# Double Slit Experiment question

• I

## Summary:

double slit experiment with quarter wave plates and polarization detector

## Main Question or Discussion Point

I read in a book the following assertion.
In a double slit experiment photons are passed through the slits and detected at the end plate.
Each of the two slits has a quarter wave plate which alters the polarization of the photons that pass through it in a way different than the other QWP.
Thus a polarizing detecting barrier at the end plate can determine which slit the photon went through.
In such an experiment, there will be no interference pattern at the end plate. i.e. the wave functions collapse.
But if one does either of two things, the interference pattern shows up. Thus if either:
1. the quarter wave plates are removed but the polarizing detecting barrier is kept.
OR
1. the polarizing detecting barrier is removed but the quarter wave plates are kept.
Then the interference pattern is back.
A. Is this assertion correct?
B. If yes, then where does the wave function collapse when both are in place? At the plates or the end detector?

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PeterDonis
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Which book?

PeterDonis
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Is this assertion correct?
Presumably this has been tested experimentally. Does the book give a reference to the published results of such an experiment?

tnich
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I wonder how the polarization detector works. Something pretty sensitive would be needed to detect the polarization of a single photon. See this paper: Single photon detector with high polarization sensitivity, for example. The problem is that (in the ideal) it would detect photons of one polarization but not photons of the orthogonal polarization. It seems to me that would certainly collapse the waveform since the only photons passing through one of the slits would be detected. The real detector described in the paper linked above only has a bias toward detecting photons of one polarization over the other, so perhaps it would only partially collapse the waveform. Over a number of trials, that might look like one bright point (collapsed waveform) superimposed over an interference pattern of reduced intensity (uncollapsed waveform).

the book is biocentrism by robert lanza (ch.8). here's a quote from there:

"If you fully learn about one, you will know nothing about the other. And just in case you’re suspicious of the quarter wave plates, let it be said when used in all other contexts, including double slit experiments but without information-providing polarization-detecting barriers at the end, the mere act of changing a photon’s polarization never has the slightest effect on the creation of an interference pattern."

can read more here (scroll down to "The Most Amazing Experiment ")

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Presumably this has been tested experimentally. Does the book give a reference to the published results of such an experiment?
see my last post

the polarizing detecting barrier is removed but the quarter wave plates are kept.
The interference pattern does not return if the detecting barrier is removed. But we can filter out a subset of photons that will exhibit interference terms.

Let $|A\rangle$ and $|B\rangle$ be the respective states of a photon travelling through slit $A$ and $B$. If the photons are polarised such that $\langle A|\mathbf{r}\rangle\langle\mathbf{r}|B\rangle = 0$ then we can talk about a photon travelling through a slit and landing on a screen at $\mathbf{r}$ with probabilities

$$p(A,\mathbf{r}) = \mathbf{Tr}[|\mathbf{r}\rangle\langle\mathbf{r}|A\rangle\langle A|\Psi\rangle\langle\Psi|A\rangle\langle A|\mathbf{r}\rangle\langle\mathbf{r}|]]$$
$$p(B,\mathbf{r}) = \mathbf{Tr}[|\mathbf{r}\rangle\langle\mathbf{r}|B\rangle\langle B|\Psi\rangle\langle\Psi|B\rangle\langle B|\mathbf{r}\rangle\langle\mathbf{r}|]]$$

where $|\Psi\rangle$ is the prepared state of the incident beam. Neither distribution will exhibit interference terms, and and neither will $p(A\lor B,\mathbf{r})$.

However, we can also talk about the photons passing through the slits in terms of the states $\{|+\rangle,|-\rangle\}$, which are symmetric and anti-symmetric states expressed as superpositions of the two slits. These terms don't carry information about which slit the photon travelled through. The corresponding probabilities are

$$p(+,\mathbf{r}) = \mathbf{Tr}[|\mathbf{r}\rangle\langle\mathbf{r}|+\rangle\langle +|\Psi\rangle\langle\Psi|+\rangle\langle +|\mathbf{r}\rangle\langle\mathbf{r}|]]$$
$$p(-,\mathbf{r}) = \mathbf{Tr}[|\mathbf{r}\rangle\langle\mathbf{r}|-\rangle\langle-|\Psi\rangle\langle\Psi|-\rangle\langle -|\mathbf{r}\rangle\langle\mathbf{r}|]]$$

These two distributions will exhibit interference fringes, though $p(+\lor -,\mathbf{r})$ won't. So if we select either distribution by filtering out the other (e.g. with a procedure similar to the one outlined here https://arxiv.org/pdf/quant-ph/0106078.pdf ) we can observe interference terms.

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PeterDonis
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PeterDonis
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the book is biocentrism by robert lanza
Which is a popular book, not a textbook, and is not a valid reference for PF discussion.

see my last post
Your link is to a post on a blog, not a textbook or peer-reviewed paper. Given some of the other content on the blog, I'm not inclined to take for granted that its explanation of the experiment in question is reliable.

PeterDonis
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Since no valid references have been provided, this thread will remain closed.