than 3r/2 the satellite will show slightly

less lapse of proper time (i.e., the above discrepancy will be

negative), whereas for higher orbits it will show slightly more

elapsed time than the corresponding interval at the North Pole.

For example, in a low Earth orbit of, say, 360 miles, we have

r/R = 0.917, so the proper time runs about 22.5 microseconds per

day slower than a clock at the North Pole. On the other hand, for

a 22,000 mile orbit we have r/R = 0.18, and so the orbit's lapse of

proper time actually EXCEEDS the corresponding lapse of proper time

at the North Pole by about 43.7 microseconds per day. Of course,

as R continues to increase the orbital velocity drops to zero and

we are left with just coordinate time for the orbit, relative to

which the North Pole on Earth is "running slow" by about 60 micro-

seconds per day, due entirely to the gravitational potential of the

earth. (This means that during a typical human lifespan the Earth's

gravity stretches out our lives to cover an extra 1.57 seconds of

coordinate time!)

___________________________________________________________

| /*\ |

| MathPages / \ http://www.seanet.com/~ksbrown/ |

|___________________________________________________________|

Apr 8, 1997, 3:00:00 AM4/8/97

to

In article <33497E...@ping.be>

Patrick...@antispam.ping.be "Patrick Van Esch" writes:

> Just modify the rho in my formula to the right value (for example,

> if you say that MIR is at only 300 km, then my rho should be 1.05.

>

> That brings my prediction to:

>

> clockrate on MIR = 1 + 6.9e-10 * (1 - 3/(2*1.05)) = 1 - 6.9e-10 * 0.428

> = 1 - 2.96e-10

>

> and this comes to about 25.5 microseconds per day...

> CONGRATULATIONS KEITH !! ONE DAY YOU WILL BE A TRUE RELATIVIST

WELL I WILL IF THEY FIND ANYTHING OVER 2O MICROSECONDS/DAY ON THE MIR PATRICK!!

but that's an awfull lot of time dilation to find, Patrick.

YOU JUST COULDN'T MISS THE 'SR TIME DILATIONS' ON THE MIR,

COULD YOU PATRICK ?

--

keith stein

Apr 8, 1997, 3:00:00 AM4/8/97

to

keith stein <ke...@sthbrum.demon.co.uk> wrote in article

<860498...@sthbrum.demon.co.uk>...

Just to put this problem in perspective,

there are 8.64 X 10^10 microseconds in a day.

I think that there are reasonable size

quartz or atomic clocks which have a stability

of about 1 part in 10^14 per day.

This should be an easy experiment to make.

Tom Potter http://pobox.com/~tdp

Apr 8, 1997, 3:00:00 AM4/8/97

to

In article <01bc4377$4a05e200$1b822399@default>,

Tom Potter <t...@earthlink.net> wrote:

>keith stein <ke...@sthbrum.demon.co.uk> wrote in article

><860498...@sthbrum.demon.co.uk>...

>> YOU JUST COULDN'T MISS THE 'SR TIME DILATIONS' ON THE MIR,

>> COULD YOU PATRICK ?

>Just to put this problem in perspective,

>there are 8.64 X 10^10 microseconds in a day.

>

>I think that there are reasonable size

>quartz or atomic clocks which have a stability

>of about 1 part in 10^14 per day.

>

>This should be an easy experiment to make.

>> COULD YOU PATRICK ?

>Just to put this problem in perspective,

>there are 8.64 X 10^10 microseconds in a day.

>

>I think that there are reasonable size

>quartz or atomic clocks which have a stability

>of about 1 part in 10^14 per day.

>

>This should be an easy experiment to make.

Easy, in principle; extremely difficult in practice -- probably impossible.

To get an experiment lifted up to MIR, you would need to convince

NASA or the Russian Space Agency that:

1. Your experiment is scientifically sound.

2. Your experiment is "worth" the resources required -

weight, astronaut time, spacecraft volume, $/Rubles, etc.

3. Your experiment is "more valuable" than other competing

experiments.

4. You (and your collaborators) are qualified and experienced

enough to make the experiment a success.

5. You have or can get the necessary funding.

6. There are probably more items on this list....

I seriously doubt such an experiment would be able to satisfy even

one of these requirements.

The first requirement above could probably be met if you

collaborate with several physicists who are experienced in

space experiments and with several physicists who are experts in

SR and GR. But that is probably an impossible selling job --

why should they work with you?

And also, as others have noted in this newsgroup, there are General

Relativistic effects which are comparable in magnitude to the

effects of Special Relativity. It is NOT clear to me that such an

experiment could ever be considered a definitive test of SR.

