Re: Hafele & Keating, Einstein, Dingle,Cocke, and Scott Murray

From: Harry (harald.vanlintel_at_epfl.ch)
Date: 06/17/04 

Date: Thu, 17 Jun 2004 16:38:20 +0200

John, see below. I may be able to clarify some points a little, although I'm
still inexperienced in GRT matters.
Please correct me if I made a mistake.

"John Kennaugh" <JKNG@kennaugh2435hex.freeserve.co.uk> wrote in message
news:NUrXQ9Ni+G0AFw7E@kennaugh2435hex.freeserve.co.uk...
>
> You may not have heard of Dr Scott Murray but he was a physicist with
> the British Scientific Civil Service who had a distinguished career in
> radio astronomy and satellite communications. This is mainly about an
> article he wrote in 1986 "If you want to know the time...." Electronics
> and Wireless World December 1986 P28 to 31 in which he looked at The
> Hafele & Keating experiment and other related matters. As far as I can
> see with my limited knowledge what he says is correct. You may judge
> otherwise, but right or wrong I am certain he was thorough in his
> researches. He ends his article:
>
> "To sum up: In 1905 Albert Einstein predicted, as a consequence of
> relativity theory, free of paradox, that an ideal clock (at sea level on
> the equator would run more slowly than an identical clock (also at sea
> level) at the earth's pole. An experiment performed in 1971, purported
> to confirm the influence of both special and general relativistic
> effects on the timekeeping of quasi-ideal clocks. The theory which was
> said to underlie that experiment was also seen to support Einstein's
> original prediction.

Most people know that Einstein's 1905 prediction was too daring as it did
not take gravitation into account (rather obvious)!
Therefore he did not specify any level, as you also show yourself below.

> However, it is observed that the differential slowing of clocks
> due to latitude alone (independent of geographic motion and altitude),
> which was predicted by Einstein, does not in fact take place. It seems
> that the explanation put forward - and apparently generally accepted -
> to account for this theoretical failure was physically unsound".

That is as clear as mud.

> As far as I can see the explanation which Murray shows to be flawed
> seems to be still generally accepted which is why I bring the article to
> your attention.
> ---------------------------------------
>
> Einstein said "Thence we conclude that a balance-clock at the equator
> must go more slowly by a very small amount than a precisely similar
> clock situated at one of the poles under otherwise identical
> conditions." - Einstein, A. On the Electrodynamics of Moving Bodies;
> trans. in The Principle of Relativity. Methuen, 1923 and Dover, 1952.
> pp.49-50.
>
>
> Herbert Dingle - who I expect everyone other than Bjoern has heard of,
> posed the question, - if speed is relative then why could not the clock
> on the equator be considered stationary and the one at the pole be
> considered as moving?
> Dingle, H. Science at the Crossroads, Martin Brian and 0'Keeffe, 1972.
> p.40ff.

Many others posed that question before him - he was a bit slow, maybe even
slower than me!

> Ian McCausland later published a brief summery of the varied
> contemporary answers to Dingle's question of 1972 which makes it clear
> that *at that time* there was no consensus answer from the physics
> community. [Wireless World October 1983 P63-65]

Nothing changed - see the FAQ.

> Hafele & Keating were faced with a similar type of question and it was
> necessary for them to choose an answer. Their report states "...the
> relative timekeeping behaviour of terrestrial clocks can be evaluated by
> reference to hypothetical co-ordinate clocks of an underlying
> nonrotating (inertial) space." Hafele & Keating, Op.cit. (4): p.166
> col.2 & p.167n(6).

The ECI coordinate system.

> They add the following footnote
>
> "It is important to emphasise that special relativity purports to
> describe certain physical phenomena only relative to (or from the point
> of view of) inertial reference systems, and the speed of a clock
> relative to one of these systems determines its timekeeping behaviour"
> Builder, G. 'Ether and relativity', Aust..l. Plys. vol. 11, 1958 p.279.
>
> Murray's comments - "Paraphrased, it says that an observer must be 'at
> rest relative to an inertial frame of reference' if the explanations of
> the physical observations are to be meaningful"
>
> This interpretation answers Dingle's question by saying that the pole is
> (or is a reasonable approximation to) an inertial frame and the equator
> isn't. H&Ks assumption is therefore consistent with Einstein's
> prediction and I understand (ref Bilge) that it is the way SR is
> generally interpreted these days.

