Constancy of c - second postulate

[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.

 

[Chronos]

I always found it simplest to assume length and time are unique to each reference frame and you need the Lorentz transform to synchronize them between different reference frames.

 

[mangaroosh]

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.

It wasn't necessarily that Maxwell's equations were defined relative to the light medium, was it? Was it not just that Maxwell believed that the equatiosn implied an ether? The equations weren't changed due to relativity were they?

[One of] the consequence of assuming Newtonian [absolute] time, was that clocks in all reference frames would tick at the same rate, wasn't it? This would have meant that a clock on a [moving] train would provided a measurement in units that was meangingful to an observer at rest on earth; such that the 's' in the definition of the speed of light would have been the same. If a clock on a moving train ticks slower, however, it would mean that that a measurement of 300, 000 km/s would not be the same as the same measurement in the Earth centred reference frame.

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."

What is meant by "adjusted" in the above, do you know?

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 wouldn't necessarily say that a clock could affect the speed of light, but it would affect how the speed of light is measured; or more precisely, the units in which that speed is expressed.

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

Again, apologies, I tend to get confused with things like that, because the MMX and the KTX usually get cited as examples of experiments which demonstrate the constancy of the speed of light, which I presume to be the second postulate.

 

[mangaroosh]

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?

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?

It's not so much concern that measurements of the speed of light don't use "the [official] second", I'm just wondering if the Maxwell's equations implicitly state that the speed of light is relative to a clock at rest on earth.

Because, a sundial is effectively just a means of breaking the daylight period into smaller segments; it effectively just breaks the "arc" of the sun, over a particular location on earth, into hours and minutes, doesn't it? So any measurement, expressed in the units measured by a sundial, could be read as a function of the movement of the sun relative to a an object at rest on earth. If that object were in motion relative to the earth, then the units would be different. The same could be said for measurements expressed in the units measured by observatories plotting the apparent motion of the fixed stars. Equally so, for an atomic clock at rest on earth, but perhaps even a more precise expression of it's location may be necessary.

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).

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.

Thanks, I think this analogy might be helpful.

This is more for myself, but I think we can imagine a plane shaped like a plus sign; such that, if the RC planes were both to start from the tail of the plane, and one of the planes turned at the intersection where the wings are, flew out to the end of the wing and then flew the distance to the end of the opposite wing, it would fly the same distance as the other RC plane flying out to the nose of the plane, returning to the midsection turning, and flying to the end of the same wing as the other RC plane; where the the detector determines if they arrived at the same time.

Staying with that analogy; what if the RC planes were of such a design (let's say they are made of massless particles) that there would be no wind resistance, they wouldn't need to assume that the plane's length had shortened, would they?

Also, if the length of time it took, for both RC planes to complete their respective trips, wasn't actually measured, rather the simple observation of whether they arrived simultaneously, or not was used; could they then conclude, when the planes arrive simultaneously, that someone on the ground would measure the speed of the RC planes to be the same as that measured by a person on the plane?

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 replied to the part above before [re-]reading this part, so take no notice of the repetition; if the RC planes were designed [from massless particles, say] such that wind resistance wasn't a factor.

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.

I try not to learn about relativity from someone who finds fault with Einstein, I generally try to learn about it from people like yourself - who are generous enough to take the time to answer posts; but I try not to accept things simply on the basis that someone says such and such is the case.

With regard to the MMX, I think what the author suggests is effectively a ballistic-like (not necessarily a ballistic) explanation for the MMX results; namely that the wavelength of the light reflected from the mirrors [in the interferometer] is the same, and so, no fringe shift would be expected.

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.

But that would be circular reasoning wouldn't it, because both clocks use light; if he were to use a very precise mechanical clock, say, even though the light was traveling at speed c, he would measure a slower speed in his reference frame, with the other clock, wouldn't he; is that how experiments would measure the speed of light?

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.)

That is one thing that I have trouble getting my head around as well, because it seems that according to relativity that both observers can assume that they are at rest in the one and only ether frame; it does seem like both observers are treated as being at absolute rest, from their own perspectives.

 

[mangaroosh]

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?

The part I don't get is how it demonstrates that it is the same in all directions, regardless of motion relative to the source.

