Light speed barrier / closing speed

[Mojo-electro]

This is something that has always bugged me about relativity... I must be missing something...

Lets say you have a space station sitting stationary out in space... a spaceship approaches it from one side at .75c...another ship approaches the station from the other side, also at .75c, still no laws of physics violated yet that I can think of... The closing speed of the 2 ships relative to each other is now 1.5c (unless I am missing something)... the 2nd ship turns on it's headlights, what would the the first ship see?

Given the invariance of the speed of light, it seems that the light from the other ship would approach at c (which, as is my understanding, it would in any reference frame) but the ship itself is approaching at 1.5c...

This leads me to something I have never understood fully... according to relativity, all descriptions of motion only make sense in terms of motion relative to some other frame of reference... yet there is an absolute speed limit, the speed of light... "nothing can move faster than the speed of light"... nothing can movine faster than light relative to what exactly? Can 2 spaceships not approach each other at faster than c? If so, than can c be exceded in some reference frames?

Is there really a state of absolute rest relative the the background universe.. is this the reference frame I am missing?

 

[Doc Al]

Lets say you have a space station sitting stationary out in space... a spaceship approaches it from one side at .75c...another ship approaches the station from the other side, also at .75c, still no laws of physics violated yet that I can think of... The closing speed of the 2 ships relative to each other is now 1.5c (unless I am missing something)...

Right. But that closing speed is according to the space station. It is not the relative speed of the spaceships.

the 2nd ship turns on it's headlights, what would the the first ship see?

Light coming at it at its usual speed.

Given the invariance of the speed of light, it seems that the light from the other ship would approach at c (which, as is my understanding, it would in any reference frame) but the ship itself is approaching at 1.5c...

From the frame of spaceship A, spaceship B is not approaching at 1.5c. The relative speed--given by the relativistic addition of velocities formula--is only 0.96c.

 

[Mojo-electro]

Right. But that closing speed is according to the space station. It is not the relative speed of the spaceships.

Light coming at it at its usual speed.


From the frame of spaceship A, spaceship B is not approaching at 1.5c. The relative speed--given by the relativistic addition of velocities formula--is only 0.96c.

Interesting.. thanks!.. so would it be correct to say that an observer at the station would see ship B beat it's own light to ship A, but the reverse is true as seen by the pilot of ship A? I'll have to research the addition of velocities a bit more...

 

[Doc Al]

so would it be correct to say that an observer at the station would see ship B beat it's own light to ship A,

No, why would you think that? An observer at the station sees ship B traveling at 0.75c. The 'closing speed' is not really the speed of anything, it's just the calculated rate at which the two ships close the distance between themselves according to the station frame. The 'closing speed' of the ships is 1.5c, but the 'closing speed' of ship A and the light from ship B is 0.75c + c = 1.75c. The light wins the race no matter how you look at it.

I'll have to research the addition of velocities a bit more...

You'll find many threads on that topic.

 

[Doc Al]

A few links to explore:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html"

http://www.edu-observatory.org/physics-faq/Relativity/SR/velocity.html"