Constancy of c - second postulate

[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

c is a constant in Maxwell's equations of Electromagnetism.
A simple derivation shows that this constant, c, is the speed of EM waves which describe the propagation of light.

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?

 

[Bread18]

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?

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.

 

[mathfeel]

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?

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.

 

[ghwellsjr]

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

c is a constant in Maxwell's equations of Electromagnetism.
A simple derivation shows that this constant, c, is the speed of EM waves which describe the propagation of light.

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?

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.

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

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.

 

[jtbell]

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

Tests of Einstein's two postulates

 

[mangaroosh]

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 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?

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.

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?

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.

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

 

[mangaroosh]

Tests of Einstein's two postulates

thanks jtbell

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

 

[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 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?

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

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

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.

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.

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?

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?

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.

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

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.

 

[mangaroosh]

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

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?

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.

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?

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?

We might have our wires crossed on this:

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.

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?

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.

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.

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

 

[ghwellsjr]

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?

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.

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?

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 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.

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.

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

That's exactly what Einstein says.

 

[mangaroosh]

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.

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?

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.

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?

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.

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.

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.

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

https://www.youtube.com/watch?v=DRDN7ceu6UU

That's exactly what Einstein says.

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?

 

[russ_watters]

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?

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.

 

[mangaroosh]

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.

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?

 

[russ_watters]

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.

 

[russ_watters]

By the way:

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?

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.

 

[ghwellsjr]

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?

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.

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?

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.

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.

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.

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

https://www.youtube.com/watch?v=DRDN7ceu6UU

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:

https://www.youtube.com/watch?v=dEhvU31YaCw

Note that each observer carries his own set of mirrors because without them, it is not possible to observe the progress of light.

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?

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?

 

[mangaroosh]

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.

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"?

 

[mangaroosh]

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.

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?

 

[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?

 

[russ_watters]

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...

Yes... As Relativity predicts.

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.

Due to Relativity, it cannot be a part of the definition, expressly or otherwise.

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

The theory demands it and experiments support it.

I echo: what's the problem?

 

[mangaroosh]

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?

I know, you mentioned that it was based on the Earth itself, but there had to be some way of measuring that second; even if we imagine a primitive sundial which basically translates the motion of the Earth into units of "time", the sundial is at rest relative to the earth.

I'm just wondering about how the second postulate is tested and how "set in stone" it actually is. It's just that as I go about trying to build an understanding of relativity, there are questions which spring to mind.

As mentioned, I've read that the second postulate was initially adopted because Maxwell's equations seemed to imply it; but the thought occurred to me that all the experiments which lead to Maxwell's equations, may have used [if only by extension] a clock at rest relative to the Earth to measure the speed of light, such that, even if Maxwell's equations didn't specify it, the instruments used in the experiments, which lead to the equations, might have carried with them, that tacit assumption.

As I say, these are just questions which arise on the way to developing a better understanding of the theory.I find it somewhat confusing though, when you say that the second postulate is essentially untestable; particularly when people point to experiments, such as the MMX, as experimental evidence of the second postulate. I've read elsewhere, also, that there are no conclusive tests of the second postulate, so I struggle with that. I wonder if there are other possible explanations for such experiments as the MMX, KTX, etc. and I read things like this

It is known that an hypothesis of a mechanical character (emissive or ballistic), according to which to the ordinary velocity of light must be added that of the source, can explain, like the theory of relativity, the failure of the above-quoted experiments [Michelson and Morley, Trouton and Noble]

Paper by Q. Majorana

 

[mangaroosh]

Yes... As Relativity predicts.

This is kind one of the areas where I have trouble.

If a clock, in motion relative to the earth, is, let's say, ticking slower, such that it doesn't measure "the second" the same as a clock on earth, how can it be used to measure the speed of light in units that are meaningful? For example, if it measures the speed of light to be approx. 300,000 km/s, but the 's' in that measurement is not the same as the 's' on earth, wouldn't it mean that the speed of light was actually different in different reference frames, by virtue of the different length of the second.

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

It might not be part of the theory, but is it a tacit assumption based on the definition of the units used?

Again, this is where I get confused; ghwells, says that it cannot actually be tested, but then others point to experiments which are supposed to affirm it.

I echo: what's the problem?

there's no problem as such, there are just issues I'm trying to resolve for myself - with the kind help of others.

 

[ghwellsjr]

I know, you mentioned that it was based on the Earth itself, but there had to be some way of measuring that second; even if we imagine a primitive sundial which basically translates the motion of the Earth into units of "time", the sundial is at rest relative to the earth.

