Is Free Will a Foundational Assumption in Quantum Theory?

[Elias1960]

And the current models of our universe that seem to be preferred in cosmology are inflationary models, which violate the premises of the singularity theorems (the energy conditions) during the inflationary epoch, so they don't have to have an initial singularity.

As far as I have understood, inflation is in standard inflation theory a particular period connected with a transition from one vacuum state to another one. So, there would be a period before, with the other vacuum state, where everything is similar, so if one does not invent some infinite sequence of such transitions, there would be nonetheless a singularity. Or are there among the inflation models also some which reverse the expansion, so that we obtain a big bounce instead of a big bang?

(It's worth noting, however, that there are some physicists, such as Freeman Dyson, who have speculated that we might not need a quantum theory of gravity, and that classical GR might in fact be the exactly correct theory of gravity.)

This is what I had in mind with my comment about "QG where classical GR remains valid".

 

[vanhees71]

I claimed that it is ill-defined on the level of theory. This is unlike in classical mechanics, where one usually takes the point of view that a preparation prepares and a measurement records an in principle arbitrarily accurate approximation of the exact value of the position and momentum. Hence one has a well-defined theoretical notion of idealized preparation and measurement. In the quantum case, this is missing.

What's the difference between QT and classical mechanics? In both cases you have abstract mathematical "universes" of states and observables. Formulating classical mechanics in terms of the Hamilton formalism and Poisson brackets as well as phase-space distributions is pretty close even to the mathematical formalism of QT.

The difference is indeed in the interpretation of the probabilities, and there people still seem to have problems after all these years to accept that probabilities do not occur due to averaging over too many details for an effective description can also be "irreducible and objective" as in the minimally interpreted QT. In CM they buy it in the mean time, because they have the rescue of the deterministic world view that the probabilities in classical statistical physics are only due to the complexity and the practical impossibility to resolve the behavior of macroscopic objects in terms of all the microscopic details of their "fundamental constituents", simply because in principle there's a deterministic dynamics behind it. From the observational/instrumental point of view, however, the difference is not all that much: It's also within classical mechanics impossible to follow all details of the $10^{24}$ molecules of a gas in all detail.

 

[A. Neumaier]

From the observational/instrumental point of view, however, the difference is not all that much

But many physicists don't take the observational/instrumental point of view. Therefore they see the missing aspects that you sweep under the carpet of instrumentalism.

 

[Morbert]

I claimed that it is ill-defined on the level of theory. This is unlike in classical mechanics, where one usually takes the point of view that a preparation prepares and a measurement records an in principle arbitrarily accurate approximation of the exact value of the position and momentum. Hence one has a well-defined theoretical notion of idealized preparation and measurement. In the quantum case, this is missing.

But we can still use this language in QM right? E.g. An accurate preparation $\rho$ of a microscopic system $s$ so that is has property $\epsilon_s$ at time $t_1$ is one where $$\mathrm{Tr}\left[\Pi_{t_1}^{\epsilon_s}\rho\right]\approx 1$$ Similarly, a device $M$ can produce an accurate record $\epsilon_M$ of this property at a later time $t_2$ if $$\frac{\mathrm{Tr}\left[\Pi^{\epsilon_M}_{t_2}\Pi^{\epsilon_s}_{t_1}\rho\right]}{\mathrm{Tr}\left[\Pi^{\epsilon_M}_{t_2}\rho\right]}\approx 1$$There are interpretational questions about the ontic status of this language due to the complementary nature of properties in QM, but the language of accurate preparations and records seems unambiguous and logically consistent so long as we respect complementarity.

 

[A. Neumaier]

But we can still use this language in QM right?

The problem is that in the standard interpretations one has no theoretical way to talk about a single measurement result, only about their distribution. Thus the notion of a record (which records a sequence of single results) is ill-defined.

In quantum information theory, one needs to augment the Hilbert space by an ancilla growing with time which simulates the record-taking process through artificial entanglement. But this ancilla is physically artificial, and becomes very awkward when used to analyze not only a small system but the system including the measuring device.

 

[PeterDonis]

nflation is in standard inflation theory a particular period connected with a transition from one vacuum state to another one

Not just the transition period, but the period before where the universe is in a "false vacuum" state. Since that state itself violates the energy conditions, it does not have to have had a beginning; it can extend indefinitely into the past. ("Eternal inflation" models are of this type.)

if one does not invent some infinite sequence of such transitions, there would be nonetheless a singularity

No. See above.

are there among the inflation models also some which reverse the expansion, so that we obtain a big bounce instead of a big bang?

There are certainly "bounce" models, but I don't know that I would consider them a subset of inflation models. They make some sort of assumption about the stress-energy tensor that leads to it violating the energy conditions, but I don't think it's the same as the SET of a scalar field, which is what inflation models use for the "false vacuum" state.

 

[Lynch101]

A class of very important questions arose when John Bell formulated his famous inequalities[1]. Indeed, when one attempts to construct models that visualize what might be going on in a quantum mechanical process, one finds that deterministic interpretations usually lead to predictions that would obey his inequalities, while it is well understood that quantum mechanical predictions violate them. In attempts to get into grips with this situation, and to derive its consequences for deterministic theories, the concept of “free will” was introduced. Basically, it assumes that any ‘observer’ has the freedom, at all times and all places, to choose, at will, what variables to observe and measure. Clashes with Bell’s inequalities arise as soon as the observer is allowed to choose between sets of observables that are mutually non commuting.

I was giving more thought to this and I'm just wondering if I'm reading it correctly. Does this say that hidden variables theories invoke the common sense notion of "Free Will" as a matter of necessity?

 

[Lynch101]

I wouldn't say it's a logical conclusion of determinism, just a special case of determinism.

