Decoherent Histories and Measurement

[A. Neumaier]

how doe we sensible _describe_ this objective invariants, without using the arbitrary choices?

By showing how the results form the different choices are related to each other,
providing in this way an observer-independent objectivity.

I had in mind times even before that, say GUT or Planck era, before we have a clear meaning of spacetime.

In my view, spacetime exists prior to everything. Whether something else has to be posited in the GUT or Planck era is pure speculation.

you are just assuming that deterministic physical law is ruling things, but to identify WHICH law like is subject of fine tuning in a huge theory space.

No. I use the well established standard model of quantum field theory, allowing for small unknown modifications to accomodate gravity. Unless I consider cosmology, where I can use any of the standard cosmological models. The foundations do not depend on the details.

 

[A. Neumaier]

A secondary incredient is the (tensor product) structure of the Hilbert space for independent systems.

This was known since before 1930. It belongs to the standard toolkit of QM, not to an interpretation.

You end-up with a mathematical structure that you can instantiate for different base fields, like the real numbers, the complex numbers, or the quaternions.

But physicists only use the complex version; the others are ruled out by experiment.

There is also some structure of the coarsening,

which structure? It cannot be significantly different from the earlier established methods, averaged second-order perturbation theory, projection formalism, or Schwinger-Keldysh formalism. They are also of the shut-up-and-calculate type, hence not part of the interpretation.

But even the more canonical part of the mathematical structure

which is just shut-up-and-calculate applied to the Born rule for histories.

 

[Fra]

By showing how the results form the different choices are related to each other,
providing in this way an observer-independent objectivity.

Yes, agreed.

But then to demonstrably show objectivity, and not just assume it. The results from the choices that are made must be collected and processed; and unless we work with fictions, I consider that to be a physical process, essentially meaning - let the acutal population of these "agents" interact for real, and see what the steady state is like. Once in place, objectivity is physically manifest, not sooner. This is how I see the "emergence".

/Fredrik

 

[A. Neumaier]

Yes, agreed.

But then to demonstrably show objectivity, and not just assume it. The results from the choices that are made must be collected and processed; and unless we work with fictions, I consider that to be a physical process, essentially meaning - let the acutal population of these "agents" interact for real, and see what the steady state is like. Once in place, objectivity is physically manifest, not sooner. This is how I see the "emergence".

All this is very high level, not theoretical physics.

Theoretical physics consists of making assumptions and deducing from these interesting things that are found (no matter how) in agreement with observations, explaining this way objectivity, rather than assuming it.

The processing needed to show the agreement is not part of theoretical physics but a side issue. If you want to study it, better observe those who bring theory and experiment into agrement than to muse about abstract information theoretial issues!

 

[gentzen]

This was known since before 1930. It belongs to the standard toolkit of QM, not to an interpretation.

That doesn't make it right. Schrödinger was careful in his "cat paper" to remain unsure whether it would remain correct for the "unification" of QM with special relativity. My understanding is that in QFT independence is modeled by commutation of measurement operators for spacelike separated spacetime regions, and the recent MIP*=RE result disproved the earlier expectations that both would be equivalent.

But physicists only use the complex version; the others are ruled out by experiment.

Can you even make this distinction and rule out the non-complex versions without a mathematical structure where this distinction exists?

which structure? It cannot be significantly different from the earlier established methods, averaged second-order perturbation theory, projection formalism, or Schwinger-Keldysh formalism. They are also of the shut-up-and-calculate type, hence not part of the interpretation.

It is not a nice structure, it is just there. It is a part of the interpretation that even its proponents try to get rid of, but it is there.

which is just shut-up-and-calculate applied to the Born rule for histories.

In the end, you are simply not interested in the consistent histories interpretation. I cannot blame you for that. But what is dangerous is to make blanket statements about interpretations that you don't really understand, nor care about. You didn't do yourself any favor with your old (2000) paper claiming Bohmian mechanics contradicts quantum mechanics. Similarly, S. Goldstein did not do himself a favor with section 2 Decoherent Histories in his Quantum Theory without Observers—Part One.

