Constancy of c - second postulate

[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.

 

[harrylin]

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.

With "pure" I simply meant a definition that is not derived from other definitions by means of assumptions - for example the standard kg in Paris I call "pure". However, it is not at rest in the ECI frame; for that you would have to measure something at for example the North Pole.

 

[mangaroosh]

@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.

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.

 

[ghwellsjr]

@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?

 

[mangaroosh]

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?


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.

 

[ghwellsjr]

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?

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

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?

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

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?

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

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

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.

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.

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.

 

[mangaroosh]

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

Apologies, I was trying to get a better understanding of the MMX without the notion of an ether wind.

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

Apologies, I thought they were different questions

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.

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.

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.

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.

 

[ghwellsjr]

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.

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.

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.

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?

 

[mangaroosh]

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.

Is there an experiment which would reveal such a violation of the PoR, given that many such experiments don't actually measure the speed of light in terms of distance/time?

I try to picutre the MMX in such a scenario, but wonder if it would reveal that the light was traveling slower relative to the carriage, because the light would still be traveling at an actual speed of c.

It sounds like you don't like either one!

sorry, I meant less attractive for proponents of Einsteinian relativity (to generalise and sterotype )

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?

I haven't tried to itemise them before, so I'm not sure if I'll label them correctly. I suppose whatever concepts you reckoned I had a good understanding of; I'm not sure what the concepts are apart from some generic terms, because my understanding is based on discussions with those more knowledgeable, on the topic, than myself, and the specific concepts might not always be named, or I might not recognise them as specific concepts.

The obvious ones would be:
- Time dilation
- Length contraction
- RoS (although that might be disputable - my level of understanding that is)
- the constancy of the speed of light
- twin paradox
- reference frames
- clock synchronisation
- Principle of Relativity
- Equivalence principle

 

[harrylin]

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. [..]

There are quite different things called "Einsteinian relativity": his philosophy and his theories of physics, and those are often mixed up - although his philosophy is perhaps not well understood and it certainly changed over time.

For example, Ives was a physicist who claimed to reject SR - until he apparently realized that what he rejected was not really the theory itself but a popular interpretation of the theory which he deemed inconsistent. In one of his later papers he even re-derived SR, using other postulates (Maxwell + conservation laws). That could be instructive.

 

[ghwellsjr]

Is there an experiment which would reveal such a violation of the PoR, given that many such experiments don't actually measure the speed of light in terms of distance/time?

There are plenty of experiments that confirm PoR, Einstein's first postulate. There are plenty of experiments that confirm the round-trip speed of light is equal to c.
There are no experiments that violate Einstein's second postulate because they cannot measure the one-way speed of light.
The purpose of this forum is to learn relativity, not to try to find ways to disprove it.

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?

I haven't tried to itemise them before, so I'm not sure if I'll label them correctly. I suppose whatever concepts you reckoned I had a good understanding of; I'm not sure what the concepts are apart from some generic terms, because my understanding is based on discussions with those more knowledgeable, on the topic, than myself, and the specific concepts might not always be named, or I might not recognise them as specific concepts.

The obvious ones would be:
- Time dilation
- Length contraction
- RoS (although that might be disputable - my level of understanding that is)
- the constancy of the speed of light
- twin paradox
- reference frames
- clock synchronisation
- Principle of Relativity
- Equivalence principle

Can you tell me what the meaning of "event" is in the context of Special Relativity?

 

[mangaroosh]

There are plenty of experiments that confirm PoR, Einstein's first postulate. There are plenty of experiments that confirm the round-trip speed of light is equal to c.
There are no experiments that violate Einstein's second postulate because they cannot measure the one-way speed of light.
The purpose of this forum is to learn relativity, not to try to find ways to disprove it.

Surely a good way to learn it is to subject it to critical questioning without any bias as to the outcome?

Can you tell me what the meaning of "event" is in the context of Special Relativity?

