# Does light must be wave-like in Einstein mirror clock thought experiment?

1. Jul 27, 2010

### Izhaki

Hi,

In attempt to understand SR, a moving mirror clock is often given as part of a thought experiment, which leads to the dismissal of absolute time.

To save people reading, the short version of my question is this: This experiment assumes light is wave-like, right?

The long version of my question is this:

Just to make sure I understand the experiment correctly, here is my version of it:

Consider a glass tube with a torch on the top, pointing at a mirror at the bottom of the tube. Whenever the torch flashes, light moves toward the bottom mirror, reflects from it, and when it hits the torch again - a time tick has gone by.

If the tube is stationary with respect to an observer, the observer will agree with the tube on the tick time. However, if the tube is moving with respect to the observer, the tick will appear to her to take longer.

Now, to my knowledge, light is not affected by Newtonian momentum. That is, if a flying plane is releasing a tennis ball and a light beam downwards at the same time - the tennis ball path will be affected by the momentum of the plane, where the light will go straight down. Similarly, light from the sun is not affected by the suns motion in the milky way.

Based on this, consider that we replace the light torch, emitting hemispherical light, with a highly directional (line-like) laser beam. If the tube is moving fast enough, and the tube height is long enough, the light will never reach the bottom mirror - by the time it reaches this point in space the mirror has already moved.

The last paragraph was taking light as a particle-like phenomenon. I guess that you can solve this issue by thinking of light as a wave-like phenomenon, in which case, it will propagate like and expending sphere once omitted. Then, the light will never miss the moving mirror (as the mirror can't travel faster than light). Is this correct?

Thanks,
Izhaki

2. Jul 27, 2010

### NanakiXIII

I'm not sure about light being affected by Newtonian momentum, but what you're saying sounds wrong. Consider your scenario from the point of view of an observer moving with the tube. He would see the light moving diagonally away, instead of in the direction the laser is pointing, without any cause.

3. Jul 27, 2010

### Izhaki

Perhaps I'm confusing wave-like with high-divergence light, and particle-like with low-divergence light.

I'm not sure why the light moving diagonally away happens without any cause - the cause is that the observer is getting away from a fixed line in space on which light travels.

Consider the following: The tube is placed on a train, with the light source being low-divergence laser beam. If the laser flashes (turned on for a fraction of time) when the tube is right in front of the stationary observer - the observer will see the light falling down while the tube will keep on moving with the train.

Surely light is not affected by newtonian momentum, or it wouldn't travel exclusively in the speed of light, with all of Einstein theories out of the window...

4. Jul 27, 2010

### Staff: Mentor

This is incorrect. If the light reaches the mirror in one frame (where the tube is stationary), then it will reach the mirror in any frame. The direction of the light--but not its speed--will depend on the frame doing the observing.

5. Jul 27, 2010

### starthaus

No, this is false. As DocAl explained, if the light hits the mirror in one frame (the carriage) , it will hit the mirror in all frames moving inertially wrt the carriage.
To add to DocAl's explanation, in the carriage, the light moves vertivcally, so it makes an angle $$\pi/2$$ with the direction of motion.
In any other frame moving wrt the carriage at speed $$v$$ there is an effect called "relativistic aberration" (google it) that makes the light beam make an angle $$cos(\theta)=v/c$$ wrt the direction of motion. The larger the $$v$$, the smaller the angle, i.e. the light beam gets more inclined wrt the vertical and closer to the direction of motion, "reaching" in the direction of motion and producing the zig-zag pattern seen in the experiment.
At $$v=0$$ (inside the carriage) $$cos(\theta)=0$$, i.e. we are back to $$\theta=\pi/2$$

6. Jul 27, 2010

### Izhaki

OK, that solves it. Apologies for carrying on asking, but I really want to get this clear:

If a spaceship traveling half the speed of light shoots a laser beam downwards right as it passes above Barcelona. What frames are involved, and what each observer will see (the one in Barcelona and the one on the spaceship)?

If direction change depending on the frame observing, shouldn't the man in Barcelona see the beam traveling diagonally away and never hitting Barcelona?

In other words, if the spaceship wants to hit Barcelona, it needs to shoot the beam before it is above it? If in the moving tube experiment point A was when the laser flashes, and B when the light hits the bottom mirror, then A is like the point where the spaceship (analog to the tube laser) beams the light, and B is where Barcelona (analog to the bottom mirror) needs to be in order to be hit?

Thanks,
Izhaki

7. Jul 27, 2010

### Staff: Mentor

Right!

Right again!

8. Jul 27, 2010

### Izhaki

OK,

That has answered my question in full.

Thank you very much!