Time dilation

[Giorgio T.]

In the experiment by Hafele & Keating to prove time dilation the frame of reference for the tests was assumed to be connected to the center of the Earth but I assume it was not rotating with the Earth. Why not assume it was connected and rotating with the Earth?

[dimreepr]

20 minutes ago, Giorgio T. said:

In the experiment by Hafele & Keating to prove time dilation the frame of reference for the tests was assumed to be connected to the center of the Earth but I assume it was not rotating with the Earth. Why not assume it was connected and rotating with the Earth?

They flew both ways.

https://en.wikipedia.org/wiki/Hafele–Keating_experiment

[swansont]

28 minutes ago, Giorgio T. said:

In the experiment by Hafele & Keating to prove time dilation the frame of reference for the tests was assumed to be connected to the center of the Earth but I assume it was not rotating with the Earth. Why not assume it was connected and rotating with the Earth?

A rotating frame is not inertial. Special relativity requires that you use an inertial frame for the analysis.

[Giorgio T.]

So are we back at Mach's principle?  The inertial frame requires that it is not rotating in relation to the stars.

[swansont]

1 hour ago, Giorgio T. said:

So are we back at Mach's principle?  The inertial frame requires that it is not rotating in relation to the stars.

You can tell if you are in an accelerating frame without referencing the stars. This is a side argument. 

[Giorgio T.]

I realize that you can tell if you are in a rotating frame in many different ways, ring lasers, gyroscope, dropping balls, etc. I find it interesting that as Mr Hafele & keating looked out the window of the aircraft going east the stars were going by at a greater rate that they were when they were going west and the clocks were going slower. Is it simply a coincidence?

[swansont]

51 minutes ago, Giorgio T. said:

I realize that you can tell if you are in a rotating frame in many different ways, ring lasers, gyroscope, dropping balls, etc. I find it interesting that as Mr Hafele & keating looked out the window of the aircraft going east the stars were going by at a greater rate that they were when they were going west and the clocks were going slower. Is it simply a coincidence?

Not at all. The earth rotates to the east. All of the clocks were moving at some speed, rather than being at rest. For the ones flying east, the speeds added. For the ones flying west, it was subtracted (since velocity is a vector)

[MigL]

Just to nit-pick...

Did they also take rotational motion about the Sun into consideration ?
And the galactic orbital motion of the Sun ?
And the Milky Way about the local cluster ?
Etc.

Why not just fly North-South ( and with a correction for the inclination of the Earth ) and eliminate some extraneous factors ?

( or maybe I should look this stuff up )

[Janus]

29 minutes ago, MigL said:

Just to nit-pick...

Did they also take rotational motion about the Sun into consideration ?
And the galactic orbital motion of the Sun ?
And the Milky Way about the local cluster ?
Etc.

Why not just fly North-South ( and with a correction for the inclination of the Earth ) and eliminate some extraneous factors ?

( or maybe I should look this stuff up )

Thee was no need to take these other motions into account as all three clocks shared them equally. It was the relative velocity difference between the clocks that was the important factor.

 Keeping one clock on the ground, while flying one clock East to West and another West to East, gave you  three clocks moving at three different relative velocities, and thus three different data points to compare. 

[Strange]

1 hour ago, Janus said:

Keeping one clock on the ground, while flying one clock East to West and another West to East, gave you  three clocks moving at three different relative velocities, and thus three different data points to compare. 

It seems that the E-to-W and W-to-E clocks travelling at the same speed relative to the clock on the ground and therefore they should both differ from the the ground clock by the same amount. (Apart from the effect of prevailing winds.)

On 27/12/2017 at 5:20 PM, swansont said:

A rotating frame is not inertial. Special relativity requires that you use an inertial frame for the analysis.

This suggests that if we choose a non-rotating frame of reference then we end up with two clocks moving West to East at different speeds (the one on the plane and the one on the ground) and one moving East to West (at a different speed than the other one being carried on a plane).

So, with respect to that frame of reference one of the planes is moving faster than the other (and, obviously, in the other direction).

