Reviewing the Hafele-Keating experiment, there's something
I don't get. Why does elapsed time depend on direction?

The planes flew identical speeds and altitudes. Why
should an east-west discrepancy occur? Isn't the earth
an arbitrary co-ordinate system?

Was this a surprising result, or standard relativity?
Did Einstein predict this?

I should add, somebody made a major effort compiling the
faq for this group. It's a real public service.

Mark

On Tuesday, November 23, 2021 at 5:51:08 PM UTC-8, Mark-T wrote:
> Reviewing the Hafele-Keating experiment, there's something
> I don't get. Why does elapsed time depend on direction?

The rotating earth is not at rest in what is called an inertial coordinate system. To use the simple equations of physics you have to express things in terms of an inertial coordinate system. Typically for a process involving movements around the world the most convenient inertial coordinate system is the Earth-Centered Inertial (ECI) coordinate system, which is a non-rotating system of coordinates with origin at the center of the Earth, which is moving nearly inertially for a sufficiently short time period in its orbit around the Sun. Any other inertial coordinate system (such as the Sun-centered inertial system, or a tangential system) would give the same answers, but it's most convenient to use the ECI for this situation.

In terms of the ECI, the surface of the earth is moving circumferentially due to the Earth's rotation, and this adds to the plane's velocity in one direction and subtracts in the other.
> The planes flew identical speeds and altitudes. Why
> should an east-west discrepancy occur?

See above.

> Isn't the earth an arbitrary co-ordinate system?

The earth is at rest in a rotating coordinate system, not an inertial coordinate system. The simple homogeneous and isotropic equations of physics apply only in local inertial coordinate systems, not in arbitrary coordinate systems.

> Was this a surprising result, or standard relativity?

Standard relativity. Some physicists mocked Hafele and Keating for carrying out this publicity stunt. Special relativity had been experimentally verified decades earlier. Of cours we, someone was bound to do it as soon as atomic clocks became accurate enough. At the time, the clocks were still just marginally accurate enough, and required sophisticated cross-corrections involving four clocks. But these days we have much more accurate clocks, and we can verify relativistic time dilation in the lab for speeds as low as 20 mph.

> Did Einstein predict this?

Einstein's special relativity unequivocally predicts this, yes. Of course, they didn't have passenger air travel back then... first airplane was only flown at Kitty Hawk about 18 months prior to Einstein's 1905 paper, and of course they didn't have atomic clocks until much later. But the outcome of such a demonstration is a trivial prediction of special relativity.

On Tuesday, November 23, 2021 at 5:51:08 PM UTC-8, Mark-T wrote:
> Reviewing the Hafele-Keating experiment, there's something
> I don't get. Why does elapsed time depend on direction?
>
> The planes flew identical speeds and altitudes. Why
> should an east-west discrepancy occur? Isn't the earth
> an arbitrary co-ordinate system?
>
> Was this a surprising result, or standard relativity?
> Did Einstein predict this?
>
> I should add, somebody made a major effort compiling the
> faq for this group. It's a real public service.
>
> Mark

The two planes had roughly equal speeds wrt the ROTATING Earth surface. That means that the plane flying E to W had a much HIGHER speed wrt to an inertial frame of reference than the plane that flew W to E. The total elapsed proper time is proportional with sqrt{1-v^2/c^2} where v is the speed of the respective plane. Thus, the higher the speed, the less total elapsed proper time.

On 11/23/21 7:51 PM, Mark-T wrote:
> Reviewing the Hafele-Keating experiment, there's something I don't
> get. Why does elapsed time depend on direction?

Because at base it is the plane's speed relative to the ECI that
matters, not relative to the (rotating) earth surface.

[The ECI frame is the locally inertial frame in
which the center of the earth is at rest. It
does not rotate relative to the "fixed stars".
It is locally inertial in the sense of GR, but
is not an inertial frame in the sense of SR;
for discussions like this that is sufficient.]