In the MMX, there is no motion relative to the source, is that accurate? There is probably something that I am missing, but it seems to suggest that the wavelenght [of the reflected light] is the same from both mirrors.

 

[mangaroosh]

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.

But, let's just say that your orientation is such that the metre stick is the same, but the clock is slower; a measurement of 300,000 km/s would mean that the light traveled a distance of 300,000km in a length of time longer than the second measured by the rest clock (and therefore the rest observer).

If the metre stick contracts and the clock slows down, and the same measurement is noted (using the same instruments) then the light will have traveled a distance shorter than 300,000km, in a period of time longer than a second.

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.

Apologies, I'm not entirely sure of the point being made.

Just for the sake of [my own] clarity, when you say the mirrors are arranged at right angles to the direction of motion, I picture them being placed on the floor and ceiling (it could also be sidewalls, I presume). If the train is in motion [near the speed of light], then, just as with the horizontal mirrors (from front to back) the distance between the mirrors is not the actual distance the light travels because the mirrors are traveling also. The time it would take for both light beams to complete a round trip would be the same, wouldn't it?

 

[mangaroosh]

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.

But the oscillations are measured by firing a laser pulse into the "cloud" and the subsequent photon hits a detector; so, even though the clock in motion might have the same frequency, the photon might have a longer distance to travel to the detector (or shorter for a clock in motion opposite to the direction of the Earth's rotation) and thus account for the change in the "passing of time".

 

[mangaroosh]

I always found it simplest to assume length and time are unique to each reference frame and you need the Lorentz transform to synchronize them between different reference frames.

I think a problem with that is, if we say that the speed of light is 300,000 km/s in the Earth centred reference frame, then, unless the units are the same in another reference frame, a measurement of 300,000km/s [in that reference frame] is not the same.

 

[mangaroosh]

@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.

I just replied, a moment ago, to a post with a point similar to this so apologies if you have read it, and this sounds like repetition.

If we take the Earth centred reference frame for example, which is the frame in which "the second" and "the metre" are defined. If there is a reference frame moving relative to that such that their clock slows down, it means that their clock measures a "second" which is longer than "the second" on earth. If, using that clock, they measure the speed of light to be 300,000km/s, it means that that 300,000km/s isn't the same as the 300,000 km/s on Earth - and so the two speeds are, in actuality, different.

If they also experience length contraction, such that their metre is shorter than the Earth metre, and, along with their slower clock, they measure the speed of light to be 300,000 km/s, it would again mean that the measurement is not the same as the Earth measurement. In fact, it would mean that it took light a little over a second to travel a distance shorter than 300,000km.

 

[Dale]

If we take the Earth centred reference frame for example, which is the frame in which "the second" and "the metre" are defined.

As has already been pointed out, this is simply not true. See the link below for the definitions of the second and the meter. Note that the Earth centered reference frame is not mentioned.

http://www.bipm.org/en/si/base_units/

Please do not repeat this incorrect assertion again.

 

[mangaroosh]

As has already been pointed out, this is simply not true. See the link below for the definitions of the second and the meter. Note that the Earth centered reference frame is not mentioned.

http://www.bipm.org/en/si/base_units/

Please do not repeat this incorrect assertion again.

the Metre
How was the length of the path traveled by light in a vacuum measured, before the metre was defined in terms of the length of the path travlled by light in a vacuum?

the Second
The atomic clock used to register the oscillations of the caesium atoms e.g. the one in NIST, is that at rest relative to the earth, or in motion relative to it?

 

[russ_watters]

Again, neither of those two questions are relevant.

 

[Dale]

the Metre
How was the length of the path traveled by light in a vacuum measured, before the metre was defined in terms of the length of the path travlled by light in a vacuum?

On the BIPM website I linked to under each unit definition there is a link on the evolution of the definition. It contains all of the historical information on previous standards.

the Second
The atomic clock used to register the oscillations of the caesium atoms e.g. the one in NIST, is that at rest relative to the earth, or in motion relative to it?

The frequency detector is at rest wrt the cesium atoms. See the linked information on practical realizations. The detector and the cesium atoms may be at rest wrt the Earth like the NIST, or not, like shipboard or orbital clocks. The Earth centered frame is not part of the definition.

 

[mangaroosh]

Again, neither of those two questions are relevant.

