Beginner Question Regarding Entanglement

[Egghead44]

TL;DR Summary

Beginner Question Regarding Entanglement

I am just starting to learn quantum mechanics. And have some questions on entanglement. I have learned that when there is two particles entangled that they share the same wave function and cannot be considered by themselves. I am having a hard time understanding some of the nuances of this concept. I have attached a diagram of the setup I have imagined. The setup uses a laser of 405nm to send photons thru a KDP crystal. This will produce two 810nm entangled photons, both having same polarity. This is then sent down two different paths, one photon (photon a) toward a 2 slit plate and the other (photon b), at half the distance, to a photon detector.

What will happen if you send one photon at a time through this setup in one of two different modes. In the first mode the APD detector is not used (taken out), and the second mode the APD detector is used. In the 1st mode, I imagine the 2 slit photons (photons a) will make a diffraction pattern. My question is in the 2nd mode, the one with the detector in place, will the photons going thru the 2 slit plate and sill interfere with each other? I am assuming that the collapse of photon B's wave function would collapse the photon A's wave function too. Or is this a wrong assumption?

 

[PeterDonis]

@Egghead44 please note that I have used moderator powers to edit your thread title and summary to remove the all caps. Using all caps is the Internet equivalent of shouting. Please don't do that.

 

[Egghead44]

@Egghead44 please note that I have used moderator powers to edit your thread title and summary to remove the all caps. Using all caps is the Internet equivalent of shouting. Please don't do that.

understood
thanks

 

[PeroK]

Summary:: Beginner Question Regarding Entanglement

I am just starting to learn quantum mechanics. And have some questions on entanglement. I have learned that when there is two particles entangled that they share the same wave function and cannot be considered by themselves. I am having a hard time understanding some of the nuances of this concept. I have attached a diagram of the setup I have imagined. The setup uses a laser of 405nm to send photons thru a KDP crystal. This will produce two 810nm entangled photons, both having same polarity. This is then sent down two different paths, one photon (photon a) toward a 2 slit plate and the other (photon b), at half the distance, to a photon detector.

What will happen if you send one photon at a time through this setup in one of two different modes. In the first mode the APD detector is not used (taken out), and the second mode the APD detector is used. In the 1st mode, I imagine the 2 slit photons (photons a) will make a diffraction pattern. My question is in the 2nd mode, the one with the detector in place, will the photons going thru the 2 slit plate and sill interfere with each other? I am assuming that the collapse of photon B's wave function would collapse the photon A's wave function too. Or is this a wrong assumption?

Why would detecting a photon at B or not affect the interference pattern at A?

Are you assuming that if a photon is detected at B, then the photon at A collapses from a wave to a particle? If so, you have not understood the basics of QM. There is no wave-particle duality in QM.

 

[Nugatory]

My question is in the 2nd mode, the one with the detector in place, will the photons going thru the 2 slit plate and sill interfere with each other?

The interference is not caused by photons interfering with one another, but instead each photon interferes with itself.

The easiest way to understand the double slit experiment is to consider that the probability of the photon being detected at any point on the screen is calculated by adding the contributions (some positive, some negative) to the probability amplitude from every possible path from source to screen. In your setup, paths through both slits are possible, and they add in such a way that we get alternating regions of high and low probability on the screen - an interference pattern. Nothing we do to photon B changes the paths available to A.

You say that you are “just starting to learn” QM. Are you working from a decent modern textbook (requires two or more years of college-level math)? If so, you’ll get better and more helpful answers if you tell us which one - it helps if we know exactly what you’ve been hearing.

If you’re trying to learn from less mathematically demanding popularizations, be warned that there’s a lot of garbage out there, like the wave-particle duality stuff that @PeroK slammed in the post above. However, two books that you may find helpful will be:
1) Feynman, “QED: the strange theory of light and matter” provides an excellent math-free intuitive picture of how a photon interferes with itself.
2) Girardi, “Sneaking a look at god’s cards“ is a layman-level overview of QM that does a decent job of explaining enough that you can see what it means to say that ”entangled particles share the same wavefunction“

 

[vanhees71]

Another hint: Don't start with photons. They are much more complicated than massive particles, which can be described with non-relativistic QM (under the constraint that you consider situations where this approximation applies). So you should start to learn non-relativistic QM first. A good starting point is vol. 3 of the Feynman lectures and a good book for the more advanced level is Sakurai, Modern quantum mechanics. Only if you have a good understanding of non-relativistic QM in Dirac's formulation in terms of operators on Hilbert space you should turn to the relativistic case, and there it's wise to skip old-fashioned attempts to formulate it in terms of the first-quantization formalism and right away learn it as relativistic QFT (e.g., starting with the book by Schwartz).