I probably can't give the exact definition, and my terminology may not be exact, but roughly I think it refers to anything that to which 3 spatial and a temporal co-ordinate can be assigned in a given frame of reference; for example, the striking of a pole by lightning can be assigned 4 co-ordinates (the point of impact that is - another location on the pole would have a different spatial co-ordinate - and possibly temporal depending on the size of the pole).

These co-ordinates can then be mathmatically transformed to give the co-ordinates of the same event from the perspective of a different reference frame.

 

[Dale]

Surely a good way to learn it is to subject it to critical questioning without any bias as to the outcome?

There is no such thing as "without any bias". SR goes against both our hard-wired nervous system and against our Newtonian training. Every student is biased against SR (including myself).

The best way to learn it is:
1) do homework problems so that you understand how it actually works (i.e. so that you don't mistakenly think that SR claims something it does not)
2) read the experimental evidence for and against it

 

[ghwellsjr]

Can you tell me what the meaning of "event" is in the context of Special Relativity?

I probably can't give the exact definition, and my terminology may not be exact, but roughly I think it refers to anything that to which 3 spatial and a temporal co-ordinate can be assigned in a given frame of reference; for example, the striking of a pole by lightning can be assigned 4 co-ordinates (the point of impact that is - another location on the pole would have a different spatial co-ordinate - and possibly temporal depending on the size of the pole).

These co-ordinates can then be mathmatically transformed to give the co-ordinates of the same event from the perspective of a different reference frame.

Good, but why did you say that another location on the pole might have a different temporal coordinate depending on the size of the pole?

 

[mangaroosh]

Good, but why did you say that another location on the pole might have a different temporal coordinate depending on the size of the pole?

In the context of the lightning pole it mightn't make sense, but if the pole was enormous say, such that one end was higher up in the gravitational potential, then time would run at different rates at either end of the pole - I've heard it, somewhat lightheartedly said, that the time at our head and our feet is slightly different .

 

[mangaroosh]

There is no such thing as "without any bias". SR goes against both our hard-wired nervous system and against our Newtonian training. Every student is biased against SR (including myself).

The best way to learn it is:
1) do homework problems so that you understand how it actually works (i.e. so that you don't mistakenly think that SR claims something it does not)
2) read the experimental evidence for and against it

The thing I have trouble with is trying to relate the maths to the physical, real world phenomena, which is why I find it helpful to discuss the physical phenomena and see what is being claimed.

 

[ghwellsjr]

These co-ordinates can then be mathmatically transformed to give the co-ordinates of the same event from the perspective of a different reference frame.

Tell me what you know about this mathematical transform, please.

 

[Dale]

The thing I have trouble with is trying to relate the maths to the physical, real world phenomena, which is why I find it helpful to discuss the physical phenomena and see what is being claimed.

That is precisely the value of homework problems, and one reason why I recommend it as the best way to learn.

 

[mangaroosh]

Tell me what you know about this mathematical transform, please.

I'm a bit sketchy on this, I think I've got a general understanding of it but not a technically detailed one.

My understanding is that it is a means of translating the co-ordinates of an event in one reference frame into the co-ordinates of another. The scaling factor gamma, or Lorentz factor is involved.

I don't know the technical details of the formula, but what I've encountered suggests that it can be derived using the Pythgorean theorem - as per the video explanation I posted (in this thread I think it was).

 

[rjaindia]

I think there is only one postulate...that of relativity...that all observers in an inertial frame will find all phenomena to be described by the same equations...from this obviously it follows that the velocity of light has to be constant for all observers...otherwise relativity will not hold...
Hence really there is only ONE postulate...that of relativity...the other (constancy of the velocity of light) is a corollary of it...

 

[Dale]

Hi rjaindia, welcome to PF!

from this obviously it follows that the velocity of light has to be constant for all observers...otherwise relativity will not hold

How so? It is not so obvious to me.

 

[ghwellsjr]

Tell me what you know about this mathematical transform, please.

I'm a bit sketchy on this, I think I've got a general understanding of it but not a technically detailed one.

