The idea of "hidden variables" that might restore determinism to quantum mechanics was proposed by David Bohm in 1952 as a solution to the Einstein-Podolsky-Rosen Paradox paper in 1935.

Bohm's new experimental method would explain the EPR paradox by providing the information needed at the distant “entangled” particle, so it can coordinate its properties perfectly with the “local” particle.

Bohm wrote in 1952,

The usual interpretation of the quantum theory is based on an assumption having very far-reaching implications, ~i.e., that the physical state of an individual system is completely specified by a wave function that determines only the probabilities of actual results that can be obtained in a statistical ensemble of similar experiments. This assumption has been the object of severe criticisms, notably on the part of Einstein, who has always believed that, even at the quantum level, there must exist precisely definable elements or dynamical variables determining (as in classical physics) the actual behavior of each individual system, and not merely its probable behavior. Since these elements or variables are not now included in the quantum theory and have not yet been detected experimentally, Einstein has always regarded the present form of the quantum theory as incomplete, although he admits its internal consistency.

"A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables. I,” Physical Review, vol.85, no.2. p.166, 1952

Einstein may have pressed Bohm to develop hidden variables as the source of nonlocal behavior. Einstein had heartily approved of Bohm’s 1951 textbook Quantum Theory and was initially supportive of Bohm’s new mechanics. Einstein thought Bohm was young enough and smart enough to produce the mathematical arguments that the older generation of “determinist” physicists like Erwin Schrödinger, Max Planck, and others had not been able to accomplish.

But when Bohm finished the work, based on Louis de Broglie’s 1924 “pilot-wave” idea (which Einstein had supported), Einstein rejected it as inconsistent with his theory of relativity.

Einstein wrote to Max Born on May 15, 1952,

Have you noticed that Bohm believes (as de Broglie did, by the way, 25 years ago) that he is able to interpret the quantum theory in deterministic terms? That way seems too cheap to me. But you, of course, can judge this better than I. 

Born-Einstein Letters, #99, p.188.

Five years later, Bohm and his Israeli student Yakir Aharonov reformulated the original EPR argument in terms of electron spin. They said experimental tests with continuous variables would be much more difficult than tests with discrete quantities, such as the spin of electrons or polarization of photons. Bohm and Aharonov described the preparation of two particles, such that a measurement of one at a later time determines a measurement in the same direction of the other particle at any distance away.

We consider a molecule of total spin zero consisting of two atoms, each of spin one-half. The wave function of the system is therefore

ψ = (1/√2) [ ψ₊ (1) ψ_- (2) - ψ_- (1) ψ₊ (2) ]                 (1)

where ψ₊ (1) refers to the wave function of the atomic state in which one particle (A) has spin +ℏ/2, etc. The two atoms are then separated by a method that does not influence the total spin. After they have separated enough so that they cease to interact, any desired component of the spin of the first particle (A) is measured. 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

Bohr and Aharonov gave a rare discussion of the role of conservation of angular momentum as explaining the fact (for the total spin zero state) that spin of the particle (B) will be found opposite to that of A. They also reacted to a hypothesis by Harvard professor Wendell Furry. Six years later Eugene Wigner also cited the conservation of angular momentum as explaining perfect correlations (or anti-correlations) in Bell-Bohm experiments.

Evidently, the foregoing interpretation is not satisfactory when applied to the experiment of ERP. It is of course acceptable for particle A alone (the particle whose spin is measured directly). But it does not explain why particle B (which does not interact with A or with the measuring apparatus) realizes its potentiality for a definite spin in precisely the same direction as that of A. Moreover, it cannot explain the fluctuations of the other two components of the spin of particle B as the result of disturbances due to the measuring apparatus.

One could perhaps suppose that there is some hidden interaction between B and A, or between B and the measuring apparatus, which explains the above behavior. Such an interaction would, at the very least, be outside the scope of the current quantum theory. Moreover, it would have to be instantaneous, because the orientation of the measuring apparatus could very quickly be changed, and the spin of B would have to respond immediately to the change. Such an immediate interaction between distant systems would not in general be consistent with the theory of relativity. This result constitutes the essence of the paradox of Einstein, Rosen, and Podolsky...

At first sight it would seem then that there exists at present no experimental proof that the paradoxical behavior described by ERP will really occur...