 

[A. Neumaier]

That doesn't make it right. Schrödinger was careful in his "cat paper" to remain unsure whether it would remain correct for the "unification" of QM with special relativity.

But decoherent histories don't even adrress relativity issues!

My understanding is that in QFT independence is modeled by commutation of measurement operators for spacelike separated spacetime regions, and the recent MIP*=RE result disproved the earlier expectations that both would be equivalent.

I dont' see how a result in quantum complexity has any bearing on this equivalence.

Can you even make this distinction and rule out the non-complex versions without a mathematical structure where this distinction exists?

No, but when you make it, you cannot reproduce standard QM, hence it is disproved and can be ignored.

In the end, you are simply not interested in the consistent histories interpretation.

Only because it adds nothing for the interpretation of the physically relevant setting of QM.

I cannot blame you for that. But what is dangerous is to make blanket statements about interpretations that you don't really understand

I think I understand the interpretation. It was not the first occasion I spent time on it.

You didn't do yourself any favor with your old (2000) paper claiming Bohmian mechanics contradicts quantum mechanics.

I still think that paper is valid; the replies from the Bohmian camp didn't convince me of the contrary.

Bohmian mechanics (on which I unfortunately spent far too many days) is a very superficial enhancement of quantum mechanics adding irrelevant extra structure. In exchange for it they lose important structure existing in QM, namely phase space symmetries and relativistic symmetries that are fundamental for a proper understanding of quantum mechanics (semiclassical approximations) and quantum field theory (conservation laws).

 

[gentzen]

I still think that paper is valid; the replies from the Bohmian camp didn't convince me of the contrary.

Did they even bother to respond? Your paper simply repeats an old misunderstanding, which already existed in the 50s, and which is well explained in many accounts of BM (even in the discussion of BM in Franck Laloë's "Do we really understand quantum mechanics").

Bohmian mechanics (which I spent many days on)

without noticing that you are not the first to raise that objection?

is a very superficial enhancement of quantum mechanics adding irrelevant extra structure.

The extra structure provides a source of randomness, even for finite dimensional systems. No need for a wavefunction of the universe like in MWI, even so you can consider one, if you really want.

 

[Morbert]

This means that nothing at all is predicted, since everything is objectively correct.
This perverts the meaning of 'objective'.

There is an analogous process in classical physics. If you have a classical theory of a 6-sided die, you can choose a coarse graining and compute probabilities for events [1 or 2], [3 or 4], [5 or 6]. Alternatively, you could choose a different coarse graining and compute probabilities for [1 or 6], [2 or 4], [3 or 5]. Both coarse grainings return objectively correct probabilities. This is uncontroversial, because the two coarse grainings aren't mutually exclusive alternatives for reality. They are addressing different claims about the same reality. The same is true for for different coarse grainings in quantum theory, only now we have different maximally fine-grained representations as well as different coarse grainings. E.g. For a detector, one might define alternative pointer outcomes {D_0, D_1}, another might define {U+, U-} which are macroscopic superpositions. These coarse grainings aren't mutually exclusive alternatives, so no inconsistency arises.

This again involves choosing additional things beyund the coordinaters of the lab, from which the state of the universe should be able to deduce what is in the lab - the arrangement, the chooser of the model and the coarse-graining, and everything else. But instead, decoherent histories has to use all this as additional input.

Given any physical theory, in order to compute probabilities for mutually exclusive alternatives, those mutually exclusive alternatives must be constructed. This does not seem like a great offense to me.

And what is the meaning of these probabilities? There is only one universe, in which some things actually happen and everything else does not happen.

Testing a cosmological theory would presumably involve experimentally testing possibilities for which the theory assigns a probability very close to 1. Even if a probability for some statement is not exactly 1, a negative result would still imply a loss of confidence in the theory.