I think so too.

> It would seem therefore that the H&K experiment not only showed that the
> predictions of SR were correct and that GR is also correct (it used GR
> to correct the data), it also showed by its success that the above
> interpretation of how SR should be applied is the correct one, thus
> potentially ending the confusion documented by McCausland.
>
> According to Murray H&K used the equation (I've written dt for delta t)
>
> dt/t = gh/c^2 - (v^2/c^2)/2 -----------------. (1)
>
> The term (v^2/c^2)/2 is Einstein's 1905 prediction due to motion at
> velocity v (by special relativity theory), where
>
> v = Omega r cos (latitude) + u --------------------- (2)
>
> Omega is the earths angular velocity, r is earths radius, and u is the
> ground speed.
>
> The term gh/c^2 is a GR correction to compensate for gravitational
> potential where h is the height of the plane above mean sea level.
> Not having read the H&K report I assume each flight was broken down into
> segments and dt/t calculated for each and this compared with the
> physical result giving good agreement. Murray assumes this was done with
> the utmost of care but does note that acceleration isn't actually
> mentioned.

Acceleration of a clock is not supposed to affect the rate of that clock.

> However Murray points out that if two planes were left on the ground at
> mean sea level at different latitudes i.e. put u = 0 and h = 0 into the
> H&K equation then you get
>
> dt/t = 1/2 (Ohmega r Cos(lattitude))^2/c^2.
>
> An experiment based on this would have the advantage that no correction
> to the data would be needed, and it could be done over a long period to
> provide any degree of accuracy required.
>
> At this point I go back to "Thence we conclude that a balance-clock at
> the equator must go more slowly ... than a precisely similar clock
> situated at one of the poles under otherwise identical conditions."
>
> Murray points out that while it is exceedingly difficult to synchronise
> clocks it is not difficult to compare their rates. A comparison via a
> two way radio link is self compensating if the comparison is mutual so
> any two observatories in line of sight with a geo-stationary satellite
> will do. While it would be nice to test Einstein's actual prediction no
> geostationary satellites are visible above the horizon at the poles but
> the same maths can be used to predict the difference expected with two
> alternative latitudes.
>
> The Observatory at Reykjavik 64deg N and one at Recife Brazil at 7deg S
> should give a difference of 82.5ns per day. (one complete cycle of a
> 12MHz oscillator). They don't and this was know to be the case prior to
> the H&KX. H&K in fact refer to it in a footnote in their report and
> explain this apparently serious failure of relativity by a reference to
> Cocke.
>
> Cocke said:
>
> "Clocks at rest on the earth's surface (at average sea level) keep the
> same relativistic time independently of latitude differences. The effect
> of the difference in surface speed at different latitudes is cancelled
> to lowest order by a corresponding effect from the difference in surface
> potential owing to the oblate figure of the earth."
> Cocke. W.J. Relativistic corrections for terrestrial clock
> synchronisation; Phas.Rw.Lett. vol.l6, 1966 p.662.

Yes, Ron Hatch (GPS specialist) claims the same:

"One of the characteristics of clock behavior clearly evident in GPS is that
all clocks in the earth-centered inertial (ECI) frame which are at sea level
run at the same rate. A clock at sea level on the equator should run slow
according to the Special Relativity Theory (SRT) due to its speed in the ECI
frame. However, a clock at sea level on the equator should run faster
according to the General Relativity Theory (GRT) due to the spin-induced
equatorial bulge which causes the clock to be higher in the earth's
gravitational potential. These two effects, explained by disjoint theories,
are of exactly equal magnitude but opposite sign and precisely cancel each
other.
A somewhat similar effect is observed regarding the clocks on board the GPS
satellites. When the satellite is near perigee, it has a faster speed; and
the SRT indicates that the clocks should run slower than nominal. But near
perigee the satellites have a lower potential in the earth's gravitational
field which, according to GRT, should also result in a slower clock rate.
Again, surprisingly, these effects explained by different theories have
precisely the same magnitude-but in this case the sign is the same and the
two effects add together."

