Why 50% of entangled photons pass through the polarizer?

[Karagoz]

Hi.

If we have 1 million entangled photons separated from their "entangled partner". We send all those photons (without their "entangled partners") through a polarizer. Each photon has has 50% chance of passing through the polarizer.
So 50% of the photons will pass through the polarizer and have a spin parallell with the axis of the polarizer, and 50% of the photons won't pass through the polarizer and become absorbed.

But wouldn't the probability of a photon passing through a polarizer be P = cos²(Φ)?

(Where Φ is the difference between spin axis of the photon and axis of the polarizer).

Why the probability is always 50%?

 

[DrChinese]

Hi.

If we have 1 million entangled photons separated from their "entangled partner". We send all those photons (without their "entangled partners") through a polarizer. Each photon has has 50% chance of passing through the polarizer.
So 50% of the photons will pass through the polarizer and have a spin parallell with the axis of the polarizer, and 50% of the photons won't pass through the polarizer and become absorbed.

But wouldn't the probability of a photon passing through a polarizer be P = cos²(Φ)?

(Where Φ is the difference between spin axis of the photon and axis of the polarizer).

Why the probability is always 50%?

The "spin axis of the photon" is in a superposition if it is entangled. Therefore it has no specific known value (if it can be said to have a value at all). When it encounters a polarizer, it randomly acquires a value as being V or H. 50% of the time it is one, 50% of the time it is the other. That is true of its partner as well. Their spin/polarization are not independent, so the results when the partners' outcomes are compared show this tight relationship.

 

[Karagoz]

The "spin axis of the photon" is in a superposition if it is entangled. Therefore it has no specific known value (if it can be said to have a value at all). When it encounters a polarizer, it randomly acquires a value as being V or H. 50% of the time it is one, 50% of the time it is the other. That is true of its partner as well. Their spin/polarization are not independent, so the results when the partners' outcomes are compared show this tight relationship.

But can't a photon have a spin axis despite being in a superposition?

Nugatory said the same thing as you said:
Exactly why FTLC is impossible with entangled photons?

He said the math behind it is complicated. But what's the math behind it?

Because it seems to me it's contradicting to what's taught to us in physics book.

This is what's written in one of two physics books used in all high-schools in Norway (translation is not exact):

We can define two polarization states for photons relative to a filter. In state P, the photons are polarized parallel to the axis of the filter. All the photons in state P will go through. In state V, the photons are polarized perpendicular to the axis of the filter. All photons in state V are blocked. In the 3rd case, the photons are in state P, and in the middle of state V. But what should we say about the 3rd situation? Here the photons polarization axis is neither parallel to nor perpendicular to the filter polarization axis.

In relation to the orientation of the filter, the photons will be in a state of superposition. This means that each photon is in a mixture of the two states P and V. Although all the photons are in an identical state of motion, frequency and polarization, we can not determine if a single photon will pass through the filter or not. Measurements indicate that the probability P for a photon to pass through the filter depends on the angle φ between the polarization axis of the photon and the filter: P = cos²φ If for example the angle between polarization axis is 60°, cos²60° = 1/4 = 25% of the photos that hit the filter pass through. After the photons have passed the filter, they are in a new state with polarization axis parallel to the filter, ie P.

Even though we know everything we can know about the photos (direction of motion, frequency and direction of polarization), we can not say what happens to each photo when it hits the filter. We can only say what statistically will result when many photons in the same state are sent to the filter.

Let's assume that the entangled photons move in opposite directions and have the same frequency and same polarization. We place a polarization filter in the way of each of the photons so that the filters have parallel polarization axes. What do you think will happen? You probably suggest that if the photons are polarized perpendicular to the filters (V), both photons are blocked and if they are polarized parallel to the filters (P), then both pass through. There you are right. But what if the photons are in a state of superposition of P and V? Then you might think that each photon will pass through with a probability of P(passing through) = cos 2 φ, and that the two photons pass through independently. For example, if the angle was 60°, one would think that the probability that each photon would pass through was 1/4 and that the likelihood that both photons would pass through was therefore (1/4)^2 = 1/16. But it is not. If one photon is passed through, then it's 100% certain that the other photon will pass through too!

 

[Nugatory]

But can't a photon have a spin axis despite being in a superposition?

No. No theory in which an entangled photon has a spin axis before it encounters the polarizer can produce the experimentally observed correlations at all angles, so any such theory must be incorrect. This is the point of Bell's theorem.

 

[Nugatory]

He said the math behind it is complicated. But what's the math behind it?

Did we not recommend Giancarlo Ghirardi's book "Sneaking a look at god's cards" in your other thread? If not, I'm recommending it now. It will get you started.

Because it seems to me it's contradicting to what's taught to us in physics book.

This is what's written in one of two physics books used in all high-schools in Norway (translation is not exact):

That quoted passage is not describing pairs of photons that have been prepared in an entangled state; it is describing single photons that have been prepared by passing them through a polarizer at a known angle. Even then, they do not have a definite polarIzation angle. That text is glossing over (appropriately, for high schoolers) the subtle but crucial mathematical difference between "the photon is V-polarized along axis $x$" and "if we measure the polarization along angle $x$ the result will be V"

 

[jimgraber]

So, please, what is the difference (in math and in words) between "the Photon is V-Polarized along axis X" and "if we measure the polarization along angle x the result will be V" ?
Thanks
jim Graber

 

[Mentz114]

So, please, what is the difference (in math and in words) between "the Photon is V-Polarized along axis X" and "if we measure the polarization along angle x the result will be V" ?
Thanks
jim Graber

If we do a measurement it tells us nothing about the state before the measurement. The first statement is true if the photon has just passed a filter.
Is it enough to know that the probability of a photon passing the filter is $\cos(\theta_{phot}-\theta_{pol})^2$ so if the photon and polarizer are aligned the probability is $\cos(0)^2=1$ ?

 

[Nugatory]

So, please, what is the difference (in math and in words) between "the Photon is V-Polarized along axis X" and "if we measure the polarization along angle x the result will be V" ?
Thanks
jim Graber

This is what's Bell's Theorem is about. We have many many threads about it, and our own @DrChinese maintains this web page. The math is in Bell's 1965 paper, the words are in the "with easy math" section.

 

[jimgraber]

Thanks for the references. It is somewhat clearer to me now, particularly in the context of entanglement.