Two Questions About Light

[tommyedison]

Does light frequency move towards lower values i.e. does it redshift after travelling big distances aside from the effects of gravitational and cosmological redshift.

Does the frequency of light change when it enters a moving object, for example, a hollow box with walls made of clear and transparent glass which is moving at a certain velocity.

[stephen_speicher]

Does light frequency move towards lower values i.e. does it redshift after travelling big distances aside from the effects of gravitational and cosmological redshift.

If you mean the old "tired-light" theories, those have been discredited. But there is a velocity-dependent Doppler redshift, or blueshift, depending on whether the object is receding or approaching the detector.

Does the frequency of light change when it enters a moving object, for example, a hollow box with walls made of clear and transparent glass which is moving at a certain velocity.

I am not sure just what the question means. Note that in standard relativity, frequency is not an intrinsic property, but rather a relationship between object and observer.

[aturner]

Not to trump the original questioner, but lets make the problem a bit more descriptive, and perhaps more complicated. Lets take a box in which is placed a pair of mirrors, between which a monochromatic beam of light is oscillating (to make it easier to visualize for physicists, lets say its a laser cavity). In the middle of this beam, place a semi-transparent mirror, which redirects some of the light out the side of the (transparent) box, so that an observer external to the box can receive the light. Lets call this redirected light the sample beam.

With the box at rest with respect to the observer, record the frequency (or wavelength) of the light. Lets say it is 530 nanometers (a favorite of mine).

Now, accelerate the box to a relativistic speed. What does the observer see? Using a single semi-transparent mirror, only the light traveling in one direction will be directed toward the observer (the other direction will be directed out the other side of the box). If the semi-transparent mirror is oriented such that the light travelling against the direction of motion is seen by the observer, is the light red-shifted? Is it blue-shifted if the light travelling in the same direction is directed to the observer?

As a subtle but important complication, the orientation of the mirror must continually change to keep the sample beam directed toward the observer as the box moves past him.

This is the cleanest way in which I can restate the problem. Otherwise, how can an external observer "see" the light in the box at all? And therein lies the solution to the question.

Because I have to redirect the light to travel toward the observer, everything depends not only on the relative velocity of the box to the observer, but also upon the viewing angle. If the observer is looking perpendicular to the direction of the motion of the box, so the sample beam is at 90 degrees to the laser cavity beam, the redirected light will have no frequency shift, as there is no motion of the source in the viewing direction. As the box travels past the observer, the viewing angle will decrease from 90 degrees, and the light will become increasingly redshifted.

The key to untangling the original question lies in understanding that in order to measure the observed frequency of the light in the box, the light itself needs to travel to the observer. In so doing, its frequency properties will change, since it will be redirected relative to the motion of the box.

What do you think, Steven? Have I got this right? Although I'm an optical engineer by profession, I haven't needed to use relativistic mechanics for about 18 years now.

[stephen_speicher]

What do you think, Steven? 

I think my name is "Stephen."

I don't mean to single you out here, but a number of people refer to me as Steve or Steven and neither of those are my name. (I do not understand why people do that. Anyone have a clue?)

Anyway, yes, the full relativistic Doppler formula depends upon the angle between the light ray path and the relative velocity vector. For the source in the primed frame, the frequency relationship is f'/f = [1 + (v/c) cos(theta)]/[1 - (v/c)^2]^1/2, where theta is the angle mentioned. As you noted, the observation is dependent on this angle. Note also that at theta = pi/2 we have just the transverse Doppler effect. This can be seen as a reduction to where the frequencies are related by simply f'/f = [1 - (v/c)^2], which is simply the time dilation.

It is instructive to see the expansion of the derived vector form where v is the instantaneous velocity and v_r is the radial velocity component. The relationship f'/f = [(1 + v_r/c]/[1 - (v/c)^2]^1/2 can be expanded to 1 + v_r/c + v^2/(2c^2) + higher order terms O(v^3/c^3). This shows that the relativistic Doppler shift can be seen as the classical Doppler of 1 + v_r/c and the relativistic effect of v^2/(2c^2), at least to the order specified.

Have I got this right?  Although I'm an optical engineer by profession, I haven't needed to use relativistic mechanics for about 18 years now.

You seem to be doing fine, but you are just not moving fast enough!

p.s. The field you are in is wonderfully inventive and as long as you continue to enjoy yourself I suspect the challenge will be there for some time.

[aturner]

Terribly sorry about the misspelling, Stephen, I actually caught the error after posting and considered sending a correction. Should have, apparently.

[stephen_speicher]

Terribly sorry about the misspelling, Stephen,  I actually caught the error after posting and considered sending a correction.  Should have, apparently.

That's okay. It's just a little annoying. I cannot figure out why so many people morph a name like mine into something else, but not do the same with other names.

[aturner]

I have a difference of opinion on Stephen being a uniquely morphed name. Apparently, Aaron = Erin = Aron = Arron. And believe me, that first mispelling eventually gets on one's nerves.

Aaron Turner

[Ed from OC]

With the box at rest with respect to the observer, record the frequency (or wavelength) of the light.  Lets say it is 530 nanometers (a favorite of mine).

Me too. It's a pretty shade of green. Have you played with a doubled Nd:YVO4? It makes a nice deep blue at 457 nm.