Is the Quantum/Classical Boundary the most important question in Physics?

[Lord Jestocost]

1. Bohr was a mumbler so understanding what he said required some effort.
2. His ideas were subtle and deep. In fact I would say verging on incomprehensible - I certainly do not understand him - and the number of papers with differing views shows that perhaps even experts in it are confuse.

It is not all that difficult to understand Bohr when taking an instrumentalist’s point of view.

 

[EPR]

As @bhobba has said quantum theory is a generalized probability theory. Sometimes a linear sum of states represents a type of statistics that doesn't appear in classical/Kolmogorov probability theory. However sometimes a state of the form:
$$|\psi\rangle = \frac{1}{\sqrt{2}}\left(|a\rangle + |b\rangle\right)$$
simply represents classical "ignorance" based probability. Such as when $|a\rangle$ and $|b\rangle$ belong to different superselection sectors.

But when is that 'sometimes'? Under what scenario and conditions?

 

[DarMM]

When is that 'sometimes'? Under what scenario and conditions?

Whenever there is a superselection rule.

 

[EPR]

This is circular reasoning - whenever classical environment-enduced superselection takes place, classical states appear.

 

[DarMM]

Even if we accept that anything can be described by quantum mechanics, quantum mechanics itself has a classical-quantum cut. So saying that anything can be described by quantum mechanics does not remove the classical-quantum cut.

What has this got to do with my original point about Bohr considering anything to be capable of being described by quantum theory?
In a given application something must be taken to select the Boolean event space, but in another application it may be the system under consideration. Thus nothing requires a classical treatment.

That is not correct. The second classical device is still required. If what you are saying is correct, then Many-Worlds or some interpretation where the entire universe is described by a unitarily evolving quantum state would be already considered viable without controversy.

Perhaps I didn't explain myself well. I'm saying that the different states of the macroscopic device belong to different superselection sectors and thus any probability due to a superposition of their states is simply classical ignorance. Thus for such degrees of freedom unitary evolution is just classical stochastic evolution concerning classical probabilities. This is nothing as such to do with Many Worlds.

EDIT: Maybe another way to say it. When Von Neumann formulated his "chain" in the 1930s at each stage in the chain we had the $n$th device necessary to select the Boolean frame choosen for the event space of the $(n - 1)$th device. However more modern study has shown that for actual devices there is only one event space, thus another device is not necessary to select out the Boolean algebra of events.

 

[bhobba]

It is not all that difficult to understand Bohr when taking an instrumentalist’s point of view.

I will take your word for it - I find him often impenetrable. The main thing for me is things have moved on since then.

Thanks
Bill

 

[DarMM]

This is circular reasoning - whenever classical environment-enduced superselection takes place, classical states appear.

I don't understand. Many superselection rules have nothing to do with the environment, such as superselection between different charge numbers.

 

[bhobba]

This is circular reasoning - whenever classical environment-enduced superselection takes place, classical states appear.

I have no idea what you mean by classical state. Do you mean a wave-packet so narrow in both the position and momentum representation for all practical purposes it has both a well defined position and momentum?

Thanks
Bill

 

[EPR]

I have no idea what you mean by classical state. Do you mean a wave-packet so narrow in both the position and momentum representation for all practical purposes it has both a well defined position and momentum?

Thanks
Bill

Mixed states

 

[Elias1960]

Personally, I think the most important question is why QM and GR don't play well together. Clearly one or the other or both need modification and so far no one has been able to do it.

No. Simply the straightforward way to do it is rejected for metaphysical reasons.

Here it is:

1.) Break diffeomorphism symmetry by adding terms that identify a preferred system of coordinates.
2.) The result is a theory with a standard, non-degenerated Lagrange resp. Hamilton formalism (no problem of time, no diff. constraint and so on).
3.) Use a lattice regularization in space in the preferred space coordinates to get rid of UV problems. Use a large cube with periodic boundary conditions to get rid of IR problems. The result is a classical theory with non-degenerated Lagrange and Hamilton formalism and a finite number of degrees of freedom.
4.) Use canonical quantization to quantize it.

The result is a well-defined quantum theory. Its continuous large distance limit will be a theory that differs from GR only by the symmetry-breaking terms added in (1). But these symmetry-breaking terms continue to break the symmetry even if we multiply them with arbitrary small constants so that with an appropriate choice of these constants they will remain undetectable for large distances, thus, the classical large distance limit will be some field theory with GR Lagrangian but in some preferred coordinates.