Photons as massless spin-1 particles have no sensible classical limit in the sense of particles. They do not even admit a position observable in the usual sense. Photons are special states of the electromagnetic field, socalled single-photon Fock states, and they are not so easy to prepare in the lab!

 

[DrChinese]

What will happen if you send one photon at a time through this setup in one of two different modes. In the first mode the APD detector is not used (taken out), and the second mode the APD detector is used. In the 1st mode, I imagine the 2 slit photons (photons a) will make a diffraction pattern. My question is in the 2nd mode, the one with the detector in place, will the photons going thru the 2 slit plate and sill interfere with each other? I am assuming that the collapse of photon B's wave function would collapse the photon A's wave function too. Or is this a wrong assumption?

A couple of things that you might not be aware of.

a. The distance on the diagram is marked as 1 foot for one apparatus, 1/2 foot for the other. The distance is not a factor in any observable (or otherwise known) fashion. In other words: the order of measurement makes no difference. You could reverse the distances, and nothing would appear different.

b. The double slit side (as drawn) always produces a double bar pattern characteristic of "no interference". While the explanation of this is somewhat complicated, there is a way to produce the characteristic interference pattern. That is: you place a single slit before the double slit. That ends the entanglement (for that particle) but leads to the coherence needed for the interference to appear.

 

[Egghead44]

Why would detecting a photon at B or not affect the interference pattern at A?

Are you assuming that if a photon is detected at B, then the photon at A collapses from a wave to a particle? If so, you have not understood the basics of QM. There is no wave-particle duality in QM.

Ahh, the latter is what I thought. The book I had talked about the entangled photon shared a wave function and that they could not be considered apart. I assumed that would mean that what happened to one could and would affect the other. Also I thought that the photon moved as a wave but is detected as a particle?
Thanks for the reply, that helps

 

[Egghead44]

The interference is not caused by photons interfering with one another, but instead each photon interferes with itself.

The easiest way to understand the double slit experiment is to consider that the probability of the photon being detected at any point on the screen is calculated by adding the contributions (some positive, some negative) to the probability amplitude from every possible path from source to screen. In your setup, paths through both slits are possible, and they add in such a way that we get alternating regions of high and low probability on the screen - an interference pattern. Nothing we do to photon B changes the paths available to A.

You say that you are “just starting to learn” QM. Are you working from a decent modern textbook (requires two or more years of college-level math)? If so, you’ll get better and more helpful answers if you tell us which one - it helps if we know exactly what you’ve been hearing.

If you’re trying to learn from less mathematically demanding popularizations, be warned that there’s a lot of garbage out there, like the wave-particle duality stuff that @PeroK slammed in the post above. However, two books that you may find helpful will be:
1) Feynman, “QED: the strange theory of light and matter” provides an excellent math-free intuitive picture of how a photon interferes with itself.
2) Girardi, “Sneaking a look at god’s cards“ is a layman-level overview of QM that does a decent job of explaining enough that you can see what it means to say that ”entangled particles share the same wavefunction“

I am learning from less mathematical publications, 1st one was “Quantum Mechanics The Physics of the Microscopic World” by Ben Schumacher 2009, and Understanding the Quantum World, by Erica Carlson 2019. I think the former talked more about duality stuff.
I will check out both of the above books you mentioned. I have a Feynman lecture of more classical physics and enjoyed listening to it, he is kinda funny.
Thanks for the reply, I knew Ii was missing something but couldn't quite figure where to look for the answer.

 

[Egghead44]

A couple of things that you might not be aware of.

a. The distance on the diagram is marked as 1 foot for one apparatus, 1/2 foot for the other. The distance is not a factor in any observable (or otherwise known) fashion. In other words: the order of measurement makes no difference. You could reverse the distances, and nothing would appear different.

b. The double slit side (as drawn) always produces a double bar pattern characteristic of "no interference". While the explanation of this is somewhat complicated, there is a way to produce the characteristic interference pattern. That is: you place a single slit before the double slit. That ends the entanglement (for that particle) but leads to the coherence needed for the interference to appear.

Ok thanks, I was thinking (or wrongly thinking) that when the photon B is detected that it would prevent photon a from interfering with itself.