The Earth is at rest relative to the earth. Long after the day was divided into 86400 equal parts called a "second", astronomers began to accurately track the apparent motion of the stars as the Earth rotated and that became the standard for a "second". Of course, they had to take into account that the length of a day based on the stars was different than based on the sun but they were smart enough to know how to figure that out. And they used this timing to calibrate their mechanical clocks.

I'm just wondering about how the second postulate is tested and how "set in stone" it actually is. It's just that as I go about trying to build an understanding of relativity, there are questions which spring to mind.

As mentioned, I've read that the second postulate was initially adopted because Maxwell's equations seemed to imply it; but the thought occurred to me that all the experiments which lead to Maxwell's equations, may have used [if only by extension] a clock at rest relative to the Earth to measure the speed of light, such that, even if Maxwell's equations didn't specify it, the instruments used in the experiments which lead to the equations might have carried that tacit assumption with them.

Maxwell (along with a lot of help from the previous work of a great many other scientists) developed his famous four equations to describe how moving charges and moving magnets interacted to create currents and voltage and magnetic fields, such things as that, and they involved very slow motion. There was no thought of connecting any of this with light until it was observed from analyzing the equations that electromagnetic waves could be generated that would propagate at a speed very close to the previously measured speed of light.

It was at that point that Maxwell proposed that light was the propagation of these waves in the EM field and that its speed relative to this field, which was presumed to be fixed in space, could be measured to determine an absolute rest state. He proposed an experiment to make this measurement but although it wasn't practical, the idea came to the attention of Michelson who devised an experiment that was practical. However, this experiment, as I said before, was not based on any Earth bound clock but rather used the round-trip speed of light in different directions to try to find a difference in the speed of light in different directions. There was no measured speed of light used anywhere in the experiment, only comparisons.

After the experimental evidence indicated that it was not possible to determine a rest state for the EM fields, Lorentz and others figured out a way to hold on to the idea of a fixed rest state by postulating that lengths contracted along the direction of motion and clocks would tick slower. This culminated in Lorentz's ether theory which explained all the evidence but was not based on the idea that the one-way speed of light was a constant in any measurement of the two-way speed of light. It was based on the idea that the one-way speed of light was a constant only in the fixed ether field.

It's important for you to realize that this theory fit perfectly with all the experimental data and that later when Einstein proposed that the one-way speed of light was constant in any measurement of the two-way speed of light, there was no way to prove that his idea was correct and Lorentz's was wrong. There is no experiment that can help us choose between these two competing ideas.

As I say, these are just questions which arise on the way to developing a better understanding of the theory.

I find it somewhat confusing though, when you say that the second postulate is essentially untestable; particularly when people point to experiments, such as the MMX, as experimental evidence of the second postulate.

I'm not the one saying it, Einstein said it over and over again in his many papers, books and speeches. Can you provide a reference of anyone actually doing an experiment as evidence of the second postulate? I realize that many people are confused and think that the second postulate is about the two-way speed of light which can be measured and does have experimental support and of which there is no controversy, especially since the science community has established the measured speed of light to be a defined constant value.

Let me put it another way: being able to identify the propagation of light is the same as being able to identify the fixed ether.

 

[ghwellsjr]

I read things like this

Paper by Q. Majorana

I see you provided a link while I was composing my previous post.

A quick read of that paper doesn't appear to me that they are making a measurement of the one-way speed of light. I know they have a mirror in their experiment.

 

[ghwellsjr]

This is kind one of the areas where I have trouble.

If a clock, in motion relative to the earth, is, let's say, ticking slower, such that it doesn't measure "the second" the same as a clock on earth, how can it be used to measure the speed of light in units that are meaningful? For example, if it measures the speed of light to be approx. 300,000 km/s, but the 's' in that measurement is not the same as the 's' on earth, wouldn't it mean that the speed of light was actually different in different reference frames, by virtue of the different length of the second.

It might not be part of the theory, but is it a tacit assumption based on the definition of the units used?

Again, this is where I get confused; ghwells, says that it cannot actually be tested, but then others point to experiments which are supposed to affirm it.

there's no problem as such, there are just issues I'm trying to resolve for myself - with the kind help of others.