 

[A. Neumaier]

Did they even bother to respond?

Yes.

I am proud of the citation of my paper in Streater's Lost Causes in and beyond Physics from 2007. Streater is one of the authors of the well-known book PCT, spin and statistics, and all that.

The extra structure provides a source of randomness

But at the cost of losing important structure. There are covariant ways of introducing noise into a system.

 

[Morbert]

Re/ Decoherent histories and relativity. For posterity: https://arxiv.org/abs/gr-qc/9304006

The interpretation can be applied to a quantum theory of mechanics, of fields, of spacetime geometries etc. so long as the theory exists. Basically the interpretation can be applied to any theory that permits the construction of boolean lattices from event algebras.

 

[A. Neumaier]

another might define {U+, U-} which are macroscopic superpositions.

How can one read a value from macroscopic superposition? (I am not really interested in the answer, or in a further continuation of this for me state discussion.)

 

[A. Neumaier]

Re/ Decoherent histories and relativity. For posterity: https://arxiv.org/abs/gr-qc/9304006

Can you please point to a page of this thick book where the discussion of relativity starts? This is new to me, so I will look at it more closely.

 

[Morbert]

How can one read a value from macroscopic superposition?

Roland Omnes, in his book "The Interpretations of Quantum Mechanics" (section 7.8) argues you would need an apparatus larger than the observable universe.

Can you please point to a page of this thick book where the discussion of relativity starts? This is new to me, so I will look at it more closely.

In section VII E (page 94), they discuss quantum mechanics of a relativistic world line. In section VIII (page 106) they discuss quantum gravity. These lecture notes make a more ambitious claim, and suggests that decoherent histories might be a generalisation of quantum mechanics (a point also made here in an interview with Gell-Mann). But the notes were from 1992 and I do not know whether it panned out.

 

[Fra]

All this is very high level, not theoretical physics.

Theoretical physics consists of making assumptions and deducing from these interesting things that are found (no matter how) in agreement with observations, explaining this way objectivity, rather than assuming it.

The processing needed to show the agreement is not part of theoretical physics but a side issue. If you want to study it, better observe those who bring theory and experiment into agrement than to muse about abstract information theoretial issues!

We disagree here in our views about that is practical matters or side issues, and what has potential deeper implications for the foundations that will allow for unification. But this I think this is due to the kind of answer we seek, I don't think we will resolve this. But agreeing on the disagreement is good enough, I think I've understood your interpretations a bit better, that was interesting enough as we shared the issues with current interpretations.

I get the difference between theoretical processing and ponderings by theorist which is indeed a side issue, but the "relational processing" one part of nature does with another part, it's the latter part I consider, and I tend to think that the description we have, hints at this. The comparasion with scientific evolution vs circularity was just to illustrate that apparent circulariry may be iteration loops.

/Fredrik

 

[A. Neumaier]

Roland Omnes, in his book "The Interpretations of Quantum Mechanics" (section 7.8) argues you would need an apparatus larger than the observable universe.

Thus this is impossible.

In section VII E (page 94), they discuss quantum mechanics of a relativistic world line. In section VIII (page 106) they discuss quantum gravity.

Thanks. But they do this for coarse-graining only. It is well-known that relativisitc coarse-graining dates back to Schwinger and Keldysh (1965), much earlier than decoherent histories. Thus this is not specific to decoherent histories but part of the general shut-up-and-calculate machinery.

Measurement is discussed in the lecture notes only in passing, on p.136, in the context of coarse-graining through a semiclassical approximation. Thus the lecture notes are silent about whether the observed fact of unique measurement results is a consequence of the unitary dynamics of the universal state.

I conclude that decoherent histories gives on the interpretation level nothing new compared to what was known earlier, namely Born's rule plus conditional probability. The only new thing is a new name.