 

[Egghead44]

Another hint: Don't start with photons. They are much more complicated than massive particles, which can be described with non-relativistic QM (under the constraint that you consider situations where this approximation applies). So you should start to learn non-relativistic QM first. A good starting point is vol. 3 of the Feynman lectures and a good book for the more advanced level is Sakurai, Modern quantum mechanics. Only if you have a good understanding of non-relativistic QM in Dirac's formulation in terms of operators on Hilbert space you should turn to the relativistic case, and there it's wise to skip old-fashioned attempts to formulate it in terms of the first-quantization formalism and right away learn it as relativistic QFT (e.g., starting with the book by Schwartz).

Photons as massless spin-1 particles have no sensible classical limit in the sense of particles. They do not even admit a position observable in the usual sense. Photons are special states of the electromagnetic field, socalled single-photon Fock states, and they are not so easy to prepare in the lab!

Thanks, I don't think I'm quite there yet, but great info to keep in mind for going forward.

 

[PeroK]

I am learning from less mathematical publications, 1st one was “Quantum Mechanics The Physics of the Microscopic World” by Ben Schumacher 2009, and Understanding the Quantum World, by Erica Carlson 2019. I think the former talked more about duality stuff.

If we look at Professor Carlson's series of lectures, the first is:

1. Particle-Wave Duality: begin your journey into the quantum world by focusing on one of its most baffling features: the behaviour of quantum entities as both particles and waves.

The interesting thing is this: suppose we throw away quantum mechanics and start again. Pretend we have never heard of QM. Is that the end of wave-particle duality?

The answer is no because wave-particle duality has to do with experimental results and the duality exists in the classical description of nature; not the quantum description of nature!

I would change that summary as follows:

1. Particle-Wave Duality: begin your journey into the microscopic world by focusing on one of its most baffling features: the behaviour of microscopic entities as both classical particles and classical waves.

1a. Continue your journey by learning how QM resolves the problem of wave-particle duality.

That's perhaps a subtle difference, but it shows that the problems all lie with classical physics - and attempting to describe the microscopic world through classical concepts. Quantum mechanics is the resolution to those problems, and in that sense there is no wave-particle duality in QM.

 

[vanhees71]

I'd rather recommend not to use a book that claims that you should begin your "journey into the microscopic world by focusing on one of its most baffling features: the behaviour of microscopic entities as both classical particles and classical waves." since it's plain wrong to think that there is something as wave-particle duality in modern quantum mechanics. It was part of the socalled "old quantum mechanics" which was an amazingly short interlude between the first discovery of quantum phenomena through the explanation of the black-body spectrum by Planck (1900) and the final formulation of modern quantum mechanics by Born and Jordan (based on an idea by Heisenberg), Schrödinger, and Dirac (1925/26).

The great achievement by these physicists was to find a consistent description instead of an unfinished theory with many "baffling features". It might make the story look more boring but the aim of science is not to create some tales with baffling features but a clear understanding of what's observed in nature.

 

[joemorin]

As another beginner, I'll follow recommended reading as noted above--thank you. Nevertheless I'd like to ask the following: What is the experimental proof that attributes (like spin for example) of entangled particles are not pre-existing and inherent within the information of the particles' wave functions from the instant of the entangled particles' creation? So, for example, while there might be only a 50% probability of some particular attribute manifesting upon observation, what proof is there that the attribute was not already pre-determined in the wave information?

 

[vanhees71]

Take as an example the polarization state of two photons,
$$|\psi \rangle=\frac{1}{\sqrt{2}}(|HV \rangle-|VH \rangle).$$
Then the single photons' polarization is completely indetermined, i.e., you have simply unpolarized photons. Nevertheless there's a 100% correlation: If you measure the polarization of one photon to be H, then with certainty the other photon's polarization is V and vice versa.

The single-photon polarization is completely indetermined before the measurement but still there's the 100% correlation. According to standard quantum mechanics that's a property of the state these two photons are prepared in.

That the polarization states are not predetermined and only unknown can be checked thanks to Bell's work on local deterministic hidden-variable theories, where you assume that there are unknown additional "hidden variables" which we don't know but whose values would determine the polarizations. Bell could show that assuming that the properties are local such a theory leads to statistical conclusions (the socalled Bell inequality) which are not valid in quantum theory, and that can be experimentally checked.

All such Bell tests ever done have shown that Bell's inequality is indeed violated in precisely the way as predicted by quantum theory, which excludes the validity of all local determinsitic hidden-variable theories.

 

[Nugatory]

what proof is there that the attribute was not already pre-determined in the wave information?

That is Bell's theorem. If the attributes are predetermined, then the measurement results must obey certain inequalities (the argument is analogous to the argument that the number of non-smoking men in a room must be less than or equal to the number of married men plus the number of unmarried non-smokers of either sex). Quantum mechanics predicts and experiments confirm that these inequalities are violated.