In fact, Einstein has (in a private communication) actually proposed such an idea; namely, that the current formulation of the many-body problem in quantum mechanics may break down when particles are far enough apart.

As Erwin Schrödinger explained to Einstein in 1935, reacting to EPR, the two-particle wave function will only separate (or decohere or decompose) into a product function when either particle is measured. For Bohm's case it will separate randomly into either ψ₊ (1) ψ_- (2) or ψ_- (1) ψ₊ (2)
The "definite" direction is created by the "free choice" of an experimenter measuring either A or B.

The consequences of such an idea have already been discussed by Furry.⁴ To illustrate Furry’s conclusions in terms of our problem, we may consider the possibility that after the molecule of spin zero decomposes, the wave function for the system is eventually no longer given by Eq. (1), which implies the puzzling correlations of the spins of the two atoms. Instead, we suppose that in any individual case, the spin of each atom becomes definite in some direction, while that of the other atom is opposite.

The molecule of spin zero is not yet in a single product. It is in a superposition of products
ψ₊ (1) ψ_- (2) and ψ_- (1) ψ₊ (2). It only decomposes (or "collapses") into one of these when a measurement is made.

The wave function will be the product

ψ = ψ_+θ,φ (1) ψ_-θ,φ (2)                 (2)

where ψ_+θ,φ (1) is a wave function of particle A whose spin is positive in the direction given by θ and φ. In other words, each particle goes into a definite spin state, while the fluctuations of the other two components of the spin are uncorrelated to the fluctuations of these components of the spin of the other particle. In order to retain spherical symmetry in the statistical sense, we shall further suppose that in a large aggregate of similar cases, there is a uniform probability for any direction of θ and φ.

It is true that in any single case, the total angular momentum will not be conserved (just because the fluctuations of the two particles are now uncorrelated). However, thus far, there has not been given an experimental demonstration of the detailed conservation of every component of the angular momentum, for particles that are far apart and not interacting.

Conservation of angular momentum must be true at all times, not only on the average as Bohr-Kramers-Slater mistakenly argued for conservation of energy in 1924.

On the other hand, with the model that we have discussed here, the uniform probability of all directions will lead to the experimentally observed fact of conservation on the average. Thus, all evidence cited up to this point is equally consistent with either theory, but the model described above has the advantage of avoiding the paradox of ERP.

Thousands of Bell tests experimentally prove that measurement of particle A in a particular direction will show perfect correlations with particle B if (and only if) B is measured in the same direction. This is true after the measurement whether the product wave function becomes ψ_+θ,φ (1) ψ_-θ,φ (2) or ψ_-θ,φ (1) ψ_+θ,φ (2)

For if this model should be correct, there will be no precise correlation of an arbitrary component of the angular momentum of each particle in every individual case, and our decision to choose a certain direction for measuring the spin of particle A will have no influence whatever on the state of particle B [since the wave function is just the product (2)].

4 W. H. Furry, Phys. Rev. 49, 393, 476 (1936).

ibid.p.1071

Eugene Wigner wrote in 1963

If a measurement of the momentum of one of the particles is carried out — the possibility of this is never questioned — and gives the result p, the state vector of the other particle suddenly becomes a (slightly damped) plane wave with the momentum -p. This statement is synonymous with the statement that a measurement of the momentum of the second particle would give the result -p, as follows from the conservation law for linear momentum. The same conclusion can be arrived at also by a formal calculation of the possible results of a joint measurement of the momenta of the two particles.

Writing a few years after Bohm, and one year before Bell, Wigner explicitly describes Einstein's conservation of momentum example as well as the conservation of angular momentum (spin) that explains perfect correlations between angular momentum (spin) components measured in the same direction

One can go even further: instead of measuring the linear momentum of one particle, one can measure its angular momentum about a fixed axis. If this measurement yields the value mℏ, the state vector of the other particle suddenly becomes a cylindrical wave for which the same component of the angular momentum is -mℏ. This statement is again synonymous with the statement that a measurement of the said component of the angular momentum of the second particle certainly would give the value -mℏ. This can be inferred again from the conservation law of the angular momentum (which is zero for the two particles together) or by means of a formal analysis.

(The Problem of Measurement, Eugene Wigner, in Wheeler and Zurek, Quantum Measurement p,340)