Implications of orthogonal clocks in rockets

[BOYLANATOR]

Hi.
If two light clocks are put on a rocket at rest and then accelerated to relativistic velocities with one of the light clocks parallel to the direction of motion and one perpendicular, will one clock continue to measure the rate of change of time in the rest plane while the other one measures a different time?
If instead grandfather clocks were used, would the result be the same?
What about mechanical clocks (i.e. with cogs of a certain orientation)
Any responses to my wondering are appreciated.

 

[ghwellsjr]

Hi.
If two light clocks are put on a rocket at rest and then accelerated to relativistic velocities with one of the light clocks parallel to the direction of motion and one perpendicular, will one clock continue to measure the rate of change of time in the rest plane while the other one measures a different time?

After the rocket achieves terminal velocity, both clocks will tick at the same rate.

If instead grandfather clocks were used, would the result be the same?

A pendulum clock requires gravity and will tick at a different rate depending on the gravity.

What about mechanical clocks (i.e. with cogs of a certain orientation)
Any responses to my wondering are appreciated.

Balance clocks will tick the same regardless of orientation under any constant velocity.

 

[BOYLANATOR]

I thought the reason a light clock orientated perpendicular to the direction of movement measured time as slower than a rest frame was due to the idea that the light beam follows the hypotenuse of a triangle as viewed by the observer at rest. What causes the parallel light clock to relatively slow?

 

[Dale]

Length contraction.

 

[ghwellsjr]

I thought the reason a light clock orientated perpendicular to the direction of movement measured time as slower than a rest frame was due to the idea that the light beam follows the hypotenuse of a triangle as viewed by the observer at rest. What causes the parallel light clock to relatively slow?

You're right about the perpendicularly oriented light clock but think about one that was moving very close to the speed of light. The triangle would be almost a flat line, wouldn't it? And if you approximated it to the parallel version, the two mirrors would have to be very close together in order to tick at the same rate, wouldn't they? But at slower speeds, you would have to move them farther apart to maintain the same rate until finally, with no motion at all, they would be the same distance apart as the perpendicular version, wouldn't they?

 

[jartsa]

Length contraction.

Well surely not. In a parallel light clock, moving at speed 0.9 c, light can travel across the clock in about half the normal time, because the clock is shortened to about half the length.

But the rate that the light - mirror distance changes is 30000 km/s (0.1 c).

So it takes about five times longer to travel across a light clock that is traveling at speed 0.9 c.


(Note: no incorrect velocity addition here)

 

[BOYLANATOR]

But at slower speeds, you would have to move them farther apart to maintain the same rate until finally, with no motion at all, they would be the same distance apart as the perpendicular version, wouldn't they?

I don't really follow this part. Is it possible to describe it in another way?

 

[BOYLANATOR]

Length contraction.

I didn't even think about length contraction. This seems like the obvious solution.

 

[Dale]

Well surely not.

Don't forget that in a parallel light clock the "forward" half of the tick takes significantly longer than the "backward" half. If you work it out, it gives the wrong time unless there is length contraction.

 

[jartsa]

Let us calculate one example case.

Rest length of a parallel light clock = 1 light second
Velocity of the clock = 0.866 c (relativistic factor is 2)

Light travels from rear to front a distance of half light seconds at speed 0.134 c.
That takes 3.73 seconds.
Then light travels from front to rear a distance of half light seconds at speed 1.866 c
That takes 0.268 seconds.

Back and forth travel takes 3.998 seconds.

We expected it to take twice the time of the time that it takes when the clock is standing still, which is 2 seconds.

 

[ghwellsjr]

But at slower speeds, you would have to move them farther apart to maintain the same rate until finally, with no motion at all, they would be the same distance apart as the perpendicular version, wouldn't they?

I don't really follow this part. Is it possible to describe it in another way?

Don't you agree that if there was no motion, there would be no difference between the perpendicular and the parallel versions? And so the mirrors would be the same distance apart. Then as the speed of the motion increases, the mirrors in the parallel case will have to move closer together in order to maintain the same tick rate as the perpendicular case? In the limit, where the speed is almost as fast as light, the mirrors will have to be very close together because the shape of the triangle will be almost a straight line and if the mirrors were as far apart in the parallel case as they were in the perpendicular case (and by that I mean the distance apart along the direction of motion, which is zero) then it would take a very long time for the light to make the round trip.

 

[BOYLANATOR]

Thanks jartsa. It's now clear to me that I have not found a flaw in the theory haha

 

[Dale]

Let us calculate one example case.

Rest length of a parallel light clock = 1 light second
Velocity of the clock = 0.866 c (relativistic factor is 2)

Light travels from rear to front a distance of half light seconds at speed 0.134 c.
That takes 3.73 seconds.
Then light travels from front to rear a distance of half light seconds at speed 1.866 c
That takes 0.268 seconds.

If there were no length contraction then we would expect the forward trip to take 7.46 s and the backwards trip to take .54 s, for a round trip duration of 8 s.

But with the length contraction factor of 2 the forward trip actually takes 3.73 s and the backward trip actually takes 0.27 s, for a round trip duration of 4 s, as expected.

Including length contraction is essential. That is the geometric piece which is different for the parallel and perpendicular clocks that BOYLANATOR was asking about.