Photon behavior after the polarizer

[San K]

Let's say we pass a photon through a 0 degree polarizer.

the photon is now oriented at 0 degrees, meaning it will pass through subsequent polarizeres oriented at 0 degrees.

(note - Not all photons will pass through the 0 degree polarizer, roughly 50% will pass through. we are talking about the ones that are able to pass through the polarizer)

1. Is the photon now in a determinate state? ...on just one axis or all?
2. If a spin is determinate on one axis, can it be indeterminate on the other axis? in QM
3. Is this possible in classical mechanics? i.e. determinate on one axis but indeterminate on another?
is indeterminacy possible, at all, in classical mechanics?
4. Can a photon, without any interaction, degrade from a determinate state to indeterminate state with time/space?
5. is it easy to convert/swap between determinate and indeterminate states?

i.e. to make a photon state determinate - pass through polarizer
to make a photon state indeterminate -- put it in superposition (i.e. half silvered mirror, ?)
6. Is the indeterminate state much more common in nature/universe? (because polarizers and similar are not so common in nature)

 

[mfb]

1. Is the photon now in a determinate state? ...on just one axis or all?

Its polarization is.

2. If a spin is determinate on one axis, can it be indeterminate on the other axis? in QM

It can.

3. Is this possible in classical mechanics?

How do you get indeterminate things in classical mechanics?

4. Can a photon, without any interaction, degrade from a determinate state to indeterminate state with time/space?

Depends on the definition of indeterminate/determinate, probably not.

5. is it easy to convert between determinate and indeterminate state?

Is it easy to send a photon through a polarizer?

6. Is the indeterminate state much more common in nature/universe?

I think that depends on the interpretation.

 

[San K]

Its polarization is.
It can.
How do you get indeterminate things in classical mechanics?
Depends on the definition of indeterminate/determinate, probably not.
Is it easy to send a photon through a polarizer?
I think that depends on the interpretation.

Thanks mfb

last question (missed it in the OP) - Can we make a photon determinate (on say, spin) on all three axis at the same time?

( I don't understand the concept of hilbert space so will stick to the 3 "classic" axis).

 

[mfb]

For photons, this is easy, they do not have a polarization component in their flight directions. A simple polarizer is enough to know the "full" polarization of the photon.

 

[vanhees71]

Here, obviously there's a severe misconception about (the "spin" of) photons in this thread. One should warn people discussing photons on a popular-science level. Massless particles with spin are an even more delicate issue than massive particles.

First of all the meaning of "spin" is different for massless particles from that for massive particles. For massless particles you have always two spin (or polarization) states (except for spin 0, where you have of course no polarization). Physically invariant is helicity, which is the projection of total angular momentum to the direction of the momentum of the (asymptotically) free particle. For spin number s \in \{0,1/2,1,\ldots \}, there are the two helicities +s and -s. Thus a photon as a massless particle with spin 1 has only two and not three polarization states.

For massless particles, to get an intuition, it's better to consider the corresponding classical wave equations to the quantum field theory. In the case of photons that's even physically sensible since that's just classical electrodynamics for free electromagnetic fields. The helicity eigenstates are best represented in this classical limit as the two circularly polarized states of a wave packet with relatively well defined wave number (i.e., a wave packet close to a plane wave but with finite total energy, momentum, and angular momentum).

 

[Khashishi]

2. If a spin is determinate on one axis, can it be indeterminate on the other axis? in QM

I'm not sure which other axis you might be referring to. If it is polarized to 0 degrees (or 180 degrees), that means it's not polarized to 90 degrees. But it is in a superposition state on the 45 degree axis.

 

[San K]

2. If a spin is determinate on one axis, can it be indeterminate on the other axis? in QM

I'm not sure which other axis you might be referring to. If it is polarized to 0 degrees (or 180 degrees), that means it's not polarized to 90 degrees. But it is in a superposition state on the 45 degree axis.

Hi Kashishi, thanks for dropping by. I'll elaborate.

Let's assume the photon is traveling along the z-axis.

Thus it would have no polarization along the z-axis (?) but have along x and y axes.

(However an electron's (which is a "mass-ful" particle) story would be different and we can discuss that later.)

Could we now manipulate the photon in such a way that - it has determinate value (for spin) along the say, x-axis but an indeterminate value (for spin) along the y-axis? .....and, of-course, no spin along the z-axis.

mfb as informed, above, that this is possible.

 

[Khashishi]

I think you are confusing spin with polarization. They are intimately related, but the terms are not interchangeable. Polarization is the direction of the electric field, whereas spin is the direction of the angular momentum. A photon that is circularly polarized, x+iy, has a z component of angular momentum of 1 hbar, and an indeterminate x and y component. You could think of the angular momentum as pointing at a 45 degree angle from the z axis, but spread out in a cone as if it was rotating around the z axis very fast.

Spin can only be fully determined in one axis. If it is measured along the x axis, it becomes indeterminate along the y and z axes.

 

[San K]

Well said and an informative reply. Thanks for clarifying Khashishi.

I think you are confusing spin with polarization. They are intimately related, but the terms are not interchangeable. Polarization is the direction of the electric field, whereas spin is the direction of the angular momentum. A photon that is circularly polarized, x+iy, has a z component of angular momentum of 1 hbar, and an indeterminate x and y component. You could think of the angular momentum as pointing at a 45 degree angle from the z axis, but spread out in a cone as if it was rotating around the z axis very fast.

Spin can only be fully determined in one axis. If it is measured along the x axis, it becomes indeterminate along the y and z axes.