Nobody understands quantum physics?

[vanhees71]

Where does the fundamental formulation of QT depend on classical physics?

Of course, the one real problem is gravity and since gravity is strongly entangled (pun intended) with the spacetime model in a sense indeed there's a classical aspect in the formulation of relativity, i.e., the spacetime model is entirely classical. Indeed in this sense there's a real scientific problem concerning the completeness of QT as the "theory of everything", but I'm pretty sure that it has nothing to do with any vaguely formulated philosophical problem about measurement.

 

[Fra]

I don't see any evidence for collapse.

Are you never suprised?

/Fredrik

 

[WernerQH]

Where does the fundamental formulation of QT depend on classical physics?

Can you refer to a formulation of quantum theory that does not use the term "measurement"? And doesn't measurement require classical apparatus?

 

[Fra]

Where does the fundamental formulation of QT depend on classical physics?

It does not depende on classical theory per see, but the theoretically perfect confidence in the distributions IMO requires a solid reference - "classical world", without it, not only is the future fuzzy, even the cloud itself is fuzzy. Thats not to imply that QM depends on newtonis mechanics as such.

in this sense there's a real scientific problem concerning the completeness of QT as the "theory of everything", but I'm pretty sure that it has nothing to do with any vaguely formulated philosophical problem about measurement.

Wether this has nothing to do with it is where we disagree. My only question is, given that one cares at all, if this ha nothing todo with QG - what does? I mean, what is the alternative? For me the path seems nasty but i see no other path.

/Fredrik

 

[vanhees71]

I'm convinced that we'll never get something physical out of a mere philosophical quibble about a pseudoproblem. Obviously no philosophical gibberish has brought us any close to an ansatz of how to formulate "quantum gravity". I think we'll need some empirical hint, but I don't see anything in sight yet.

 

[LittleSchwinger]

@vanhees71 , this is more out of curiosity about how you would phrase it, I'm not debating as such.

We commonly say quantum theory is a probability theory where not all quantities take well-defined values at once. So if we start with a particle in an eigenstate of z-axis spin, $S_{z}$, such as $\ket{\uparrow}$ then we know that $S_{x}$ doesn't have a well-defined value.

If we do an $S_{x}$ measurement however we do end up in a state with a well-defined value for $S_{x}$. "When" in the measurement process do you think this well-defined value was obtained?

 

[vanhees71]

It's just by filtering. Take the Stern-Gerlach experiment which can be designed as an almost perfect filter measurement, i.e., you use an inhomogeneous magnetic field with the right properties to split the beam in two spatially well separted parts, of which you know (from unitary quantum dynamics by the way) that position and spin-component (which one is selected by the direction of the large homogeneous part of the magnetic field) are almost perfectly entangled, i.e., blocking one partial beam prepares a beam with determined spin component. It's clear that you can prepare only one spin component and not more, i.e., the spin components in other directions don't take determined values, and the so prepared quantum state implies the and only the probabilities for the results of measurements of any spin component. Measuring the prepared spin component gives with 100% probability the prepared value, i.e., this and only this spin component takes a determined value. The preparation is obtained after the beams got sufficiently well separated due to the (unitary) dynamics of the particles moving in the magnetic field.

 

[LittleSchwinger]

The preparation is obtained after the beams got sufficiently well separated due to the (unitary) dynamics of the particles moving in the magnetic field.

Okay thanks. That basically lines up with what I first learned from Gottfried (1st Ed sans Yan) and the old Schwinger "Humpty-Dumpty" paper.

 

[A. Neumaier]

If we do an $S_{x}$ measurement however we do end up in a state with a well-defined value for $S_{x}$. "When" in the measurement process do you think this well-defined value was obtained?

Measuring the prepared spin component gives with 100% probability the prepared value, i.e., this and only this spin component takes a determined value. The preparation is obtained after the beams got sufficiently well separated due to the (unitary) dynamics of the particles moving in the magnetic field.

This does not answer the query. Prepared is a superposition without definite values of $S_x$. But measured is one of the values $\pm1$, let us say $+1$. The question is when, in a quantum description of the detector, the definite value $+1$ is obtained.

 

[vanhees71]

After the magnet the spin component in direction of the field is (almost completely) entangled with position, i.e., in each of the two partial beams "selected" by the magnet you have a well-prepared spin component.

 

[Morbert]

This does not answer the query. Prepared is a superposition without definite values of $S_x$. But measured is one of the values $\pm1$, let us say $+1$. The question is when, in a quantum description of the detector, the definite value $+1$ is obtained.

To quote the Schwinger essay mentioned by @LittleSchwinger:

"Therefore, the mathematical scheme for microscopic measurements can certainly not be the representation of physical properties by numbers. [...] we must instead look for a new mathematical scheme in which the order of performing physical operations is represented by an order of performance of mathematical operations. The mathematical scheme that was finally found to be necessary and successful is the representation, in a very abstract way, of physical properties not by numbers but by elements of an algebra for which the sense of multiplication matters."