For more on this subject, Google for "Bell's theorem" (pay particular attention to the website maintained by our own @DrChinese), try this Scientific American article, and look at some of the many threads here.

 

[joemorin]

That is Bell's theorem. If the attributes are predetermined, then the measurement results must obey certain inequalities (the argument is analogous to the argument that the number of non-smoking men in a room must be less than or equal to the number of married men plus the number of unmarried non-smokers of either sex). Quantum mechanics predicts and experiments confirm that these inequalities are violated.

For more on this subject, Google for "Bell's theorem" (pay particular attention to the website maintauned by our own @DrChinese), try this Scientific American article, and look at some of the many threads here.

Much thanks--will do.

 

[PeroK]

As another beginner, I'll follow recommended reading as noted above--thank you. Nevertheless I'd like to ask the following: What is the experimental proof that attributes (like spin for example) of entangled particles are not pre-existing and inherent within the information of the particles' wave functions from the instant of the entangled particles' creation? So, for example, while there might be only a 50% probability of some particular attribute manifesting upon observation, what proof is there that the attribute was not already pre-determined in the wave information?

The question of a quantity like spin not having a well-defined value before measurement goes to the heart of QM. The debate on entanglement brought the issue into sharp focus, but most physicist believed this before it was proved by the experiments that confirmed it: i.e. by contradicting Bell's Theorem. Here's one reason why:

If an electron has a definite spin before measurement, then you would not expect the uncertainty principle to apply, in terms of the amount of spin about different axes:

If the x-spin, y-spin and z-spin all have definite values, then why does measuring the z-spin scramble the x and y-spin? Also, the probability of getting a particular spin value about an intermediate axes fits perfectly with the QM formalism. Whereas, it's difficult to make a good case for the general behaviour being controlled by hidden variables.

QM explains this behaviour perfectly and many physicists, such as Niels Bohr, took this as a sign that this was telling them something fundamental about the nature of reality.

The problem with hidden variables starts as soon as you analyse electron spin and it seems (to some at lesat) more natural to accept this and move on. The alternative, to insist on hidden variables, feels like an insistence that nature at the fundamental level must have the properties that we expect in advance.

With all these debates about QM, the real problems start when you try to discard QM - because then you have little or no explanation for the behaviour of elementary particles. It's not like everything can be explained otherwise. If you want well-defined electron spin before measurement, then you lose the explanation for all particle physics since 1900 or so!

 

[DrChinese]

What is the experimental proof that attributes (like spin for example) of entangled particles are not pre-existing and inherent within the information of the particles' wave functions from the instant of the entangled particles' creation?

The "experimental" proof is built around 3 steps, which I will paraphrase liberally from their essential sources in order to keep it relatively simple (details are dropped, interpretations are ignored, etc). All of these are built around entangled particle pairs and their spins (measured respectively by Alice & Bob).

1) Einstein et al (1935, a/k/a EPR): QM limits simultaneous knowledge of non-commuting observables, essentially saying they don't exist until measured. But Alice can choose to measure ANY spin component (i.e. any of all possible angles), and therefore predict with certainty what Bob will observe at the same angle. So that outcome (as well as all other outcomes that can be predicted with certainty) must have been determined at entangled pair creation [this was your starting point].

2) Bell (1964): Assuming 1) is true: Yes, that works when Alice and Bob measure at the same angle settings. However, a contradiction with the predictions of QM occurs when the Alice/Bob angle settings are different. Basically: if all of those outcomes (at all angles) were determined at pair creation, what are they? Turns out that even if you hand pick them (for all possible angles, but 3 is enough), they will NOT match QM's statistical predictions for particle pairs. For Alice/Bob angles 120 degrees apart: the QM prediction (for the Alice & Bob match rate) is at least 8% different than the prediction would be if 1) is true.

3) Aspect et al (1982): Experiments are performed on actual entangled particle pairs, and confirm QM's predictions (it took this many years to put together a suitable setup). Therefore per 2): assumption 1) must be rejected. QED.

 

[joemorin]

You have all been generously helpful with intuitive lay explanations (to the degree possible) and guidance to new contemplations for me, e.g. Bell theorem, uncertainty principle, locality, Counterfactual definiteness (wow), no-conspiracy -- some of which I've gained vague understanding in last 24 hours -- thank you all! Then the arguments meld into the philosophical: determinism, free will, realism ... Simply put in my own lay words it appears that uncertainty has become demonstrably more certain, much to the consternation of those (like myself) on a potentially futile quest to know absolute truth. My sincere thanks to all contributing to this forum.