My understanding is that it is a means of translating the co-ordinates of an event in one reference frame into the co-ordinates of another. The scaling factor gamma, or Lorentz factor is involved.

I don't know the technical details of the formula, but what I've encountered suggests that it can be derived using the Pythgorean theorem - as per the video explanation I posted (in this thread I think it was).

We're talking about the Lorentz Transform and there are actually two formulas (really four but the other two are trivial), one for the new time coordinate and one for the new x-coordinate, and both are functions of the old time coordinate, the x-coordinate, and the speed difference between the old frame and the new frame. They are really very simple, especially if you use compatible units where c=1. I'm assuming, like everyone else, that you only doing the standard convention.

But the reason I asked is because there is no provision for gravity in the Lorentz Transform or in Special Relativity. We pretend like the effects gravity don't exist when we're doing transforms in SR so you don't need to worry about how time is effected by height.

 

[ghwellsjr]

I think there is only one postulate...that of relativity...that all observers in an inertial frame will find all phenomena to be described by the same equations...from this obviously it follows that the velocity of light has to be constant for all observers...otherwise relativity will not hold...
Hence really there is only ONE postulate...that of relativity...the other (constancy of the velocity of light) is a corollary of it...

The constancy of the measured two-way velocity of light is covered under the first postulate, which is the principle of relativity--not Special Relativity. The second postulate concerns the one-way speed of light or the propagation of light which cannot be measured but is defined to be the same as the two-way velocity of light. It takes both of these postulates, the principle of relativity and the constancy of the propagation of light, in order to get Special Relativity, according to Einstein.

 

[harrylin]

[..] Hence really there is only ONE postulate...that of relativity...the other (constancy of the velocity of light) is a corollary of it...

No, the second postulate is not that the speed of light is the same for all observers; and it's not a corollary of the first postulate, but it is in apparent contradiction with it.

See my earlier posts in this thread:
https://www.physicsforums.com/showthread.php?p=3742805 #29
https://www.physicsforums.com/showthread.php?p=3187482 #2

 

[Dale]

The constancy of the measured two-way velocity of light is covered under the first postulate

How so?

 

[DrGreg]

The second postulate asserts that, within any single inertial frame, the one-way speed of light is a constant value. (So it doesn't depend on the motion of the source or the direction of propagation.) It doesn't assert that the constant value is the same in every frame, but that is something that follows from the first postulate (otherwise you would have a method for distinguishing one frame from another). So to obtain the invariance of the speed of light in all frames you need both postulates.

The second postulate (without the first postulate) implies that, within any single inertial frame,

• the two-way speed of light is constant (something we can confirm or falsify by experiment)
• we will, by convention, use a clock-synchronisation method to make the one-way speed of light equal the two-way speed (a definition, once (a) is assumed)

 

[ghwellsjr]

The constancy of the measured two-way velocity of light is covered under the first postulate

How so?

In his 1905 paper, near the end of section 1, Einstein makes the following statement:

In agreement with experience we further assume the quantity

to be a universal constant—the velocity of light in empty space.

He's talking about the measured round-trip speed of light. "A" is the location of the clock, "B" is the location of the mirror, so "2AB" is the round-trip distance the light has to travel, "t_A" is the time the light starts from the clock at "A" and "t'_A" is the time the reflection arrives back at the clock at "A", and the calculation, by experience always yields c no matter what was the inertial state of motion under which the measurement was made.

This was the measurement that lead to the Lorentz Transformation as the basis for the new Principle of Relativity because the old one based on the Galilean Transformation didn't work any more. In the Lorentz Ether Theory, the presumed second postulate was that light propagated at c only in one absolute ether rest state but due to length contraction and time dilation, the measured round-trip speed of light always came out the same even when the experiment was done in motion through the ether.

When Einstein proposed his second postulate, it was a follow-on to the first one and he noted that it was apparently irreconcilable with the first one because it seemed impossible that light could make both parts of the trip in the same amount of time under differing states of inertial motion in any measurement of the round-trip speed of light.