This is summarised well in the Wikipedia page linked above:

Quote

Considering the Hafele–Keating experiment in a frame of reference at rest with respect to the center of the earth, a clock aboard the plane moving eastward, in the direction of the Earth's rotation, had a greater velocity (resulting in a relative time loss) than one that remained on the ground, while a clock aboard the plane moving westward, against the Earth's rotation, had a lower velocity than one on the ground.

But this is where I am now struggling to get my head round this. We don't have a clock that is not rotating with the Earth to compare with. (Do we?)

We only have a clock that is rotating with the Earth. And relative to that clock, it seems that the two plane-bound clocks are both moving at the same relative speed (in opposite directions) and so they should both have the same time dilation relative to that clock.

What am I not getting? (*)

 

(*) I am quite amused by the fact that a not-insignificant number of people would, at this point, be saying: "AND THEIR FOR EISENSTEIN WAS RONG!!!1!" 

[koti]

30 minutes ago, Strange said:

...it seems that the two plane-bound clocks are both moving at the same relative speed (in opposite directions) and so they should both have the same time dilation relative to that clock.

I might be wrong but I think the airplane moving east moves at a higher velocity than the plane which moves west because the earths rotation velocity adds to it.

[Strange]

Just now, koti said:

I might be wrong but I think the airplane moving east moves at a higher velocity than the plane which moves west because the earths rotation velocity adds to it.

That's why I added the "prevailing wind" comment. Planes fly at a speed relative to the Earth (the air moves with the Earth - but you know that!) so I don't think that is the answer.

[koti]

3 minutes ago, Strange said:

That's why I added the "prevailing wind" comment. Planes fly at a speed relative to the Earth (the air moves with the Earth - but you know that!) so I don't think that is the answer.

Excerpt from wiki, seems pretty straight forward to me unless Im missing what your actual concern is:

”...a clock aboard the plane moving eastward, in the direction of the Earth's rotation, had a greater velocity (resulting in a relative time loss) than one that remained on the ground, while a clock aboard the plane moving westward, against the Earth's rotation, had a lower velocity than one on the ground”

[Strange]

Just now, koti said:

Excerpt from wiki, seems pretty straight forward to me unless Im missing what your actual concern is:

”...a clock aboard the plane moving eastward, in the direction of the Earth's rotation, had a greater velocity (resulting in a relative time loss) than one that remained on the ground, while a clock aboard the plane moving westward, against the Earth's rotation, had a lower velocity than one on the ground”

If they said "had a lower velocity [than the other plane] relative to the one on the ground" then I would certainly agree.

But they seem to be saying that the westbound plane was moving slower than the clock on the ground (relative to a frame of reference that is not rotating, I assume). 

I have just realised that this is a version of the Twin's Paradox: we are not comparing time dilation (which would, I assume, be symmetrical for the two planes relative to the ground), but the total elapsed time experienced by each clock. This depends on the accelerations each makes to get up to speed and then come back together again. And that will presumably be different in each direction because all three clocks are in an accelerating (rotating) frame of reference.

Is that it?

[koti]

2 minutes ago, Strange said:

If they said "had a lower velocity [than the other plane] relative to the one on the ground" then I would certainly agree.

But they seem to be saying that the westbound plane was moving slower than the clock on the ground (relative to a frame of reference that is not rotating, I assume). 

I have just realised that this is a version of the Twin's Paradox: we are not comparing time dilation (which would, I assume, be symmetrical for the two planes relative to the ground), but the total elapsed time experienced by each clock. This depends on the accelerations each makes to get up to speed and then come back together again. And that will presumably be different in each direction because all three clocks are in an accelerating (rotating) frame of reference.

Is that it?

But its all just time dillation...the twin paradoxes and this experiment does deal with exactly the same issue. Total elapsed time for plane A and plane B are different in relation to the clock on the ground. They got a result with clock A vs ground clock and compared it with clock B vs ground clock. The velocity of clock A on one plane was different  from the velocity of clock B on the other plane - in relation to the ground clock. I don’t get what you don’t get  

[swansont]

 

59 minutes ago, Strange said:

It seems that the E-to-W and W-to-E clocks travelling at the same speed relative to the clock on the ground and therefore they should both differ from the the ground clock by the same amount. (Apart from the effect of prevailing winds.)

This suggests that if we choose a non-rotating frame of reference then we end up with two clocks moving West to East at different speeds (the one on the plane and the one on the ground) and one moving East to West (at a different speed than the other one being carried on a plane).

