We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by “explaining” how it works. We will just tell you how it works. In telling you how it works we will have told you about the basic peculiarities of all quantum mechanics.

(Lectures on Physics, vol. I, ch 37, and vol. III, Ch. 1)

I will take just this one experiment, which has been designed to contain all of the mystery of quantum mechanics, to put you up against the paradoxes and mysteries and peculiarities of nature one hundred per cent. Any other situation in quantum mechanics, it turns out, can always be explained by saying, 'You remember the case of the experiment with the two holes? It's the same thing'. I am going to tell you about the experiment with the two holes. It does contain the general mystery; I am avoiding nothing; I am baring nature in her most elegant and difficult form.

The Character of Physical Law, chapter 6, p.129
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What then is this "only mystery?" And why doesn't Feynman tell us more about it beyond simply describing the two-slit experiment? Information philosophy reframes the question and proposes a deeper question that is without an answer...

Now we know how the electrons and light behave. But what can I call it? If I say they behave like particles I give the wrong impression; also if I say they behave like waves. ...They behave in a way that is like nothing that you have ever seen before.

The Character of Physical Law, chapter 6, p.128

Feynman says particles don't behave like oscillating weights on a spring, nor tiny planets going around in orbits (p.128). What he knows and might have said is that the waves (actually the wave functions Ψ that are the solutions to Schrödinger's wave equation HΨ = EΨ) are not forces like those moving weights or planets! They are just mathematical probabilities for different possible places where experimental measurements will find the particles.

As information philosophy sees it, the deepest mystery is how abstract mathematical predictions (information) about where particles will be found is "influencing" the particles to move to those predicted positions, without concrete forces to push or pull them!

Should Feynman have explained this mystery as something immaterial affecting something material? Do you see the resemblance to René Descartes' Mind-Body Problem?

Feynman explicitly says "The question now is, how does it really work? What machinery is actually producing this thing? Nobody knows any machinery."(Character of Physical Law, p.144)

We can compare John Bell's paper on the EPR Paradox, which also claimed there must be a mechanism...

In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant.

"On the Einstein Podolsky Rosen Paradox," Physics Vol. 1, No. 3, pp. 195—200, 1964

Did Feynman think that entanglement is just another "situation in quantum mechanics [which] can...be explained by saying, 'You remember the case of the experiment with the two holes? It's the same thing'"? Not entirely. In his very brief comments on Bell's Theorem, Feynman said it was "no big deal," just another way of presenting what quantum mechanics already knows. See YouTube.com. But entanglement involves something more than the mysterious wave function.

A scientific theory can only be judged by its agreement with experiments. Although the experimental results are only statistical, quantum theory predictions are more accurate by several orders of magnitude than classical physics!

And entanglement is no exception. The two-particle wave function Ψ₁₂ predicts the outcomes perfectly and completely. First, it predicts that the sequence of spins for each particle will be completely random! Secondly (and counterintuitively) it predicts that the total spin will be the same as it was at initial entanglement, conserving total spin angular momentum.

Quantum mechanics predicts that although the first measurement is perfectly random, the second measurement, no matter how far away when measured, will be exactly what is needed to conserve total spin, leading so many thinkers for nearly a century to believe that the first measurement must have "influenced" the second, that the particles are "communicating" at faster than light speed!

And thousands of Bell experiments have confirmed these theoretical predictions perfectly!

Is the "weirdness" of entanglement a part of the "only mystery" of quantum mechanics? It is, but not the only part, because quantum mechanics tells us precisely what causes the two particles to always appear perfectly correlated. The total spin of the particles is a constant of the motion that is conserved at all times, constraining the spins to always agree. We can view this constraint as a common cause in the past light cone of the two particles, coming from the apparatus that initially entangled them, located centrally between the two measurements.

The great exaggeration of entanglement capabilities comes from thinking that Alice and Bob are communicating at faster than light speed with one another. They are not. Alice and Bob's measurements are creating bits of information when they collapse the two-particle wave function coming from the entanglement apparatus located centrally between them. Neither is any meaningful information being communicated from the causal center to Alice and Bob, since the bits are randomly generated. Nevertheless, these randomly generate bit strings have value as quantum keys for cryptography.

Starting most prominently with Einstein himself, critics of the Copenhagen Interpretation say that it denies a "reality" independent of (conscious) "observers." This is extreme and seriously flawed, especially the absurd claim that particles "do not exist" when they are not being observed. What does not exist is the particular value of properties which quantum mechanics says has different possible values when measured.

The conservation of matter and energy means that aA material particle cannot go in and out of "existence."

"Do you really believe the moon is not there when you are not looking at it?," Einstein famously asked his colleague and later biographer, Abraham Pais (Rev. Mod. Phys. 51, 863–914 (1979), p. 907).

N David Mermin

What "doesn't exist" when no one is observing is up-to-date information (knowledge) about a particle's properties, where is it exactly, how is it moving, what is its internal state, etc.

And when an observer does make a measurement, the so-called collapse of the wave function does not mean that anything physical is moving! It is just information changing!

The foolish idea that a particle goes out of existence and returns when observed contradicts a basic principle of physics, more fundamental then the mechanical laws of motion, namely the conservation of mass and energy, as well as conservation of properties like angular momentum and electron spin, which are critical to explaining entanglement.