But it is obvious that GR defenders will never accept this theory. It is not background-independent, and background independence is a sort of Holy Grail among the GR guys. The other camp, the string theory guys, will also not accept this, because they could no longer claim that string theory is the only theory able to quantize gravity (in fact, they don't even have a rigorous proof that string theory is able to do this).

 

[A. Neumaier]

It is unclear. I am tempted to say with von Neumann that the cut is in the observer's head. The cut is of course absurd, but standard quantum mechanics is formulated with a cut, which is subjective, just like notions of measurement and measurement outcome.

This is what Heisenberg and von Neumann said about the cut.

Um zur Beobachtung zu gelangen, muss man also irgendwo ein Teilsystem aus der Welt ausschneiden und über dieses Teilsystem eben 'Aussagen' oder 'Beobachtungen' machen. Dadurch zerstört man dort den feinen Zusammenhang der Erscheinungen und an der Stelle, wo wir den Schnitt zwischen dem zu beobachtenden System einerseits, dem Beobachter und seinen Apparaten andererseits machen, müssen wir Schwierigkeiten für unsere Ansschauung erwarten. [...] Jede Beobachtung teilt in gewisser Weise die Welt ein in bekannte und unbekannte oder besser: mehr oder weniger genau bekannte Grössen.

wir müssen die Welt immer in zwei Teile teilen, der eine ist das beobachtete System, der andere der Beobachter. In der ersteren können wir alle physikalischen Prozesse (prinzipiell wenigstens) beliebig genau verfolgen, in der letzteren ist dies sinnlos. Die Grenze zwischen beiden ist weitgehend willkürlich

Aus diesem Zwiespalt ergibt sich die Notwendigkeit, bei der Beschreibung atomarer Vorgänge einen Schnitt zu ziehen zwischen den Messapparaten des Beobachters, die mit den klassischen Begriffen beschrieben werden, und dem Beobachtungsobjekt, dessen Verhalten durch eine Wellenfunktion dargestellt wird. Während nun sowohl auf der einen Seite des Schnittes, die zum Beobachter führt, wie auf der anderen, die den Gegenstand der Beobachtung enthält, alle Zusammenhänge scharf determiniert sind - hier durch die Gesetze der klassischen Physik, dort durch die Differentialgleichungen der Quantenmechanik -, äussert sich die Existenz des Schnittes doch I am Auftreten statistischer Zusammenhänge. An der Stelle des Schnittes muss nämlich die Wirkung des Beobachtungsmittels auf den zu beobachtenden Gegenstand als eine teilweise unkontroIlierbare Störung aufgefasst werden. [...] Entscheidend ist hierbei insbesondere, dass die Lage des Schnittes - d.h. die Frage, welche Gegenstände mit zum Beobachtungsmittel und welche mit zum Beobachtungsobjekt gerechnet werden - für die Formulierung der Naturgesetze gleichgültig ist.

Though they wrote in German (maybe someone wants to translate these quotes into English?), it is clear that they regard the cut as being fairly arbitrary, not in the observer's head.

 

[bhobba]

Mixed states

Gotcha.

Thanks
Bill

 

[atyy]

What has this got to do with my original point about Bohr considering anything to be capable of being described by quantum theory?
In a given application something must be taken to select the Boolean event space, but in another application it may be the system under consideration. Thus nothing requires a classical treatment.

But in every application there is a cut, so one could just as well say that everything requires a classical treatment. Basically, there is a classical-quantum cut, the topic of this thread.

Perhaps I didn't explain myself well. I'm saying that the different states of the macroscopic device belong to different superselection sectors and thus any probability due to a superposition of their states is simply classical ignorance. Thus for such degrees of freedom unitary evolution is just classical stochastic evolution concerning classical probabilities. This is nothing as such to do with Many Worlds.

EDIT: Maybe another way to say it. When Von Neumann formulated his "chain" in the 1930s at each stage in the chain we had the $n$th device necessary to select the Boolean frame choosen for the event space of the $(n - 1)$th device. However more modern study has shown that for actual devices there is only one event space, thus another device is not necessary to select out the Boolean algebra of events.

Are you just saying that with decoherence, unitary evolution gives a reduced density matrix that is almost diagonal, the same as if measurement had collapsed the state?