I don't see why not.

 

[mangaroosh]

On the BIPM website I linked to under each unit definition there is a link on the evolution of the definition. It contains all of the historical information on previous standards.

The frequency detector is at rest wrt the cesium atoms. See the linked information on practical realizations. The detector and the cesium atoms may be at rest wrt the Earth like the NIST, or not, like shipboard or orbital clocks. The Earth centered frame is not part of the definition.

If we trace the evolution back, we can see that the Earth centred frame, although not expressly part of the any definition, is, as a result of the practicalities of the measurements, a tacit assumption of the definitions.

With regard to the atomic clock, the proper second is still defined in terms of an atomic clock at rest on earth, even correcting for the velocity of the atom in the lab - as a matter of interest, the velocity relative to what? - because it isn't defined in terms of the clocks traveling relative to the earth; that is, the clocks used in the Hafele-Keating epxeriment can't be said to have counted "the proper second" when they return to rest on earth.

 

[Dale]

If we trace the evolution back

The definitions of previous standards are not relevant to the definition of the current standard, except in terms of backwards compatibility. The current standard is not based on the Earth centered frame.

With regard to the atomic clock, the proper second is still defined in terms of an atomic clock at rest on earth

Please cite your source. This is either a personal misunderstanding or a non-mainstream source.

 

[harrylin]

It wasn't necessarily that Maxwell's equations were defined relative to the light medium, was it? Was it not just that Maxwell believed that the equatiosn implied an ether? The equations weren't changed due to relativity were they?

The equations were not changed but generalised. Originally they were assumed to be valid relative to one inertial frame (retained with the second postulate), nowadays they are assumed (neglecting gravitation) to be valid relative to any inertial frame (the first postulate). Effectively that is what the combination of the two postulates means.

[One of] the consequence of assuming Newtonian [absolute] time, was that clocks in all reference frames would tick at the same rate, wasn't it? This would have meant that a clock on a [moving] train would provided a measurement in units that was meangingful to an observer at rest on earth; such that the 's' in the definition of the speed of light would have been the same. If a clock on a moving train ticks slower, however, it would mean that that a measurement of 300, 000 km/s would not be the same as the same measurement in the Earth centred reference frame.

The combination of relativity of simultaneity + time dilation + Lorentz contraction assures that the same speed of light will be measured. The best way (probably the only way!) to fully understand that, is to do an example calculation yourself, for example with v=0.8c.

What is meant by adjusted" in the above, do you know?

That refers to the freely chosen simultaneity: when we set up a standard inertial reference system, we make the time for a light signal along that system in one direction equal to that in the opposite direction by means a convenient adjustment of clocks (clock synchronisation procedure).

Again, apologies, I tend to get confused with things like that, because the MMX and the KTX usually get cited as examples of experiments which demonstrate the constancy of the speed of light, which I presume to be the second postulate.

What some textbooks mean with "the constancy of the speed of light" is not exactly the second postulate. The confusion is due to such sloppy textbooks. A few years ago there was a physics paper (I think in the AJP) that did a futile(?) attempt to correct such misunderstandings... The second postulate of special relativity is just what I cited: in a single inertial frame is the (operationally defined) speed of light in vacuum everywhere and in all directions the same constant.

The part I don't get is how it demonstrates that it is the same in all directions, regardless of motion relative to the source.

In the MMX, there is no motion relative to the source, is that accurate? There is probably something that I am missing, but it seems to suggest that the wavelenght [of the reflected light] is the same from both mirrors.

What you are missing - probably because the book you read forgot to mention it - is that the Fizeau experiments supports the fact that the speed of light is incompatible with ballistic light models. Michelson and Morley also repeated that experiment. Thus they assumed it to be a proven fact that light propagates as a wave with speed of propagation c according to Maxwell's model. Next they tried in vain to detect a small anisotropy of the two way speed of light in different directions at different times of the year.

- http://en.wikisource.org/wiki/Influence_of_Motion_of_the_Medium_on_the_Velocity_of_Light
- http://en.wikisource.org/wiki/On_the_Relative_Motion_of_the_Earth_and_the_Luminiferous_Ether

 

[harrylin]

the Metre
How was the length of the path traveled by light in a vacuum measured, before the metre was defined in terms of the length of the path travlled by light in a vacuum?

the Second
The atomic clock used to register the oscillations of the caesium atoms e.g. the one in NIST, is that at rest relative to the earth, or in motion relative to it?

