Is light time dilated?

[Vorpal]

Yup; I'm being dumb. Thanks to both you.

 

[sol invictus]

Except we can't apply the same logic, because circular polarizers (ie, quarter-wave plates) don't work by absorbing the "wrong" circular polarization. They work by retarding one of the linear photons so they have the right phase difference.

That's not really a circular polarizer, because it leaves some linear polarizations invariant. In other words if you send in some incoherent light the result will still be incoherent. To get only circularly polarized light out of a quarter wave plate you have to send in only a particular linear polarization.

But even with a linear polarizer attached it's still not a projector onto circular polarization.

 

[sol invictus]

Yup; I'm being dumb. Thanks to both you.

I'm finding this confusing too... am I actually correct that I can detect the change in the phase of a photon as it propagates along? Zig has shaken my faith...

The set-up I have in mind now is a series of identical lasers situated along the beam path, aimed perpendicular to it. Those are my clock readers.

To read the "clock" at some point, you turn on the laser at that point and insert a mirror there that reflects the traveling photon at 90 degrees, out of the beam path but parallel to the beam from the laser, and then interfere the two. It seems to me the result will depend on where along the beam I do this.... am I missing anything?

 

[Ziggurat]

That's not really a circular polarizer

It's what gets used experimentally to circularly polarize light, and it's the relevant one in terms of Vorpal's objections (of it not behaving like a linear polarizer in terms of transmission rates).

 

[ben m]

That's not really a circular polarizer, because it leaves some linear polarizations invariant. In other words if you send in some incoherent light the result will still be incoherent. To get only circularly polarized light out of a quarter wave plate you have to send in only a particular linear polarization.

But even with a linear polarizer attached it's still not a projector onto circular polarization.

I think that a three-element stack {QWP, linear polarizer, QWP} is a projector onto circular polarization.

 

[Ziggurat]

Yes, I think you're right. But that doesn't affect my point so long as I can construct experiments which are sensitive to how far the photon has traveled. But I'm pretty sure I can - for example, I could interfere it with another photon, or with itself traveling along some other path, and the interference pattern that results will depend on the length it propagated down the pipe.

Yes, it will. But how do you turn that into a clock?

Let's start with a simple example. I shoot a photon with a fixed frequency to the right, and another photon with the same frequency to the left. As they cross over each other, they interfere, creating nodes. I can time how long it takes the photon to pass each node, and extract a frequency (and hence a clock rate) from that. All well and good. But does that mean my clock was traveling with the photon?

Well, what happens if I look at that same experiment, but now travelling at 0.5 c to the right. I want to measure the "clock rate" of the right-propagating photon. Its frequency is now 2/3rds of what it was in my original frame. But nodes in one frame are nodes in another frame, so the nodes are closer together by a factor of gamma. Furthermore, the nodes are no longer stationary, but are now moving towards me at 0.5 c. So the frequency at which my photon passes nodes is now about 70% greater. But the photon's frequency should be less in this reference frame.

You can't get the kind of interference you want unless you're interfering two photons travelling in different directions. The interference depends upon the frequency of both photons, and hence the reference frame in which you're observing them. I'm not sure how you think you can construct a clock from this which can be thought of as moving with the photon.

 

[Ziggurat]

I'm finding this confusing too... am I actually correct that I can detect the change in the phase of a photon as it propagates along?

To the best of my understanding, you cannot. Classically, the field profile of an electromagnetic plane wave traveling in a vacuum should only translate, it should not otherwise time-evolve. I don't see how going to quantum mechanics would change that.

Zig has shaken my faith...

That doesn't happen very often, so I'm kinda proud right now.

The set-up I have in mind now is a series of identical lasers situated along the beam path, aimed perpendicular to it. Those are my clock readers.

To read the "clock" at some point, you turn on the laser at that point and insert a mirror there that reflects the traveling photon at 90 degrees, out of the beam path but parallel to the beam from the laser, and then interfere the two. It seems to me the result will depend on where along the beam I do this.... am I missing anything?

It will depend upon where you place the laser, but it will also depend upon what phase the laser is in when you turn it on (or, if the laser always starts in the same phase, when you turn it on). So in this scenario, you can get constructive or destructive interference at all points along the path.

 

[Ziggurat]

I think that a three-element stack {QWP, linear polarizer, QWP} is a projector onto circular polarization.

I think this is correct (assuming the proper relative orientations of those elements). If you come in with the correct circular polarization, you get transformed into the correct linear polarization, transmitted through the linear polarizer, then transformed back into the circular polarization direction you started with. If you come in with the wrong circular polarization, you get transformed into the wrong linear polarization and blocked at the linear polarizer.

 

[sol invictus]

I think that a three-element stack {QWP, linear polarizer, QWP} is a projector onto circular polarization.

Yes, of course you're right (if the first QWP is the inverse of the last). Thanks!

And that kind of filter will let through 50% of any linearly polarized beam, regardless of its phase or orientation.

To the best of my understanding, you cannot. Classically, the field profile of an electromagnetic plane wave traveling in a vacuum should only translate, it should not otherwise time-evolve. I don't see how going to quantum mechanics would change that.

I agree that QM shouldn't change anything here. So let's see... a classical EM pulse moving in (say) the +x direction will have a profile that's some function of u=x-ct, where u is a lightcone coordinate, and which doesn't depend on v. Which means... which means you're absolutely correct, and I was being an idiot. That is exactly like a frozen clock moving at speed c, because the phase at (say) the center of the pulse doesn't change.