Understanding Light's Motion in a Moving Clock

[member 529879]

When light is moving up and down in a light clock, it has no horizontal speed to an observer at rest relative to it. If that light clock starts moving, the light must be moving with the clock because at rest, the light and clock both have no horizontal speed. How does the light convert its vertical speed into horizontal speed as the clock moves?

 

[PeroK]

How does the light convert its vertical speed into horizontal speed as the clock moves?

It doesn't. Think about someone in a vehicle (moving relative to you) throwing a ball up and down. You see the ball going up and down at an angle, but the person throwing the ball sees it going straight up and down.

The horizontal motion of the ball comes from the relative motion of the observers.

 

[member 529879]

But with a ball in a car, the speed of the car is added to the ball causing that to happen for an observer watching the car go by, where as the speed of light is constant.

 

[PeroK]

But with a ball in a car, the speed of the car is added to the ball causing that to happen for an observer watching the car go by, where as the speed of light is constant.

Correct. So, what's your question?

 

[member 529879]

The reason that the ball moves with the car is because the horizontal speed of the car is added to the ball. You can't just add the horizontal speed of the clock to the light because then it would move faster than light. When the clock moves the vertical speed is converted to horizontal speed. I'm confused why in the reference frame of an observer watching the clock move, the light doesn't just move vertically at the speed of light not with the clock.

 

[PeroK]

The reason that the ball moves with the car is because the horizontal speed of the car is added to the ball. You can't just add the horizontal speed of the clock to the light because then it would move faster than light. When the clock moves the vertical speed is converted to horizontal speed. I'm confused why in the reference frame of an observer watching the clock move, the light doesn't just move vertically at the speed of light not with the clock.

So, something has got to give. If we assume that transverse distance (distance up and down) is the same for both observers, then the variable in the equation is time. So, if the speed of light is the same for both observers, then the time elapsed cannot be the same for both observers.

 

[ghwellsjr]

When light is moving up and down in a light clock, it has no horizontal speed to an observer at rest relative to it. If that light clock starts moving, the light must be moving with the clock because at rest, the light and clock both have no horizontal speed. How does the light convert its vertical speed into horizontal speed as the clock moves?

If a light clock accelerates, as you described, then the light that was hitting both mirrors before the acceleration will not continue to hit both mirrors during or after the acceleration and the light clock will stop working.

 

[PeroK]

The reason that the ball moves with the car is because the horizontal speed of the car is added to the ball. You can't just add the horizontal speed of the clock to the light because then it would move faster than light. When the clock moves the vertical speed is converted to horizontal speed. I'm confused why in the reference frame of an observer watching the clock move, the light doesn't just move vertically at the speed of light not with the clock.

Note that there is a physical reality underpinning this. Either the light hits both mirrors for both observers or neither. One observer can't see the beam of light go straight up while the other (moving) observer sees it go straight up, hit the mirror, and reflect.

So, if the moving observer sees the light go straight up, the stationary observer must see it go at an angle. That's the same for light and for the ball.

 

[A.T.]

If a light clock accelerates, as you described, then the light that was hitting both mirrors before the acceleration will not continue to hit both mirrors during or after the acceleration and the light clock will stop working.

To deal with this problem, one can replace the mirrors with detectors & omnidirectional flash lights. Now the signal can reach the other detector even with acceleration.

 

[WhatIsGravity]

http://www.nist.gov/pml/div688/grp50/primary-frequency-standards.cfm

 

[phyti]

When light is moving up and down in a light clock, it has no horizontal speed to an observer at rest relative to it. If that light clock starts moving, the light must be moving with the clock because at rest, the light and clock both have no horizontal speed. How does the light convert its vertical speed into horizontal speed as the clock moves?

If the 1st postulate of SR is true, then the clock should work at any speed, since it is already working at a random speed.
research "solar sail" on wikipedia.
Light has momentum which provides a horizontal velocity component, after it has accelerated. Since it is matched by clock/observer speed, the observer is only aware of the vertical light component, which explains why the clock runs slower than the identical clock at rest.

 

[PeterDonis]

with a ball in a car, the speed of the car is added to the ball causing that to happen for an observer watching the car go by, where as the speed of light is constant.

Velocities don't add in relativity the way they do in Newtonian physics. Yes, the speed of the car is "added" to the ball, but not linearly; it "adds" in such a way that the speed of light "added" to any speed slower than light, still gives the speed of light. See here:

http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_theory_of_relativity

 

[bahamagreen]

This question usually comes from reading the translated German to English writings of Einstein, or other writings that use the same translated words.

The German word for simple "speed" was translated to English as "velocity" in the informal sense of just "speed"... the problem is that in technical English, velocity is a vector with a direction.

When you read that "the velocity of light is independent of the motion of the source", that just means its speed. If you assume that meant that the direction of the light was independent of the source motion, then yes; you might very well wonder why the light would not appear to emit from the lower moving mirror and simply move straight up from that static fixed coordinate, and miss the upper mirror that would have moved out of the way by the time the light reached where the upper mirror was when the light was emitted..

 

[harrylin]

This question usually comes from reading the translated German to English writings of Einstein, or other writings that use the same translated words.

The German word for simple "speed" was translated to English as "velocity" in the informal sense of just "speed"... the problem is that in technical English, velocity is a vector with a direction.

It's not an "informal" translation: different from German, in English one may choose "speed" for magnitude, and because of that, more and more physics books choose to use "velocity" as a label for "speed + direction" for that book.

When you read that "the velocity of light is independent of the motion of the source", that just means its speed. If you assume that meant that the direction of the light was independent of the source motion, then yes; you might very well wonder why the light would not appear to emit from the lower moving mirror and simply move straight up from that static fixed coordinate, and miss the upper mirror that would have moved out of the way by the time the light reached where the upper mirror was when the light was emitted..

Probably that was a typo: the direction of light is dependent on the motion of the source - see also past threads such as https://www.physicsforums.com/threa...irection-and-wave-source.735118/#post-4642866

However, as ghwellsjr already noticed, that was not the question. ;)