# B How can the measurement of c be measured from Earth?

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1. Nov 1, 2016

### jahrudz

I understand that c is the "ultimate speed" and that it is a result of the fundamental constant, the permeability of free space. But if this is a constant only to a "stationary" frame of reference, how can we accurately measure it from Earth? Since Earth is moving relative to a supposed "fixed" point in the Universe, shouldn't our measurement of the speed of light be off somehow? And is the difference between this measurement and the derived speed of light related to the relative speed of the Earth?

2. Nov 1, 2016

### Orodruin

Staff Emeritus
There is no such point. Not in special relativity nor in classical mechanics.

3. Nov 1, 2016

### jahrudz

Then how can we know if our measurement of light is off from the "true" speed of light since we're measuring from a moving reference point, Earth?

4. Nov 1, 2016

### Staff: Mentor

Google for "Michelson-Morley experiment", and also check the sticky thread on experimental support for relativity at the top of this subforum: https://www.physicsforums.com/threads/faq-experimental-basis-of-special-relativity.229034/

The speed of light is the same for all observers regardless of their speed, so we don't need a "really stationary" reference point to measure it.

The Michelson-Morley experiment confirms this by showing that the motion of the earth does not affect the measured speed of light. In this experiment we compare the speed of light in a direction crosswise to the direction of the earth's motion with the speed of light in the direction of the earth's motion, ad it comes out the same both ways.

5. Nov 1, 2016

### Workingstiff

I think the point that confuses people is that the speed of light is distance divided by time. As your velocity increases, time slows down, so one second is only the same amount of time to those travelling at the same velocity. The general assumption is that time is a constant and one second is one second for everyone. Gravity also impacts time with higher gravity slowing time. The light from the sun takes about 8.5 minutes to reach us. However if you left the sun and traveled at the speed of light to earth you would realize almost no time had passed for your journey, you would arrive almost instantaneously.

6. Nov 1, 2016

### Mister T

We can't. Which is why you were asked to look at the Michealson-Morley experiment. It was done in 1889, but there have been been lots of others both like it and unlike it, all searching for the same answer you are searching for. The answer to the question, How fast are we really moving?

Earth's motion relative to the sun is pretty small compared to a light beam's motion. About one part in 10 thousand. And yet these experiments are sensitive enough to easily detect that small of a difference. Yet no such difference has ever been observed. Hence the explanation put forth in 1905 for why we'll never detect a difference. The speed of light is absolute, not relative. It makes no difference how fast we move, we will always measure the same speed for a light beam.

So, to answer your question, one way is to take the distance traveled by a light beam and divide it by the time spent travelling. That will give you the "true" speed of light. As for the "true" speed of Earth, that doesn't exist. There is nothing "truly" at rest for us to measure Earth's speed relative to. As long as the motion is along a straight line and is constant in magnitude, it's equivalent to a state of rest. That's known as the Principle of Relativity. It's the foundation for our understanding of how moving clocks behave and without it we wouldn't have a GPS. Or a lot of other things, either.