Conceptual SR question (2 cyclists)

[RoyalCat]

This is a conceptual question in special relativity.

Let's say we have 2 cyclists riding parallel to each other, separated by a distance D, at a constant velocity directed along the x axis, v.

Cyclist A has a laser, and he points it at cyclist B and presses the button so that a short pulse comes out. A pale red dot flickers on cyclist B's forehead, to no one's surprise.

However, looking at this from the frame at rest, rather than the cyclists' frame causes some confusion for me.

I understand that the laser beam simply travels at an angle, thus traversing a longer distance, and taking longer to do so. In the cyclists' frame, t'=D/c, in the rest frame, the time it takes the pulse to reach cyclist B is t=γt'

Now, the conceptual difficulty for me is the question of aim. In the cyclists' frame, A point directly towards B, perpendicular to their direction of travel. If so, then how does the laser beam in the rest frame follow an angled trajectory?

A photon-based approach makes things a bit simpler to follow, allowing the photons to have momentum along the direction of motion as they are emitted, but the simple light-pulse view gives me a headache.

I'd greatly appreciate a clarification of what's happening and a way to put the process together in my mind.
With thanks in advance,
Anatoli

 

[hikaru1221]

I don't quite get it. If that's the question of aim, then the aim of A is to have the laser pulse arriving at B, and that is satisfied in both frames.

I think we should be aware that A cannot perceive his motion. Instead, A can perceive the motion of a point C which is stick to the black line where A is "moving" on. See the attached picture. A wants the laser pulse to be perpendicular to the traveling direction of C in A's viewpoint, but that doesn't necessarily have to be what happens in C's viewpoint (I'm not sure if it's correct to call that "the relativity of space"). Anyway, what happens in BOTH frames is that A emits a laser pulse and then B receives the laser pulse, and that matches logic and our intuition. That's the aim of A.

How light travels has loose connection with A's aim. Light always travels in such a way that its speed in vacuum is always constant, but its direction has nothing to do with that. The laser pulse travels in the way that satisfies both A's aim and the invariance of c.

Anyway, what do I know? 2 cents from an amateur