Constancy of c - second postulate

the Metre
How was the length of the path travelled 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 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.

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

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.

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.

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.

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/Influe...ocity_of_Light
- http://en.wikisource.org/wiki/On_the...niferous_Ether

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.

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.

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

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;

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 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.

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.

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.

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.

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.

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.

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?

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?

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?

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]:

American Journal of physics

Are you familiar with the paper by any chance?

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.

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.



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?




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.



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 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?



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.

@George - just wondering if you had a chance to read this post by any chance; I had a few questions on the analogy you used.

Yes, I read your post and was impressed by your level of understanding. I've said before, you seem to understand a lot about relativity. Am I right?

Thanks George, I think I've got a half decent understanding of certain concepts, but obviously far from a full understanding. Based on that understanding though, Einsteinian relativity doesn't seem to sit well with me, so I'm hoping that through discussing it in depth I'll either confirm my bias or resolve those issues.

Just referring back to the RC plane analogy, with the planes that don't experience wind resistance, if the RC planes making their journey across the "big" plane in flight were to arrive simultaneously at the detector, I don't think we would conclude that length contraction and/or time dilation occurred, would we?

Also could we conclude that a person on the ground would measure the same speed of the planes as the RC operators? I think based on our previous discussions, that we couldn't; I'm just trying to figure out, what a reasonable conclusion would be from that scenario?

Also, just wondering if you had any thoughts on the issue of the moving observer measuring the speed of light; we mentioned that he would measure the speed to be c if he used a light clock, but if he were to use a mechanical clock, for example, an infinitely precise pendulum clock, then he would measure a speed different to c. I'm wondering if there are any issues that mean we couldn't use such an idealised pendulum clock? Is the fact that it wouldn't work in an inertial reference frame in deep space sufficient reason to exclude it?

Not a pendulum-clock, which is physically a system to which the Earth belongs. This case had to be excluded.

Also, just on the point of being at absolute rest in the ether frame, this is something which also doesn't sit too well with me; I often hear that Lorentzian relativity contains the superfluous assumption of an undetectable, absolute rest frame, but Einsteinian relativity seems to include the assumption that reference frames are at rest in that rest frame, which doesn't seem to be any less of an assumption - to my mind it seems more objectionable.

Planes that don't experience wind resistance are not a part of my analogy and you shouldn't be introducing them into the discussion.

I covered the situation where the measurement was made while stationary on the ground. You shouldn't be asking about this again.

It's not just in deep space but at different altitudes on earth. Note 7 of Einstein's 1905 paper says:

You shouldn't be bringing this up. Isn't it obvious that if you want to use a mechanical clock, it must be one that is not going to be influenced by environmental factors? You could use a mechanical clock that has a balance wheel in it, the type that Einstein says to use.

Why do you object to any assumption that doesn't conflict with experimental evidence? You are free to adopt ether Lorentzian relativity or Einsteinian relativity (or both) since they both comport with reality identically (they both stand or fall together) but to argue that one should be excluded because it "doesn't sit too well with me" or because "to my mind it seems more objectionable" is the height of arrogance.

In the scenario of the moving train, where the slower relative [to the train carriage] speed of light would be offset by the slower ticking light clock, would the use of such a mechanical clock to measure the speed of light lead to the observer measuring a slower speed.

I don't think it's a matter of arrogance, rather a matter of reason.

The objection to Lorentzian relativity, that usually seems to get cited as the reason for preferring Einsteinian relativity, is the fact that it doesn't have the undetectable, absolute rest frame; while Einsteinian relativity appears to treat each reference frames as though they are that absolute rest frame - that doesn't appear to be too different from my own reasoning.

However, that I find it more objectionable is not necessarily a conscientious preference for one over the other, rather that from trying to develop an understanding of both theories, the process of assimiltation of information has lead, for some reason, to Einsteinian relativity not sitting well; that could be, in part, due to the reasons that are given for preferring Einsteinian relativity over Lorentzian.

EDIT: also possibly because it seems like the superfluous assumption [of an absolute rest frame] that seems to make Lorentzian relativity less attractive, could probably be done away with, within the context of Lorentzian relativity.

Now if that were the case, then there would be an experiment that would violate the Principle of Relativity in different Frames of Reference. You can rest assured that any type of accurate clock that isn't influence by environment factors will give identical results.

It sounds like you don't like either one!!

You said earlier, "I think I've got a half decent understanding of certain concepts, but obviously far from a full understanding". Could you please itemize those concepts that you feel you half-way understand?