# Constancy of c - second postulate

1. Jan 30, 2012

### mangaroosh

I'm trying to get a better handle on the second postulate of relativity.

I've read that Einstein adopted it because Maxwell's equations appeared to suggest that this was the case. I just read the below quote in another thread

The speed of light is measured, or defined, as 299792458 m/s; but the 's', or "the second" in that measurement is defined in terms of the oscillations of a caesium atom, in an atomic clock, at rest relative to the earth. Does this not mean then, that the speed of light is, by definition, relative to a clock at rest on earth?

I'm also, wondering, how is the [assumption of the] second postulate actually tested?

2. Jan 30, 2012

Einstein's second postulate is that the speed of light is a constant for all frames of reference. This means no matter where you are in the universe, you will always measure the speed of light to be 299792458 m/s. If I was to travel in a rocket at 0.5c away from the earth, I will still measure the speed of light to be 299792458 m/s.

3. Jan 30, 2012

### mathfeel

Carry your atomic clock and meter stick to a spaceship that's chasing the light at any speed (subluminal, of course). You will still measure it to that value.

4. Jan 30, 2012

### ghwellsjr

The value of the speed of light, 299792458 m/s, used to be determined in a round-trip measurement involving a single timing device at one end of a measuring rod with a reflector at the other end, but since the value always came out the same, it has been defined to be an absolute constant of nature and is now used to define the length of a meter along with the definition of the second. So if you use the oscillations of a caesium atom as your timing device, then you can now measure the length of your rod in the same experiment that used to measure the round-trip speed of light.

What turns out to be relative is the definition of the second. If we compare the seconds produced by different atomic clocks at different altitudes on the earth, we find that they do not track. So this means that the definition of a meter is also relative since the definition of the speed of light is defined to be constant.
The second postulate states that the propagation of light, that is, the one-way speed of light, is equal to the value of the two-way speed of light. What this is really concerned with is knowing that the time that it takes for the light to traverse the distance from our timing device to the reflector is exactly equal to the return time from the reflector back to our timing device. This would require that we have a second timing device located at the reflector that has the same "time" on it as the first timing device. Einstein stated that we we need to define the time on this second clock by asserting that those two time intervals are equal and that is what is second postulate does. We cannot then turn around and say that we have some way to measure that those two times are equal or we will negate everything that Einstein said.

5. Jan 30, 2012

### Staff: Mentor

Tests of Einstein's two postulates

6. Jan 30, 2012

### mangaroosh

What kind of a clock was used to measure the speed in the first instance? Presumably it was a clock at rest relative to the earth also, which would have the same implications, no?

Also, in measuring the round trip speed, is there the possibility that the speed was higher in one direction than the other?

Does that not just mean that the clock which ticks slower (or faster as the case may be) doesn't actually measure "the second", but either a longer or shorter unit; because the second is defined by the oscillations of a specific atomic clock, at a certain altitude?

Apologies, to the untrained eye that appears to be assuming the conclusion, but I presume there is something I'm missing.

7. Jan 30, 2012

### mangaroosh

thanks jtbell

Just having a look at those experiments. Do they all invoke length contraction and/or time dilation, or just some if them?

8. Jan 30, 2012

### ghwellsjr

Notice that I didn't say a clock was used to measure the round-trip speed of light, I said a timing device which is much broader. Clocks were no where near accurate or precise enough to make this measurement almost two hundred years ago. What they did use was a rotating device that would essentially chop the light at the source and chop the returned reflection and then they would vary the speed of the device so that the light that got chopped by one blade or mirror face would let the light through on the next one. This would allow them to multiply the resolution of the time measurement by seeing how long it took the rotating device to spin a very large number of times. They also used distances of several miles to increase the resolution. You can read about some of these early measurements done in the middle of the nineteenth century here:

http://en.wikipedia.org/wiki/Fizeau–Foucault_apparatus
Now this is a loaded question.

From the time of those early measurements up until the time of Maxwell's equations, I would guess the scientists would say no, mainly because they had no reason to suppose otherwise.

But between the time of Maxwell's equations which suggested that light traveled in a medium and the time of Einstein when he showed that this did not have to be the case, scientists would answer your question by saying that light would travel at a constant speed relative to the medium and if you happened to be stationary in that medium, then the two speeds would be equal but there was very little chance of that happening since the earth's surface was constantly changing its velocity through this presumed medium. So they would say yes, the two times would not be equal and therefore the calculated speed of light would be different, however, they wouldn't think that the speed of light was actually different, they would recognize this as the normal kind of apparent speed difference that you get with any motion through a medium.

But they had another problem, they still didn't have clocks precise to be used in such a measurement but that didn't stop them because some very smart scientists figured out that since the earth was changing direction daily predominately only along the direction of the equator, they could compare the difference in the round-trip measurement of the speed of light along the direction of the poles of the earth to the round-trip measurement of the speed of light along the direction of the equator. They didn't have to know what the actual speed of light was, just that it would show a difference in the different directions at different times of the day. But when they did the experiment, it acted just like they were stationary in the ether and they couldn't determine the answer to your question even though they insisted that the answer was yes.

