The False Asymmetry in Entanglement

In 1935 Albert Einstein and Erwin Schrödinger mistakenly introduced an asymmetry into a perfectly symmetric situation, making entanglement the mystery that it is considered today. Every follower of their early thinking introduces this false asymmetry.

Almost every presentation of the EPR paradox begins with something like "Alice observes one particle..." and concludes with the question "How does the second particle get the information needed so that Bob's later measurements correlate perfectly with Alice's?"

In between the two experimenters, two entangled particles leave the center in opposite directions. Alice makes a measurement and finds an electron or photon in a certain spin state (say up). When Bob makes his measurement, at the same time or later, he always finds a spin state (say down) that is perfectly correlated (or anti-correlated) with Alice's. The final spin is the same as at the start of the experiment (say zero). Spin is a conserved quantity.

The simplest explanation of the mystery of entanglement is that any measurement, either Alice or Bob, whichever is actually first, "collapses" the two-particle wave function and determines both particles' properties. Conservation of those properties means that they have been continuously correlated perfectly since the experiment started, unless an external interaction changes one or both of them.

It is a surprise that Einstein, who was so good at seeing deep symmetries, did not consider how to remove the false asymmetry favoring the supposed "first" measurement..

This description privileges the "here" and the "now" of Alice's point of view. In the special frame of reference in which Alice's and Bob's labs are at rest along with the central source emitting the entangled particles, the two-particle wave function Ψ12 "collapses" in both places at the same instant in "world-time." Either Alice or Bob "collapses" the wave function, depending on who measures first in this special frame. We can say that like the initial entanglement, disentanglement affects both particles simultaneously.

Bob's "then" and "there" are thought by Alice to happen later because they are in a space-like separation and it takes time for Bob's results to reach Alice. But the overall situation is perfectly symmetric. Bob can think his measurement is first when it is not, unless it is actually made at a later time t1 in the special frame above.

Einstein's 1935 EPR paper asked about two electrons fired in opposite directions from a central source with equal velocities. He imagined them starting at t0 some distance apart and approaching one another with high velocities. Then for a short time interval from t1 to t1 + Δt the particles are in contact with one another and become entangled.

Einstein said correctly in the EPR paper that at a later time t2, a measurement of one electron's position would instantly establish the position of the other electron - without measuring it explicitly. And this is correct, just as after the collision of two billiard balls, measurement of one ball tells us exactly where the other one is due to conservation of momentum. But this is not "action at a distance." It is more properly "knowledge at a distance."

Note that Einstein used conservation of linear momentum to calculate the position of the second electron. Although conservation laws are rarely cited as the explanation, they are the physical reason that entangled particles always produce correlated results. If the results were not always correlated, the implied violation of a fundamental conservation law would be a much bigger story than the mysterious entanglement itself, as interesting as that is.

Now linear momentum is not the only quantity that is always strictly conserved. Others are mass, energy, angular momentum, and particle spin. It is the spin (of electrons or photons) that is measured in the modern tests of entanglement inspired by Bell's 1964 theorem and inequality.

Now Einstein's idea of an "objective reality" is that the particles have properties like position, momentum, and spin at all times. By contrast, Niels Bohr's "Copenhagen Interpretation" claims that particles have no such properties until they are measured.

While it is true that particles acquire some specific properties that depend on what the experimenter measures for, conservation laws require that particle motions and other properties are continuous in space and time. It is only our knowledge of the particle positions that appears to be discontinuous (the "quantum jumps").

But just because we cannot know their properties does not mean, as Einstein insisted, that they do not have objective properties. We cannot prove (without continuous measurements) that the particle ceases to exist or has discontinuous properties, between measurements. What forces would cause such changes? We imagine the particles are not interacting with other particles!

One property that is particularly difficult to visualize as conserved is spin. When measured in a particular direction, electrons always are measured as having a spin of +1/2 or -1/2. They can be measured in the x, y, or z direction, so it is tempting to see them as having spin 1/2 simultaneously in these directions, but that is not the case. They have a certain probability of measuring 1/2 or -1/2 in any direction, but it is the measurement that "projects" the spin 1/2 into the direction of measurement.

left right
σx σy σz σx σy σz
+ +/- +/- - +/- +/-
+/- + +/- +/- - +/-
+/- +/- + +/-- +/- -
- +/- +/- + +/- +/-
+/- - +/- +/- + +/-
+/- +/- - +/-- +/- +
Below is an animation that starts with two electrons produced with the left spin up in the y direction and the right spin down (the yellow row). The animation illustrates the assumption, unprovable but consistent with conservation principles, that particles remain in those states no matter how far they separate, provided neither interacts with anything else before the measurement.

This illustrates Einstein's "objective reality" idea, that particles have properties like position before they are measured. Spin is different, in that the measurement projects the electron spins along the chosen measurement direction, with projection preserving the opposite directions of spin.

Since each electron has only one unit of electron spin (a magnetic moment equal to one Bohr magneton), we can only say that if measured in a given direction, the spin will be instantly projected, in our example as spin up (1/2 ) for the left electron and the opposite spin down (-1/2) for the right electron.

The table shows six possible outcomes. The spins in directions not measured are indeterminate. A superposition of spin up and down is our best possible prediction +/-.

Werner Heisenberg and later Paul Dirac and others refer to the "free choice" of the experimenter as to which direction is chosen to measure. But then Dirac adds that nature makes an indeterministic choice as to whether we find the electron spin is up (1/2 ) or down (-1/2) in that freely chosen direction.

In his description of three polarizers, Dirac showed that unmeasured directions are in a superposition of states.

Now entanglement adds the nonlocality and non-separability that is caused by the (single) two-particle wave function Ψ12 collapsing symmetrically and simultaneously into single-electron wave functions Ψ1 and Ψ2 in our special frame.

Normal | Teacher | Scholar