The Mirror Paradox: Exploring Special Relativity Theory

[Demystifier]

Let's imagine that there are two people who has the same biological age.

That assumption is not as clear as you think it is. When I was 20, I had the same biological age as my dad when he was 20. But we didn't have the same biological age at the same time. Perhaps you wanted us to imagine two people who have the same biological age at the same time, but then you have to specify what do you mean by the "same time". The notion of "same time" is relative in the theory of relativity. As others told you, you will not get very far before you understand this central idea.

 

[Piet Venter]

The GPS clocks are only synchronized in the earth centered inertial frame. @mfb is correct that “you can never have them synchronized both for the stars and the spacecraft , or more generally for multiple observers that move (in the connecting direction) relative to each other”. The GPS is not a counterexample. The GPS clocks are not synchronized in any inertial reference frame where the earth is moving.

“The GPS clocks are only synchronized in the earth centered inertial frame.“

Perhaps you meant here the center of earth non rotating frame (which is approximately non inertial)? The surface of earth is of course not an inertial frame.

According to SR the earth clocks would be moving relative to the GPS satellite, hence the earth clocks must be unsynchronized due to relativity of simultaneity?

Yet the GPS system seems to work everywhere on earth, hence the predicted unsynchronization of earth clocks never happens?

 

[Ibix]

“The GPS clocks are only synchronized in the earth centered inertial frame.“

Perhaps you meant here the center of earth non rotating frame (which is approximately non inertial)? The surface of earth is of course not an inertial frame.

Yes.

According to SR the earth clocks would be moving relative to the GPS satellite, hence the earth clocks must be unsynchronized due to relativity of simultaneity?

Unsynchronized with respect to what?

Yet the GPS system seems to work everywhere on earth, hence the predicted unsynchronization of earth clocks never happens?

The GPS satellite clocks are deliberately set to tick the time of the Earth centered inertial frame, even though that is not their natural tick rate or simultaneity convention (there is no unique convention for orbiting bodies).

However, the "receiver" end of a GPS system has no need of high precision clocks, or consumer GPS units would have to be hundreds of thousands of pounds each. Relativistic effects on the receiver clocks are negligible compared to the inaccuracy of quartz clocks, and the GPS system is built to tolerate those much larger errors. So, while there are uncorrected relativistic issues with GPS receivers, they are completely negligible.

 

[PeroK]

Yet the GPS system seems to work everywhere on earth, hence the predicted unsynchronization of earth clocks never happens?

there's a nice story that the politicians and senior managers who commissioned the GPS system didn't believe in the theory of relativity, so they insisted that the system was first tried without the relativistic corrections. I.e. letting each clock run at its normal rate. Only when this failed did they allow the relativitistic corrections to be made. I.e. each satellite clock continually adjusts itself to take account of relativity.

I don't know whether the politicians and senior managers still doubt relativity. Quite what is the purpose of physicists lying about the laws of physics escapes me.

 

[Dale]

Perhaps you meant here the center of earth non rotating frame (which is approximately non inertial)? The surface of earth is of course not an inertial frame.

ECI is a pretty standard term. It is non-rotating and approximately inertial. The surface of the earth would be an earth-fixed frame, sometimes ECEF for earth centered earth fixed frame. It is non-inertial.

According to SR the earth clocks would be moving relative to the GPS satellite, hence the earth clocks must be unsynchronized due to relativity of simultaneity?

More explicitly and correctly, according to SR clocks synchronized in the momentarily co-moving inertial frame (MCIF) of any earth clock will be unsynchronized in the ECI frame because those clocks are moving relative to the ECI frame.

This is the relativity of simultaneity. Two inertial frames moving with respect to each other (like the ECI and the MCIF) disagree on simultaneity.

Note that the ECEF frame is a non-inertial frame, so that statement doesn't apply. The ECEF frame is designed to have the same simultaneity as the ECI frame. So clocks synchronized in the non-inertial ECEF frame will also be synchronized in the ECI frame but not in their own MCIFs.

Yet the GPS system seems to work everywhere on earth, hence the predicted unsynchronization of earth clocks never happens?

The GPS system doesn't interact with any system of clocks that are synchronized in the MCIF of any earth clocks. So why would that "unsynchronization" matter? The earth clocks in the GPS use the ECI time, not the synchronization of their MCIF. In fact, many of the earth clocks don't even measure their own time, they simply use multiple signals from the space clocks to calculate the ECI time at their location. In that sense, they aren't even actually clocks.

 

[Piet Venter]

What is the MCIF? Does the MCIF differ from ECEF? Why is the MCIF inertial?

 

[Piet Venter]

Yes.

Unsynchronized with respect to what?

The GPS satellite clocks are deliberately set to tick the time of the Earth centered inertial frame, even though that is not their natural tick rate or simultaneity convention (there is no unique convention for orbiting bodies).

