Albert Einstein: "If a ray of light be sent along the embankment, we see from the above that the tip of the ray will be transmitted with the velocity c relative to the embankment. Now let us suppose that our railway carriage is again travelling along the railway lines with the velocity v, and that its direction is the same as that of the ray of light, but its velocity of course much less. Let us inquire about the velocity of propagation of the ray of light relative to the carriage. It is obvious that we can here apply the consideration of the previous section, since the ray of light plays the part of the man walking along relatively to the carriage. The velocity W of the man relative to the embankment is here replaced by the velocity of light relative to the embankment. w is the required velocity of light with respect to the carriage, and we have w = c - v. The velocity of propagation of a ray of light relative to the carriage thus comes out smaller than c. But this result comes into conflict with the principle of relativity set forth in Section 5." http://www.bartleby.com/173/7.html

The result w = c - v (Newton's variable speed of light) does not "come into conflict" with the principle of relativity. Rather, it is perfectly consistent with this principle. In 1887, prior to the introduction of the length-contraction fudge factor, Newton's variable speed of light was the only speed-of-light concept able to explain the null result of the Michelson-Morley experiment:

"Emission theory, also called emitter theory or ballistic theory of light, was a competing theory for the special theory of relativity, explaining the results of the Michelson–Morley experiment of 1887. [...] The name most often associated with emission theory is Isaac Newton. In his corpuscular theory Newton visualized light "corpuscles" being thrown off from hot bodies at a nominal speed of c with respect to the emitting object, and obeying the usual laws of Newtonian mechanics, and we then expect light to be moving towards us with a speed that is offset by the speed of the distant emitter (c ± v)." https://en.wikipedia.org/wiki/Emission_theory

Banesh Hoffmann, Einstein's co-author, admits that, originally ("without recourse to contracting lengths, local time, or Lorentz transformations"), the Michelson-Morley experiment was compatible with Newton's variable speed of light, c'=c±v, and incompatible with the constant speed of light, c'=c:

"Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether." Banesh Hoffmann, Relativity and Its Roots, p.92 https://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768

See more here: https://twitter.com/pentcho_valev

Pentcho Valev

On Wednesday, September 21, 2022 at 1:17:28 PM UTC-7, Pentcho Valev wrote:
> Albert Einstein: "If a ray of light be sent along the embankment, we see from the above that the tip of the ray will be transmitted with the velocity c relative to the embankment. Now let us suppose that our railway carriage is again travelling along the railway lines with the velocity v, and that its direction is the same as that of the ray of light, but its velocity of course much less. Let us inquire about the velocity of propagation of the ray of light relative to the carriage. It is obvious that we can here apply the consideration of the previous section, since the ray of light plays the part of the man walking along relatively to the carriage. The velocity W of the man relative to the embankment is here replaced by the velocity of light relative to the embankment. w is the required velocity of light with respect to the carriage, and we have w = c - v. The velocity of propagation of a ray of light relative to the carriage thus comes out smaller than c. But this result comes into conflict with the principle of relativity set forth in Section 5." http://www.bartleby.com/173/7.html
>
> The result w = c - v (Newton's variable speed of light) does not "come into conflict" with the principle of relativity. Rather, it is perfectly consistent with this principle. In 1887, prior to the introduction of the length-contraction fudge factor, Newton's variable speed of light was the only speed-of-light concept able to explain the null result of the Michelson-Morley experiment:
>
> "Emission theory, also called emitter theory or ballistic theory of light, was a competing theory for the special theory of relativity, explaining the results of the Michelson–Morley experiment of 1887. [...] The name most often associated with emission theory is Isaac Newton. In his corpuscular theory Newton visualized light "corpuscles" being thrown off from hot bodies at a nominal speed of c with respect to the emitting object, and obeying the usual laws of Newtonian mechanics, and we then expect light to be moving towards us with a speed that is offset by the speed of the distant emitter (c ± v)." https://en.wikipedia.org/wiki/Emission_theory
>
> Banesh Hoffmann, Einstein's co-author, admits that, originally ("without recourse to contracting lengths, local time, or Lorentz transformations"), the Michelson-Morley experiment was compatible with Newton's variable speed of light, c'=c±v, and incompatible with the constant speed of light, c'=c:
>
> "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether." Banesh Hoffmann, Relativity and Its Roots, p.92 https://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768
>
> See more here: https://twitter.com/pentcho_valev
>
> Pentcho Valev
When Einstein says, "If a ray of light be sent along the embankment, we see from the above that the tip of the ray will be transmitted with the velocity c relative to the embankment," has has conceded that light shares the motion of the embankment in obedience to Galileo's principle of shared momentum and contrary to the second postulate.

On Wednesday, September 21, 2022 at 1:17:28 PM UTC-7, Pentcho Valev wrote:
>"The result w = c - v (Newton's variable speed of light) does not "come into conflict" with the principle of relativity. Rather, it is perfectly consistent with this principle. "
> Pentcho Valev
It is consistent with Galileo's principle of shared momentum. Is it clearly consistent with Poincare's reformulation of that principle? Not if the equations have to be kept the same across frames of reference (pretending relative motion does not exist).