 

[EPR]

I don't understand. Many superselection rules have nothing to do with the environment, such as superselection between different charge numbers.

I don't mean to derail the thread(if needed i will start a new one) - what happens to conserved quantities like charge during superposition of states e.g. of electrons? If you insist that superpositions aren't real, why are we observing fringes in the double slit experiment?

 

[atyy]

Though they wrote in German (maybe someone wants to tranlate these quotes into English?), it is clear that they regard the cut as being fairly arbitrary, not in the observer's head.

Double meaning of "in the observer's head"

 

[bhobba]

I don't mean to derail the thread(if needed i will start a new one) - what happens to conserved quantities like charge during superposition of states e.g. of electrons? If you insist that superpositions aren't real, why are we observing fringes in the double slit experiment?

The pure states form a vector space so of course superposition's are real - its in the very definition of a vector space. Charge is a scaler observable so is always the same when observed.

Thank
Bill

 

[A. Neumaier]

Double meaning of "in the observer's head"

How? Unless all physics is in the observer's head, the cut is not in the observer's head in any sense.

 

[A. Neumaier]

Charge is a scaler observable so is always the same when observed.

Distance is also a scalar variable but not always the same when observed. Charge is special in that there is a superselection rule for charge.

 

[DarMM]

But in every application there is a cut, so one could just as well say that everything requires a classical treatment. Basically, there is a classical-quantum cut, the topic of this thread.

Genuinely I am lost. Let me try again.

So originally I quoted Bohr saying that anything can be treated in a quantum way. Are you still disagreeing with this being Bohr's opinion or something else?

I don't understand what you mean by "everything requires a classical treatment". In Quantum Theory the treatment of microscopic systems require an external system to select the Boolean algebra so as to have well defined events/a well defined statistical model. Some degrees of freedom, for example charge, total angular momentum and macroscopic properties, do not seem to require such an external system since their probability theory is Kolmogorovian. However all of this is predicted/given by quantum theory itself, what do you mean by they "require a classical treatment"?

Are you just saying that with decoherence, unitary evolution gives a reduced density matrix that is almost diagonal, the same as if measurement had collapsed the state?

No, although some relation. First of all it is not state reduction, since you'd still have each outcome with a certain probability, up until you update the state yourself after an observation. Secondly it's more that decoherence combined with relativistic constraints generates a superselection rule among macroscopic properties.

 

[DarMM]

I don't mean to derail the thread(if needed i will start a new one) - what happens to conserved quantities like charge during superposition of states e.g. of electrons? If you insist that superpositions aren't real, why are we observing fringes in the double slit experiment?

I'm not at all saying superpositions is not real. That would be daft, equivalent to denying QM.

I'm saying that for certain quantities a linear sum of states with specific values, e.g.
$$|\psi\rangle = \frac{1}{\sqrt{2}}\left(|a\rangle + |b\rangle\right)$$
where $a$ and $b$ are two values for such a quantity $Q$, the statistics described by such a state are just those of Kolmogorovian/classical statistics. They're not quantum superposition. Again this is for some quantities. Examples are charge, total angular momentum, macroscopic properties. There are some others, but often it is a complex problem to verify something is "superselected" like this.

 

[A. Neumaier]

decoherence combined with relativistic constraints generates a superselection rule among macroscopic properties.

I'd be interested in references substantiating this. Or is it just your impression?

 

[atyy]

So originally I quoted Bohr saying that anything can be treated in a quantum way. Are you still disagreeing with this being Bohr's opinion or something else?

No.

I don't understand what you mean by "everything requires a classical treatment". In Quantum Theory the treatment of microscopic systems require an external system to select the Boolean algebra so as to have well defined events/a well defined statistical model. Some degrees of freedom, for example charge, total angular momentum and macroscopic properties, do not seem to require such an external system since their probability theory is Kolmogorovian. However all of this is predicted/given by quantum theory itself, what do you mean by they "require a classical treatment"?

Quantum theory has a classical-quantum cut. Hence the use of quantum theory itself means the assumption of a classical "something".

No, although some relation. First of all it is not state reduction, since you'd still have each outcome with a certain probability, up until you update the state yourself after an observation.

But are you talking about the reduced density matrix?

Secondly it's more that decoherence combined with relativistic constraints generates a superselection rule among macroscopic properties.