The problem with so many of the people who post to this newsgroup

is that they assume the world is a "simple" place which conforms to

their wishes. It simply ain't so.

Tom Roberts tjro...@lucent.com

Apr 8, 1997, 3:00:00 AM4/8/97

to

Tom Potter (t...@earthlink.net) wrote:

: I think that there are reasonable size

: quartz or atomic clocks which have a stability

: of about 1 part in 10^14 per day.

: This should be an easy experiment to make.

The point is, there are already 24 such clocks up there.

It is called the GPS system. So it is "feasible".

That doesn't mean it is cheap. While I think that

the accuracy of the best clocks is of the order

of what you quote, that doesn't mean that they're

of the size of a wrist watch.

What I don't know if these clocks can keep their

calibration during the violent motions at takeoff

and landing. I think the clocks keep their integrity,

but I don't know if they don't get offset by all those

vibrations and accelerations. It is not easy

to do an experiment with a precision of 14 digits

while getting a kick in the butt.

After all, the GPS clocks were only switched

on AFTER they were in orbit.

Moreover, I think that the best place to do such

an experiment is NOT the MIR, but is good old

space shuttle. The orbit is similar, the time

is ok (a few days) and the take off and landings

aren't too violent.

Now I would also like to see the experiment done

if it isn't too difficult. But putting something

on the shuttle isn't really that cheap.

Nevertheless, it would be fun if it were done.

Not because I have the slightest doubt about the

outcome, but it would have other advantages:

1) We would have a clearcut experiment to show to

the ARNs. Well, that won't cut it.

2) MUCH MORE IMPORTANT: it could be a great

public relations stunt. After all, I'm quite

convinced that 99% of the population hasn't got

the slightest idea of what time dilatation is.

So if it could break the news that Einstein's

theory has been confirmed (once more) by the

advances in technology and space crafts and so

on blah blah blah, the great nation etc...,

has shown the STARTLING RESULT THAT TIME IS NOT

ABSOLUTE, which should shock the average citizen.

KEITH's principle shown false ! Big astonishment !

It is just weird enough to tickle fantasies in

the public, and not too complicated so that nobody

actually understands what it is all about.

If well organised, sales of "dilatation T-shirts"

with sqrt(1-v^2/c^2) written on it, TV - shows

in which old professors come and explain the

twin paradox to people, in between dazzling spectacles

etc...

We could also add a lot of bullshit like infinity

lifetime when reaching c, and asking people to fund

research to reach c.

And by the end of the day, requests to Congress to

fund more fundamental research etc...

Yes... if well handled, the money spend on a clock

on the shuttle could very well be a good investment.

cheers,

Patrick.

Apr 8, 1997, 3:00:00 AM4/8/97

to

In sci.physics.relativity keith stein <ke...@sthbrum.demon.co.uk> wrote:

[snip]

> velocity = SQR(G * m / (R + h))

> gamma# = (1 - velocity ^ 2 / c ^ 2) ^ -.5

> SRtd = (gamma# - 1) * 24 * 60 * 60

This computation is not well coded; it will suffer significant loss of

accuracy due to cancellation errors : if the double precision number

can represent about 13 significant figures, errors in gamma will be

a few times 10^-13; and as gamma-1 is not much larger than that, the

numeric noise will be appreciable in the result. In this sort of

circumstance it's better to expand

(1 + x)^p -1 as

px + p(p-1)x^2/2! + p(p-1)(p-2)^p^3/3! ....

and compute as many terms as make a difference.

> GRtd = G * m * (1 / (R + h) - 1 / R) / c ^ 2 * 24 * 60 * 60

similarly were h/R smaller here it would be worth doing the trick for

(Gm/R)( (1+h/R)^-1 - 1).

> i would be gratefull to see your suggested

> modification to my little BASIC program.

See comments about the sources of numerical error above.

--

Personal mail to steve#windsong.demon.co.uk (encrypted mail preferred)

PGP public key at http://www.windsong.demon.co.uk/ or on keyservers

pegwit v8 public key =74e039aa21adac343be35a|My opinions, not those of GDS

f006fb0ade30df0401d6306f690c9beec49fb1ef11 |Corporation or its affiliates.

Apr 9, 1997, 3:00:00 AM4/9/97

to

In article <5ie5j8$gj5$1...@enterprise.desy.de>

van...@jamaica.desy.de (Patrick van Esch) writes:

> 2) MUCH MORE IMPORTANT: it could be a great

> public relations stunt.

3) Much much more important: with the results Keith might admit he was

wrong and SR and GR are right?