However, the "receiver" end of a GPS system has no need of high precision clocks, or consumer GPS units would have to be hundreds of thousands of pounds each. Relativistic effects on the receiver clocks are negligible compared to the inaccuracy of quartz clocks, and the GPS system is built to tolerate those much larger errors. So, while there are uncorrected relativistic issues with GPS receivers, they are completely negligible.

 

[Ibix]

What is the MCIF? Does the MCIF differ from ECEF? Why is the MCIF inertial?

MCIF is the Momentarily Comoving Inertial Frame, which is the inertial frame in which some chosen object (in this case, your GPS receiver) is instantaneously at rest.

 

[Piet Venter]

MCIF is the Momentarily Comoving Inertial Frame, which is the inertial frame in which some chosen object (in this case, your GPS receiver) is instantaneously at rest.

Thanks for your reply.
Your GPS device is on the surface of Earth, and we know the surface of Earth is definitely not an inertial frame! Earth is rotating as well as orbiting the sun. The term MCIF is therefore a misnomer.

 

[Piet Venter]

ECI is a pretty standard term. It is non-rotating and approximately inertial. The surface of the earth would be an earth-fixed frame, sometimes ECEF for earth centered earth fixed frame. It is non-inertial.More explicitly and correctly, according to SR clocks synchronized in the momentarily co-moving inertial frame (MCIF) of any earth clock will be unsynchronized in the ECI frame because those clocks are moving relative to the ECI frame.

This is the relativity of simultaneity. Two inertial frames moving with respect to each other (like the ECI and the MCIF) disagree on simultaneity.

Note that the ECEF frame is a non-inertial frame, so that statement doesn't apply. The ECEF frame is designed to have the same simultaneity as the ECI frame. So clocks synchronized in the non-inertial ECEF frame will also be synchronized in the ECI frame but not in their own MCIFs.The GPS system doesn't interact with any system of clocks that are synchronized in the MCIF of any earth clocks. So why would that "unsynchronization" matter? The earth clocks in the GPS use the ECI time, not the synchronization of their MCIF. In fact, many of the earth clocks don't even measure their own time, they simply use multiple signals from the space clocks to calculate the ECI time at their location. In that sense, they aren't even actually clocks.

“The GPS system doesn't interact with any system of clocks that are synchronized in the MCIF of any earth clocks. So why would that "unsynchronization" matter? ”,

In the real physical world it does not matter, of course, as the unsynchronization of earth clocks predicted by SR can never happen.

Everything in the universe is moving relative to each other. The earth is orbiting the sun etc. Hwnce it is not possible to find an inertial frame anywhere in the universe. This implies that SR cannot be applied anywhere in the universe. Hence the predicted unsynchronization of the earth clocks in a GPS satellite frame can never occur in physical reality , because the GPS satellite is not in an inertial frame!

 

[Ibix]

Thanks for your reply.
Your GPS device is on the surface of Earth, and we know the surface of Earth is definitely not an inertial frame! Earth is rotating as well as orbiting the sun. The term MCIF is therefore a misnomer.

You misunderstand. The MCIF is the frame in which you are instantaneously at rest. The Earth's rest frame is not inertial, but every point is instantaneously at rest in some inertial frame.

 

[Ibix]

Everything in the universe is moving relative to each other. The earth is orbiting the sun etc. Hwnce it is not possible to find an inertial frame anywhere in the universe. This implies that SR cannot be applied anywhere in the universe. Hence the predicted unsynchronization of the earth clocks in a GPS satellite frame can never occur in physical reality , because the GPS satellite is not in an inertial frame!

This is just nonsense. There are objections to the notion of global Inertial frames (GR, in short), but "stuff moves" is not one of them.

 

[Piet Venter]

This is just nonsense. There are objections to the notion of global Inertial frames (GR, in short), but "stuff moves" is not one of them.

No, the prediction of SR in the GPS satellite is nonsense.
The GPS satellite observes that all the synchronized clocks on the surface of Earth are moving relative to the satellite. Hence SR predicts, using the relativity of simultaneity, that the earth clocks must all become unsynchronized!
Of course in the real physical world we never observe the earth clocks becoming unsynchronized die to the presence of GPS satellites!

 

[Ibix]

The GPS satellite observes that all the synchronized clocks on the surface of Earth are moving relative to the satellite.

Yes.

Hence SR predicts, using the relativity of simultaneity, that the earth clocks must all become unsynchronized!

In its own MCIF, yes.

Of course in the real physical world we never observe the earth clocks becoming unsynchronized die to the presence of GPS satellites!

Correct (although we do see relativity of simultaneity, it is not due to the presence or absence of satellites). If you think that contradicts the parts you wrote earlier then you have a catastrophic misunderstanding of relativity and I would strongly suggest studying Einstein's train thought experiment until you understand what the relativity of simultaneity is. A Minkowski diagram will probably help.

 

[Drakkith]

Thread locked for moderation.

 

[Drakkith]

Thread will remain locked. Thanks everyone.