Let's suppose that your concern is valid, that of making a measurement of the speed of light with a clock that is ticking at different rates depending on the condition of the measurement. Let's also suppose that there is a fixed ether and that the only valid measurement of the speed of light would be when you were stationary in that ether because only then would your clock be ticking at the true one-second rate and only then would your meter stick be the true length. But let's suppose that you are traveling at some high rate of speed with respect to the ether and your meter stick is contracted when you place it along the direction of motion and your clock is experiencing time dilation but in spite of all this, you go ahead and make a measurement of the round-trip speed of light, which cancels out all those issues with the meter stick and the clock (according to theory), and you get a value. Now you slow down with respect to the ether and you make another measurement and you get the same value, even though your meter stick is a different length and your clock ticks at a different rate. Remember, this is all according to Lorentz Ether Theory (LET). And you slow down some more and get another identical reading for the speed of light. Finally you slow down and are at rest with respect to the ether and you still get the same value. Well if you always get the same value, how could all of them be wrong, except the one done under the correct condition?

And here's another thing to consider: according to both LET and Special Relativity (SR), when a measuring device is in motion with respect to the ether (for LET) or any frame (for SR), then lengths contract only along the direction of motion but the tick rate of the clock is independent of the orientation of the clock. So why don't you get a different answer depending on the orientation of your measurement of the speed of light?

 

[mangaroosh]

The Earth is at rest relative to the earth. Long after the day was divided into 86400 equal parts called a "second", astronomers began to accurately track the apparent motion of the stars as the Earth rotated and that became the standard for a "second". Of course, they had to take into account that the length of a day based on the stars was different than based on the sun but they were smart enough to know how to figure that out. And they used this timing to calibrate their mechanical clocks.

smart arse the sundial could be in motion relative to the earth.

I presume that the plotting of the apparent motion of the stars was also done relative to an observer, or observatory, at rest relative to the earth, which would presumably have the same implications, no?

Maxwell (along with a lot of help from the previous work of a great many other scientists) developed his famous four equations to describe how moving charges and moving magnets interacted to create currents and voltage and magnetic fields, such things as that, and they involved very slow motion. There was no thought of connecting any of this with light until it was observed from analyzing the equations that electromagnetic waves could be generated that would propagate at a speed very close to the previously measured speed of light.

It was at that point that Maxwell proposed that light was the propagation of these waves in the EM field and that its speed relative to this field, which was presumed to be fixed in space, could be measured to determine an absolute rest state. He proposed an experiment to make this measurement but although it wasn't practical, the idea came to the attention of Michelson who devised an experiment that was practical. However, this experiment, as I said before, was not based on any Earth bound clock but rather used the round-trip speed of light in different directions to try to find a difference in the speed of light in different directions. There was no measured speed of light used anywhere in the experiment, only comparisons.

I still have difficulty getting my head around the MMX and similar experiments, and how they demonstrate that an observer will measure the speed of light to be c regardless of their motion relative to the source. It's probably because I'm trying to reconcile it with the example of two cars traveling along a road, where a faster car (traveling at 80km/k) passes the slower car (traveling at 60km/h) and the slower car measures the speed of the faster one as 20km/h; while if the faster car was replaced with a beam of light they wouldn't measure it in the same manner. I know the MMX is completely different, but the consequences of it are similar.

It's also probably down to how I am imagining the experiments, because I imagine them to be measuring the wavelength of the light. In the example of the cars, if a car was stationary with respect to the source of light and it simply used some means of detecting the light wave (without actually measuring its speed), then I imgaine that if the car started moving relative to the light source, then, using the same means of detecting the light wave, there wouldn't be any discernable difference in how the wave is detected because the wavelenght of the light would be unchanged. I know that is a gross oversimplification, but I have trouble then taking the step towards the Michelson interferometer, because I imagine that there would be no fringe shift because the speed of light (and the wavelength) of the reflected light in the interferometer would be the same.

I know ballisitic theory has effectively been disproved, but would the below explanation make any sense?

A simpler explanation for the constancy of the speed of light in the Michelson-Morley experiment, however, is that there is no relative net motion or changes in density of the molecules within the apparatus, creating no cause for Coulomb chain reactions to be accelerated or decelerated...

...the vectoring of the propagation of light has nothing to do with the motion of the source once the signal has been released...

For an analogy, consider a line of people shaking hands.(See Figure 7.) Each shakes hands with the guy on the left for exactly 2.5 seconds and then the guy on the right for 2.5 seconds. If the series of handshakes starts, and somebody pushes on the line from the point of origin, the “signal” will not change its rate of propagation unless the pushing force is fast enough to overtake the “wave front.”

