I Is the Theory of Everything necessarily deterministic?

[SEYED2001]

Hi
I am aware that QM isn't deterministic. Should a theory of everything be deterministic to be a theory of everything, and if yes, then how can it be when QM as a part of it is not deterministic?

Thanks in advance
Seyed

 

[PeroK]

Should a theory of everything be deterministic to be a theory of everything?

Why should it?

 

[SEYED2001]

Why should it?

Maybe because it must predict everything to be a theory for them? That's what theories do, to predict don't they?

 

[PeroK]

Maybe because it must predict everything to be a theory for them? That's what theories do, to predict don't they?

Maybe they predict probabilities.

 

[atyy]

A classical heuristic is that there is no fundamental difference between deterministic and probabilistic theories, in the sense that one could see the most fundamental theory as deterministic, with the probabilistic theories arising due to our inability to fully know the state of all variables in the fundamental deterministic theory. The variables whose state one does not know can be considered "hidden variables" of the probabilistic theory.

It is unclear at the moment whether hidden variables can be constructed for quantum theory. Bohmian mechanics is one well known proposal for hidden variables for non-relativistic quantum mechanics. It is not well understood whether hidden variable theories can be constructed for other types of quantum theory.

 

[SEYED2001]

Maybe they predict probabilities.

Great. I see what you mean. If probabilities are the only things out there then a theory of everything is a theory for no more than probabilities. Thanks.

 

[SEYED2001]

A classical heuristic is that there is no fundamental difference between deterministic and probabilistic theories, in the sense that one could see the most fundamental theory as deterministic, with the probabilistic theories arising due to our inability to fully know the state of all variables in the fundamental deterministic theory. The variables whose state one does not know can be considered "hidden variables" of the probabilistic theory.

It is unclear at the moment whether hidden variables can be constructed for quantum theory. Bohmian mechanics is one well known proposal for hidden variables for non-relativistic quantum mechanics. It is not well understood whether hidden variable theories can be constructed for other types of quantum theory.

Thank you for your reply. Is any relation between the existence of hidden variables and existence of a theory of everything ever established?

 

[SEYED2001]

Thank you for your reply. Is any relation between the existence of hidden variables and existence of a theory of everything ever established?

I asked this since I think I can establish one and so wondering if is worth spending time on.

 

[atyy]

Thank you for your reply. Is any relation between the existence of hidden variables and existence of a theory of everything ever established?

Deterministic hidden variables and theories of everything are usually considered attempts to solve different types of problems.

Usually, by a theory of everything, we mean a quantum theory of everything. Whether a quantum theory of everything is possible is a matter of research. String theory is a research area that attempts to construct a quantum theory of everything.

Deterministic hidden variables are usually discussed with respect to attempts to solve the "measurement problem" present in all quantum theories (including string theory, if it were to succeed). A good description of the "measurement problem" of quantum theory is John Bell's article Against 'measurement'.

 

[SEYED2001]

Usually, by a theory of everything, we mean a quantum theory of everything. Whether a quantum theory of everything is possible is a matter of research. String theory is a research area that attempts to construct a quantum theory of everything.

Deterministic hidden variables are usually discussed with respect to attempts to solve the "measurement problem" present in all quantum theories (including string theory, if it were to succeed). A good description of the "measurement problem" of quantum theory is John Bell's article Against 'measurement'.

Thank you!

 

[bayakiv]

I am aware that QM isn't deterministic. Should a theory of everything be deterministic to be a theory of everything, and if yes, then how can it be when QM as a part of it is not deterministic?

Here you can reason from the opposite and refer to the next example. Suppose we have a theory of everything that describes the dynamics of a vector field on an infinite cylinder. Moreover, the dynamic laws of motion of the singularities of the vector field (prototypes of particles) are both deterministic, since they follow from some integral variational equation, and probabilistic, since the free motions of the singularities are arbitrary in the choice of speed and direction. Now imagine that the feature of the vector field, which serves as the prototype of the particle, is the streamline of the vector field, outlining the defining circle on the cylinder, and the observer can only see the linear coordinate of the cylinder (straight or helical line). Now what can we say about the dynamic behavior of "particles" on the line of the observer, is it deterministic or not?