Apr 10, 1997, 3:00:00 AM4/10/97

to

ale2 wrote:

>

> 3) Much much more important: with the results Keith might admit he was

> wrong and SR and GR are right?

Of course not. He will insist that the clock had to be

painted in pink. Blue clocks don't count.

cheers,

Patrick.

Apr 10, 1997, 3:00:00 AM4/10/97

to

In article <334CB0...@ping.be>

Patrick...@antispam.ping.be "Patrick Van Esch" writes:

HOW MANY TIMES HAVE I GOT TO SAY THIS PATRICK!

"If clocks on the Mir lose anything over 20 microseconds/day then

I'M A RELATIVIST."

--

keith stein

Apr 10, 1997, 3:00:00 AM4/10/97

to

keith stein (ke...@sthbrum.demon.co.uk) wrote:

: HOW MANY TIMES HAVE I GOT TO SAY THIS PATRICK!

: "If clocks on the Mir lose anything over 20 microseconds/day then

: I'M A RELATIVIST."

I DON'T BELIEVE YOU !

Apr 12, 1997, 3:00:00 AM4/12/97

to

Patrick van Esch <van...@jamaica.desy.de> wrote:

: keith stein (ke...@sthbrum.demon.co.uk) wrote:

: : HOW MANY TIMES HAVE I GOT TO SAY THIS PATRICK!

: : "If clocks on the Mir lose anything over 20 microseconds/day then

: : I'M A RELATIVIST."

: I DON'T BELIEVE YOU !

: cheers,

: Patrick.

(No comments regarding whether your belief is correct, but ...)

Well said, Patrick.

--

John August

Fate may be arbitrary; but it is not biased.

Apr 12, 1997, 3:00:00 AM4/12/97

to

: Now I would also like to see the experiment done

: if it isn't too difficult. But putting something

: on the shuttle isn't really that cheap.

: Nevertheless, it would be fun if it were done.

: Not because I have the slightest doubt about the

: outcome, but it would have other advantages:

: 1) We would have a clearcut experiment to show to

: the ARNs. Well, that won't cut it.

: public relations stunt. After all, I'm quite

: convinced that 99% of the population hasn't got

: the slightest idea of what time dilatation is.

: So if it could break the news that Einstein's

: theory has been confirmed (once more) by the

: advances in technology and space crafts and so

: on blah blah blah, the great nation etc...,

: has shown the STARTLING RESULT THAT TIME IS NOT

: ABSOLUTE, which should shock the average citizen.

: KEITH's principle shown false !

Maybe I'm a little off base here, but I think that the

experiments in question have been pretty much done long ago. Didn't the

early "Timation" satellites settle most of the fundamental question about

velocity and time wrt Einstein and the rest? I was under the impression

that by the mid 70s gathered data was so close to prediction that managers

figured there was no more point in continuing tests--at least until a

whole new generation of timekeeping technology had come around.

I was under the impression that the Time Gods (NRL and NRO gurus)

had pretty much given up on trying to disprove basic relativity and were

into better engineering rather than "pure science"---once again because

everything was checking out. I could hardly believe that anything

approaching 20 microseconds a day could be "lost" ( or not lost as

expected) without a great deal of whooping and hollering---in large part

by designers who would *love* to have an excuse to abandon the

complications of designing in relativistic corrections.

Could you give a little more precise description of the kind of

experiment you would like? If you mean running two clocks, one on the

ground and one in orbit, and comparing them---that should be old hat. How

many decimal places do you want, and with what parameters?

: Big astonishment !

: It is just weird enough to tickle fantasies in

: the public, and not too complicated so that nobody

: actually understands what it is all about.

: If well organised, sales of "dilatation T-shirts"

: with sqrt(1-v^2/c^2) written on it, TV - shows

: in which old professors come and explain the

: twin paradox to people, in between dazzling spectacles

: etc...

: We could also add a lot of bullshit like infinity

: lifetime when reaching c, and asking people to fund

: research to reach c.

: And by the end of the day, requests to Congress to

: fund more fundamental research etc...

: Yes... if well handled, the money spend on a clock

: on the shuttle could very well be a good investment.

Hmmmm. You are starting to sound an awful lot like Leon Lederman :-).

regards,

-------------------------------------------------------------------

Steven j Forsberg at au...@imap2.asu.edu wizard 87-01

Apr 12, 1997, 3:00:00 AM4/12/97

to

au...@imap2.asu.edu wrote:

> Maybe I'm a little off base here, but I think that the

> experiments in question have been pretty much done long ago.

You are absolutely correct. However, these news groups have several

people who make a job out of denying all this stuff.

