Light Clock Confusion in Special Relativity

[subzero0137]

When students are first introduced to special relativity, the first thing they are taught is the derivation of the gamma factor and time-dilation, and it goes something like this:

Suppose there are 2 observers in space, let's call them Alice and Bob. Let's assume Alice is stationary from our perspective, and Bob, who is holding a light clock in his hands, is traveling past Alice at some finite speed. Since the speed of light is constant, the time taken for the light beam to bounce between the 2 mirrors is longer for Bob from Alice perspective...

But doesn't this thought experiment assume that light has mass, and therefore inertia? Because if light has no inertia, how can it travel diagonally (to match Bob's speed) from Alice point of view? If light is emitted in a direction perpendicular to the direction of motion of Bob, shouldn't the light beam go straight up, and miss the mirror that has moved ahead?

 

[A.T.]

If light is emitted in a direction perpendicular to the direction of motion of Bob, shouldn't the light beam go straight up, and miss the mirror that has moved ahead?

If the light hits the mirror in the rest frame of the clock, then it must hit the mirror in every other frame of reference.

 

[subzero0137]

If the light hits the mirror in the rest frame of the clock, then it must hit the mirror in every other frame of reference.

Is that to do with the 2nd postulate of SR, which states that the laws of physics shouldn't change in any inertial reference frame? But why assume this to be the case, especially since light has no mass and shouldn't be subject to Newton's 1st law ∴ it shouldn't be traveling along with the rocket?

I think the source of my confusion is the idea of massless particles having inertia.

 

[Bill_K]

If light is emitted in a direction perpendicular to the direction of motion of Bob, shouldn't the light beam go straight up, and miss the mirror that has moved ahead?

The direction of a light beam is also frame-dependent. This effect is called aberration. A light beam that is traveling straight up in Alice's frame will not travel straight up in Bob's frame.

 

[A.T.]

Is that to do with the 2nd postulate of SR, which states that the laws of physics shouldn't change in any inertial reference frame?

It is far more basic: SR is not a multiverse theory. Different frames must agree on the events that occur, they are merely allowed to assign different space & time coordinates to those events.

Assume it is a high power laser and replace the mirror with Bob himself as target. He can't be killed in his frame, but survive in Alice's frame. There is only one Bob.

 

[jtbell]

If the light hits the mirror in the rest frame of the clock, then it must hit the mirror in every other frame of reference.

Is that to do with the 2nd postulate of SR, which states that the laws of physics shouldn't change in any inertial reference frame?

It is far more basic: SR is not a multiverse theory. Different frames must agree on the events that occur, they are merely allowed to assign different space & time coordinates to those events.

Assume it is a high power laser and replace the mirror with Bob himself as target. He can't be killed in his frame, but survive in Alice's frame. There is only one Bob.

Or attach a bomb to the mirror, and set it up so that if light hits the mirror, the bomb explodes. All observers agree on whether the bomb explodes or not, at some point in time, although they probably disagree on when it happens because each has his own time coordinate.