Is the speed of light really constant?

[Goliatbagge]

Imagine this race.

A beam of light is emitted from a planet (point A). Of course this beam will travel in the speed of light relative to the planet until it reaches point B. Starting at the same time as the beam, a spaceship travel from point A to point B (its speed is arbitrary). The speed of this light relative to the spaceship cannot be c? Otherwise the light would come to point B at different times? Doesn't this interfere with Special Relativity claiming that light has a constant speed (c) relative to all observers?

Where do I make the wrong assumptions?

 

[Ich]

Imagine this race.

A beam of light is emitted from a planet (point A). Of course this beam will travel in the speed of light relative to the planet until it reaches point B. Starting at the same time as the beam, a spaceship travel from point A to point B (its speed is arbitrary). The speed of this light relative to the spaceship cannot be c? Otherwise the light would come to point B at different times? Doesn't this interfere with Special Relativity claiming that light has a constant speed (c) relative to all observers?

Where do I make the wrong assumptions?

You assume that the time of the light beam's arrival could not be different when jugded by the rocket's clocks. But it is.

 

[neutrino]

Assuming the planets are at rest with respect to each other, then certainly the light would take a shorter time to reach planet B as seen from the spaceship. But that is due to the distance between the planets as measured from the spaceship.

If radar measurements from planet A suggest that planet B is at a distance L_o away, then the spaceship observer would measure a distance of {L_o}\sqrt{1-\frac{v^2}{c^2}} between them.

 

[Goliatbagge]

Thanks for your answers! I totally forgot Lorentz' length contraction. I get what you mean.

So here is a follow-up question. At point B, we have a bomb that detonates when struck by a photon. From the spaceship observer's perspective the bomb will detonate before the photon from Planet A:s perspective has reached point B. What will happen to this photon? Or do I make the same mistake again? Does it have to do with the light cones?

Sorry, if I bother you, maybe I should read more. But I like discussing...

 

[neutrino]

So here is a follow-up question. At point B, we have a bomb that detonates when struck by a photon. From the spaceship observer's perspective the bomb will detonate before the photon from Planet A:s perspective has reached point B. What will happen to this photon? Or do I make the same mistake again? Does it have to do with the light cones?

Events are the same for all inertial observers, in the sense that both the planet observer and the one on the spaceship will see a photon impinge the detector on the bomb, which in turn will trigger an explosion. They agree on the things that happen, it's just their space and time coordinates they attribute to those events do not always agree.

If you assume that a photon is emitted when the origins of the frames coincide and t = t' = 0. Then the planet observer's coordinates of the explosion are (L_o/c, L_o). Now it's simple algebra to find out the coordinates of the same event with respect to the spaceship observer using Lorentz transformation. You can also do this with spacetime diagrams, if you find them easier.

 

[Ich]

At point B, we have a bomb that detonates when struck by a photon. From the spaceship observer's perspective the bomb will detonate before the photon from Planet A:s perspective has reached point B. What will happen to this photon?

What photon from Planet A's perspective? There is only one photon, one bomb, one reality: photon hits, bomb explodes.
It's just that this happened at, say, 14:00 from planet A's perspective, and at 13:15 from the rocket's perspective.

 

[Goliatbagge]

I get fooled by the time dilation. It's just hard to imagine that an event (e.g. an explosion) in one perspective can take place "before" it happened in another perspective. It "feels" like you can prevent something that already took place in another perspective. I know this reasoning is wrong. Maybe I can draw parallells to thunder...

 

[jtbell]

If event A could cause event B, that is, if it is possible to send a signal from event A to event B at a speed less than or equal to c, then event A precedes event B in all inertial reference frames.

However, if event A cannot cause event B, that is, if a signal from A to B would have to travel faster than c, then it doesn't make any difference which event comes first. In this case, A precedes B in some inertial reference frames but B precedes A in other inertial reference frames.