Dan Evens

Apr 12, 1997, 3:00:00 AM4/12/97

to

> : Now I would also like to see the experiment done

> : if it isn't too difficult. But putting something

> : on the shuttle isn't really that cheap.

> : Nevertheless, it would be fun if it were done.

> : Not because I have the slightest doubt about the

> : outcome, but it would have other advantages:

> : 1) We would have a clearcut experiment to show to

> : the ARNs. Well, that won't cut it.

> : 2) MUCH MORE IMPORTANT: it could be a great

> : public relations stunt. After all, I'm quite

> : convinced that 99% of the population hasn't got

> : the slightest idea of what time dilatation is.

> : So if it could break the news that Einstein's

> : theory has been confirmed (once more) by the

> : advances in technology and space crafts and so

> : on blah blah blah, the great nation etc...,

> : has shown the STARTLING RESULT THAT TIME IS NOT

> : ABSOLUTE, which should shock the average citizen.

> : KEITH's principle shown false !

>

> Maybe I'm a little off base here, but I think that the

> experiments in question have been pretty much done long ago.

No way. If they had anything like the predicted 24,000 ns/day on Mir,

they wouldn't be offering these very dubious experiments on planes

were the total time dilations were never more than a few hundred ns,

if anything.

The GPS satelites do have an even larger (claimed) dilation

than the Mir, but that one is opposite in direction to the 'SR' time

dilations. Also in the case of the GPS we are relying on the accuracy

of a time keeping signal transmitted over 20,000 km which is a very

long way. In the case of the Mir it would be possible to compare the

clocks while they were adjacent on the Mir, eliminating any possible

error to signal transmission.

the Mir experiment would be a much more accurate and direct test of

relativity than anything previously published.

Didn't the

> early "Timation" satellites settle most of the fundamental question about

> velocity and time wrt Einstein and the rest? I was under the impression

> that by the mid 70s gathered data was so close to prediction that managers

> figured there was no more point in continuing tests

They have nothing comparable with the decisiveness of the MIR TEST,for sure.

--at least until a

> whole new generation of timekeeping technology had come around.

> I was under the impression that the Time Gods (NRL and NRO gurus)

> had pretty much given up on trying to disprove basic relativity

That's the problem. Where they ever trying to 'disprove' basic relativity ?

I rather think that they were trying to 'prove' it, but they never did eh!

and were

> into better engineering rather than "pure science"---once again because

> everything was checking out.

Right 'better engineering' puts in things like automatic recalibration

of GPS system, so that the system will work whatever the clocks do. I

can't beleive any engineer would really rely on a clock not to lose

the odd nonosecond in ten years, but some scientists seem to think that's

how it works eh!

> I could hardly believe that anything

> approaching 20 microseconds a day could be "lost" ( or not lost as

> expected) without a great deal of whooping and hollering---in large part

> by designers who would *love* to have an excuse to abandon the

> complications of designing in relativistic corrections.

Exactly if it was there, someone would have been hollering about it

before now eh!

> Could you give a little more precise description of the kind of

> experiment you would like?

Sure. 1.Syncronise two clocks

2.Take one to the Mir.

3.Some days later take, on the next lauch,take up the other.

4.Compare the clocks in space.

If the clocks are still syncronised then SR IS WRONG!

If you mean running two clocks, one on the

> ground and one in orbit, and comparing them---that should be old hat. How

> many decimal places do you want, and with what parameters?

I really don't care how many decimal places,i just want to be convinced

that SR clock slowing, like claimed for those twins happens 'at all'.

So far all test haven't even added up to 1 microsecond, and you expect

people to beleive in tales of travelling twins saving years.It's not true,

i think

--

keith stein

Apr 13, 1997, 3:00:00 AM4/13/97

to

ksb...@seanet.com (Kevin Brown) wrote:

>Now for each test particle, one sitting at the North Pole and one

>in a circular orbit of radius R, the path parameter s is the local

>proper time, so the ratio of the orbital proper time to the North

>Pole's proper time is

> _______________

> d s_orbit / 1 - 3M/R

> ------------- = / --------------

> d s_earth \/ 1 - 2M/r

By the way, it's interesting to note that this ratio goes to zero

when the orbit radius R equals 3M. That's because 3M is the radius

of the orbit of light. This suggests that even if something prevented

a massive object from collapsing within its Schwarzschild radius 2M,

it would still be a very remarkable object if it was just within

3M, because then it could (theoretically) support circular light

orbits, although I don't know how stable such orbits would be (even

neglecting interference from infalling matter). If neutrinos are

massless I suppose there could also be neutrinos in 3M orbit around

such an object.

