Elementary question - Special relativity

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Elementary question -- Special relativity

Hi, I have a really elementary question on the theory of special relativity.
Here is an excerpt from the website einstein-online.info that confused me:

"For light, it would be natural to expect that one could similarly add and subtract velocities. Suppose that I measure a particular light signal's speed, and find the usual value of 299,792.458 kilometers (186,000 miles) per second. If I see a fast spaceship chase right after that signal, moving at half the speed of light (c/2), I would expect that an observer on that spaceship would measure the speed of my light signal at merely c - c/2 = c/2, half the value that I measured.

Not so, according to special relativity! Simply subtracting speeds would only give the correct answer if the observer on that space-ship measured space and time, distance and duration in the same way that I do. As we have seen on the previous page, that's not the case. From my point of view, for instance, the measuring rods on the speeding spaceship are shorter than my own, and its clocks run more slowly than mine. Taken together, all of these relativistic effects combine in precisely the right way to result in a surprising phenomenon: Even from the point of view of an observer on the speeding spaceship, my light signal moves with exactly the same speed, c=299,792.458 kilometers per second."

-- http://www.einstein-online.info/elementary/specialRT/speed_of_light

The question is: How do we know that the light signal moves at the absolute speed? What proof is there that the person and the spaceship are seeing light traveling at the same speed and not a relative one? I'm really confused when I think of the cars and how they move at relative speeds

 

[Passionflower]

The question is: How do we know that the light signal moves at the absolute speed? What proof is there that the person and the spaceship are seeing light traveling at the same speed and not a relative one? I'm really confused when I think of the cars and how they move at relative speeds

We only know that the roundtrip speed, or average speed, of light is constant, the one way speed of light depends on how you synchronize the two clocks, so there is no one correct answer. Of course in order to measure a speed you need some time and some distance.

How do we know the roundtrip speed is c, well we measured it many times and also with relative movement. Take a look at the article on Wikipedia on the speed of light here to get some info: http://en.wikipedia.org/wiki/Speed_of_light

 

[bcrowell]

How do we know that the light signal moves at the absolute speed?

The Michelson-Morley experiment.

What proof is there that the person and the spaceship are seeing light traveling at the same speed and not a relative one?

It *is* a relative speed. It just happens to be the same speed relative to everything. Take a look at the relativistic equation for adding velocities: http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_theory_of_relativity In the special case where one of the velocities equals c, the combined velocity is also c.