So to explain how this could happen, they came up with the idea that the lengths of their apparatus in the two directions were changing to make the differences disappear. They also concluded that clocks would slow down as they moved through the ether. Thus, they came up with a scheme to validate their answer of yes.

Now when Einstein came along, he said that the answer to your question was impossible to determine. It doesn't have an answer, not that the answer is either yes or no. He said that until we make up an answer, there will never be an answer. So he said let's just make the answer be no. That seemed impossible but he showed the way. You can read about it in his 1905 paper introducing Special Relativity.
You're right, these atomic clocks are not measuring "the second" as previously defined, which was such that there were exactly 86400 seconds in the average day determined by the rotation of the earth. But since the rotation of the earth is slowing down, that means the definition of a second was getting longer. Would you rather go back to the previous definition?
You're not missing anything, we are assuming the conclusion. According to Einstein, if we want a conclusion, we have to provide our own because nature won't reveal one to us.

9. Jan 31, 2012

### mangaroosh

Thanks gh, I'll check that out.

You mention that they varied the speed of the device; presumably this speed would have been defined in terms of a clock at rest relative to the earth, which, by extension, would have the same implication, no?

Could the experiments [along the equator and at the poles] not be explained by the possibility that the speed of light is constant with respect to it's source; given the negligible speed of the rotation of the earth compared to the speed of light, we wouldn't expect there to be any difference in the speeds, would we?

We might have our wires crossed on this:

The point was that the definition of a meter may not necessarily be relative; it would only be relative if we assume that the clocks tick at the same rate in their own reference frames; alternatively, a slower ticking clock might count a longer interval than "the second" in its own reference frame as well as from the perspective of the other reference frame; this would mean that "a meter" would not actually be measured in the reference frame of the slower ticking clock but a length longer than a meter.

Does this mean that there are no real tests of the second postulate?

10. Jan 31, 2012

### ghwellsjr

That is correct. But the change in the clock rate due to altitude is so small that they could never detect that difference with any clock they had at the time.
I probably should have said along the east-west orientation compared to the north-south orientation because the experiment was done in Cleveland Ohio so it wasn't near the equator or the poles. But the experiment was more than sensitive enough to detect the expected differences in the speed of light at right angles. They rotated the entire apparatus and watched for variations because a static measurement would not have been stable enough.
We don't have to assume that clocks can tick at different rates, we can easily demonstrate this. However, I was talking about an effect due to gravity which is the purview of general relativity and what I thought you were alluding to in your opening thread when you asked about the speed of light...relative to a clock at rest on earth.

I can't understand what you are talking about in this previous paragraph. In Special Relativity, frames are symmetrical, clocks at rest in one frame will determine that moving clocks run slower and vice versa. Also, rulers at rest in one frame will determine that moving rulers are contracted along the direction of motion and vice versa.
That's exactly what Einstein says.

11. Jan 31, 2012

### mangaroosh

We might have our wires crossed again.

I'm referring more to the assumption that the speed of light is constant regardless of the motion of the observer with respect to the source. From what I can gather Maxwell's equations don't appear to make any distinction between motion with respect to the source and being at rest with respect to the source; I'm just wondering if the definition of the speed of light, in terms of a clock at rest on earth, does implicity make this distinction?

I know you said they didn't use clocks to directly measure the speed of light, but they presumably used them to measure the speed of the rotating device, which, I would imagine, affected their calculations of the speed of light. Again, I presume that these clocks would have been at rest relative to the earth?

Ah no worries, that is effectively what I had pictured.

If the speed of light was constant with respect to the source of the light, would the results be the same?

apologies, I mightn't have been very clear about it. I'm more wondering if the use of a clock at rest on earth, to measure the speed of light [or the speed of a rotating device used to measure the speed of light] carries with it the implicit assumption that the speed of light is relative to a clock at rest on earth, and therefore an observer? To me it seems as though it does.

Is the light clock thought experiment in the video below (around the 3min 40 mark) a good explanation of that phenomenon, do you know?

This seems to be a pretty bold statement! Are there specific citations which support that?

I thought things like the MMX, KTX, Brillet and Hall, etc. were supposed to be tests of the second postulate, no?

12. Jan 31, 2012

### Staff: Mentor

No because if you travel with the clock, you won't notice the change. The key here isn't that the clock is at the surface of the earth, but rather that the clock and you are in the same reference frame. It just happens that the reference frame we are usually in is at the surface of the earth.

A clock is a device that tells time. So whatever reference frame it is in, that's where the clock is telling time and due to Relativity that time may not be the same as the time in another frame.