But, if the universe is deterministic, presumably the chain of causality/determinism stretches all the way back to the Big Bang?

 

[Lynch101]

I've been considering the question of Free Will in QM (and perhaps empiricism) further, in the context of other discussions that I've been having on here and I wanted to subject my current understanding to questioning.

The understanding I have thus far is that there are, broadly speaking, two general paradigms under which QM is interpreted a) determinism and b) indeterminism.

In general, the notion of free will is usually understood to be incompatible with determinism because in a deterministic universe, of which our will is a part, our will is determined by prior causes. "Compatibilism" seeks to rescue the notion of free will but it seems only to attempt a redefinition of the term. It doesn't however, succeed in restoring the freedom of the will because the will is still determined by prior causes.

Realist-indeterministic interpretations don't seem to fare any better. In stochastic interpretations of QM grounded in realism, the choice of an observer would be governed by the random collapse of the wave function and not their own free choice.

This would leave us with non-realist-indterministic interpretations. An issue with these interpretations (indeed with any interpretation) is that "our decision" i.e. our will, cannot be caused by anything prior to it. This would mean that it must be free from the causal influence of the physical world yet able to act as a causal influence in the world. Does this seem to sound dangerously close to a form of Cartesian Dualism, or would it seem to point to the necessity of an alternative paradigm in physics? Or is there another way to look at it?

 

[Elias1960]

Realist-indeterministic interpretations don't seem to fare any better. In stochastic interpretations of QM grounded in realism, the choice of an observer would be governed by the random collapse of the wave function and not their own free choice.

Why do you think that stochastic interpretations have some collapse?

For example, Caticha's entropic dynamics has no physical collapse, the wave function has an epistemic interpretation. It has some sort of Brownian motion of what really exists - the configuration. What defines this Brownian motion is not specified, we simply don't know.

 

[A. Neumaier]

our will is determined by prior causes

Isn't the will of most people strongly determined by their past experience, and quite often very well predictable? Only that we (and they) cannot pin it down to the last detail. But most people can give a quite rational account of why they will what they will...

Nondeterminism would be an explanation for whimsicality, but not for will.

 

[bhobba]

What's the difference between QT and classical mechanics? In both cases you have abstract mathematical "universes" of states and observables. Formulating classical mechanics in terms of the Hamilton formalism and Poisson brackets as well as phase-space distributions is pretty close even to the mathematical formalism of QT.

That was Dirac's view, and mine as well. QM is what we get if we introduce q numbers like Dirac did in his early papers extending Heisenberg before he (along with Jordan independently) came up with his transformation theory. It's interesting if you do that it only really makes sense if you introduce probilities as Kochen-Specker would suggest.

Thanks
Bill

 

[Lynch101]

Why do you think that stochastic interpretations have some collapse?

For example, Caticha's entropic dynamics has no physical collapse, the wave function has an epistemic interpretation. It has some sort of Brownian motion of what really exists - the configuration. What defines this Brownian motion is not specified, we simply don't know.

Thanks Elias, I am not familiar with that particular interpretation. I'll give it a look.

How would it address the issue pertaining to free will, though? If decision making is the result of a truly stochastic process then there doesn't appear to be any room for free will. We either have the situation where
a) some stochastic process causes us to make a particular choice
b) what we label "our choice" is the result of a purely stochastic process, with no will involved

For the will to be free it cannot be caused by prior events. This would appear to mean that the will can act in a causal way upon the world but cannot be acted upon .

 

[PeterDonis]

For the will to be free it cannot be caused by prior events.

This is not correct. It is one particular definition of the term "free will", but not the only possible one, and should not be asserted as though it were fact.

 

[Lynch101]

Isn't the will of most people strongly determined by their past experience, and quite often very well predictable? Only that we (and they) cannot pin it down to the last detail. But most people can give a quite rational account of why they will what they will...

I would very much agree, but that is an argument against the will being free. If the will is determined by prior causes then there is merely the illusion of choice.

If we picture a deterministic chain of events in which "the will" is a single "link", then "the will" doesn't freely choose anything, it is caused to "choose", with no real choice being open. We would no more freely choose than a domino freely chooses to knock over another domino.

We don't even need to define what "the will" means here because in the paradigm of determinisim it would simply be another link in a deterministically causal chain.

 

[PeterDonis]

f the will is determined by prior causes then there is merely the illusion of choice.

Again, this is one particular definition of "free will", but not the only possible one, and should not be asserted as if it were fact.

 

[Lynch101]

This is not correct. It is one particular definition of the term "free will", but not the only possible one, and should not be asserted as though it were fact.

Forgive the assumption, but based on some of your previous posts I think you might be referring to the compatibilist notion? Am I correct in that?

The issue with the compatibilist notion of free will appears to be that it doesn't rescue freedom from the jaws of determinism. A choice that is causally determined by prior events isn't free.

 

[PeterDonis]

I've been considering the question of Free Will in QM (and perhaps empiricism) further, in the context of other discussions that I've been having on here and I wanted to subject my current understanding to questioning.

Before doing so you should first go back and read through this thread again. You seem to have forgotten a lot of what has already been discussed. There is no point in re-discussing it all again.

 

[PeterDonis]

Forgive the assumption, but based on some of your previous posts I think you might be referring to the compatibilist notion? Am I correct in that?

The issue with the compatibilist notion of free will appears to be that it doesn't rescue freedom from the jaws of determinism. A choice that is causally determined by prior events isn't free.

As I said in my previous post just now, go back and read through the thread again. You have evidently forgotten a lot of what has already been discussed. We are not going to discuss it again; that would be a waste of everybody's time.

Once you have read through the thread again, if you have additional questions, start a new thread. This thread is now closed.