Einsteins's relativity: the special and general theories - pdf file

After the experimental evidence indicated that it was not possible to determine a rest state for the EM fields, Lorentz and others figured out a way to hold on to the idea of a fixed rest state by postulating that lengths contracted along the direction of motion and clocks would tick slower. This culminated in Lorentz's ether theory which explained all the evidence but was not based on the idea that the one-way speed of light was a constant in any measurement of the two-way speed of light. It was based on the idea that the one-way speed of light was a constant only in the fixed ether field.

It's important for you to realize that this theory fit perfectly with all the experimental data and that later when Einstein proposed that the one-way speed of light was constant in any measurement of the two-way speed of light, there was no way to prove that his idea was correct and Lorentz's was wrong. There is no experiment that can help us choose between these two competing ideas.

I've come across that point before alright, and thought your comment:

6) Einstein promoted the idea of assuming that any inertial observer was at rest with respect to the ether and everyone else who was moving with respect to that observer was experiencing the time dilation and length contraction. Of course, he didn't word it precisely that way, but that is the equivalent of what he was saying.

in a thread on the Michelson-Morley experiment was interesting, because it does seem as though observers are treated as being at absolute rest, from their own perspective; or at least the consequences appear to be somewhat similar.

I'm not the one saying it, Einstein said it over and over again in his many papers, books and speeches. Can you provide a reference of anyone actually doing an experiment as evidence of the second postulate? I realize that many people are confused and think that the second postulate is about the two-way speed of light which can be measured and does have experimental support and of which there is no controversy, especially since the science community has established the measured speed of light to be a defined constant value.

Let me put it another way: being able to identify the propagation of light is the same as being able to identify the fixed ether.

I don't doubt you are correct; I suppose I just found it somewhat strange that there appeared to be circular reasoning incorporated in the theory. It just starts me wondering again if such an assumption could affect the conclsusions drawn from experiments.

For example, the light clock on the train thought experiment, as per the video posted earlier - incidentally, your own video you posted subsequently, which you'd shown me before, is very helpful for trying to visualise the issue of the expanding spheres of light; thanks.

For both observers the path length of the photon in the light clocks is given as 2d, which means that, from the perspective of each observer [in their own reference frames] the clocks tick at the same rate, while the clock of the other observer ticks slower, because the photon in the clock has to travel a longer distance between mirrors - as given by Pythagoras's theorem.

If we imagine things just from the observer on the platform's perspective, for a moment, and assume that this is actually how things are; he is at rest and the train is moving relative to him. In this case the trains clock would tick slower because the photon of the light clock has to travel a longer distance. If this were actually the case, then the observer on the train wouldn't know that his clock was ticking slower because he has nothing to compare it to - assuming a similar scenario to Galileo's observer on the ship e.g. a windowless carriage. The light would still travel a speed of c between mirrors, but it would travel a longer distance, unbeknownst to the observer. But that would mean that if he were to measure the speed of light in the light clock he would not measure the speed of light to be c, because he would measure the distance the photon has to travel as being twice the distance between the mirrors, when it actually travels a longer distance.

It seems that as though the second postulate is the reason why that can't be the case; because he would have to measure the speed of light to be c. Does the fact that the second postulate is assumed have any bearing on that?

 

[mangaroosh]

Let's suppose that your concern is valid, that of making a measurement of the speed of light with a clock that is ticking at different rates depending on the condition of the measurement. Let's also suppose that there is a fixed ether and that the only valid measurement of the speed of light would be when you were stationary in that ether because only then would your clock be ticking at the true one-second rate and only then would your meter stick be the true length. But let's suppose that you are traveling at some high rate of speed with respect to the ether and your meter stick is contracted when you place it along the direction of motion and your clock is experiencing time dilation but in spite of all this, you go ahead and make a measurement of the round-trip speed of light, which cancels out all those issues with the meter stick and the clock (according to theory), and you get a value. Now you slow down with respect to the ether and you make another measurement and you get the same value, even though your meter stick is a different length and your clock ticks at a different rate. Remember, this is all according to Lorentz Ether Theory (LET). And you slow down some more and get another identical reading for the speed of light. Finally you slow down and are at rest with respect to the ether and you still get the same value. Well if you always get the same value, how could all of them be wrong, except the one done under the correct condition?

And here's another thing to consider: according to both LET and Special Relativity (SR), when a measuring device is in motion with respect to the ether (for LET) or any frame (for SR), then lengths contract only along the direction of motion but the tick rate of the clock is independent of the orientation of the clock. So why don't you get a different answer depending on the orientation of your measurement of the speed of light?