So, with respect to that frame of reference one of the planes is moving faster than the other (and, obviously, in the other direction).

This is summarised well in the Wikipedia page linked above:

But this is where I am now struggling to get my head round this. We don't have a clock that is not rotating with the Earth to compare with. (Do we?)

We only have a clock that is rotating with the Earth. And relative to that clock, it seems that the two plane-bound clocks are both moving at the same relative speed (in opposite directions) and so they should both have the same time dilation relative to that clock.

What am I not getting? (*)

The ground clock is not a stationary frame. And the effect of motion is nonllinear  - it's a (v/c)^2 term 

 

3 hours ago, MigL said:

 Why not just fly North-South ( and with a correction for the inclination of the Earth ) and eliminate some extraneous factors ?

There is no differential effect going N-S. No point in doing an experiment that doesn't show what you wish to measure.

29 minutes ago, koti said:

I might be wrong but I think the airplane moving east moves at a higher velocity than the plane which moves west because the earths rotation velocity adds to it.

Precisely. I said this earlier.

15 minutes ago, Strange said:

I I have just realised that this is a version of the Twin's Paradox: we are not comparing time dilation (which would, I assume, be symmetrical for the two planes relative to the ground), but the total elapsed time experienced by each clock. This depends on the accelerations each makes to get up to speed and then come back together again. And that will presumably be different in each direction because all three clocks are in an accelerating (rotating) frame of reference.

Is that it?

Yes. Each clock is moving at a different speed relative to some inertial frame (a frame moving with the earth was chosen for ease of analysis) and the accrued time was measured. Dilation integrated over the trip.

[Janus]

23 minutes ago, Strange said:

If they said "had a lower velocity [than the other plane] relative to the one on the ground" then I would certainly agree.

But they seem to be saying that the westbound plane was moving slower than the clock on the ground (relative to a frame of reference that is not rotating, I assume). 

I have just realised that this is a version of the Twin's Paradox: we are not comparing time dilation (which would, I assume, be symmetrical for the two planes relative to the ground), but the total elapsed time experienced by each clock. This depends on the accelerations each makes to get up to speed and then come back together again. And that will presumably be different in each direction because all three clocks are in an accelerating (rotating) frame of reference.

Is that it?

The thing to keep in mind is that none of the three clocks are in an inertial frame of reference.  They all are in rotating frames.  Each with a different angular velocity with respect to the non-rotating Earth centered frame.   If you examine this scenario from that inertial frame, then it is clear that if the clocks are all synced when they start off, they will all be out of sync when they pass each other again.  And if this in true in the non-inertial frame, it is true in all the frames.  

The respective time dilation each clock measures for the other clocks will only be symmetrical at the moment that the clocks are passing each other.  The clocks, each in their own rotating frame, are each undergoing different accelerations, and when they are at different points of their paths, their acceleration vectors are all pointing in different directions.  The rate at which any given clock will determine another clock as ticking will depend on its own rotational acceleration and the relative position of the other clock respective position to  the acceleration vector.    At different moments during the clock's separation, they will measure the other clocks as sometime ticking slower and sometimes ticking faster.  The accumulative time difference will be the sum of all those different tick rates and when they meet up again, all three clocks will agree on their respective time readings.

[Strange]

9 hours ago, Janus said:

If you examine this scenario from that inertial frame, then it is clear that if the clocks are all synced when they start off, they will all be out of sync when they pass each other again.  And if this in true in the non-inertial frame, it is true in all the frames.  

Excellent answer, as always!

So the confusion seen so often (and which I just fell into) comes from only thinking of the simple "special relativistic" case (which only applies at one moment) and not taking into account the accelerations. Thanks.

[MigL]

Lesson learned.

Don't argue with Janus about SR.
Don't argue with Swansont about clocks.

By the way, I gotta know...
You being a former James Bond, and me being a watch collector, Swansont.
Is it Rolex or Omega ?

[swansont]

2 hours ago, MigL said:

 By the way, I gotta know...

You being a former James Bond, and me being a watch collector, Swansont.
Is it Rolex or Omega ?

Connery Bond was a Rolex. Craig Bond was Omega.