In a simplified H-K experiment in which gravity can be ignored, the
elapsed time of each trip is just
\integral sqrt(1-v(t)^2/c^2) dt
where v(t) is the speed of the plane relative to the ECI coordinates,
and t is the ECI time coordinate. Due to the rotation of the earth,
v(westbound) < v(eastbound), which accounts for the difference.

NOTE: That equation holds ONLY for inertial coordinates, such as the ECI
coordinates used by the GPS.

In the real H-K experiment, the effect of gravity is small compared to
the above effect of SR. Gravity must be included to obtain numerical
consistency, but it can be ignored for the basic idea.

> The planes flew identical speeds and altitudes.

Relative to the earth's surface. But the their speeds are quite
different relative to the ECI, and that's what matters.

[They were not precisely equal relative to the earth
surface, but were close enough for an elementary
discussion like this.]

> Why should an east-west discrepancy occur? Isn't the earth an
> arbitrary co-ordinate system?

I suppose just about anything could be an "arbitrary coordinate system".
But in physics like this what matters is an INERTIAL coordinate system.
The rotating earth is not such a coordinate system, but the ECI is.

[Again, close enough for a discussion like this.]

> Was this a surprising result, or standard relativity?

It is unsurprising and simply standard relativity.

> Did Einstein predict this?

Not specifically, because he was long dead. But he did discuss similar
situations, and his theory of General Relativity certainly does
accurately predict the H-K result.

> I should add, somebody made a major effort compiling the faq for this
> group. It's a real public service.

It was an effort by many people. I wrote the FAQ entry on the
experimental basis of SR.

Tom Roberts

On Tuesday, November 23, 2021 at 8:30:32 PM UTC-8, tjrob137 wrote:
> In the real H-K experiment, the effect of gravity is small compared to
> the above effect of SR.

Not so. In the real H-K experiment the effect of gravity was roughly the same size as the effect of velocity. In very rough numbers, compared to the ground time, the predicted elevation effect added about 140-180 nsec to both flights (they didn't hold the same altitudes), and the effects of motion added another 100 nsec to the westbound flight and subtracted about 180 from the eastbound flight.

On Wednesday, 24 November 2021 at 05:30:32 UTC+1, tjrob137 wrote:
> On 11/23/21 7:51 PM, Mark-T wrote:
> > Reviewing the Hafele-Keating experiment, there's something I don't
> > get. Why does elapsed time depend on direction?
> Because at base it is the plane's speed relative to the ECI that
> matters, not relative to the (rotating) earth surface.
>
> [The ECI frame is the locally inertial frame in
> which the center of the earth is at rest. It
> does not rotate relative to the "fixed stars".
> It is locally inertial in the sense of GR, but
> is not an inertial frame in the sense of SR;
> for discussions like this that is sufficient.]
>
> In a simplified H-K experiment in which gravity can be ignored, the
> elapsed time of each trip is just
> \integral sqrt(1-v(t)^2/c^2) dt
> where v(t) is the speed of the plane relative to the ECI coordinates,
> and t is the ECI time coordinate. Due to the rotation of the earth,
> v(westbound) < v(eastbound), which accounts for the difference.
>
> NOTE: That equation holds ONLY for inertial coordinates, such as the ECI
> coordinates used by the GPS.
>
> In the real H-K experiment, the effect of gravity is small compared to
> the above effect of SR. Gravity must be included to obtain numerical
> consistency, but it can be ignored for the basic idea.
> > The planes flew identical speeds and altitudes.
> Relative to the earth's surface. But the their speeds are quite
> different relative to the ECI, and that's what matters.

In the meantime in the real world, however, forbidden by
your moronic religion GPS clocks keep measuring t'=t,
just like all serious clocks always did. Your screams
"We're FORCED!!!" simply didn't work.

> But in physics like this what matters is an INERTIAL coordinate system.

Sure, what matters in physics is a gedanken nowhere.

> It was an effort by many people. I wrote the FAQ entry on the
> experimental basis of SR.

