Let's just read the passage in its entirety:
We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system; for we have not as yet furnished the proof that the principle of the constancy of the velocity of light is compatible with the principle of relativity.
At the time when the origin of the coordinates is common to the two systems, let a spherical wave be emitted therefrom, and be propagated with the velocity c in system K.
Transforming this equation with the aid of our equations of transformation we obtain [a solution].
The wave under consideration is therefore no less a spherical wave with velocity of propagation c when viewed in the moving system. This shows that our two fundamental principles are compatible. |
— Equations deleted.
Source.
Looks to me like Einstein claimed to have proved "that any ray of light, measured in the moving system, is propagated with the velocity c." :idunno:
Are you saying that Einstein did not prove the constancy of the speed of light?
Stripe, I will now nurse that puppy that was abused back to health, by including some details you are ignorant of or misrepresenting.
Michael Faraday (1791 – 1867) was a British fellow who was intensely interest in science from his youth. He was poorly educated, but as a young man he managed to get a job as an assistant to a prominent British scientist. In spite of his lack of education, he proved to be brilliant at thinking up and performing experiments, often dealing with magnets and electricity. His lack of mathematical training forced him to document what he discovered about E&M (electricity and magnetism) as best he could in journals without the benefit of concise equations. Yet he still managed to produce a wealth of data and discoveries about E&M.
James Clerk Maxwell, also a British scientist, was born 40 years after Faraday, and was well trained in mathematics and physics. Maxwell soon focused on the data and discoveries that Faraday had produced, and was able to reduce most of Faraday’s E&M discoveries to just 4 concise mathematical equations. The equations involve multi-variable calculus (sometimes called “Advanced Calculus), but in fact they depend on mathematical concepts (gradient and curl) that all physicists, and probably most engineers should be comfortable with.
Several new realizations about light quickly became evident, based on Maxwell’s equations. One was that the speed at which light travels (commonly denoted as just the letter “c”) could be computed by a simple equation involving two measurable constants (called permittivity and permeability). Permittivity deals with electricity and permeability deals with magnetism. It was not a big step then to realize that a light wave could be composed of a transverse magnetic field wave (which simply means the wave “crests” and “valleys” were up and down, similar to waves on the surface of a pond), and a perpendicular transverse electric field wave (meaning it also had crests and valleys like water waves, except these crests and valley were left and right). Embedded in this video it touches on this (plus a bit of other stuff - sorry):
But now comes the kicker that is directly relevant to Stripe’s rant. If the speed of light can be computed by the simple equation involving permittivity and permeability I alluded to above, now let’s have someone in a travelling train measure those two constants involved in the speed-of-light equation. Is he gonna get a different value than some scientist sitting in a lab at work will get? Not if Newton was right. Newton said the laws of nature do not change if someone is in uniform motion. But that means the train guy must measure the speed of light to be the same as the guy by the track, even though the train guy is racing along towards the oncoming beam of light.
TILT. That idea conflicts with Newton, since Newton (and “logic” and “common sense”, etc.) all said that the train's speed must be added to the speed of the oncoming beam of light.
This apparent constancy of c was recognized from Maxwell’s equations before Einstein was even born. For several decades physicists struggled with this incompatibility between Newton and Maxwell’s equations. Before Einstein was old enough to get involved there were experiments performed trying to understand this apparent anomaly (see MIchelson-Morley).
When Einstein was old enough, he became aware of and interested in this issue. He struggled with it, and reviewed the development of Maxwell’s equations. Satisfied that Maxwell was not in error, finally Einstein took the rather bold step of assuming that the constancy of c was not just an artifact due to how we measure speeds, but was a fundamental property of how nature worked. Once that light popped into his head, then he rather quickly followed what the math told him based on this radical new idea, and soon submitted the paper that Stripe misunderstands to a German Physics Journal.
It is significant to note that in his work Einstein derived some mathematical equations that are now referred to as the Lorentz Transformations. Why weren’t they named after Einstein? Because several physicists and mathematicians (including Hendrik Lorentz) were struggling with the incompatibility between E&M and Newton long before Einstein showed up. Lorentz decided to simply see if he could derive some equations which would convert E&M answers into Newton-compatible answers. He did that when Einstein was still a toddler. Had Lorentz taken the daring step of saying his equations were not just a useful mathematical tool, but instead they were a fundamental correction to Newton’s ideas, then we would be singing the praises of Lorentz, while Einstein might have been remembered as a minor figure in the history of physics.
Now on to the puppy-dog paper that Stripe keeps abusing. Once Einstein had fleshed out for himself the conclusions his radical idea led to, then he turned to the task of how to present it in a formal paper to be submitted to “The Annals of Physics” (English equivalent of the German Journal title). He starts his paper by mentioning some of the apparent incompatibilities between Maxwell’s E&M and Newtonian Mechanics. In the second paragraph of his paper, he explicitly mentions the constancy of c in Newtonian frames (meaning when measurements can be taken when moving, but not when accelerating). In that same second paragraph he first introduces the concept of what he calls “The Principle of Relativity”. He then proceeds to show how concepts which had long seemed to be without question were, in fact not valid, such as the idea that length is an absolute quantity. He shows how the constancy of c requires that the length of an object as measured from a non-moving observer has to contract when the object being measured is moving at a steady velocity. He concurrently shows that the measurement of time itself is altered when one of two originally identical clocks measures time differently than the other if either is put in motion.
A couple of pages later we come to the place that Stripe is interested in. Notice Stripe’s claim:
Looks to me like Einstein claimed to have proved "that any ray of light, measured in the moving system, is propagated with the velocity c." :idunno:
What Stripe has no clue about is that in the paper in question Einstein had just introduced a distinctly new way of understanding length and time, based on c being constant, and based on velocity. Einstein’s coming-in position was that c was a constant in the Newtonian world, but he had not showed that c was still invariant under this radical new “Relativistic” way of thinking. In Stripe’s reply he omitted the accompanying equations, probably because they involve mathematical symbols that would be hard to show in a TOL post. But he did link to the Einstein’s paper, so if anyone is interested, they can go to it.
As I noted a couple of posts back, the first equation in the section Stripe is concerned with is an equation used to describe an expanding spherical wave, similar to the wave that spreads out across the surface of a pond when a rock is tossed into it. The wave spreads out uniformly in all directions. But that first equation was for a wave in Newtonian space, not in the Relativistic system Einstein was proposing. But within a few paragraphs Einstein showed that even in his new Relativistic way of looking at things, the light wave still spreads out uniformly. Immediately thereafter, as Stripe’s quote shows Einstein did say “any ray of light, measured in the moving system, is propagated with the velocity c”. Einstein’s mention of “the moving system” is in direct reference to the whole subject he was addressing – a moving system as viewed from the standpoint of relativity.
It is interesting why Einstein would do no more than show light wave spreads out uniformly in his new system, and then declare that c was therefore a constant. It is because, unlike some amateur rabid dog-abusing doubters, Einstein knew that years before it had been shown that one of the simplest acid tests for any proposed solution to the conflict between Newton and E&M would be to show that a spherical wave would still be spherical when viewed from a moving reference frame. An earlier attempt to resolve the Newton-E&M conundrum was to postulate the existence of an ether – the substance that was believed to be what light waves were “waving” in. The famous Michelson-Morley experiment was an attempt to show that “ether” (but it failed). Had the ether existed, the speed of light in different directions would have been measurably different, and a spherical wave would deform as it spread.
So yeah, Einstein proved c was STILL a constant, IN THE NEW RELATIVITISTIC SYSTEM he was proposing. And the equations he used were the simplest ones that conclusively established that.
