I Is quantum entanglement just like ordering Schrodinger's Slice pizza?

[Wallace]

TL;DR Summary

What's missing from this simplistic analogy for entanglement? Does this correctly guide intuition, of not, why not?

Here's a simple story. I'm running a pizza delivery store and hit upon a gimmick to increase sales, I call it "Schrodiners Slice". You call up and get paired up with the next caller and your orders are randomly shuffled. Maybe you get your order, but maybe you get the next persons order instead. Alice rings up and orders a Pepperoni and Bob calls in and orders a Margarita. The boxes are identical so I take the two, shuffle them so that I don't know which is which. They are now "entangled", once you know the flavour of one you'd know the flavour of the other instantly, regardless of how far away the second box is at the time.

The orders are delivered and Alice measures the flavour of her order by opening the box, revealing the piping hot Margarita. She knows instantly that Bob has the Pepperoni.

So, my questions is, is this a reasonable analogy for entanglement, but using everyday macroscopic objects, and therefore demonstrating that entanglement is about knowledge of the observer, rather than there being some fundamental physical process "the collapse of the wavefunction" that happens upon observations? Or, maybe this is a flawed and misleading explanation that missing some key ingredient of what makes quantum entanglement fundamentally different from this classical and macroscopic scenario. I think vaguely there's something about Bell's inequality that is relevant here, but can't make it work with the analogy (i.e. add some extra details that show that the quantum version is weirder than just lazy Pizza order fulfilment).

I'm asking for understanding. I studied all this years ago, although Quantum was never my speciality. I'm getting back into thinking about this stuff via Sean Carroll's book on Many Worlds and I'm trying to wrap my head around the concepts again.

 

[atyy]

Here's a simple story. I'm running a pizza delivery store and hit upon a gimmick to increase sales, I call it "Schrodiners Slice". You call up and get paired up with the next caller and your orders are randomly shuffled. Maybe you get your order, but maybe you get the next persons order instead. Alice rings up and orders a Pepperoni and Bob calls in and orders a Margarita. The boxes are identical so I take the two, shuffle them so that I don't know which is which. They are now "entangled", once you know the flavour of one you'd know the flavour of the other instantly, regardless of how far away the second box is at the time.

The orders are delivered and Alice measures the flavour of her order by opening the box, revealing the piping hot Margarita. She knows instantly that Bob has the Pepperoni.

The remarkable thing about quantum entanglement is that your analogy is incomplete. Quantum mechanics violates Bell inequalities, which means that scenarios such as the one you suggested, where everything occurs in accord with classical relativistic causality, cannot explain all entanglement phenomena. Because of the violation of classical relativistic causality, quantum mechanics is nonlocal in that sense. Amazingly, although classical relativistic causality is violated, quantum mechanics does not allow faster-than-light communication, so it preserves relativity at an operational level.

 

[PeterDonis]

is this a reasonable analogy for entanglement

No, because any model of the kind you describe will make predictions that satisfy the Bell inequalities; that was the point of Bell's papers that derived those inequalities. But the predictions of QM, which have been verified in actual experiments, violate the Bell inequalities; therefore, those predictions cannot be explained by any model of the type you describe. (Bell describes such models in another paper as "Bertlmann's socks" type models, named for a professor who always wore socks of different colors.)

 

[PeterDonis]

entanglement is about knowledge of the observer, rather than there being some fundamental physical process "the collapse of the wavefunction" that happens upon observations?

How "collapse of the wavefunction" is treated depends on which interpretation of QM you adopt. Discussion of QM interpretations belongs in a separate thread in the QM interpretations forum. But all interpretations must account for the fact that quantum entanglement can violate the Bell inequalities.

 

[Wallace]

Thanks for the responses everyone. Maybe I gave a bum steer in bringing up Bell's inequality, what I'm after is an intuition as to what is incomplete/wrong with the analogy. Imagine someone had only encountered Quantum Physics at a "read New Scientist occasionally" level and came up with the Pizza thing as an explanation to teach people with. Is there a plain English description of the flaw in the analogy that doesn't require pointing to some detailed maths or reference to some theorem.

Maybe putting it another way, if the Pizza's were quantum systems, what weird/unexpected behaviour might you see that is not as described here?

I realize I may be Not Even Wrong here and trying to get to some pithy explanation for something that is just fundamentally hard to explain.

 

[PeroK]

Thanks for the responses everyone. Maybe I gave a bum steer in bringing up Bell's inequality, what I'm after is an intuition as to what is incomplete/wrong with the analogy. Imagine someone had only encountered Quantum Physics at a "read New Scientist occasionally" level and came up with the Pizza thing as an explanation to teach people with. Is there a plain English description of the flaw in the analogy that doesn't require pointing to some detailed maths or reference to some theorem.

Maybe putting it another way, if the Pizza's were quantum systems, what weird/unexpected behaviour might you see that is not as described here?

I realize I may be Not Even Wrong here and trying to get to some pithy explanation for something that is just fundamentally hard to explain.

This is covered in almost any material on quantum enganglement: hidden variables, Bohr-Einstein debates, EPR paper, Bell's theorem, tests thereof. Where have you been reading about quantum entanglement if you haven't come across this?

You've raised this as an "A" (postgraduate level) thread, but what you seem to want is something below a B level answer.

My suggestion is to do some reading on the subject.

 

[Nugatory]

Maybe putting it another way, if the Pizza's were quantum systems, what weird/unexpected behaviour might you see that is not as described here?

A violation of Bell’s inequality IS the weird unexpected behavior here. To see just how weird that is...

Suppose that when someone calls in their order, they specify not only the type of pizza but also whether they want it with extra cheese and/or extra sauce. Think about it for a moment and you’ll agree that the number of pepperoni pizzas with extra sauce can be no more than the number of pizzas with extra sauce and extra cheese plus the number of pepperoni pizzas without extra cheese. That inequality is analogous to Bell’s inequality, and it would be quite weird and unexpected to find it violated... But it is violated by quantum entanglement.

You might try https://static.scientificamerican.com/sciam/assets/media/pdf/197911_0158.pdf for a non-technical explanation of how Bell’s inequality relates to analogies such as this pizza one.

 

[vanhees71]

Thanks for the responses everyone. Maybe I gave a bum steer in bringing up Bell's inequality, what I'm after is an intuition as to what is incomplete/wrong with the analogy.

The problem is that we don't have "quantum intuition" from everyday-experience, because in everyday-experience we deal with macroscopic objects which are (effectively) very well described by classical physics (mostly classical mechanics and some electrodynamics). The only way to build "quantum intuition" is to learn the mathematical formalism and analyze a lot of real-world "quantum experiments" with it (and be it only gedanken experiments). If it comes to entanglement any "naive intuition" fails!

 

[EPR]

Here is something for your intuition - because of fundamental uncertainty in qm, systems which have interacted in the past have now joint uncertainties. This was clear way before the first entanglement experiment proved it.