I always get a bit thrown at the mention of an ether, because I don't see the necessity of it; but sticking with it, if your clock slowed down such that it measured a unit longer than a second, and your metre stick contracted, such that it measured less than a metre; if you measured the speed of light to be approx. 300,000 km/s, using those instruments, would that not mean that it had actually traveled a distance shorter than 300,000 km (as measured by the metre stick at rest relative to the ether) in a longer time (than the second measured by the rest clock). If the time interval is longer, shouldn't it travel a longer distance?

 

[mangaroosh]

thanks for the patince btw, in answering questions I'm sure ye've probably addressed countless times before.

Another question on the MMX; I'm just wondering where length contraction comed into it? If the MMX shows that the speed of light is the same in all directions, what role does length contraction play?

I can see why LET might necessitate it, but without an ether, where does it come into relativity? The results of the MMX demonstrate that the speed of light is the same in all directions without invoking length contraction, don't they?

 

[harrylin]

[..] 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? [..]

Maxwell assumed that time is absolute (Newtonian time). Maxwell's equations were defined relative to the light medium, and he thought that it would be possible to detect motion relative to that medium. According to SR (first postulate), that is not possible.

What was retained of Maxwell's theory in SR is that relative to an inertial reference system, the speed of light is everywhere the same constant - thus independent of the motion of the source (second postulate). SR uses the wave model of light propagation as opposed to the ballistic (particle) emission model of light, which had been effectively disproved by then.

He later (1907) phrased it as follows:

"We [...] assume that the clocks can be adjusted in such a way that
the propagation velocity of every light ray in vacuum - measured by
means of these clocks - becomes everywhere equal to a universal
constant c, provided that the coordinate system is not accelerated."

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.

According to the wave model of light, the speed of clocks or observers cannot affect the speed of light. In SR we may apply the wave model relative to any inertial reference system, such as the Earth Centered Inertial frame. For example, GPS uses that reference system and people as well as clocks on Earth move relative to that virtual medium.

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

They were tests of the relativity principle (the first postulate).

Harald

 

[ghwellsjr]

The Earth is at rest relative to the earth. Long after the day was divided into 86400 equal parts called a "second", astronomers began to accurately track the apparent motion of the stars as the Earth rotated and that became the standard for a "second". Of course, they had to take into account that the length of a day based on the stars was different than based on the sun but they were smart enough to know how to figure that out. And they used this timing to calibrate their mechanical clocks.

smart arse the sundial could be in motion relative to the earth.

I'm not trying to be funny or trite. A sundial is not portable. You can't just pick it up and plop it down somewhere else. There's a reason why they are always firmly attached to the ground. Every sundial is custom fitted to its location, if it's going to keep accurate time. Of course you can buy decorative sundials but they are useless for keeping time. Why don't you read the wikipedia article on sundials?

I presume that the plotting of the apparent motion of the stars was also done relative to an observer, or observatory, at rest relative to the earth, which would presumably have the same implications, no?

Yes, observatories designed for the purpose of keeping track of time, even ancient ones, were firmly fixed to the ground. They are measuring the motion of the Earth and are used to calibrate other clocks that are portable.

But now that we have atomic clocks that can detect the difference in altitude and that can show that the Earth is slowing down and therefore the previous official second is getting longer, we can no longer rely on the Earth as our definition for a second. You seem concerned that measurements of the speed of light do not use "the [official] second". What would you propose if you don't like the way it is done now?

Maxwell (along with a lot of help from the previous work of a great many other scientists) developed his famous four equations to describe how moving charges and moving magnets interacted to create currents and voltage and magnetic fields, such things as that, and they involved very slow motion. There was no thought of connecting any of this with light until it was observed from analyzing the equations that electromagnetic waves could be generated that would propagate at a speed very close to the previously measured speed of light.

It was at that point that Maxwell proposed that light was the propagation of these waves in the EM field and that its speed relative to this field, which was presumed to be fixed in space, could be measured to determine an absolute rest state. He proposed an experiment to make this measurement but although it wasn't practical, the idea came to the attention of Michelson who devised an experiment that was practical. However, this experiment, as I said before, was not based on any Earth bound clock but rather used the round-trip speed of light in different directions to try to find a difference in the speed of light in different directions. There was no measured speed of light used anywhere in the experiment, only comparisons.

I still have difficulty getting my head around the MMX and similar experiments, and how they demonstrate that an observer will measure the speed of light to be c regardless of their motion relative to the source.