- http://www.egtphysics.net/Mechanism/ClockRel.htm (in the conservative
introduction for his own theory)

> This it appears is the standard text book explanation of the failure of
> Einstein's prediction. Murray followed up the reference to see how
> Cocke came to his conclusion. The equation he uses is:
>
> dt/t = gH/c^2 - (v^2/c^2)/2 = 0
>
> What it is saying is that the (first) GR term conveniently cancels the
> (second) SR prediction because of the shape of the earth.
>
> Note H is not as in the H&K equation the height above sea level but the
> difference between local earths radius and polar radius. v is the speed
> of the earths surface.
>
> The following is my limited understanding of Murray's calculations. If I
> have got it wrong don't blame Murray, look up what he actually wrote. I
> do not feel confident to convert them into a suitable text format which
> can be posted. While I think I understand the maths, even if I don't the
> final conclusion he comes to appears to me to be blatantly obvious as
> you will see.
>
> He calculates the total gravitational potential at the surface of the
> earth as (gH - (v^2)/2) - the first term coming from gravitational of
> the earth and the second from centrifugal acceleration.

I have the imprsssion that he uses an uncommon definition of gravitational
potential...

> This means that
> Cocke's equation is wrong and should be:
>
> dt/t = (gH - 1/2 v^2)/c^2) - (v^2/c^2)/2
> = gH/c^2 - (v^2/c^2)/2 - (v^2/c^2)/2
>
> The first term is the GR correction for potential due to the mass of the
> earth, the second term is the GR correction due to centrifugal
> acceleration and the third term is the SR term for time dilation. It
> turns out that the last two terms are identical.
>
> Cocke is correct when he says
> gH/c^2 - (v^2/c^2)/2 = 0
>
> so the equation reduces to
> dt/t = 0 - (v^2/c^2)/2
>
> In effect that is saying that there is no GR correction for clocks at
> mean sea level. Mean sea level is a unipotential surface. Whether I have
> understood the maths or not surely that is blatantly obvious. Water is
> free to flow so some of it is not going to remain at a different
> gravitational potential to the rest. The essential shape of the earth is
> the shape the water takes up with a combination of mass and spin. The
> land is simply bits of sea floor which poke through that surface. A
> clock at mean sea level anywhere in the world is at the same
> gravitational potential. Or as Murray puts it "The precise statement is
> that the geoid is defined as a unipotential surface in Earth co-
> ordinates - if one understands potential in its usual field theory
> sense".

Likely it is not a coincidence that this "unipotential" surface corresponds
to identical clock rate - that's what Hatch meant with "disjoinct theories".
One would expect it should be possible to put it forward as one theory with
one calculation. But not like Murray, IMO it really should be dt/t = 0.

> "...the difference in surface potential" caused by the oblate figure of
> the earth which Cocke says cancels to lower order the effect of
> difference speeds does not in fact exist.
>
> This means that Einstein's prediction is proved wrong and there is no
> comforting explanation to come to the rescue.

Which of his predictions is proved wrong?!

> H&K's equations predict a change in rate of clocks at different
> latitudes which does not occur

Indeed, they took the wrong H if I understand well.

> and the interpretation of SR (Builder's)
> which they used, supports Einstein's prediction which turns out to be
> false.

No, SR is admittedly incomplete.

> I read the article in 1986 and was somewhat surprised when, having asked
> in this NG as to the current explanation of the apparent failure of
> Einstein's prediction Paul Anderson came up with Cocke's explanation
> unmodified. While I am not qualified in these matters the argument does
> not appear to depend on anything sophisticated. I therefore feel
> competent to bring the matter to your attention and hope that I have
> done justice to Murray's article.
>
> If anyone would like a copy of the complete article - 89 kBytes - email
> me by converting the number in my return address from Hex to decimal or
> if you can't manage that by adding 6834 and removing 'hex' :o).

Please send it to me - regretfully I didn't think of spam protection, and
now it doesn't matter anymore...

Harald

Quantcast