I Did Einstein Formulate an Aberration of Light Using Tangents?

[Clovis]

TL;DR Summary

Did Einstein ever give a formula for the aberration of light in terms of tangents?

Hello, everyone. I am trying to find an aberration of light formula in Einstein's writings that is given in terms of tangents. I did a fairly thorough internet search and all I could find was the formula he wrote in terms of cosines. Yet I have a vague memory that somewhere he did give the formula in terms of tangents.

Am I misremembering this or did he write such a tangents formula? Thank you. Any help would be appreciated.Clovis

 

[SiennaTheGr8]

No idea whether he ever expressed it explicitly in terms of tangents rather than cosines, but—at the risk of stating something you already know—the expressions are mathematically equivalent and follow from combining the Lorentz transformation with basic trigonometry.

 

[Clovis]

Thank you, Sienna. The reason for my question was merely to give proper credit for the tangent equation in a website that I am working on. But I appreciate your reply, all the same.

Clovis

 

[PAllen]

Thank you, Sienna. The reason for my question was merely to give proper credit for the tangent equation in a website that I am working on. But I appreciate your reply, all the same.

Clovis

The point is that modifying an equation by high school math is not considered a new result in need of crediting. The Pythagorean theorem can be written with or without square root. Does anyone care who first happened to write it using the modern symbol for square root, rather than in terms of squares?

 

[Histspec]

As far as I know:

The tangens aberration formula in terms of half angles: Plummer, 1910, On the Theory of Aberration and the Principle of Relativity, p. 258:

$$\tan\frac{1}{2}\phi'=\sqrt{\left(\frac{U-v}{U+v}\right)}\tan\frac{1}{2}\phi$$

The tangens aberration formula: Max von Laue, 1911, Das Relativitätsprinzip, p. 90:

$$\rm{tg}\,\vartheta=\frac{\sin\vartheta'\sqrt{1-\beta^{2}}}{\cos\vartheta'+\beta}$$

 

[vanhees71]

The point is that modifying an equation by high school math is not considered a new result in need of crediting. The Pythagorean theorem can be written with or without square root. Does anyone care who first happened to write it using the modern symbol for square root, rather than in terms of squares?

Hm, the first part of Einstein's 1905 paper is just algebraic and should be doable at high-school level. Are you saying that thus Einstein's first (and in a sense most important) part of this paper should not be "considered a new result in need of crediting", only because it's doable with high-school math? That's pretty ridiculous, isn't it?

 

[vanhees71]

Be careful with formulae which use tan rather than cos and sin! What you usually really need is not simply arctan but what's called atan2 in many computer languages (including my still beloved FORTRAN ;-))).

 

[PAllen]

Hm, the first part of Einstein's 1905 paper is just algebraic and should be doable at high-school level. Are you saying that thus Einstein's first (and in a sense most important) part of this paper should not be "considered a new result in need of crediting", only because it's doable with high-school math? That's pretty ridiculous, isn't it?

Come on, I meant that rearranging an equation using trig identities doesn't make it a new result. Otherwise, look at all the papers one could publish for trivialities.