"If you know the state, you can then predict what the result of repeated trials of measurement of a particular physical property will be. You will have perfectly determinate, statistical predictions but no longer individual predictions."

"The knowledge of the state does not imply a detailed knowledge of every physical property but merely, in general, of what the average or statistical behavior of physical properties may be."

I read this to mean:

i) We should be careful not to attribute a property like $S_x = +1$ to the object of measurement. $+1$ would only be attributed to the classical datum post-measurement. If we want to speak about properties of the object of measurement, we would use a representation like $\Pi_{S_x=+1}$. This more robust representation frees us of worrying about when a particular property does or doesn't obtain. Only the ordering in consideration of measurement operations is important.

ii) We do not have to associate the preparation of the object of measurement with the moment a microscopic property obtains. The quantum state is not an assertion of what properties the system has at any given time. It is only an assertion of what future statistics can be expected.

[edit] - Tidied up a bit

 

[vanhees71]

To quote the Schwinger essay mentioned by @LittleSchwinger:

"Therefore, the mathematical scheme for microscopic measurements can certainly not be the representation of physical properties by numbers. [...] we must instead look for a new mathematical scheme in which the order of performing physical operations is represented by an order of performance of mathematical operations. The mathematical scheme that was finally found to be necessary and successful is the representation, in a very abstract way, of physical properties not by numbers but by elements of an algebra for which the sense of multiplication matters."

"If you know the state, you can then predict what the result of repeated trials of measurement of a particular physical property will be. You will have perfectly determinate, statistical predictions but no longer individual predictions."

"The knowledge of the state does not imply a detailed knowledge of every physical property but merely, in general, of what the average or statistical behavior of physical properties may be."

That's the most precise no-nonsense statement I can think of. Indeed, this introductory chapter of Schwinger's textbook is a must-read for anybody interested in the interpretational issues of QT.

I read this to mean:

i) We should be careful not to attribute a property like $S_x = +1$ to the object of measurement. $+1$ would only be attributed to the classical datum post-measurement. If we want to speak about properties of the object of measurement, we would use the representation $\Pi_{S_x=+1}$. This more robust representation frees us of worrying about when a particular property does or doesn't obtain. Only the ordering in consideration of measurement operations is important.

Yes, the state implies the probabilities for the outcome of any measurement you can do on the prepared system. If the state is such that the outcome for an observable like $P(s_x=+\hbar/2)=1$, then this observable takes a determined values $\hbar/2$, otherwise it's value is indetermined, and only the probalities for either possible outcome is given by the preparation in that state.

ii) We do not have to associate the preparation of the object of measurement (e.g. by blocking the other beam) with the moment a microscopic property obtains. The quantum state is not an assertion of what properties the system has at any given time. It is only an assertion of what future statistics can be expected.

The state represents a preparation procedure. It predicts probablistic and only probabilistic properties about the outcome of future measurements.

 

[Couchyam]

It's just by filtering. Take the Stern-Gerlach experiment which can be designed as an almost perfect filter measurement, i.e., you use an inhomogeneous magnetic field with the right properties to split the beam in two spatially well separted parts, of which you know (from unitary quantum dynamics by the way) that position and spin-component (which one is selected by the direction of the large homogeneous part of the magnetic field) are almost perfectly entangled, i.e., blocking one partial beam prepares a beam with determined spin component. It's clear that you can prepare only one spin component and not more, i.e., the spin components in other directions don't take determined values, and the so prepared quantum state implies the and only the probabilities for the results of measurements of any spin component. Measuring the prepared spin component gives with 100% probability the prepared value, i.e., this and only this spin component takes a determined value. The preparation is obtained after the beams got sufficiently well separated due to the (unitary) dynamics of the particles moving in the magnetic field.

Remember that the signal produced in the original Stern Gerlach experiment consisted of two well separated clusters of points on a screen, not a single pair. The experiment strongly hints at the existence of a spin degree of freedom that is entangled, but it also hints at the existence of a number of other configurational degrees of freedom associated with the wave function that ultimately must somehow collapse to a point with each trial in order for any experimental data to be obtained at all. It's possible that similar (uncontrolled) filtering mechanisms are at work in separating each measurement outcome, but verifying that requires performing a second experiment (trying to 'dissect' the wave function collapse process, to determine each filtering mechanism in turn.)

At a certain point, you need to explain why the Hamiltonian of a system is definite and not itself described by a wave function or density operator. It could be that the Hamiltonian is a macroscopic statistical average that emerges from a random ensemble of definite (observed) events, or that it is somehow connected to the ability of the experimenter to both modulate a system and 'read' its character, or something else entirely, but quantum mechanics in its traditional formulation makes it very difficult to tell which of these perspectives if any is in fact closest to the truth.

 

[PeterDonis]

At a certain point, you need to explain why the Hamiltonian of a system is definite

I'm not sure what you mean by "definite". The Hamiltonian is an operator.