The second postulate asserts that, within any single inertial frame, the one-way speed of light is a constant value. (So it doesn't depend on the motion of the source or the direction of propagation.) It doesn't assert that the constant value is the same in every frame, but that is something that follows from the first postulate (otherwise you would have a method for distinguishing one frame from another). So to obtain the invariance of the speed of light in all frames you need both postulates.

The second postulate (without the first postulate) implies that, within any single inertial frame,

• the two-way speed of light is constant (something we can confirm or falsify by experiment)
• we will, by convention, use a clock-synchronisation method to make the one-way speed of light equal the two-way speed (a definition, once (a) is assumed)

Here's Einstein's first formulation of the second postulate from the introduction of his paper:

light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body

And here is his second formulation of the second postulate from the beginning of section 2:

Any ray of light moves in the “stationary” system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body.

Note that in both of these formulations, Einstein specifically states that the speed is c, the same as the measured round-trip speed of light.

However, Einstein calls this second postulate "the principle of the constancy of the velocity of light", which I presume is the same as "the invariance of the speed of light", as you called it. I would repeat that the second postulate is a follow-on to the first one in which the value of the speed of light has already been "determined" (as Einstein says) to be c and so I agree with your two-part summary but I would say that (a) is part of the first postulate and (b) is the second postulate.

It is obvious from Einstein's elaboration of the second postulate in section 2 that he is excluding the two-way speed of light from it since he calls it a "ray" of light and defines its velocity as:

where the time interval is one-half of the measured round-trip interval.

 

[harrylin]

The second postulate asserts that, within any single inertial frame, the one-way speed of light is a constant value. (So it doesn't depend on the motion of the source or the direction of propagation.) It doesn't assert that the constant value is the same in every frame, but that is something that follows from the first postulate (otherwise you would have a method for distinguishing one frame from another). So to obtain the invariance of the speed of light in all frames you need both postulates.

The second postulate (without the first postulate) implies that, within any single inertial frame,

• the two-way speed of light is constant (something we can confirm or falsify by experiment)
• we will, by convention, use a clock-synchronisation method to make the one-way speed of light equal the two-way speed (a definition, once (a) is assumed)

Yes, that is exact.
Recycling in part my post #29, that directly follows from Einstein's 1907 formulation of the second postulate:

"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."

As we discussed in the past, for this to be possible the two-way speed must be the same in all directions.

 

[harrylin]

[..] Einstein calls this second postulate "the principle of the constancy of the velocity of light", which I presume is the same as "the invariance of the speed of light" [..]

George, please take note that with "invariant" people do not mean the same as "constant".

See my post #132 here:
https://www.physicsforums.com/showthread.php?t=575332&page=9&highlight=invariantHarald

 

[Dale]

In his 1905 paper, near the end of section 1, Einstein makes the following statement:

He's talking about the measured round-trip speed of light. "A" is the location of the clock, "B" is the location of the mirror, so "2AB" is the round-trip distance the light has to travel, "t_A" is the time the light starts from the clock at "A" and "t'_A" is the time the reflection arrives back at the clock at "A", and the calculation, by experience always yields c no matter what was the inertial state of motion under which the measurement was made.

This was the measurement that lead to the Lorentz Transformation as the basis for the new Principle of Relativity because the old one based on the Galilean Transformation didn't work any more. In the Lorentz Ether Theory, the presumed second postulate was that light propagated at c only in one absolute ether rest state but due to length contraction and time dilation, the measured round-trip speed of light always came out the same even when the experiment was done in motion through the ether.

When Einstein proposed his second postulate, it was a follow-on to the first one and he noted that it was apparently irreconcilable with the first one because it seemed impossible that light could make both parts of the trip in the same amount of time under differing states of inertial motion in any measurement of the round-trip speed of light.

Yes, I understand all of that, but that was not what I was asking. I was asking how the constancy of the measured two-way velocity follows from the first postulate as you claimed. Einstein did the definition of simultaneity using the two-way speed of light in the section before introducing his postulates, so it is not clear to me how the claim follows merely from the first postulate. I certainly don't see anything to that effect in his writing.