Could you give a reference?

 

[EPR]

The pure states form a vector space so of course superposition's are real - its in the very definition of a vector space. Charge is a scaler observable so is always the same when observed.

Thank
Bill

When observed... But what happens to electron's charge when for example an electron is in a state of definite momentum and so is in a superposition of states of many many different positions?

I am not sure if understand this correctly - how do we know electrical charge can induce superselection(and say resolve the measurement problem) if we don't know what happens to charge between observations/measurements?

 

[A. Neumaier]

But what happens to electron's charge when for example an electron is in a state of definite momentum and so is in a superposition of states of many many different positions?

An electron always has charge $-e$, independent of the state it is in.

 

[DarMM]

I'd be interested in references substantiating this. Or is it just your impression?

Even charge superselection is not "proved" as such. Nor lepton number superselection. Do you consider the usual arguments where by the appropriate interference observables can be shown to be unphysical acceptable? If so I can provide references, if not I'll ask more about what you would consider acceptable.

 

[DarMM]

Quantum theory has a classical-quantum cut. Hence the use of quantum theory itself means the assumption of a classical "something".

Describe this cut explicitly though. To my mind in modern quantum theory we require a system to select the Boolean frame to constitute events, however this is not an invocation of classical mechanics. It's that QM doesn't have a single sample space, thus something must select the sample space to give a well-define set of outcomes. That something is the "frame-selector" in one application doesn't mean quantum theory can't be applied to it in another application.
Thus anything can be given a quantum treatment.

But are you talking about the reduced density matrix?

Could you give a reference?

Not exactly with reference to the first part. For the second I shall after the discussion with @A. Neumaier above to see what he is looking for.

 

[EPR]

An electron always has charge $-e$, independent of the state it is in.

Indeed, charge has only 1 possible value so cannot be in a supperposition of different states.

But... since charge also behaves non-classically and obeys the Rules of Quantum Mechanics, how do we know it may lead to superselection? We must assume, right?
In the end, John von Neumann and Niels Bohr had the best clarity of these concepts and this is why their ideas found their way into the textbooks. And Everett's didn't.
Is decoherence taught in textbooks?

 

[A. Neumaier]

Even charge superselection is not "proved" as such. Nor lepton number superselection. Do you consider the usual arguments where by the appropriate interference observables can be shown to be unphysical acceptable? If so I can provide references, if not I'll ask more about what you would consider acceptable.

I just wanted to know what you consider as evidence for your previous assertion since I haven't seen decoherence discussed in a relativistic context.

Isn't the charge superselection rule a theorem?

 

[DarMM]

Isn't the charge superselection rule a theorem?

Yes basically. I should say that wasn't intended to imply doubt about charge superselection. There are remaining issues with characterizing plausible or permitted states, for which there are no stringent criterion. Issues about if QED exists do the appropriately constructed local field operators in a rigorous analogue of the Gupta-Beuler gauge obey enough of the expected properties of that formalism.

Under such "assumptions" as such it is proved here:
https://aip.scitation.org/doi/10.1063/1.1666601
However these arguments are so plausible that this is in essence a proof.

I just wanted to know what you consider as evidence for your previous assertion since I haven't seen decoherence discussed in a relativistic context.

It's the proof given in Chapter 7 of Omnès's text as I mentioned before. Whereby the interference observables for a real device would require a second device with at least $\mathcal{O}\left(10^{10^{18}}\right)$ atoms. Thus such observables do not belong to the observable algebra due to both the actual limit of material in the universe and relativistic reasons, e.g. under General Relativity are so large as to collapse in on themselves and under Special Relativity are too large to operate on the time scales required.

Again Chapter 7 of Omnès's book or Chapter 4 of Streater's Lost Causes (only noticed there that he cites you in that book!)

 

[atyy]

Describe this cut explicitly though. To my mind in modern quantum theory we require a system to select the Boolean frame to constitute events, however this is not an invocation of classical mechanics. It's that QM doesn't have a single sample space, thus something must select the sample space to give a well-define set of outcomes. That something is the "frame-selector" in one application doesn't mean quantum theory can't be applied to it in another application.
Thus anything can be given a quantum treatment.

As far as I can tell, that is the same as saying that every application of quantum mechanics has a classical-quantum cut. Frame selector = classical apparatus.