Question about relativity example

[ivans]

Hello,

I apologize in advance for what is probably a boneheaded question, but I'm just a little bit confused.

I just started reading The Elegant Universe and in the chapter on the theory of relativity, the author uses an example of a photon-based clock to illustrate how the perception of time changes based on the observer. In the example (which I think I also remember from another book on general relativity), there is a clock made of a photon that travels back and forth between two plates. The clock is moving relative to an observer, and to illustrate the distortion in time, the author states that from the observer's point of view the photon would have to travel sideways to reach the other plate, therefore taking longer to get there than it would in a straight path.

What I'm confused about is that just before this example, the author gave another example where a light traveling to both sides of a table on a moving train would get to one side faster than the other because the speed of light is always constant and the side moving along with the train would get to the light faster than the side moving away from the light because the movement of the train has no effect on the light.
So what's confusing is why the photon in the clock example would be traveling sideways if the movement of the clock has no effect on it.

Once again, I apologize for asking something like this when I barely read anything of the book, but there is no explanation of it and I'm curious about it.

 

[HallsofIvy]

Hello,

I apologize in advance for what is probably a boneheaded question, but I'm just a little bit confused.

I just started reading The Elegant Universe and in the chapter on the theory of relativity, the author uses an example of a photon-based clock to illustrate how the perception of time changes based on the observer. In the example (which I think I also remember from another book on general relativity), there is a clock made of a photon that travels back and forth between two plates. The clock is moving relative to an observer, and to illustrate the distortion in time, the author states that from the observer's point of view the photon would have to travel sideways to reach the other plate, therefore taking longer to get there than it would in a straight path.

What I'm confused about is that just before this example, the author gave another example where a light traveling to both sides of a table on a moving train would get to one side faster than the other because the speed of light is always constant and the side moving along with the train would get to the light faster than the side moving away from the light because the movement of the train has no effect on the light.
So what's confusing is why the photon in the clock example would be traveling sideways if the movement of the clock has no effect on it.

It is not that the movement of the clock is causing the photon to be "travelling sideways". The fact that the photon keeps hitting the same two points on the mirrors means that the beam of light must have been aimed slightly sideways.

Once again, I apologize for asking something like this when I barely read anything of the book, but there is no explanation of it and I'm curious about it.

 

[yuiop]

So what's confusing is why the photon in the clock example would be traveling sideways if the movement of the clock has no effect on it.

The movement of the clock has no effect on the speed of the emitted photon but it does have an effect on the direction that the photon is emitted in.

 

[ivans]

So, wait... does that mean that the photon was initially fired to match the movement of the clock? If it wasn't, I'm still confused as to why, if it was fired directly upward, it would travel along with the clock's body.

(I know that this is an extremely theoretical example, but it's confusing me nonetheless)

 

[Ich]

So, wait... does that mean that the photon was initially fired to match the movement of the clock?

It was aimed directly upward in the clock's frame. That looks different in other frames.

 

[Al68]

So what's confusing is why the photon in the clock example would be traveling sideways if the movement of the clock has no effect on it.

As an analogy, if I were to throw a ball straight up and catch it, the ball will travel a straight line and return to its starting point in my rest frame, but it's trajectory will be at an angle in a reference frame in relative motion to me, and it's trajectory will look like an upside down vee.

So if I were on a moving train when I tossed the ball straight up, it will move at an angle as seen from the ground.

The photon in a light clock does the same thing.

 

[ivans]

Sure I understand that, I was just confused because I thought that the author stated that light was not affected that way.

 

[Saw]

I think we need to explain Ivans a little more, because he has raised a very common concern.

The movement of the clock has no effect on the speed of the emitted photon but it does have an effect on the direction that the photon is emitted in.

Yes, but that is a way of describing what happens, it doesn’t say why it happens.

The fact that the photon keeps hitting the same two points on the mirrors means that the beam of light must have been aimed slightly sideways.

It was aimed directly upward in the clock's frame. That looks different in other frames.

Take two tubes of identical length and place them on platforms A and B moving wrt each other, at right angles to the direction of relative motion. When the bottoms of the tubes are perfectly lined up, the tops are also aligned. Right then light pulses are sent upward inside both tubes by the corresponding laser guns. At this instant, the bottoms of the tubes (and the exit half-silvered mirrors of the laser guns) are aiming at their respective targets in perfectly parallel directions. Why do the trajectories of the pulses diverge afterwards?

As an analogy, if I were to throw a ball straight up and catch it, the ball will travel a straight line and return to its starting point in my rest frame, but it's trajectory will be at an angle in a reference frame in relative motion to me, and it's trajectory will look like an upside down vee.

Yes, the same happens to the light pulses. In frame A, its light A follows a vertical trajectory inside its tube A, but light B follows a diagonal path. In frame B, its light B follows a vertical trajectory inside its tube B, but light A follows a diagonal path. Forcefully, once each pulse hits its respective target, those will be the pictures that the two frames will paint in their corresponding coordinate systems. If that happens, you’ll paint it that way. But the question is precisely whether that will happen or not and why.

In the case of a massive ball, there is a reason for that. As observed by me, before you threw the ball, it was traveling with you by inertia in a certain direction and with a certain speed wrt me. When you apply a force onto it, you give it a certain direction and speed wrt you that, in my frame, combine with your original direction and speed wrt me. Ok, in SR the combination of speeds follows the relativistic formula, not a simple addition, but it is still a combination of states of motions, including both direction and speed. The two things go together with balls. Why can your massless light be accelerated wrt me in terms of direction, although not in terms of speed?

Before DaleSpam warns that in physics you don’t care about why-questions, I’d say I’d be satisfied with the following explanation:

It has to do with the fact that light is created in an instrument that reproduces, at a smaller scale, the trajectory that it should follow afterwards, in the outer world (in the clock or the tube). Photons are created initially in random directions but only those that follow the line between the two extremes of the instrument succeed in coming out through the hole at the exit. Hence they maintain outside the trajectory that they followed inside, the successful trajectory, one enabling them to hit the target again. In particular, lasers, instead of relying on luck, are good at producing many photons with the right trajectory: they generate very little diverging beams that follow a thing straight line because their mechanism favours that photons bounce between a bottom and top mirror and create by stimulated emission new photons that acquire the same direction.

So, in the end, yes, as some posters said, the photon is “aimed at” the target, but it needs to be explained how.