Jarrett thus defines what he calls the constraint "DETERMINISM" not as the familiar philosophical idea that every event or state of affairs, including every human decision and action, is the inevitable and necessary consequence of antecedent states of affairs, a chain of causes and event, with one possible future.

Instead, Jarrett defines determinism as the fact that the measurement outcomes of a Bell test is limited to two possible values 0 and 1.

Using Mermin's notation, where P is probability, i and j are the inputs/switches of the Mermin contraption at A and B, and x and y are the measurement outcomes, which are "determined" to be 0 or 1, Jarrett defines what he calls a DETERMINISM "constraint" in Mermin notation...

Jarrett similarly defines new constraints for the terms "CONSERVATION," "LOCALITY," and "COMPLETENESS." And he adds a new version of locality that he calls "STRONG LOCALITY," declaring it to be a "Bell-type Inequality."

Jarrett defines a constraint he calls CONSERVATION, noting that it is not the physical conservation of angular momentum

The conservation condition (or "constraint?") derives its name from the quantum-theoretic analysis of these experiments, wherein it expresses the conservation of angular momentum. This quantum-theoretic analysis is not, however, to be assumed in any of what follows. Instead, I tentatively offer as warrant for this condition (subject to a qualification to be mentioned later) this simple empirical fact: In the data of Mermin contraption experiments, in each trial in which the A and B switch settings are the same, the lights which come on at A and B agree in color. Hence for the time being, conservation is put forward as a necessary condition for empirical adequacy.

Bell's Theorem, A Guide to the Implications, 1987, p.70.

Here Jarrett's constraint has become a "condition." And he says the condition is necessary, a logical concept with little connection to empirical facts.

An empirical fact of great importance is that the outcomes of Bohm-version EPR experiments are always perfectly correlated, in opposite spin directions with a 50-50 chance of particle 1 being spin-up and particle 2 spin-down, or vice versa.

The Bohm version of EPR starts with a hydrogen molecule in a spherically symmetric "singlet" state, with total spin angular momentum zero, which disassociates into two hydrogen atoms. Bohm-EPR is describable by a two-particle wave function we can call ψ₁₂ which is the linear combination of two terms, each the product of two single-particle wave functions, ψ₁ and ψ₂.

The coefficients 1/√2, when squared, tell us there is a 50-50 chance of finding the separated atoms in ψ₁ψ₂ or in ψ₂ψ₁. In either case the atomic spins are always found in opposite directions, when measurements are made in the same direction, preserving the symmetry, and conserving the total spin angular momentum as zero, the same as the original molecule.

It is this physical fact that led Bohm in 1951 to write...

Suppose that we have a molecule containing two atoms in a state in which the total spin is zero and that the spin of each atom is ℏ/2. Roughly speaking, this means that the spin of each atom points in a direction exactly opposite to that of the other, insofar as the spin may be said to have any definite direction at all. [Indeed, we can only say that the total spin zero of the two atoms means that their two-particle wave function ψ₁₂ is spherically symmetric with no preferred direction - the singlet state.] Now suppose that the molecule is disintegrated by some process that does not change the total angular momentum. The two atoms will begin to separate and will soon cease to interact appreciably. [But Erwin Schrödinger tells us that they will not become independent and "cease to interact" until some measurement disentangles them, decohering their phases, and allowing their two-particle wave function ψ₁₂ to be replaced with the product of two single-particle wave functions ψ₁₂ψ₂ or ψ₂ψ₁.] Their combined spin angular momentum, however, remains equal to zero, because no torques have acted on the system...

Suppose now that one measures the spin angular momentum ofany one of the particles, say No.1. Because of the existence of correlations we can immediately conclude that the angular momentum vector of the other particle (No.2) is equal and opposite to that on No.1. In this way, we can indirectly measure the angular momentum of particle No.2 by measuring the corresponding vector of particle No.1.

Quantum Theory, p.614

Bohm and Aharonov say the equivalent in 1957

Then, because the total spin is still zero, it can immediately be concluded that the same component of the spin of the other particle (B) is opposite to that of A.

"Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky,” Physical Review, vol.108, no.4. p.1070, 1957

Finally Bell in 1964 says...

With the example advocated by Bohm and Aharonov, the EPR argument is the following. Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite directions. Measurements can be made, say by Stern-Gerlach magnets, on selected components of the spins σ₁ and σ₂. If measurement of the component σ₁ • a, where a is some unit vector, yields the value + 1 then, according to quantum mechanics, measurement of σ₂ • a must yield the value — 1 and vice versa.

"On the Einstein-Podolsky-Rosen Paradox," Physics, 1.3, p.195. /div>

Now why, we may ask, did not Bohm, or Bell, or modern commentators on Bell's theorem, like Jarrett, consider the conservation of total spin angular momentum zero as a "common cause" explaining the perfect measurement correlations? The conservation is true at all times for the "separating" particles up to the moment of measurements (It is known as a "quasi-molecule" because it is described with a molecular wave function and not the product of two atomic wave functions). Conservation will remain true as long as the forces involved in Stern-Gerlach spin measurements are symmetric, the two SG devices oriented in the same plane to preserve the symmetry. When the devices measure in planes at an angle to one another, the correlations fall off as the cosine squared of that angle (Malus's law).

This "common cause" is just a shared/joint property of the two particles, true at all times, not just for measurements. It is not one particle's measurement acting (instantaneously at a distance) on the other particle.

The constant total spin zero is thus a "constant of the motion." Since it achieves the goal of hypothetical "local hidden variables" traveling with the particles, we might call it a "hidden" constant of the motion.

Some of these philosophers of science, starting with Jarrett himself, simply redefine "Bell's locality," claiming it contains more than simple "locality." Some also redefined "locality." Again following Jarrett, many decided that Bell's theorem and his "locality" can not be understood without understanding other complicated phenomena, such as Einstein's "realism," Bohr's "completeness," Bohm's "hidden variables," and of course philosophical "determinism."

The mathematical derivation of Bell's theorem and its meaning is not easily seen. But Bell's stated goal was to find an explanation for Einstein's "spooky action at a distance" as close as possible to Einstein's idea of "realism."

So instead of suggesting new terminology for future philosophical debates, we propose reviewing Einstein's own insights into

1. nonlocal behavior between a particle and its single-particle wave function, between 1905 and 1927
2. nonlocal behavior between two particles and their two-particle wave function ψ₁₂, starting in 1933
3. his "separability principle" (Trennungsprinzip), starting with EPR in 1935, about which,
4. Erwin Schrödinger in his 1935 reply to EPR, told Einstein that the particles are "entangled," that is, they are not separable, until some disturbance or some measurement "disentangles" the two-particle wave function ψ₁₂ into the product of two single-particle wave functions, either ψ₁ψ₂ or ψ₂ψ₁, after which they are separated and no longer influence one another.
5. However, Schrödinger said, measurements of one particle may still reveal properties of the separated particle, using conservation laws.

Don Howard, who follows Jarrett's thinking and new terminology in many ways, also gave us the clearest history of Einstein's nonlocality and his nonseparability.

We should compare Jarrett's constraints, claims, and logical map with the central physical issues of quantum entanglement.

COMPLETENESS, LOCALITY, and STRONG LOCALITY