 

[harrylin]

[..] it is not clear to me how the claim follows merely from the first postulate. I certainly don't see anything to that effect in his writing.

It's quite the contrary. The PoR is perfectly consistent with Galilean relativity and the issue was how to combine Maxwell's laws with the PoR.

Harald

 

[John232]

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

Wow, this video is amazing, they actually solve for the Lorentz and assigned the time vairables correctly in the light clock experiment like I mentioned in another thread. Every other source I have seen on this doesn't. Guess you can't win them all.

I would have to say that Newton rigged physics to allow the equation of velocity to work for light, he did this by dividing the amount of length something traveled by the amount of time it traveled. It's funny people say Einstein overturned Newtonian Physics, but to start out he had to use this same equation to do it.

Say you drew the line of velocity on a coordinate plane, the line is true from -∞ to ∞. If you draw out the function for the lorentz transform on a coordinate plane, it has a hole at c. At the hole the two sides of the triangle become the same line, this line then gives the same values for spacetime dialation, so then you get your original equation for velocity. The concept of v=d/t may be more true for light than it is for anything else in the known universe.

You could show this by drawing where these two functions intersect at v=c. The Lorentz Transformation isn't true, but the velocity equation is true at this point.

 

[Dale]

The Lorentz Transformation isn't true, but the velocity equation is true at this point.

Then kindly explain the outcome of each of these experiments without using the Lorentz transform or formulas derived from it:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

 

[ghwellsjr]

In his 1905 paper, near the end of section 1, Einstein makes the following statement:

He's talking about the measured round-trip speed of light. "A" is the location of the clock, "B" is the location of the mirror, so "2AB" is the round-trip distance the light has to travel, "t_A" is the time the light starts from the clock at "A" and "t'_A" is the time the reflection arrives back at the clock at "A", and the calculation, by experience always yields c no matter what was the inertial state of motion under which the measurement was made.

This was the measurement that lead to the Lorentz Transformation as the basis for the new Principle of Relativity because the old one based on the Galilean Transformation didn't work any more. In the Lorentz Ether Theory, the presumed second postulate was that light propagated at c only in one absolute ether rest state but due to length contraction and time dilation, the measured round-trip speed of light always came out the same even when the experiment was done in motion through the ether.

When Einstein proposed his second postulate, it was a follow-on to the first one and he noted that it was apparently irreconcilable with the first one because it seemed impossible that light could make both parts of the trip in the same amount of time under differing states of inertial motion in any measurement of the round-trip speed of light.

Yes, I understand all of that, but that was not what I was asking. I was asking how the constancy of the measured two-way velocity follows from the first postulate as you claimed. Einstein did the definition of simultaneity using the two-way speed of light in the section before introducing his postulates, so it is not clear to me how the claim follows merely from the first postulate. I certainly don't see anything to that effect in his writing.

Before developing the definition of simultaneity, Einstein said in the introduction of his 1905 paper:

...unsuccessful attempts to discover any motion of the Earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate...

I assumed that he was talking about such experiments as MMX which compared the two-way speed of light along two paths at right angles to each other and established them to be the same.

 

[Dale]

Before developing the definition of simultaneity, Einstein said in the introduction of his 1905 paper:

I assumed that he was talking about such experiments as MMX which compared the two-way speed of light along two paths at right angles to each other and established them to be the same.

Sure, that gives some historical background that the measured invariance of the two way speed of light was already experimentally established. It does not support your claim that said invariance follows from the first postulate.

 

[ghwellsjr]

Sure, that gives some historical background that the measured invariance of the two way speed of light was already experimentally established. It does not support your claim that said invariance follows from the first postulate.

It's not my claim, I got it from Einstein.

If experiments indicated that the measured speed of light was not the same under different inertial states, wouldn't that disprove the Principle of Relativity? Isn't that what Maxwell thought his equations would lead to?