In the meantime in the real world, however, forbidden by
your moronic religion GPS clocks keep measuring t'=t,
just like all serious clocks always did. Your screams
"We're FORCED!!!" simply didn't work.

Den 24.11.2021 02:51, skrev Mark-T:
> Reviewing the Hafele-Keating experiment, there's something
> I don't get. Why does elapsed time depend on direction?
>
> The planes flew identical speeds and altitudes. Why
> should an east-west discrepancy occur? Isn't the earth
> an arbitrary co-ordinate system?
>
> Was this a surprising result, or standard relativity?
> Did Einstein predict this?
>
> I should add, somebody made a major effort compiling the
> faq for this group. It's a real public service.
>
> Mark
>

https://paulba.no/pdf/H&K_like.pdf

--
Paul

https://paulba.no/

On Wednesday, 24 November 2021 at 08:59:29 UTC+1, Paul B. Andersen wrote:
> Den 24.11.2021 02:51, skrev Mark-T:
> > Reviewing the Hafele-Keating experiment, there's something
> > I don't get. Why does elapsed time depend on direction?
> >
> > The planes flew identical speeds and altitudes. Why
> > should an east-west discrepancy occur? Isn't the earth
> > an arbitrary co-ordinate system?
> >
> > Was this a surprising result, or standard relativity?
> > Did Einstein predict this?
> >
> > I should add, somebody made a major effort compiling the
> > faq for this group. It's a real public service.
> >
> > Mark
> >
> https://paulba.no/pdf/H&K_like.pdf

In the meantime in the real world, however, forbidden by
your moronic religion GPS clocks keep measuring t'=t,
just like all serious clocks always did.

On Tuesday, November 23, 2021 at 9:48:53 PM UTC-8, Townes Olson wrote:
> On Tuesday, November 23, 2021 at 8:30:32 PM UTC-8, tjrob137 wrote:
> > In the real H-K experiment, the effect of gravity is small compared to
> > the above effect of SR.
> Not so. In the real H-K experiment the effect of gravity was roughly the same size as the effect of velocity. In very rough numbers, compared to the ground time, the predicted elevation effect added about 140-180 nsec to both flights (they didn't hold the same altitudes), and the effects of motion added another 100 nsec to the westbound flight and subtracted about 180 from the eastbound flight.

Tom was most likely thinking about GPS, he is clearly off on his remark on HK: https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment#Results

On Wednesday, November 24, 2021 at 8:49:13 AM UTC-8, Dono. wrote:
> On Tuesday, November 23, 2021 at 9:48:53 PM UTC-8, Townes Olson wrote:
> > On Tuesday, November 23, 2021 at 8:30:32 PM UTC-8, tjrob137 wrote:
> > > In the real H-K experiment, the effect of gravity is small compared to
> > > the above effect of SR.
> > Not so. In the real H-K experiment the effect of gravity was roughly the same size as the effect of velocity. In very rough numbers, compared to the ground time, the predicted elevation effect added about 140-180 nsec to both flights (they didn't hold the same altitudes), and the effects of motion added another 100 nsec to the westbound flight and subtracted about 180 from the eastbound flight.
> Tom was most likely thinking about GPS, he is clearly off on his remark on HK: https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment#Results

What seems to explain is the Allan discrepancy, why what is so for
the "atomic clock" and how it's measured and what it is as measuring
relativistic acceleration, or acceleration relativistically, it's as much
space contraction what's predicted by relativity then, instead of a length
contraction and a time dilation. (Along with that the machinery of an atomic
clock is a relativistic device, then for also explaining Pound Rebka, again
so a device, carries a common theme for validating and making falsifiable
and having a theory with space contraction.)

About the East-West tracks, again it's remarkable why the time added back
up, then with respect to what tracks they took that the great Hafele-Keating
experiment which doesn't falsify relativity as for what follows its predictions.