But MMX and similar experiments were not trying to measure the speed of light relative to the source. They were trying to measure it relative to the ether. They carried the source with them (which was a flame, by the way).

It's probably because I'm trying to reconcile it with the example of two cars traveling along a road, where a faster car (traveling at 80km/k) passes the slower car (traveling at 60km/h) and the slower car measures the speed of the faster one as 20km/h; while if the faster car was replaced with a beam of light they wouldn't measure it in the same manner. I know the MMX is completely different, but the consequences of it are similar.

A better analogy would be some crazy people doing an experiment on top of an airplane:

Suppose they have a couple radio-controlled model airplanes that go somewhat faster than the airplane but at a constant speed relative to the stationary air. They get on top of their airplane near the tail and they send one of the RC planes to fly toward the front and to turn around and come back to the tail. At the same time, they send another identical RC plane to fly from the end of the left wing to the end of the right wing and turn around and come back. The length of the airplane is the same as the wingspan so when they test this on the ground, it takes the same amount of time for each RC plane to make its round trip.

They figure that when the airplane is in flight, there will be a headwind that will slow the RC plane leaving from the tail and make it take a long time to get the the front but when it comes back it will have a tailwind that will make the trip very short. On the other hand, they figure that the RC plane flying along the wings will take the same amount of time to go in each direction and it will take longer than it did on the ground but it should still be faster than the RC plane going along the length of the plane. They reason that if the airplane was going just a hair under the speed that the RC planes could travel, the RC plane flying along the wings could make the round trip before the other RC plane even got to the front of the big plane. And they'd be right.

But let's suppose, just for the sake of argument that when they did their experiment, both RC planes made their individual round trips in exactly the same length of time, no matter how fast or slow the airplane was traveling. How would they explain that? Well, obviously, if the airplane were to shorten its length, depending on its actual wind speed, then both RC planes could make their round trips in the same amount of time.

It's also probably down to how I am imagining the experiments, because I imagine them to be measuring the wavelength of the light. In the example of the cars, if a car was stationary with respect to the source of light and it simply used some means of detecting the light wave (without actually measuring its speed), then I imgaine that if the car started moving relative to the light source, then, using the same means of detecting the light wave, there wouldn't be any discernable difference in how the wave is detected because the wavelenght of the light would be unchanged. I know that is a gross oversimplification, but I have trouble then taking the step towards the Michelson interferometer, because I imagine that there would be no fringe shift because the speed of light (and the wavelength) of the reflected light in the interferometer would be the same.

If there were a motion of the car relative to the light source, there would be a change in the wavelength of the light detected, but this is not a factor in MMX because they carried the light source with them. However, there should be a change in the wavelength if the whole apparatus were to change its speed or if the round-trip times for the two legs were to change differently while the whole apparatus was rotated.

Think about the airplane analogy. Of course while the airplane is flying, the headwind will always come from the front of the airplane but suppose they put the airplane in a large wind tunnel and allowed the airplane to rotate. They would expect that whenever the airplane was aligned with the wind, the front-to-back RC plane would take longer and whenever the airplane was aligned at right angles to the wind, the RC plane flying along the wingspan would take longer. But with MMX it always took the same amount of time.

I know ballisitic theory has effectively been disproved, but would the below explanation make any sense?

A simpler explanation for the constancy of the speed of light in the Michelson-Morley experiment, however, is that there is no relative net motion or changes in density of the molecules within the apparatus, creating no cause for Coulomb chain reactions to be accelerated or decelerated...

...the vectoring of the propagation of light has nothing to do with the motion of the source once the signal has been released...

For an analogy, consider a line of people shaking hands.(See Figure 7.) Each shakes hands with the guy on the left for exactly 2.5 seconds and then the guy on the right for 2.5 seconds. If the series of handshakes starts, and somebody pushes on the line from the point of origin, the “signal” will not change its rate of propagation unless the pushing force is fast enough to overtake the “wave front.”

Einsteins's relativity: the special and general theories - pdf file

Makes no sense to me. That pdf file appears to be a review of Einstein's book in which the reviewer complains of Einstein's analogies and examples which I have no problem with but his own counter analogies and examples I find incomprehensible. I think it might be because he just doesn't understand relativity and so he thinks he can explain the experiments in a better way, but to someone who understands relativity, his review looks like the ramblings of a confused mind. You really shouldn't try to learn relativity from someone who finds fault with Einstein.