 

[Dale]

It's not my claim, I got it from Einstein.

For brevity let's use the abbreviation 2C for the statement that the measured two way speed of light is invariant. I see in the introduction Einstein's statements that 2C was an established experimental fact in his mind. After he introduced the two postulates 2C clearly follows from the second postulate. I don't see anywhere where he shows that the first postulate alone is sufficient to show 2C.

 

[ghwellsjr]

For brevity let's use the abbreviation 2C for the statement that the measured two way speed of light is invariant. I see in the introduction Einstein's statements that 2C was an established experimental fact in his mind. After he introduced the two postulates 2C clearly follows from the second postulate. I don't see anywhere where he shows that the first postulate alone is sufficient to show 2C.

Whenever Einstein discusses the second postulate, he always specifically refers to 1C and not 2C. He always uses terms like "propagation of light" or "a ray of light" or "how light travels" or "the progress of light" or "tracking light" or other similar terms. The point about 2C is that it establishes the universal constant value of c, the speed of light, a value that needs to be determined before the second postulate can be introduced. The second postulate does not say anything about the value of c or how to determine it or even what its value is. Instead, it establishes that the two portions of the round-trip measurement of the speed of light (whatever that is) takes the same amount of time in either direction.

 

[Dale]

Yes, I understand the relationship between 2C and 1C and I understand that the second postulate refers to 1C. That is not a point of disagreement.

I can see how you can easily arrive at 2C from only the second postulate. I cannot see how you can arrive at 2C from only the first postulate. That is the point of disagreement, and so far nothing you have shown even remotely resembles proof of that point.

I am not looking for more quotes from Einstein's OEMB, I am looking for a clear derivation that starts only with the first postulate and arrives at 2C. It is not in OEMB.

 

[ghwellsjr]

Yes, I understand that you can easily arrive at 2C from only the second postulate. That is not a point of disagreement.

I won't give you more quotes from Einstein's OEMB, but I will repeat some that I quoted earlier and provide your responses and then you can explain to me why you don't think Einstein was claiming that 2C comes out of the first postulate and does not require the second postulate. And I would like answers to my previous questions that you ignored.

Ok, here's the quote from the introduction:

...unsuccessful attempts to discover any motion of the Earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate...

to which you replied:

Sure, that gives some historical background that the measured invariance of the two way speed of light was already experimentally established.

and:

I see in the introduction Einstein's statements that 2C was an established experimental fact in his mind.

So if he wasn't talking about 2C when he said (previously quoted in post #86):

In agreement with experience we further assume the quantity c to be a universal constant—the velocity of light in empty space.

then what "laws of electrodynamics and optics" was he referring to when he conjectured they "will be valid for all frames of reference for which the equations of mechanics hold good"?

And finally, I would appreciate answers to my previous questions:

If experiments indicated that the measured speed of light was not the same under different inertial states, wouldn't that disprove the Principle of Relativity? Isn't that what Maxwell thought his equations would lead to?

 

[Dale]

I will repeat some that I quoted earlier and provide your responses and then you can explain to me why you don't think Einstein was claiming that 2C comes out of the first postulate and does not require the second postulate.

I don't think that he was claiming that 2C comes out of the first postulate alone because none of those quotes are even a vague outline of a proof that 2C comes out of the first postulate.

If experiments indicated that the measured speed of light was not the same under different inertial states, wouldn't that disprove the Principle of Relativity?

Not necessarily. The alternative is that Maxwells equations as written are not a law of nature, and that the real laws of electrodynamics were Galilean invariant.

Isn't that what Maxwell thought his equations would lead to?

I have no idea what Maxwell thought.

I have revisited the quotes and answered your questions, now answer mine: Can you or can you not provide a proof that 2C follows from the first postulate alone? I am not interested in history nor expert opinion (even Einstein's), either there is such a proof or there is not such a proof. To me the reasoning doesn't seem sound. I see no way to start only with the first postulate alone and follow a logical chain to get 2C