Commutativity of frequency measurement

[zonde]

Let's say we have photon beam with certain frequency. Now we make a choice to perform one of two noncomuting measurements, say polarization measurement in H/V basis or polarization measurement in +45°/-45° basis. After that measurement we perform frequency measurement.
From QM perspective it is not possible that frequency measurement can commute with both polarization measurements. Therefore we necessarily filter out some photons at least in case of one of two polarization measurements if not both.

Does this reasoning seem correct?

 

[zonde]

Didn't get any response but this question still bothers me.

Is it possible to change frequency of photon by performing polarization measurement considering that different polarization measurements can be non-commuting?

 

[sweet springs]

Hi, zonde.

I am sorry it is not answer you want but teach me. Do polarization and frequency not commute? We cannot measure frequency of polarized light? I've been thinking that these two operators commute.

Regards.

 

[zonde]

Hi, zonde.

I am sorry it is not answer you want but teach me. Do polarization and frequency not commute? We cannot measure frequency of polarized light? I've been thinking that these two operators commute.

Regards.

Your question contains the part that is confusing me. Can we really talk about polarization operator? We can measure polarization in H/V basis and we can measure polarization in +45°/-45° basis and those two measurements do not commute.
Shouldn't we talk about two operators - HVpolarization operator and +-polarization operator?
In that case we can say for example that frequency and +-polarization operators commute but frequency and HVpolarization operators don't.

Physical similarity between HVpolarization measurement and +-polarization measurement just adds more confusion. You just rotate polarizer by 45° and you switch from one measurement to other.

 

[sweet springs]

Hi, zonde.
From Wiki light
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Five primary properties of light are intensity, frequency or wavelength, polarization, phase and orbital angular momentum.
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I understood you are stating frequency , e.g.　10＾14　Hz and　polarization, e.g. z-axis linear polarization are not determined simultaneously due to HUP. For example blue rays are not blue after passing a light polarization sheet.

I should appreciate your suggestion on my (mis)understanding of what you want to say.

Regards.

 

[zonde]

Let's say it that way.
Assume we have polarized light with certain frequency. We pass it through polarizer that is at 45° relative to polarization axis of light. Now the frequency is not certain anymore.
That's how it seems to me.

 

[DrDu]

zonde, frequency measurement commutes with both H/V polarization measurement and with +45/-45 measurements. That the latter two do not commute does not mean that they don't commute with frequency measurement.
There is a similar example with spin. The operator $$\sigma^2$$ commutes with any of $$\sigma_x$$, $$\sigma_y$$, $$\sigma_z$$, but none of the latter 3 commute among themselves.

 

[sweet springs]

Assume we have polarized light with certain frequency. We pass it through polarizer that is at 45° relative to polarization axis of light. Now the frequency is not certain anymore.

I do not think it happens.

From Wiki 3-D film
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In the case of RealD a circularly polarizing liquid crystal filter which can switch polarity 144 times per second is placed in front of the projector lens. Only one projector is needed, as the left and right eye images are displayed alternately.
-----

In my experience color of light does not change whether I wear polarization glass or not for 3-D movies in attraction theater.
I will try to wear glasses in 45 degree angle next time for confirmation.
Regards.

 

[zonde]

zonde, frequency measurement commutes with both H/V polarization measurement and with +45/-45 measurements. That the latter two do not commute does not mean that they don't commute with frequency measurement.
There is a similar example with spin. The operator $$\sigma^2$$ commutes with any of $$\sigma_x$$, $$\sigma_y$$, $$\sigma_z$$, but none of the latter 3 commute among themselves.

Thanks for the answer.
Just to check that I understand it correctly. Frequency operator can have two different eigenbasis where one is common eigenbasis with H/V operator but the other one is common eigenbasis with +45/-45 operator, right?

 

[DrDu]

Yes, because H and V or +45 and -45 polarized waves all have the same frequency. Hence any linear combination of them will have the same frequency, too.
Btw, this does not hold true in dichroic materials. There, frequency depends on polarization and only rays of a fixed polarization can propagate.