Can the speed of light be exceeded by relative velocities?

[Garen]

Just wondering, if photon A and B are traveling towards each other head on (at the speed of light) why isn't the velocity of B relative to A exceed the speed of light? And no, it is not homework related.

 

[Doc Al]

Imagine this scenario, which makes the same point. Spaceship A moves at 0.99c with respect to Earth heading north. Someone on Earth shines a flashlight pointing south, directly at the oncoming spaceship A. What will be the speed of the photons with respect to spaceship A?

To answer this you need to understand the basic postulates of special relativity which has implications for how velocities add.

 

[Garen]

Imagine this scenario, which makes the same point. Spaceship A moves at 0.99c with respect to Earth heading north. Someone on Earth shines a flashlight pointing south, directly at the oncoming spaceship A. What will be the speed of the photons with respect to spaceship A?

To answer this you need to understand the basic postulates of special relativity which has implications for how velocities add.

Understood, thank you!

 

[HallsofIvy]

What do you mean "Understood"? He asked you a question. Can you answer that question?

 

[Sakha]

Light speed is the same in all references frames.
Check http://www.math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html" for some understanding of it.

 

[shreason]

Special theory of relativity from Einstein will help you.

 

[atyy]

Just wondering, if photon A and B are traveling towards each other head on (at the speed of light) why isn't the velocity of B relative to A exceed the speed of light? And no, it is not homework related.

Imagine this scenario, which makes the same point. Spaceship A moves at 0.99c with respect to Earth heading north. Someone on Earth shines a flashlight pointing south, directly at the oncoming spaceship A. What will be the speed of the photons with respect to spaceship A?

To answer this you need to understand the basic postulates of special relativity which has implications for how velocities add.

Doc Al seems to be answering a slightly different question. For a human experimentalist O measuring two photons going in opposite directions, he will measure both photons going at the same speed, no matter what his velocity relative to another human experimentalist P.

The question was about photon B "relative" to photon A. The "standard answer" is that the question is meaningless. To be honest, I don't know why - and actually, if it is meaningless, there shouldn't be a reason. But here is my attempt to "prove" that it is meaningless anyway!

If we take an inhuman experimentalist on photon A. For all photons going the same direction as himself, they will go at the same speed, so he will measure their speed to be 0. For photons coming towards him, maybe he can measure a speed c_i, where the subscript stands for "inhuman". So he can measure c_i > 0, and the "speed of light" will be greater than the "speed of light". But we can never test it, so maybe that's why the standard answer is that the question is "meaningless".

I can imagine another "more fundamental" reason the question is meaningless. To establish a measure of "distance", two experimentalists must send signals to each other. So if an inhuman experimentalist Y sits on one peak of a light wave, and another inhuman experimentalist Z sits on another peak "in front" of Y. Then Z can send a signal to Y, but Y can never send a signal to Z, since light will not move forwards relative to him.

Criticisms obviously expected and welcome! Just in case this misleads anyone, let me say, obviously, don't write this on your exam!

 

[Doc Al]

Doc Al seems to be answering a slightly different question. For a human experimentalist O measuring two photons going in opposite directions, he will measure both photons going at the same speed, no matter what his velocity relative to another human experimentalist P.

I modified the question to make it answerable.

The question was about photon B "relative" to photon A. The "standard answer" is that the question is meaningless. To be honest, I don't know why - and actually, if it is meaningless, there shouldn't be a reason. But here is my attempt to "prove" that it is meaningless anyway!

Generally, the speed of B "relative to" A means the speed of B as measured from a frame in which A is at rest. But there's no such inertial frame for a photon--they are never at rest and always move at speed c with respect to any frame. That's the problem. You are essentially denying a basic postulate of SR. Once you've done that, all else is fantasy.

http://www.math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/headlights.html"

 

[atyy]

I modified the question to make it answerable.

Yes, I forgot to mention that. Very good of you to do so!