Does the energy of light depend on the observer's reference frame?

[blarpityblorp]

Hi, Physics Forums! This is my first post here and I know just about zero physics, so I apologize in advance if the question is a little daft/naïve.

Ok, so here's what I'm wondering: suppose you have a light source that produces EM waves in all directions at some frequency ν, and a camera set up very far away to observe the frequency. If the camera is at rest, the light appears to have an incoming velocity c and frequency v, but if the camera is moving at a constant velocity towards the light source, it appears to have velocity c and the frequency is blueshifted to something greater than v. So the same number of photons pass the moving camera each second, but they appear to have more energy. Moreover, they should actually have more momentum, and the capacity to do more work on the camera (suppose there's something like a solar sail mounted to it—then the light "pushes the moving camera harder.") How is this extra energy accounted for? I'm clearly missing something big, and it's gone right over my head.

Thanks!

 

[PAllen]

You are not missing anything. Replace it with baseballs. Person A throws ball in all directions at 80 mph. Person B is moving toward A at some speed. B will be hit by balls with more energy and momentum. With light, it is the same (except the speed doesn't change). Energy and momentum are frame dependent in Newtonian physics and relativistic physics. 'only the details change' (big details...)

 

[Dale]

How is this extra energy accounted for? I'm clearly missing something big, and it's gone right over my head.

As PAllen mentioned, energy and momentum are frame-variant. What you are probably missing is the difference between "frame invariant" and "conserved". Roughly speaking, a quantity is called "conserved" if its value in a given reference frame does not change over time. A quantity is called "frame invariant" if it is the same in different reference frames. Frame invariance and conservation are two entirely different concepts.

Energy is frame variant, but it is still conserved.

 

[elfmotat]

In any particular reference frame, energy will be conserved. This does not mean it will have the same value in every frame. Energy and momentum have always been frame-dependent quantities, even in Newtonian physics. For example:

Bob, at rest in frame A, throws a 0.1 kg ball to the right towards Alice (also at rest) at 10 m/s. The kinetic energy and momentum of the ball are 5 J and 1 Ns respectively. Now consider the same situation from frame B, which is moving at 10 m/s to the left with respect to A: Bob (moving at 0+10 m/s = 10 m/s to the right) throws the ball to Alice (also moving at 10 m/s) at 10 m/s + 10 m/s = 20 m/s. The kinetic energy and momentum of the ball are 20 J and 2 Ns respectively.

When solving a physics problem you generally need to pick a reference frame to work in first, before doing anything else. This frame is usually chosen for convenience (i.e. where certain things are at rest), and in most problems you will only need to work within this single frame. If you should need to switch frames for any reason, then you can do so with the corresponding transformation laws (Lorentz transformation in relativity and Galilean transformation in Newtonian physics).