Travelling at 0.5c or .43c? Unraveling the Mystery

[kaleidoscope]

A particle traveling at 0.5c for 1 second covers 1.3E8m (speed=.5*3E8 and gamma=.866) and not 1.5E8. The average speed was then 1.3E8 m/s = .43c and not .5c. What is going on here? Was it travelilng at 0.5c or at .43c?

 

[talk2glenn]

This is relativity.

The particle, from its perspective, travels .5*3e^8m in 1 sec. From your perspective, the particle travels the distance in more time (a lower average speed). Both the particle and the observer agree that it reached a point in space, and disagree on the time it took to get there.

The Lorentz factor (your gamma) tells you the degree of the relativistic effect.

 

[Dale]

A particle traveling at 0.5c for 1 second at its frame of reference covers 1.3E8m (speed=.5*3E8 and gamma=.866). The average speed was then 1.3E8 m/s = .43c and not .5c. What is going on here? Was it travelilng at 0.5c or at .43c? (Notice that all the calcualtions are done at the particles frame of reference).

By definition the particle's speed in the particle' frame of reference is 0. And yes, it is 0 in one frame and 0.5 c in another and 0.999 c in yet another. There is even a frame where it's speed is 0.43 c, but that is not the particle's frame.

 

[I_am_learning]

A particle traveling at 0.5c for 1 second covers 1.3E8m (speed=.5*3E8 and gamma=.866) and not 1.5E8. The average speed was then 1.3E8 m/s = .43c and not .5c. What is going on here? Was it travelilng at 0.5c or at .43c?

Suppose you are observing the particles motion over a road And you are stationary above the road. For you the particle covers 1.5E8m on the road in one second. But in the particles perspective, the road moves past a distance of 1.5E8 * 0.866 = 1.3E8m in a time of 1 * 0.866 = 0.866 seconds. So, the particle concludes, the road is moving at 0.5c.

So, Neither the particle nor the road sees any velocity at 0.43c.

BTW 0.866 is 1/gamma. From what I remember, gamma is always greater than 1.