speed of light

[Josh5v]

If two space travelers are traveling in opposite directions at 60% the speed of light, is the relative speed of one to the other 120% of the speed of light.

 

I know there is a problem with this statement but I don't know what it is.

[timo]

There is actually no problem with this statement. However, you are used to relative velocities being constant when you switch to a moving frame: If you see two cars approaching each other with 50 km/h in opposite directions their relative velocity is 100 km/h. This holds true in relativity. But you are used to think even more, namely that then the cars' drivers see the other car approaching with a velocity of 100 km/h, too. That simple transferring of relative velocities to other observers does not hold in relativity, anymore.

 

Oh, and welcome to sfn. According to my system clock and your user profile you are about to register here tomorrow .

Edited December 14, 2009 by timo

[iNow]

Josh - If you're into math, it's explained here:

 

http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

In non-relativistic mechanics the velocities are simply added and the answer is that A is moving with a velocity w = u+v relative to C. But in special relativity the velocities must be combined using [a different] formula

 

<...>

 

Naively the relativistic formula for adding velocities does not seem to make sense. This is due to a misunderstanding of the question which can easily be confused with the following one: Suppose the object B above is an experimenter who has set up a reference frame consisting of a marked ruler with clocks positioned at measured intervals along it. He has synchronised the clocks carefully by sending light signals along the line taking into account the time taken for the signals to travel the measured distances. He now observes the objects A and C which he sees coming towards him from opposite directions. By watching the times they pass the clocks at measured distances he can calculate the speeds they are moving towards him. Sure enough he finds that A is moving at a speed v and C is moving at speed u. What will B observe as the speed at which the two objects are coming together? It is not difficult to see that the answer must be u+v whether or not the problem is treated relativistically. In this sense velocities add according to ordinary vector addition.

 

But that was a different question from the one asked before. Originally we wanted to know the speed of C as measured relative to A not the speed at which B observes them moving together. This is different because the rulers and clocks set up by B do not measure distances and times correctly in the reference from of A where the clocks do not even show the same time. To go from the reference frame of A to the reference frame of B you need to apply a Lorentz transformation on co-ordinates

 

<...>

 

A feature of the formula is that if you combine two velocities less than the speed of light you always get a result which is still less than the speed of light. Therefore no amount of combining velocities can take you beyond light speed.

 

 

 

http://en.wikipedia.org/wiki/Velocity-addition_formula

According to the theory of special relativity, the frame of the ship has a different clock rate and distance measure, and the notion of simultaneity in the direction of motion is altered, so the addition law for velocities is changed. This change isn't noticeable at low velocities but as the velocity increases towards the speed of light it becomes important. The addition law is also called a composition law for velocities.

[ajb]

If two space travelers are traveling in opposite directions at 60% the speed of light, is the relative speed of one to the other 120% of the speed of light.

 

What you have said is acceptable, but be aware that the 120% the speed of light is not a speed that can be measured by an inertial observer. So it is not really a relative speed.

 

To find out what an inertial observer would measure, you need the velocity addition formula already given.

[Josh5v]

I think I understand your explanation. It certainly does not follow common sense but then what in relativity does.

 

Thanks for your help.