13. Jan 31, 2012

### mangaroosh

But, if "the second" is defined in terms of a clock at rest on the earth, and a clock in motion relative to it ticks at a different rate, let's say slower, then, by necessity, the clock in motion won't measure "the second", but a different interval of time. That an observer in motion with that clock can't tell the difference just means they don't know if their clock is ticking slower, faster, or at the same rate, no? It could be ticking slower i.e. not measuring a true "second" as per the units used in experiments.

No?

14. Jan 31, 2012

### Staff: Mentor

No. We know our clocks really do measure time accurately and don't just have a dependency on speed or gravity that makes them inaccurate because multiple types of clocks and other time dependent experiments agree with each other.

15. Jan 31, 2012

### Staff: Mentor

By the way:
The bolded part is not part of the definition of a second. No one pointed it out probably because they didn't realize where you were going with this.

16. Jan 31, 2012

### ghwellsjr

You can take any rigid measuring rod and any stable clock and use them to measure the speed of light in any place you want to do it in any orientation and you will get a speed that is so many rods per tick. You can then take that rod and that clock and move it to any other location and/or any other orientation and repeat the measurement and you will get exactly the same number of rods per tick. You don't have to be concerned about whether the rod is changing its "actual" length or the clock is changing its "actual" tick rate due to motion or gravity. You don't even have to know anything about relativity or Maxwell's equations. All you have to be concerned with is that you don't accelerate the apparatus during the time of the measurement and that the rod isn't so long that the gravity field is different at one end than the other (which would be very hard to do). Oh, and we're assuming that the experiment is performed in vacuum and that the rod and clock are not effected themselves by temperature or other environmental factors. You also can't use a remote clock such as GPS as your timing source--it has to be a clock that is experiencing the same motion and gravity as the rod and the mirror.

You can also use light that is coming from a source that is remote to your measuring device. It does not have to be a light that is stationary with respect to the rod and clock. You would just need a way to shutter the light as opposed to switching the light on.

So these experiments have been done in all kinds of situations and the result is always the same, the speed of light is measured to be the same constant value.
If?? I'm not sure what you're asking here since the speed of light is constant with respect to the source of the light. Experiments have been done to verify this even for the one-way propagation of light from two different sources with a relative speed difference. What we can't measure is what that constant value is unless we use a reflector and measure the "average" round-trip speed of those lights.
After you collect all the experimental evidence and you want to build a theory to explain all the facts, there are many different options you can take and as long as the theory comports with all the facts, no one can discount the theory. But building theories is very difficult work. I'm not sure if you were starting from scratch that you could come up with any theory that explains all the facts. I know I couldn't. And you can't just be fuzzy, you have to come up with precise mathematical equations.

The amazing thing to me is that these scientists from the last couple of centuries were able to figure out that clocks would run slow in different situations before they had clocks to test the idea.

But the bottom line is that if you treat the speed of light to be an exact constant with a defined value as we do now, it makes so many other aspects of science much simpler.
It's good as far as it goes. I wish they had shown how even in Einstein's ground frame, you can illustrate how Lorentz measures Einstein's clock to be running slow but instead, they switch to Lorentz's frame. I have the same complaint about the beginning of the video where they point out that both Einstein and Lorentz will each think they are in the center of an expanding sphere of light even though they are in different places.

So I made my own video to illustrate this:

Note that each observer carries his own set of mirrors because without them, it is not possible to observe the progress of light.
No, they were testing the round-trip speed of light. The second postulate deals with the one-way speed of light.

Have you read section 1 of Einstein's 1905 paper introducing Special Relativity?

17. Jan 31, 2012

### mangaroosh

But do experiments, like Hafele-Keating, not demonstrate that clocks moving relative to the earth will tick at different rates from one at rest on earth, which measures "the [official] second" and therefore that they will not measure "the [official] second"?

18. Jan 31, 2012

### mangaroosh

I don't think it is expressly part of the definition of the speed of light, but the speed of light is expressed in seconds, and "the [official] second" is determined by a clock at rest relative to the earth.

As ghwellsjr pointed out, they didn't use clocks to measure the speed of light "back in the day" but rather a rotating object with varying speeds; the speed of this rotating object however would, presumably, have been measured using a clock at rest relative to the earth and so, I would imagine, this would implicitly mean that the speed of light is relative to a clock at rest on earth.

There is presumably a reason why that isn't the case?

19. Jan 31, 2012

### ghwellsjr

I also pointed out in post #8 that the official second was never based on a clock at rest on the earth but rather on the earth itself, until it was discovered that the earth was not a stable clock.

I'm curious--what is your real concern?

20. Jan 31, 2012

### Staff: Mentor

Yes... As Relativity predicts.
Due to Relativity, it cannot be a part of the definition, expressly or otherwise.
The theory demands it and experiments support it.

I echo: what's the problem?

Last edited: Jan 31, 2012