# Did Einstein Formulate an Aberration of Light Using Tangents?

• I
• Clovis
In summary: What's the big deal?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. What's the big deal?
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

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.

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

Clovis said:
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?

PeroK
PAllen said:
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?

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 ;-))).

SiennaTheGr8
vanhees71 said:
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.

SiennaTheGr8

## What is the Einstein aberration formula?

The Einstein aberration formula is a mathematical equation that describes the effect of relative motion on the apparent position of objects in space. It was developed by Albert Einstein as part of his theory of special relativity.

## How does the Einstein aberration formula work?

The formula takes into account the speed of an observer and the speed of light to calculate the angle at which an object will appear to be positioned. It is based on the principle that the speed of light is constant for all observers, regardless of their relative motion.

## What is the significance of the Einstein aberration formula?

The formula is significant because it helps to explain the observed phenomenon of aberration, which is the apparent displacement of stars due to the Earth's motion around the Sun. It also supports Einstein's theory of special relativity and has been confirmed through various experiments and observations.

## Can the Einstein aberration formula be applied to everyday situations?

Yes, the formula can be applied to everyday situations involving relative motion, such as the Doppler effect in sound waves or the apparent motion of objects while driving in a car. However, its effects are only noticeable at very high speeds, close to the speed of light.

## Are there any limitations to the Einstein aberration formula?

While the formula accurately describes the effects of aberration in most cases, it does not take into account gravitational effects or the motion of objects at speeds approaching the speed of light. It is also not applicable to objects that are not moving at a constant velocity.

• Special and General Relativity
Replies
4
Views
2K
• Special and General Relativity
Replies
58
Views
4K
• Special and General Relativity
Replies
29
Views
2K
• Calculus and Beyond Homework Help
Replies
4
Views
1K
• Special and General Relativity
Replies
13
Views
2K
• Special and General Relativity
Replies
6
Views
1K
• Special and General Relativity
Replies
7
Views
2K
• Special and General Relativity
Replies
43
Views
4K
• Special and General Relativity
Replies
1
Views
2K
• Quantum Physics
Replies
78
Views
3K