The original (and more pure or fundamental) definitions are the standard meter and kg as well as the solar day. For convenience (increased precision) impure (indirect) definitions are used nowadays. For theoretical discussions it is often better to stick to the pure definitions in order to avoid circular arguments as well as discrepancies with the definitions that were used for the formulation of the theory; however this should of course be clarified at the start.

Atomic clocks as used by NIST are at rest on the earth, and corrected for such things as altitude, pressure, temperature,...
Thanks to a lucky fact of the shape of the earth, it is not necessary to make a correction for the rotational speed: the clock slowdown due to rotation speed is compensated by the rate increase due to the higher potential from the bulging of the Earth as a result of that same rotation.

 

[mangaroosh]

The definitions of previous standards are not relevant to the definition of the current standard, except in terms of backwards compatibility. The current standard is not based on the Earth centered frame.

They are relevant though if they form part of the basis for the new measurement; for example, the measurement of the path length of light in a vacuum first has to be measured using the existing standard.

Please cite your source. This is either a personal misunderstanding or a non-mainstream source.

If it is a misunderstanding, then it is a personal one. It could probably easily be cleared up though by asking if the clocks flown in planes in the Hafele-Keating experiment can be said to have measured the proper second. I presume the answer has to be no, because if they did they wouldn't have had net losses or gains.

 

[mangaroosh]

The equations were not changed but generalised. Originally they were assumed to be valid relative to one inertial frame (retained with the second postulate), nowadays they are assumed (neglecting gravitation) to be valid relative to any inertial frame (the first postulate). Effectively that is what the combination of the two postulates means.

That's not so much to do with the equations themselves, but rather the interpretation of them isn't it? Isn't is possible that the measurements which lead to the derivation of the equations could carry certain tacit assumptions with them?

The combination of relativity of simultaneity + time dilation + Lorentz contraction assures that the same speed of light will be measured. The best way (probably the only way!) to fully understand that, is to do an example calculation yourself, for example with v=0.8c.

Is RoS a result of time dilation and Lorentz contractions?

Just on that point, and this is somewhere I might lack clarity, but if someone uses a slower clock and a smaller ruler (than similar instruments at rest on earth) and if they measure the speed of light to be 300,000 km/s with those instruments, would it not mean that the speed of light in both frames is actually different; because it would mean that the light in the reference frame moving relative to the Earth actually took longer than a second to travel a distance shorter than 300,000 km?

That refers to the freely chosen simultaneity: when we set up a standard inertial reference system, we make the time for a light signal along that system in one direction equal to that in the opposite direction by means a convenient adjustment of clocks (clock synchronisation procedure).

What some textbooks mean with "the constancy of the speed of light" is not exactly the second postulate. The confusion is due to such sloppy textbooks. A few years ago there was a physics paper (I think in the AJP) that did a futile(?) attempt to correct such misunderstandings... The second postulate of special relativity is just what I cited: in a single inertial frame is the (operationally defined) speed of light in vacuum everywhere and in all directions the same constant.

The uni-directional speed of light is, essentially, an untestable assumption though isn't it? If it was abandoned, because it is untestable, and replaced with the notion that the round trip speed of light is the same for all observers,would that affect any of the conclusions drawn from experiments?

What you are missing - probably because the book you read forgot to mention it - is that the Fizeau experiments supports the fact that the speed of light is incompatible with ballistic light models. Michelson and Morley also repeated that experiment. Thus they assumed it to be a proven fact that light propagates as a wave with speed of propagation c according to Maxwell's model. Next they tried in vain to detect a small anisotropy of the two way speed of light in different directions at different times of the year.

- http://en.wikisource.org/wiki/Influence_of_Motion_of_the_Medium_on_the_Velocity_of_Light
- http://en.wikisource.org/wiki/On_the_Relative_Motion_of_the_Earth_and_the_Luminiferous_Ether

I came across this abstract when looking up the Fizeau experiment, but unfortunately I can't find the full paper [without having to pay for it]:

The motivation and interpretation of the Fizeau experiment are reviewed, and its status as a test of special relativity is discussed. It is shown, with the aid of a simplified, purely mechanical, model of the propagation of light in matter, that the experiment actually cannot discriminate between Galilean and relativistic kinematics.

http://ajp.aapt.org/resource/1/ajpias/v48/i12/p1059_s1?isAuthorized=no

Are you familiar with the paper by any chance?