Again, it's remarkable the prediction, when, it's only after the discrepancy,
which is not predicted, that makes for that it's only in the regime of the
atomic clock, and not for example the crystal clock, why it neatly holds so..

Then the fact that the atomic clocks are used to detect changes in Earth's
frame, is again remarkable.

On Friday, November 26, 2021 at 8:44:35 AM UTC-8, Ross A. Finlayson wrote:
> On Wednesday, November 24, 2021 at 8:49:13 AM UTC-8, Dono. wrote:
> > On Tuesday, November 23, 2021 at 9:48:53 PM UTC-8, Townes Olson wrote:
> > > On Tuesday, November 23, 2021 at 8:30:32 PM UTC-8, tjrob137 wrote:
> > > > In the real H-K experiment, the effect of gravity is small compared to
> > > > the above effect of SR.
> > > Not so. In the real H-K experiment the effect of gravity was roughly the same size as the effect of velocity. In very rough numbers, compared to the ground time, the predicted elevation effect added about 140-180 nsec to both flights (they didn't hold the same altitudes), and the effects of motion added another 100 nsec to the westbound flight and subtracted about 180 from the eastbound flight.
> > Tom was most likely thinking about GPS, he is clearly off on his remark on HK: https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment#Results
> What seems to explain is the Allan discrepancy, why what is so for
> the "atomic clock" and how it's measured and what it is as measuring
> relativistic acceleration, or acceleration relativistically,

Clocks are not affected by acceleration, doddering crank.

On Friday, 26 November 2021 at 18:16:16 UTC+1, Dono. wrote:
> On Friday, November 26, 2021 at 8:44:35 AM UTC-8, Ross A. Finlayson wrote:
> > On Wednesday, November 24, 2021 at 8:49:13 AM UTC-8, Dono. wrote:
> > > On Tuesday, November 23, 2021 at 9:48:53 PM UTC-8, Townes Olson wrote:
> > > > On Tuesday, November 23, 2021 at 8:30:32 PM UTC-8, tjrob137 wrote:
> > > > > In the real H-K experiment, the effect of gravity is small compared to
> > > > > the above effect of SR.
> > > > Not so. In the real H-K experiment the effect of gravity was roughly the same size as the effect of velocity. In very rough numbers, compared to the ground time, the predicted elevation effect added about 140-180 nsec to both flights (they didn't hold the same altitudes), and the effects of motion added another 100 nsec to the westbound flight and subtracted about 180 from the eastbound flight.
> > > Tom was most likely thinking about GPS, he is clearly off on his remark on HK: https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment#Results
> > What seems to explain is the Allan discrepancy, why what is so for
> > the "atomic clock" and how it's measured and what it is as measuring
> > relativistic acceleration, or acceleration relativistically,
> Clocks are not affected by acceleration, doddering crank.

Where did you get this information, poor halfbrain?

Maciej Wozniak wrote:

>> Clocks are not affected by acceleration, doddering crank.
>
> Where did you get this information, poor halfbrain?

why should they, inertia? Do you have a perimeter institute?

On November 23, Townes Olson wrote:
>> In the real H-K experiment, the effect of gravity is small compared to
>> the above effect of SR.
>
> Not so. In the real H-K experiment the effect of gravity was roughly the same size as the effect of
> velocity. In very rough numbers, compared to the ground time, the predicted elevation effect added
> about 140-180 nsec to both flights (they didn't hold the same altitudes), and the effects of motion
> added another 100 nsec to the westbound flight and subtracted about 180 from the eastbound flight.

So we remove the earth, and reference the ECI, which is empty space, pure geometry,
like GPS.

Then each flight had return to the exact same spot, in the ECI.
Not JFK airport <--> JFK airport

How did they manage the precise location control?

Mark

On Monday, November 29, 2021 at 5:53:47 PM UTC-8, Mark-T wrote:
> So we remove the earth...

No, we don't "remove the earth". It's still here.

> and reference the ECI...

Any inertia-based coordinate system would do just as well, but yes, the ECI will work as an inertial reference system.