After the experimental evidence indicated that it was not possible to determine a rest state for the EM fields, Lorentz and others figured out a way to hold on to the idea of a fixed rest state by postulating that lengths contracted along the direction of motion and clocks would tick slower. This culminated in Lorentz's ether theory which explained all the evidence but was not based on the idea that the one-way speed of light was a constant in any measurement of the two-way speed of light. It was based on the idea that the one-way speed of light was a constant only in the fixed ether field.

It's important for you to realize that this theory fit perfectly with all the experimental data and that later when Einstein proposed that the one-way speed of light was constant in any measurement of the two-way speed of light, there was no way to prove that his idea was correct and Lorentz's was wrong. There is no experiment that can help us choose between these two competing ideas.

I've come across that point before alright, and thought your comment:

6) Einstein promoted the idea of assuming that any inertial observer was at rest with respect to the ether and everyone else who was moving with respect to that observer was experiencing the time dilation and length contraction. Of course, he didn't word it precisely that way, but that is the equivalent of what he was saying.

in a thread on the Michelson-Morley experiment was interesting, because it does seem as though observers are treated as being at absolute rest, from their own perspective; or at least the consequences appear to be somewhat similar.

I'm not the one saying it, Einstein said it over and over again in his many papers, books and speeches. Can you provide a reference of anyone actually doing an experiment as evidence of the second postulate? I realize that many people are confused and think that the second postulate is about the two-way speed of light which can be measured and does have experimental support and of which there is no controversy, especially since the science community has established the measured speed of light to be a defined constant value.

Let me put it another way: being able to identify the propagation of light is the same as being able to identify the fixed ether.

I don't doubt you are correct; I suppose I just found it somewhat strange that there appeared to be circular reasoning incorporated in the theory. It just starts me wondering again if such an assumption could affect the conclsusions drawn from experiments.

For example, the light clock on the train thought experiment, as per the video posted earlier - incidentally, your own video you posted subsequently, which you'd shown me before, is very helpful for trying to visualise the issue of the expanding spheres of light; thanks.

For both observers the path length of the photon in the light clocks is given as 2d, which means that, from the perspective of each observer [in their own reference frames] the clocks tick at the same rate, while the clock of the other observer ticks slower, because the photon in the clock has to travel a longer distance between mirrors - as given by Pythagoras's theorem.

If we imagine things just from the observer on the platform's perspective, for a moment, and assume that this is actually how things are; he is at rest and the train is moving relative to him. In this case the trains clock would tick slower because the photon of the light clock has to travel a longer distance. If this were actually the case, then the observer on the train wouldn't know that his clock was ticking slower because he has nothing to compare it to - assuming a similar scenario to Galileo's observer on the ship e.g. a windowless carriage. The light would still travel a speed of c between mirrors, but it would travel a longer distance, unbeknownst to the observer. But that would mean that if he were to measure the speed of light in the light clock he would not measure the speed of light to be c, because he would measure the distance the photon has to travel as being twice the distance between the mirrors, when it actually travels a longer distance.

But you see, measuring the speed of light in the light clock is identical to measuring the time of the ticks of the light clock. Let's say the traveling observer has a second identical light clock to measure the speed of light in the first light clock. He will conclude that the speed of light is c because it takes the same amount of time to make a tick-tock as it did when the train was stopped. In other words, whether the train is stopped or traveling, both clocks always track--they always tick-tock together.

It seems that as though the second postulate is the reason why that can't be the case; because he would have to measure the speed of light to be c. Does the fact that the second postulate is assumed have any bearing on that?

The second postulate has no bearing on the outcome of any experiment. Lorentz says that time is going slower for the traveler and his light clock as determined by the ground frame and Einstein agrees. Lorentz says that the ground frame represents the one and only ether frame and that, chances are, nobody is on the ground, we're all on moving trains. Einstein says we on the moving train can assume that we are stationary in the one and only ether frame and our clock is ticking at a normal rate and the other guy's clock on the ground is the one that is ticking slower than normal. (I'm speaking here of the actual Lorentz and Einstein, not the ones in the video.)

 

[harrylin]

thanks for the patince btw, in answering questions I'm sure ye've probably addressed countless times before.

Another question on the MMX; I'm just wondering where length contraction comed into it? If the MMX shows that the speed of light is the same in all directions, what role does length contraction play?

I can see why LET might necessitate it, but without an ether, where does it come into relativity? The results of the MMX demonstrate that the speed of light is the same in all directions without invoking length contraction, don't they?