 

[mangaroosh]

The original (and more pure or fundamental) definitions are the standard meter and kg as well as the solar day. For convenience (increased precision) impure (indirect) definitions are used nowadays. For theoretical discussions it is often better to stick to the pure definitions in order to avoid circular arguments as well as discrepancies with the definitions that were used for the formulation of the theory; however this should of course be clarified at the start.

Atomic clocks as used by NIST are at rest on the earth, and corrected for such things as altitude, pressure, temperature,...
Thanks to a lucky fact of the shape of the earth, it is not necessary to make a correction for the rotational speed: the clock slowdown due to rotation speed is compensated by the rate increase due to the higher potential from the bulging of the Earth as a result of that same rotation.

When you say the pure definitions, do you mean things like the metre being defined in terms of the meridian (was it?) of the earth?

It seems, although not expressly stated, that measurements expressed in those units tacitly assume the Earth centred reference frame as the rest frame; as you mention atomic clocks are at rest on earth, and the "pure" definitions would have been relative to the Earth centred rest frame too.

 

[Dale]

the measurement of the path length of light in a vacuum first has to be measured using the existing standard.

No, it doesn't. The current standard stands on its own. There is no need to do any measurements using previous standards in order to implement the current standard.

It could probably easily be cleared up though by asking if the clocks flown in planes in the Hafele-Keating experiment can be said to have measured the proper second. I presume the answer has to be no, because if they did they wouldn't have had net losses or gains.

The correct answer is "yes, the clocks flown in planes in the Hafele-Keating experiment measured proper seconds". Proper time is defined as the time measured by a clock, and identified with the spacetime interval in both special and general relativity. It has nothing to do with the Earth centered reference frame, except coincidentally for clocks which happen to be at rest in the Earth centered reference frame.

 

[Dale]

Just on that point, and this is somewhere I might lack clarity, but if someone uses a slower clock and a smaller ruler (than similar instruments at rest on earth) and if they measure the speed of light to be 300,000 km/s with those instruments, would it not mean that the speed of light in both frames is actually different;

What you say would be correct except that you are forgetting the relativity of simultaneity. The Lorentz transform is not just length contraction and time dilation, but it also includes the relativity of simultaneity. You cannot just ignore it and get correct conclusions.

 

[mangaroosh]

No, it doesn't. The current standard stands on its own. There is no need to do any measurements using previous standards in order to implement the current standard.

The previous standard, however, forms the basis for the current standard. Again, the path length of light in a vacuum had to be measured using the existing standard, before the path length of light in a vacuum could be used as the standard. This would be so right the way back the line, and so the implications would be the same.

The correct answer is "yes, the clocks flown in planes in the Hafele-Keating experiment measured proper seconds". Proper time is defined as the time measured by a clock, and identified with the spacetime interval in both special and general relativity. It has nothing to do with the Earth centered reference frame, except coincidentally for clocks which happen to be at rest in the Earth centered reference frame.

The seconds measured by the clocks in the Hafele-Keating experiment did not measure seconds equal to that of the clock at rest on earth, so both cannot be said to have measured proper seconds, because that would mean that proper seconds are different in each reference frame. That would infer that a measurement of 300,000 km/s in one reference frame is materially different to that in another.

What you say would be correct except that you are forgetting the relativity of simultaneity. The Lorentz transform is not just length contraction and time dilation, but it also includes the relativity of simultaneity. You cannot just ignore it and get correct conclusions.

Forgive me for copying and pasting someone else's response [on another forum] to this point; I'd effectively just be saying the same thing anyway - the emphases are the other persons.

ROS is a subsidiary shorthand way of using distance contraction and time dilation and is not a separate stand-alone component of SR. ROS is a SUBSTITUTE for distance contraction and/or time dilation. It is NOT an additional function.

 

[Dale]

Again, the path length of light in a vacuum had to be measured using the existing standard, before the path length of light in a vacuum could be used as the standard.

