Is the Location of Light relative due to its speed being constant

[Sicktoaster]

Sorry if this turns out to be a colossally stupid question. I'm a newbie.

But since light has a constant speed in all inertial frames wouldn't that mean where it would end up would have to be relative?

A famous example of relativity for things in inertial frames of reference other than light is throwing a ball out of a car. To someone on the side of the road the ball will appear to go faster than it would from the perspective of a person in the car.

Yet as the ball travels the ball lands will always be exactly the same location for any given amount of elapsed time since it is emitted.

Replace the ball with a photon and now it travels at the same speed regardless of the observer. Does this mean that the location that the photon at any given point of elapsed time after it is emitted is relative?

If not, if the photon post-emission is still in the same exact place relative to either observer what accounts for this?

 

[Doc Al]

Replace the ball with a photon and now it travels at the same speed regardless of the observer. Does this mean that the location that the photon at any given point of elapsed time after it is emitted is relative?

Yes. Time and distance are relative (frame-dependent) in just the right ways so that everyone measures the same speed for that photon.

 

[Nugatory]

Just as with the ball, the path of the light signal through space-time is invariant; all observers agree about which points in space-time the light signal passes through, and they all agree that after an interval of time $\Delta{t}$ has passed since the emission of the light, the light will have traveled a distance $c\Delta{t}$ (this is just distance equals speed times time).

Where you're getting in trouble is when you say "for any given amount of elapsed time"; because the observers moving relative to one another see time passing at different rates, they all have a different notion of elapsed time. Thus, there is no such thing as a "given amount of elapsed time" unless you specify which observer's time you're using - and even then the amount of elapsed time is specific to that observer.