> which is empty space, pure geometry, like GPS.

The ECI is just a system of inertia-based coordinates, it isn't empty space, it isn't pure geometry, and it isn't like GPS (whatever that might mean).

> Then each flight had return to the exact same spot, in the ECI.

Nope. The earth is rotating, so their home base airport moved significantly in terms of the ECI during the trip.

> How did they manage the precise location control?

Again, the airport moved (in terms of the ECI) by thousands of miles between departure and arrival. If you are asking how the airplanes managed to navigate all the way and land on the correct runway, well, they used ordinary navigation techniques. The planes have steering wheels and rudders, so they can steer where they want to go (fortunately, or they wouldn't be much use for transportation).

On Tuesday, 30 November 2021 at 03:31:06 UTC+1, Townes Olson wrote:
> On Monday, November 29, 2021 at 5:53:47 PM UTC-8, Mark-T wrote:
> > So we remove the earth...
>
> No, we don't "remove the earth". It's still here.
>
> > and reference the ECI...
>
> Any inertia-based coordinate system would do just as well

Sure, poor halfbrain; any of none.

On November 29, 2021 at 6:31:06 PM UTC-8, Townes Olson wrote:
> > So we remove the earth...
>
> No, we don't "remove the earth". It's still here.
>
> > and reference the ECI...
>
> Any inertia-based coordinate system would do just as well, but yes, the ECI will work as
> an inertial reference system.
>
> > which is empty space, pure geometry, like GPS.
>
> The ECI is just a system of inertia-based coordinates, it isn't empty space, it isn't pure geometry,
> and it isn't like GPS (whatever that might mean).

GPS ignores the earth, it's pure x-y-z 3-D geometry.

> > Then each flight had return to the exact same spot, in the ECI.
>
> Nope. The earth is rotating, so their home base airport moved significantly in terms of the ECI during the trip.

Something doesn't add up here.

It's a demonstration of the twins paradox, is it not? It uses the ECI frame
as the reference. The twins fly at different speeds, relative to the origin of that
frame. Hence show different aging, in conclusion.

So the twins must depart and return at the same point, in that frame. Otherwise
it's a mashup. As you note, that point isn't their home base airport.

Mark

On Tuesday, November 30, 2021 at 6:04:55 PM UTC-8, Mark-T wrote:
> > The ECI is just a system of inertia-based coordinates, it isn't empty space, it isn't pure geometry,
> > and it isn't like GPS (whatever that might mean).
>
> GPS ignores the earth, it's pure x-y-z 3-D geometry.

The global positioning system is geometry? It consists of satellites, etc. Are you confusing it with the ECI? The earth centered inertial coordinates surely don't "ignore the earth", making allowances for the weird anthropomorphism.

> > The earth is rotating, so their home base airport moved significantly in
> > terms of the ECI during the trip.
>
> Something doesn't add up here. It's a demonstration of the twins paradox,
> is it not?

It's a demonstration of time dilation... a very old and obsolete one... really just a publicity stunt.

> It uses the ECI frame as the reference.

Well, it can be analyzed and described in terms of any coordinate system we like, but it's most convenient to describe it in terms of the ECI.

> The twins fly at different speeds, relative to the origin of that frame.
> Hence show different aging, in conclusion.

Yes, although the ground station is also moving in terms of the ECI. In fact, it is moving faster than one of the planes.

> So the twins must depart and return at the same point, in that frame. Otherwise
> it's a mashup.

Nope. Nothing is absolutely at rest, so any situation involves movement in terms of some system of coordinates. We can use any system of coordinates we like, but if we want the laws of physics to take their simplest form we use inertia-based coordinate systems. But there are infinitely many of those. The twins just show that you can have different elapsed proper times along two different paths between two given events.

> As you note, that point isn't their home base airport.

There is no "absolute rest", so we can't identify absolute "points" in space from one time to another.

On Saturday, 4 December 2021 at 08:46:29 UTC+1, Townes Olson wrote:

> It's a demonstration of time dilation... a very old and obsolete one... really just a publicity stunt.

