# Does Bohmian Mechanics yield the existence of a multiverse?

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Summary:
Did David Bohm ever propose or agree with the existence of some kind of multiverse?
David Deutsch, a theoretical physicist, talks about David Bohm in his book "the Fabric of Reality":

"[w]orking out what Bohm’s invisible wave will do requires the same computations as working out what trillions of shadow photons will do. Some parts of the wave describe us, the observers, detecting and reacting to the photons; other parts of the wave describe other versions of us, reacting to photons in different positions. Bohm’s modest nomenclature – referring to most of reality as a ’wave’ – does not change the fact that in his theory reality consists of large sets of complex entities, each of which can perceive other entities in its own set, but can only indirectly perceive entities in other sets. These sets of entities are, in other words, parallel universes. (Deutsch 1997, p. 56)"

Does this mean that Bohmian Mechanics or any other "Bohmian" ideas (like the Implicate-Explicate order) yields the existence of some kind of multiverse?

Minnesota Joe

## Answers and Replies

Demystifier
Gold Member
No. The Deutch's view of Bohmian mechanics is a distortion of the usual view of Bohmian mechanics. Deutch thinks that all the empty branches of the wave function are as real as the one non-empty branch filled with the Bohmian particle. From the Bohmian perspective, this would be analogous to saying that all the meals described in a cook book are as real as an actual meal made out of real foodstuff.

Minnesota Joe and bhobba
DarMM
Gold Member
I never understood this either. Especially if you piece together Deutsch's claims.

Many Worlds is local
Bohmian Mechanics is nonlocal
Bohmain mechanics is just Many-Worlds in disguise/denial.

It's some disguise that it can turn a local theory into a nonlocal one.

Minnesota Joe and Demystifier
No. The Deutch's view of Bohmian mechanics is a distortion of the usual view of Bohmian mechanics. Deutch thinks that all the empty branches of the wave function are as real as the one non-empty branch filled with the Bohmian particle. From the Bohmian perspective, this would be analogous to saying that all the meals described in a cook book are as real as an actual meal made out of real foodstuff.
The analogy fails because the menu in a cook book has far lower information content than an actual meal. Deutsch's point is that the information content of Bohmian mechanics is equal or higher than Everett's scheme - there is no collapse in Bohm, hence Everett's multiverse is contained within BM. A point originally made by Everett, who expressed the sentiment that the Bohmian particle(s) is(are) unobservable, hence Okhamatically superfluous.

Heikki Tuuri and akvadrako
Demystifier
Gold Member
The analogy fails because the menu in a cook book has far lower information content than an actual meal. Deutsch's point is that the information content of Bohmian mechanics is equal or higher than Everett's scheme - there is no collapse in Bohm, hence Everett's multiverse is contained within BM. A point originally made by Everett, who expressed the sentiment that the Bohmian particle(s) is(are) unobservable, hence Okhamatically superfluous.
Then take another analogy. First, consider a classical field
$$\psi(x,y)=\frac{y^2}{2m}+\frac{kx^2}{2}$$
Second, consider a classical particle with a trajectory ##X(t)## described by the Hamiltonian
$$H(X,P)=\frac{P^2}{2m}+\frac{kX^2}{2}$$
Would you say that the system described by the second theory (which is an analog of Bohmian mechanics) contains the system described by the first theory (which is an analog of many-worlds)?

Then take another analogy. First, consider a classical field
$$\psi(x,y)=\frac{y^2}{2m}+\frac{kx^2}{2}$$
Second, consider a classical particle with a trajectory ##X(t)## described by the Hamiltonian
$$H(X,P)=\frac{P^2}{2m}+\frac{kX^2}{2}$$
Would you say that the system described by the second theory (which is an analog of Bohmian mechanics) contains the system described by the first theory (which is an analog of many-worlds)?
Only if the particle is unobservable, as Everett claimed. The particle is unobservable because, although it is pushed around (influenced) by the wavefunction, the wavefunction is not influenced by the particle.

Demystifier
Gold Member
The particle is unobservable because, although it is pushed around by (influenced) the wavefunction, the wavefunction is not influenced by the particle.
In my analogy above, it would be like saying that the classical particle is unobservable because, although it is governed by the Hamiltonian, the Hamiltonian is not influenced by the particle. Do I need to explain why is that wrong?

In my analogy above, it would be like saying that the classical particle is unobservable because, although it is governed by the Hamiltonian, the Hamiltonian is not influenced by the particle. Do I need to explain why is that wrong?
The Hamiltonian defines the dynamics, it is not the solution. You wouldn't expect the solution to the dynamical equations to influence the equations themselves. But the Bohmian particle doesn't influence the other part of the solution (the wavefunction). Throw the B-particle away and the wavefunction's evolution is unaffected. Throw you classical particle away and you don't have a solution at all.

Demystifier
Gold Member
The Hamiltonian defines the dynamics, it is not the solution.
Well, it's a philosophical prejudice that something which defines dynamics cannot be a solution. This prejudice may be true in classical mechanics, but it does not necessarily need to be true in quantum (or Bohmian) mechanics.

Moreover, even in classical mechanics you have the solution ##S(x,t)## of the Hamilton-Jacobi equation, which governs the particle trajectory but is not influenced by the particle.

DarMM
DarMM
Gold Member
It's also not true in General Relativity right? There the dynamical structure is also solved for.

Demystifier
Gold Member
It's also not true in General Relativity right? There the dynamical structure is also solved for.
That's not a good example, because the metric is solved as a functional of matter degrees of freedom, the same matter degrees that the metric determines the motion of.

DarMM
Well, it's a philosophical prejudice that something which defines dynamics cannot be a solution. This prejudice may be true in classical mechanics, but it does not necessarily need to be true in quantum (or Bohmian) mechanics.

Moreover, even in classical mechanics you have the solution ##S(x,t)## of the Hamilton-Jacobi equation, which governs the particle trajectory but is not influenced by the particle.
AFAIK this prejudice holds true in QFT: the field operators are distinct from the field values/wavefunction. (The Hamilton-Jacobi example seems the same as the earlier classical particle_example.)

The basic idea of David Bohm is that the number of particles is fixed and that there are markers for each particle. The markers sail according to the instructions which the markers read from the (Schrödinger equation) wave function of the particles.

The markers do not affect the development of the wave function at all. The markers are like miniature ships sailing on large waves in the sea.

The canonical example is the double slit experiment. The marker for a photon takes a course through just one of the slits. The interference pattern forms because the path of the marker after the slit is strongly affected by the wave which went through both slits.

I would say that the wave and the markers "exist" as physical entities in the Bohm model.

The markers single out the "branch", where I, as an observing subject, live.

What about the other branches? Do they "exist"? They certainly exist as a part of the wave function.

It is a matter of taste, if the other branches "exist as strongly" as the branch where I live with my markers.

The Bohm model is the Many Worlds interpretation plus an exact method for picking one designated branch where the observing subject lives.

One can say that a kind of a "multiverse" exists in the branches of the wave.

Thus, Dürr et al. (1999) showed that it is possible to formally restore Lorentz invariance for the Bohm–Dirac theory by introducing additional structure. This approach still requires a foliation of space-time. While this is in conflict with the standard interpretation of relativity, the preferred foliation, if unobservable, does not lead to any empirical conflicts with relativity. In 2013, Dürr et al. suggested that the required foliation could be covariantly determined by the wavefunction.[23]
https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory

There are problems in lifting the Bohm model from the non-relativistic Schrödinger equation to relativistic quantum mechanics.

Last edited:
Demystifier