# Envariance vs Bohm: Is Quantum Mechanics Truly Deterministic?

• atyy
In summary, the Bohmian interpretation says quantum mechanics is deterministic, while the environmental darwinism approach tries to derive the Born rule and make quantum mechanics deterministic. If darwinism succeeds, it would be compatible with Bohmian mechanics because both aim to make QM deterministic.
atyy
The Bohmian interpretation says quantum mechanics is deterministic.

The environmental darwinism approach tries to derive the Born rule, and make quantum mechanics deterministic.

If darwinism succeeds, would it be compatible with Bohm, since both aim to make QM deterministic?

atyy said:
The Bohmian interpretation says quantum mechanics is deterministic.

Can you quote a reliable source?

Can you quote a reliable source?

http://arxiv.org/abs/quant-ph/0312059
"Bohmian mechanics, on the other hand, upholds a unitary time evolution of the wavefunction, but introduces an additional dynamical law that explicitely governs the always-determinate positions of all particles in the system."

But this statement in the paper:

"Thus the particles follow determinate trajectories described by Q(t), with the distribution of Q(t) being given by the quantum equilibrium distribution $$\rho=|\psi|^2$$"

is inaccurate. To make it accurate one would have to add: "provided it is given by this distribution at some time instant t0."

Last edited:
Quoting from Goldestein, Struyve, "On the Uniqueness of Quantum Equilibrium in Bohmian Mechanics", Journal of Statistical Physics 128, 1197-1209 (2007)

"Bohmian mechanics (often called the deBroglie-Bohm theory) yields the same predictions as standard quantum theory provided the conﬁguration of a system with wave function ψ is random, with distribution given by $$|\psi|^2$$ This distribution, the quantum equilibrium distribution [1, 2], satisfies the following natural property: If the distribution of the conﬁguration at some time t0 is given by $$|\psi_{t_0}|^2$$, then the distribution of the conﬁguration at any other time t will be given by $$|\psi_t|^2$$ — i.e., with respect to the wave function it will have the same functional form at the other time—provided, of course, that the wave function evolves according to Schrodinger’s equation between the two times and the conﬁguration evolves according to the law of motion for Bohmian mechanics."

atyy said:
If darwinism succeeds, would it be compatible with Bohm, since both aim to make QM deterministic?
Probably not, because the two approaches have different ontologies. Yet, there could be a relation between the two approaches not yet seen explicitly (at least by me).

Demystifier said:
Probably not, because the two approaches have different ontologies. Yet, there could be a relation between the two approaches not yet seen explicitly (at least by me).

Thanks, Demystifier. I guess have to wait and see, but I would hope it'd be something like a different foliation of the same spacetime.

## 1. What is the main difference between Envariance and Bohm interpretations of quantum mechanics?

The main difference between Envariance and Bohm interpretations lies in their understanding of the role of hidden variables in determining the behavior of quantum systems. Envariance proposes that the environment, or the collection of all other particles in the universe, plays a crucial role in determining the behavior of a quantum system. In contrast, Bohmian mechanics suggests that there are hidden variables, such as the position of particles, that determine the behavior of quantum systems.

## 2. Is quantum mechanics truly deterministic in either the Envariance or Bohm interpretation?

Neither Envariance nor Bohmian mechanics can definitively claim that quantum mechanics is truly deterministic. While Envariance suggests that the environment may determine the behavior of quantum systems, it does not provide a complete explanation for all quantum phenomena. Similarly, Bohmian mechanics may propose hidden variables, but it is unable to explain certain quantum phenomena such as entanglement. Ultimately, the true nature of quantum mechanics remains a topic of debate and research.

## 3. How do Envariance and Bohmian mechanics account for the uncertainty principle?

Envariance and Bohmian mechanics both propose that the uncertainty principle is a fundamental aspect of quantum mechanics. However, they offer different explanations for it. Envariance suggests that the uncertainty principle arises from the entanglement between a quantum system and its environment. In contrast, Bohmian mechanics explains the uncertainty principle as a result of the limitations of our ability to measure the hidden variables that determine the behavior of quantum systems.

## 4. Are there any experiments that can distinguish between the Envariance and Bohmian interpretations of quantum mechanics?

Currently, there are no known experiments that can definitively distinguish between the Envariance and Bohmian interpretations of quantum mechanics. This is due to the fact that both interpretations make similar predictions for many quantum phenomena. However, ongoing research in the field may lead to the development of experiments that can potentially differentiate between the two interpretations.

## 5. How do Envariance and Bohmian mechanics address the measurement problem in quantum mechanics?

The measurement problem in quantum mechanics refers to the paradoxical nature of wavefunction collapse and the role of the observer in determining the outcome of a measurement. Envariance and Bohmian mechanics offer different solutions to this problem. Envariance suggests that the environment is responsible for the collapse of the wavefunction, while Bohmian mechanics proposes that the wavefunction is a real physical entity that evolves according to deterministic equations. However, both interpretations are still subject to ongoing debate and research.

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