In the meantime in the real world, however, forbidden by your
insane religion GPS clocks keep measuring t'=t, just like all
serious clocks always did.

On Friday, November 26, 2021 at 8:44:35 AM UTC-8, Ross A. Finlayson wrote:
> On Wednesday, November 24, 2021 at 8:49:13 AM UTC-8, Dono. wrote:
> > On Tuesday, November 23, 2021 at 9:48:53 PM UTC-8, Townes Olson wrote:
> > > On Tuesday, November 23, 2021 at 8:30:32 PM UTC-8, tjrob137 wrote:
> > > > In the real H-K experiment, the effect of gravity is small compared to
> > > > the above effect of SR.
> > > Not so. In the real H-K experiment the effect of gravity was roughly the same size as the effect of velocity. In very rough numbers, compared to the ground time, the predicted elevation effect added about 140-180 nsec to both flights (they didn't hold the same altitudes), and the effects of motion added another 100 nsec to the westbound flight and subtracted about 180 from the eastbound flight.
> > Tom was most likely thinking about GPS, he is clearly off on his remark on HK: https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment#Results
> What seems to explain is the Allan discrepancy, why what is so for
> the "atomic clock" and how it's measured and what it is as measuring
> relativistic acceleration, or acceleration relativistically, it's as much
> space contraction what's predicted by relativity then, instead of a length
> contraction and a time dilation. (Along with that the machinery of an atomic
> clock is a relativistic device, then for also explaining Pound Rebka, again
> so a device, carries a common theme for validating and making falsifiable
> and having a theory with space contraction.)
>
> About the East-West tracks, again it's remarkable why the time added back
> up, then with respect to what tracks they took that the great Hafele-Keating
> experiment which doesn't falsify relativity as for what follows its predictions.
>
> Again, it's remarkable the prediction, when, it's only after the discrepancy,
> which is not predicted, that makes for that it's only in the regime of the
> atomic clock, and not for example the crystal clock, why it neatly holds so.
>
> Then the fact that the atomic clocks are used to detect changes in Earth's
> frame, is again remarkable.

Though, there is account for drift, why Michelson Morley is accurate,
about the right tracks here the solloidal, which flights.

All of course quite well held up by GR.

(In an ideal world where the interpretation of GR was independent
and free for example also SR, "the" theory.)

I.e., invalidating GR isn't falsifiable in the Newtonian of course.

(The theory.)

On November 23, Paul B. Andersen wrote:
>> Reviewing the Hafele-Keating experiment, there's something
>> I don't get. Why does elapsed time depend on direction?
>
> > The planes flew identical speeds and altitudes. Why
> > should an east-west discrepancy occur? Isn't the earth
> > an arbitrary co-ordinate system?
>
> https://paulba.no/pdf/H&K_like.pdf

Very good.

The special relativity explanation produces the same answer, fortunately.
However, the general relativity analysis must be the truth, so to speak.

What are the assumptions and approximations made in the former case,
in order to arrive at the same result?

Mark

On Saturday, December 11, 2021 at 4:28:30 PM UTC-8, Mark-T wrote:
> On November 23, Paul B. Andersen wrote:
> >> Reviewing the Hafele-Keating experiment, there's something
> >> I don't get. Why does elapsed time depend on direction?
> >
> > > The planes flew identical speeds and altitudes. Why
> > > should an east-west discrepancy occur? Isn't the earth
> > > an arbitrary co-ordinate system?
> >
> > https://paulba.no/pdf/H&K_like.pdf
>
> Very good.
>
> The special relativity explanation produces the same answer, fortunately.
> However, the general relativity analysis must be the truth, so to speak.
>
> What are the assumptions and approximations made in the former case,
> in order to arrive at the same result?
>
> Mark
SR does not account for the accumulated proper time due to changer in altitude (changes in gravitational potential), so it must assume constant altitude of plane flight.