This is not true. By historical accident the previous standard was measured before the current standard was, but there is no reason that it had to have happened that way. Back in Romer's day, in 1676, long before the BIPM ever made the first meter standard, someone could have defined a unit of length based on the distance light travels in 1/299792458 second and named it the meter.

The seconds measured by the clocks in the Hafele-Keating experiment did not measure seconds equal to that of the clock at rest on earth, so both cannot be said to have measured proper seconds, because that would mean that proper seconds are different in each reference frame.

Proper time is frame invariant but path dependent. The different clocks in the HK experiment measured different amounts of proper time because they took different paths. See: http://en.wikipedia.org/wiki/Proper_time

Please read the wikipedia article to begin. It is clear that you have some misunderstanding of what proper time is, and it is one of the most important concepts of relativity. If you have any questions, I would be glad to clarify.

ROS is a subsidiary shorthand way of using distance contraction and time dilation and is not a separate stand-alone component of SR. ROS is a SUBSTITUTE for distance contraction and/or time dilation. It is NOT an additional function.

Completely incorrect. I can easily come up with a coordinate transformation which has length contraction and time dilation, but not relativity of simultaneity. Likewise, I can easily come up a coordinate transform which does not have length contraction nor time dilation but does have the relativity of simultaneity.

They are three separate features of the Lorentz transform, and all three are required. You cannot simply use length contraction and time dilation and assume that relativity of simultaneity is somehow autmoatically included.

 

[harrylin]

That's not so much to do with the equations themselves, but rather the interpretation of them isn't it? Isn't is possible that the measurements which lead to the derivation of the equations could carry certain tacit assumptions with them?

That's always possible; however both postulates were based on a long history of measurements and successful theories that were based on each.

Is RoS a result of time dilation and Lorentz contractions?

In a certain way, but it's also the result of a human choice. Thanks to time dilation and Lorentz contraction the PoR applies to all laws of nature; consequently no absolute simultaneity can be established. Thus we can freely choose to make a relativity of simultaneity, as is the custom. Alternatively one could define for example the centre of the universe as in rest, and synchronize our clocks accordingly.

Just on that point, and this is somewhere I might lack clarity, but if someone uses a slower clock and a smaller ruler (than similar instruments at rest on earth) and if they measure the speed of light to be 300,000 km/s with those instruments, would it not mean that the speed of light in both frames is actually different; because it would mean that the light in the reference frame moving relative to the Earth actually took longer than a second to travel a distance shorter than 300,000 km?

You forgot the RoS, and according to the PoR we can't determine what is actually true for such cases. Instead, we can only operationally define such things as "speed of light" without any metaphysical meaning as to what "really" occurs. That is the basic message of the introduction of Einstein's 1905 paper.
However, necessarily the velocity of a light ray relative to both frames as measured with an independent reference system is indeed different. As a matter of fact, that velocity (also called "closing velocity" in modern jargon) is equal to the vector subtraction (c-v).

The uni-directional speed of light is, essentially, an untestable assumption though isn't it? If it was abandoned, because it is untestable, and replaced with the notion that the round trip speed of light is the same for all observers,would that affect any of the conclusions drawn from experiments?

That would change nothing as you can easily understand by you re-reading my 1907 citation of the second postulate.

Effectively Einstein assumed that when setting up a reference system we can make the one-way speed equal to the round trip speed which is postulated (as a law of physics) to be constant (everywhere and in all directions, independent of the motion of the source); and we postulate also that all laws of physics must be valid for all inertial reference systems. Combining those two postulates, we find that the round trip speed must be the same constant in all inertial reference systems, and we can make the one-way speed equal to the measured two-way speed by convenient clock synchronization. That is important to keep the laws of physics free from unnecessary complexity.

I came across this abstract when looking up the Fizeau experiment, but unfortunately I can't find the full paper [without having to pay for it]:

http://ajp.aapt.org/resource/1/ajpias/v48/i12/p1059_s1?isAuthorized=no

Are you familiar with the paper by any chance?

Sorry no, but it's likely irrelevant: it is well known that such tests are too imprecise to distinguish between the Galilean transformation and the Lorentz transformation. Much more relevant are the introductions of the papers to which I gave you the links and which explain why ballistic light theory was disproved before the end of the 19th century.