 

[Sunil]

The point that a theory which predicts only probabilities is not a theory of everything given that there exist, in reality, also actual values, is a nice one. But one should not forget that "theory of everything" has a slightly different established meaning - simply a theory which covers all the particles and fields observed up to now, that means, at least all those of the SM together with gravity. In this sense, even an obviously incomplete theory could count as a "theory of everything", once it covers everything observed up to now.

A classical heuristic is that there is no fundamental difference between deterministic and probabilistic theories, in the sense that one could see the most fundamental theory as deterministic, with the probabilistic theories arising due to our inability to fully know the state of all variables in the fundamental deterministic theory. The variables whose state one does not know can be considered "hidden variables" of the probabilistic theory.

Similarly, the most fundamental theory may be probabilistic, and deterministic theories may appear on the large scale for averages.

It is unclear at the moment whether hidden variables can be constructed for quantum theory. Bohmian mechanics is one well known proposal for hidden variables for non-relativistic quantum mechanics. It is not well understood whether hidden variable theories can be constructed for other types of quantum theory.

No, that's clear. De Broglie-Bohm theory works for relativistic field theory too. The classical reference for this is Bohm.D., Hiley, B.J., Kaloyerou, P.N. (1987). An ontological basis for the quantum theory, Phys. Reports 144(6), 321-375

 

[Demystifier]

I am aware that QM isn't deterministic. Should a theory of everything be deterministic to be a theory of everything, and if yes, then how can it be when QM as a part of it is not deterministic?

1. The theory of everything does not necessarily need to be deterministic.
2. Some formulations of QM, such as Bohmian mechanics, are deterministic.
3. Even if we accept that QM is not deterministic, the theory of everything may be deterministic by saying that QM is emergent, very much like classical statistical mechanics (which is probabilistic) emerges form deterministic classical mechanics.

 

[Demystifier]

Is any relation between the existence of hidden variables and existence of a theory of everything ever established?

Yes. A hint is given in Sec. 4.3 of http://de.arxiv.org/abs/1703.08341 and the idea is further elaborated in http://de.arxiv.org/abs/1811.11643 .

 

[Demystifier]

It is unclear at the moment whether hidden variables can be constructed for quantum theory. Bohmian mechanics is one well known proposal for hidden variables for non-relativistic quantum mechanics. It is not well understood whether hidden variable theories can be constructed for other types of quantum theory.

It's quite clear to me that Bohmian mechanics works for relativistic QFT as well. See e.g. my non-technical lecture http://thphys.irb.hr/wiki/main/images/3/3d/QFound5.pdf

 

[phinds]

... a theory of everything is a theory for no more than probabilities. Thanks.

And why is that necessarily a bad thing?

 

[Morbert]

As an aside: This is certainly outside my comfort zone, but this paper[1] discusses QFT without the insistence that we must be able to define a quantum state evolving unitarily through spacelike surfaces (which, sans some fancy theory like string theory, runs into problems if there is a topology change induced e.g. by a black hole). Hartle seems to be happy to drop that condition, and compute amplitudes via a sum-over-histories approach (see eq 4.2). He argues that even though information might appear lost on specific spacetime surfaces, it is still present throughout spacetime.

I.e. A unitarily evolving quantum state is desirable even if a probabilistic interpretation is adopted. But even this might not be necessary, or at least not enforced by the formalism.

There might be a million things wrong with this, or it might just be a project that has generated little scientific interest (only 8 citations)

[1] https://arxiv.org/abs/gr-qc/9808070

 

[Demystifier]

As an aside: This is certainly outside my comfort zone, but this paper[1] discusses QFT without the insistence that we must be able to define a quantum state evolving unitarily through spacelike surfaces (which, sans some fancy theory like string theory, runs into problems if there is a topology change induced e.g. by a black hole). Hartle seems to be happy to drop that condition, and compute amplitudes via a sum-over-histories approach (see eq 4.2). He argues that even though information might appear lost on specific spacetime surfaces, it is still present throughout spacetime.

I.e. A unitarily evolving quantum state is desirable even if a probabilistic interpretation is adopted. But even this might not be necessary, or at least not enforced by the formalism.

There might be a million things wrong with this, or it might just be a project that has generated little scientific interest (only 8 citations)

[1] https://arxiv.org/abs/gr-qc/9808070

For a similar approach see also my
http://de.arxiv.org/abs/0905.0538
http://de.arxiv.org/abs/0912.1938

 

[RUTA]

See this ScienceX News article for a general audience explanation as to why we must obtain probabilistic results for Bell states.