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Clock Paradox Thought Experiment

GarretKadeDupre
Posts: 2,023
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11/10/2014 6:15:03 PM
Posted: 2 years ago
Here is a graphic for illustration purposes:

http://i.imgur.com...

The experiment works as follows. All observations are from the observer's perspective (the blue figure).

Clock A and Clock B are in sync. Clock B moves linearly at a constant velocity to the left until it is side by side with Clock A, then it stops.

Clock B went out of sync with Clock A while it was moving to the left (it slowed relative to A). As soon as Clock B stops, what is the relation between the times displayed by the clocks?

From the observer's perspective, it seems that Clock B should remain behind Clock A. But since all three entities represent the same inertial frame, this means Clock B's perspective of Clock A should be the same as that of the observer's. From Clock B's perspective, treating it as an inertial frame, it was Clock A and the observer that moved towards Clock B. Therefore, Clock B perceives that Clock A is lagging behind.

This is a contradiction, since, once all entities represent the same inertial frame, they should all see the same times on both clocks. Yet, this does not seem (to me) to be the case.

What you think?
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Enji
Posts: 1,022
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11/11/2014 12:35:40 AM
Posted: 2 years ago
At 11/10/2014 6:15:03 PM, GarretKadeDupre wrote:
Here is a graphic for illustration purposes:

http://i.imgur.com...

The experiment works as follows. All observations are from the observer's perspective (the blue figure).

Clock A and Clock B are in sync. Clock B moves linearly at a constant velocity to the left until it is side by side with Clock A, then it stops.

Clock B went out of sync with Clock A while it was moving to the left (it slowed relative to A). As soon as Clock B stops, what is the relation between the times displayed by the clocks?

From the observer's perspective, it seems that Clock B should remain behind Clock A. But since all three entities represent the same inertial frame, this means Clock B's perspective of Clock A should be the same as that of the observer's. From Clock B's perspective, treating it as an inertial frame, it was Clock A and the observer that moved towards Clock B. Therefore, Clock B perceives that Clock A is lagging behind.

This is a contradiction, since, once all entities represent the same inertial frame, they should all see the same times on both clocks. Yet, this does not seem (to me) to be the case.

What you think?

If, from the observer's perspective, the two clocks are in sync at the start of this shenanigans (and assuming an isocoles triangle as illustrated), then from A's perspective B is lagging behind and from B's perspective A is lagging behind. This is because it it takes time for information to transmit along each leg of the triangle. When clock A registers time T it takes time t for this information to travel to clock B, so when B sees A reach time T only when clock B registers time T+t (and vice versa).

When B moves towards A, clock B sees A counting faster and A sees B counting faster until, when clock B stops at A, they are in sync. The observer would observe clock A and B in sync once clock B stops. As B is travelling, the observer would see first clock B counting faster until its path is orthogonal to the observer; then clock B would be counting slower until it stopped in sync with A.

Things get more complicated with different geometries, but that would only serve to obfuscate the issue -- not to establish any legitimate contradiction or paradox.
chui
Posts: 507
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11/12/2014 6:26:07 PM
Posted: 2 years ago
At 11/10/2014 6:15:03 PM, GarretKadeDupre wrote:
Here is a graphic for illustration purposes:

http://i.imgur.com...

The experiment works as follows. All observations are from the observer's perspective (the blue figure).

Clock A and Clock B are in sync. Clock B moves linearly at a constant velocity to the left until it is side by side with Clock A, then it stops.

Clock B went out of sync with Clock A while it was moving to the left (it slowed relative to A). As soon as Clock B stops, what is the relation between the times displayed by the clocks?

From the observer's perspective, it seems that Clock B should remain behind Clock A. But since all three entities represent the same inertial frame, this means Clock B's perspective of Clock A should be the same as that of the observer's. From Clock B's perspective, treating it as an inertial frame, it was Clock A and the observer that moved towards Clock B. Therefore, Clock B perceives that Clock A is lagging behind.

This is a contradiction, since, once all entities represent the same inertial frame, they should all see the same times on both clocks. Yet, this does not seem (to me) to be the case.

What you think?

This is nothing new its just the same old twin paradox that has been refuted for nearly a century now. Just google Twin paradox and you will find the refutation.
chui
Posts: 507
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11/12/2014 6:26:07 PM
Posted: 2 years ago
At 11/10/2014 6:15:03 PM, GarretKadeDupre wrote:
Here is a graphic for illustration purposes:

http://i.imgur.com...

The experiment works as follows. All observations are from the observer's perspective (the blue figure).

Clock A and Clock B are in sync. Clock B moves linearly at a constant velocity to the left until it is side by side with Clock A, then it stops.

Clock B went out of sync with Clock A while it was moving to the left (it slowed relative to A). As soon as Clock B stops, what is the relation between the times displayed by the clocks?

From the observer's perspective, it seems that Clock B should remain behind Clock A. But since all three entities represent the same inertial frame, this means Clock B's perspective of Clock A should be the same as that of the observer's. From Clock B's perspective, treating it as an inertial frame, it was Clock A and the observer that moved towards Clock B. Therefore, Clock B perceives that Clock A is lagging behind.

This is a contradiction, since, once all entities represent the same inertial frame, they should all see the same times on both clocks. Yet, this does not seem (to me) to be the case.

What you think?

This is nothing new its just the same old twin paradox that has been refuted for nearly a century now. Just google Twin paradox and you will find the refutation.