MMX showed that the return speed of light is the same in all directions at different times of the year. Thus whatever inertial reference system you use, the apparatus is moving at considerable speed during some of the experiments. Without invoking length contraction and based on the second postulate, how do you think can the return time of the light rays be the same in all directions?

 

[ghwellsjr]

Let's suppose that your concern is valid, that of making a measurement of the speed of light with a clock that is ticking at different rates depending on the condition of the measurement. Let's also suppose that there is a fixed ether and that the only valid measurement of the speed of light would be when you were stationary in that ether because only then would your clock be ticking at the true one-second rate and only then would your meter stick be the true length. But let's suppose that you are traveling at some high rate of speed with respect to the ether and your meter stick is contracted when you place it along the direction of motion and your clock is experiencing time dilation but in spite of all this, you go ahead and make a measurement of the round-trip speed of light, which cancels out all those issues with the meter stick and the clock (according to theory), and you get a value. Now you slow down with respect to the ether and you make another measurement and you get the same value, even though your meter stick is a different length and your clock ticks at a different rate. Remember, this is all according to Lorentz Ether Theory (LET). And you slow down some more and get another identical reading for the speed of light. Finally you slow down and are at rest with respect to the ether and you still get the same value. Well if you always get the same value, how could all of them be wrong, except the one done under the correct condition?

And here's another thing to consider: according to both LET and Special Relativity (SR), when a measuring device is in motion with respect to the ether (for LET) or any frame (for SR), then lengths contract only along the direction of motion but the tick rate of the clock is independent of the orientation of the clock. So why don't you get a different answer depending on the orientation of your measurement of the speed of light?

I always get a bit thrown at the mention of an ether, because I don't see the necessity of it; but sticking with it, if your clock slowed down such that it measured a unit longer than a second, and your metre stick contracted, such that it measured less than a metre; if you measured the speed of light to be approx. 300,000 km/s, using those instruments, would that not mean that it had actually traveled a distance shorter than 300,000 km (as measured by the metre stick at rest relative to the ether) in a longer time (than the second measured by the rest clock). If the time interval is longer, shouldn't it travel a longer distance?

Well, I said you don't have to use the concept of ether, you can use any frame, it doesn't matter. And I just pointed out that depending on your orientation with respect to your motion in the defined frame, your meter stick may or may not be shortened. If you do a measurement at right angles to the direction of motion, only your clock takes longer, since the light has to travel on a diagonal. But if you rotate your apparatus 90 degrees, if your meter stick didn't get shorter (remember the airplane analogy) then you would measure a different speed for light or a different time interval.

Another way to think about this is when the mirrors of a light clock are arranged at right angles to the direction of motion, the mirrors stay the same distance apart as they were at rest or at any speed. But when you rotate the mirrors 90 degrees, if they didn't come closer together and you were going very nearly the speed of light, it would take nearly forever for the light to travel from the rear mirror to the front mirror and remember also that the distance between the mirrors is not the actual distance the light travels because the mirrors are traveling also. The light hits the rear mirror and the point of impact travels away from the mirror behind the light clock and eventually the light hits the front mirror but the distance between the mirrors is no where near the length that the light had to travel to get from one to the other. Then the opposite effect happens for the light traveling from the front mirror to the rear mirror--it doesn't have to go as far as the spacing between the mirrors because the rear mirror is moving toward the point of impact of the light with the front mirror.

 

[ghwellsjr]

thanks for the patince btw, in answering questions I'm sure ye've probably addressed countless times before.

Another question on the MMX; I'm just wondering where length contraction comed into it? If the MMX shows that the speed of light is the same in all directions, what role does length contraction play?

I can see why LET might necessitate it, but without an ether, where does it come into relativity? The results of the MMX demonstrate that the speed of light is the same in all directions without invoking length contraction, don't they?

You posted this before I had a chance to respond to your earlier concerns so hopefully your questions have already been answered. Just remember that traveling through the ether in LET is identical to traveling in a Frame of Reference in SR. But if I didn't answer your questions to your satisfaction, ask again.

 

[mananvpanchal]

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?

Time meas "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom".

So motion clock have the same frequency, but time period between two hyperfine levels would slow down. So resulting time slow down.

 

[mananvpanchal]

@mangaroosh

By reading conversation it seems that "second is different every where then how one can say that speed of light is same everywhere".

But there is other factor: Length Contraction.

Time Dilation and Length Contraction is different for different frames. So Speed of light is same for all frames because Length and Time is different for them than other frames.