Please Explain to me this thought experiment

[Jewlian]

Suppose a rocket is moving away from Earth at 0.5c. The rocket is moving towards a beam of light. There are two clocks on the rocket placed 1m apart. Each clock stops ticking when the beam of light hits it. The speed of light is then calculated as d/t = 1/(t1-t2). What effects occur for the calculation to yield c instead of 1.5c , and what is going on on a more intuitive level?

 

[tiny-tim]

Hi Jewlian!

Tell us what you think, and then we'll comment!

 

[yuiop]

Also tell us how you intend to synchronise the clocks.

 

[GTOM]

Well I'm not him, but i would synchronise them on Earth, and i would except a measured value of 1.5 c / length contradiction.

 

[Goodison_Lad]

One way is to image that you are observing things from somewhere nearby to the speeding rocket (but is stationary with respect to the Earth.)

Suppose the spaceship flies past you from left to right. The astronauts will, hopefully, have synchronised their two clocks with each other - but they would be synchronised only in reference frames that are stationary with respect to the spaceship. Relativity tells us that the clocks would not appear to us to be synchronised – the leftmost (rear) clock would appear to be running ahead of the forward clock. However, the astronauts see nothing of the sort – to them, the clocks still appear to be synchronised.

(Another thing we’d notice is that the spaceship would appear very foreshortened. Because of this length contraction, to us, the light would take even less time to get from the front clock to the back clock. Again, the astronauts notice nothing unusual about the length of their ship.)

When the two (now stopped) clocks are compared with each other they will show a bigger difference in time than would have been the case had this relativistic asynchronisation not been happening.

In other words, the asynchronisation is of the just the right amount to make sure that the readings on the clocks tell the astronauts that the light took exactly the expected amount of time to get from front to back, giving a velocity of c. The amount of asynchronisation compensates precisely for both the rocket’s velocity toward the light source and its length contraction (as observed by us).

 

[darkhorror]

Suppose a rocket is moving away from Earth at 0.5c. The rocket is moving towards a beam of light. There are two clocks on the rocket placed 1m apart. Each clock stops ticking when the beam of light hits it. The speed of light is then calculated as d/t = 1/(t1-t2). What effects occur for the calculation to yield c instead of 1.5c , and what is going on on a more intuitive level?

the speed of light is c in all inertial frames of reference. The light is moving towards the rocket at c in the rocket's frame of reference. The light is moving towards the rocket at 1.5c in the Earth's frame of reference.