Recognizing that there are probably all kinds of reasons why this

couldn't actually occur, I wonder if theoretically there would be

any reason to expect orbiting photons and/or neutrinos to be

concentrated in one plane, or if the orbits would be distributed

evenly about all axes. In other words, could there be a stable

solution consisting of a solid mass inside 3M surrounded by a

spherical "shell" of orbiting photons at 3M? Presumably this

could only work as long as the energy content of the shell was

small enough that it didn't significantly affect the field.

Also, how would a photon get INTO a circular orbit at 3M? Maybe

if it was emitted by a decay of some infalling particle right

at 3M and in precisely the right direction, but that seems

highly improbable. Is there be any mechanism by which a free

photon could be "captured" into a circular orbit?

Apr 13, 1997, 3:00:00 AM4/13/97

to

au...@imap2.asu.edu writes:

}

} Maybe I'm a little off base here, but I think that the

} experiments in question have been pretty much done long ago.

Exactly. But Keith thinks that only *his* experiment will test

the theory, ignoring the fact that it relies on exactly the

same principles as the GPS satellites.

ke...@sthbrum.demon.co.uk writes:

>

>No way. If they had anything like the predicted 24,000 ns/day on Mir,

>they wouldn't be offering these very dubious experiments on planes

>were the total time dilations were never more than a few hundred ns,

>if anything.

When was the first time the US flew on Mir?

When were the airplane experiments done? What is the relative cost?

What other experiments have been done with satellites?

This will suggest why experiments were done with an economical

and accessible mode of transportation, and why it is not realistic

to expect people to pay for two shuttle launches to test Keith's

theory that everything about GPS is wrong.

>The GPS satelites do have an even larger (claimed) dilation

>than the Mir, but that one is opposite in direction to the 'SR' time

>dilations.

Keith is able to reject that GPS navigation works, but is sometimes

willing to accept evidence that time intervals are affected by gravity

and uses this to argue that time intervals are absolute.

--

James A. Carr <j...@scri.fsu.edu> | "Whatever."

http://www.scri.fsu.edu/~jac/ |

Supercomputer Computations Res. Inst. | George Herbert Walker Bush

Florida State, Tallahassee FL 32306 |

Apr 14, 1997, 3:00:00 AM4/14/97

to

>In article <5inrvo$3...@news.asu.edu> au...@imap2.asu.edu writes:

> The GPS satelites do have an even larger (claimed) dilation

>than the Mir, but that one is opposite in direction to the 'SR' time

>dilations. Also in the case of the GPS we are relying on the accuracy

>of a time keeping signal transmitted over 20,000 km which is a very

>long way. In the case of the Mir it would be possible to compare the

In the case of GPS satellites, it looks like you are confusing TD ("in

the opposite direction") with the artificially induced error in the

civilian band of the GPS signal. The GPS system broadcasts at two

frequencies:1.023 MHz (civilian) and 10.23 MHz (military). The

civilian frequency has random errors purposely inserted into the data

stream to REDUCE accuracy in order to maintain military security. The

random errors produce an uncertainty of approximately 25 meters,

however, recent techniques using differential measurement have yielded

accuracies up to 1 cm (as of 1995). The military frequency uses an

encrypted code to prevent foreign militaries from achieving high

accuracy from our GPS.

In addition to the above induced delay, sensitive measurements need to

be calibrated to account for delays due to changing ionosphere

conditions. This is done by a comparison of both the civilian and

military signals (since they are at different frequencies).

Incidentally, after achieving centimeter accuracy in 1995, the next

step was to get it down to one millimeter ... haven't heard any word

on that though.

_______________________________________________________________

Todd Spohnholtz roo...@wwa.com

Mechanical Engineering

University of Illinois at Chicago

_______________________________________________________________

Apr 14, 1997, 3:00:00 AM4/14/97

to

foramp.net>:

Distribution:

: > Maybe I'm a little off base here, but I think that the

: > experiments in question have been pretty much done long ago.

: You are absolutely correct. However, these news groups have several

: people who make a job out of denying all this stuff.

Ahhhhhh. Of course, it's Usenet! And to think, I was going to

look up the guy that used to subject me to long lectures on the travails

of relativistic corrections when trying to statistically correlate

spaceborne clocks.

"How's it going Fred?"

"I'm glad you asked. If a geosynch Hydrogen Maser fails to 3

sigma with an overpolar LEO c-beam......"

"Uh, Yeah, nice talkin' to you Fred. Gotta go!"

regards,

----------------------------------------------------------------------

Steven j Forsberg at au...@imap2.asu.edu Wizard 87-01

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