 

[Couchyam]

I'm not sure what you mean by "definite". The Hamiltonian is an operator.

What I mean is that the Hamiltonian is (conventionally understood as) a 'definite operator', as opposed to an operator-valued random number generator, or a wave function over a space of operators (or part of some larger wave function of the universe.) It might change over time, and it might be impossible to measure its components exactly, but at every instant it has (in principle) a well-defined value. If a formulation of quantum mechanics existed in which the Hamiltonian wasn't definite, the authors of the theory would need to explain the exact nature of its indefiniteness very carefully (possibly by appealing to a more fundamental mechanism for time evolution.) There may be some way for a Hamiltonian to 'emerge' from a wave function that either lacked inherent dynamics or was described by some completely strange-looking but unitary 'super-Hamiltonian', but that would mark a departure from the conventional picture.

 

[hutchphd]

After the magnet the spin component in direction of the field is (almost completely) entangled with position, i.e., in each of the two partial beams "selected" by the magnet you have a well-prepared spin component.

I do not understand the term "after the magnet" in the above. I believe this goes to the fundamental disagreement in much of this discussion. Is this temporal? Spatial?

 

[Couchyam]

I do not understand the term "after the magnet" in the above. I believe this goes to the fundamental disagreement in much of this discussion. Is this temporal? Spatial?

I guess you could say that conditional on the particle having been measured (at some point away from the magnet, after it has been emitted by whatever source is used), it must have been influenced by the magnetic field to some extent (barring somewhat contrived neutral Aharonov-Bohm field configurations.) Speaking of the Aharonov-Bohm effect and spatial/temporal ambiguities...

 

[gentzen]

I do not understand the term "after the magnet" in the above. I believe this goes to the fundamental disagreement in much of this discussion. Is this temporal? Spatial?

Is there a disagreement (in this thread)? Between whom? I guess "after the magnet" is Spatial. Probably near the hole in some imaginary aperture, which blocks the unwanted part of the particle beam.

 

[gentzen]

At a certain point, you need to explain why the Hamiltonian of a system is definite and not itself described by a wave function or density operator. It could be that the Hamiltonian is a macroscopic statistical average that emerges from a random ensemble of definite (observed) events, or that it is somehow connected to the ability of the experimenter to both modulate a system and 'read' its character, or something else entirely, but quantum mechanics in its traditional formulation makes it very difficult to tell which of these perspectives if any is in fact closest to the truth.

My answer would be that preparation does not just determine the initial state, but also the Hamiltonian.

And in general, I guess that the failure to distinguish between preparation and measurement is responsible for some of the confusion with QM and its interpretation. Using measurement to emulate preparation seems so convenient and straightforward, just like an additional quantum symmetry. But you risk a totally unnecessary circularity in this way.

 

[Fra]

At a certain point, you need to explain why the Hamiltonian of a system is definite

My answer would be that preparation does not just determine the initial state, but also the Hamiltonian.

And in general, I guess that the failure to distinguish between preparation and measurement is responsible for some of the confusion with QM and its interpretation. Using measurement to emulate preparation seems so convenient and straightforward, just like an additional quantum symmetry. But you risk a totally unnecessary circularity in this way.

This illustrates the problem of the paradigm where one has a timeless evolution law (represented by hamiltonian flow), that works on timeless statespaces.

The problem from the perspective of inference is that, ANY "input" counts. "Specfiying the hamiltonian" is no less "input" than is "speciying the initial state". The difference is though that the hamiltonian is given much more weight (by construction). But it is pretty obvious that any process tomographic process can not with perfect confidence infer a timeless hamiltonian, how could it? I think effectively the inference limited by a certain capacity implies an energy cutoff (or large time limit), that I interpret as physically related to the agents complexity. Perhaps one can also interpret this as a decoupling between agents that fails to decode each other, due to running out of processing time on the dynamical scale.

(As I see the solution to this, it does seem circular at first, but i would say it can be evolutionary. Ie its no more circular than the relation between how the dynamics IN spacetime, changes the dynamics OF spacetime - but applie to a more abstract "information space", that involves all information, not just positions. I see it as a possible feedback loop of learning. this is very different than "circular reasoning")

What happens is when you think this is too complicated, you can truncate or "freeze" the process from a given observer, and the effective theory - frozen - looks like a normal hamiltonian paradigm. It happens when you say that, ignore some marginal uncertainty and consider anything that is "sufficiently certain" as completely certain.

/Fredrik

 

[Fra]

But you risk a totally unnecessary circularity in this way.

I agree, but there is a possible benefit as well. To connect two different effective theories or allow for emergent hamiltonian as part of the physics. And I think this is sort of what one needs in the quest for unification. But it certainly makes it more complicated with a feedback. This is already why GR is quite complicated, we have problems of time etc.

/Fredrik

 

[gentzen]

I agree, but there is a possible benefit as well. To connect two different effective theories or allow for emergent hamiltonian as part of the physics. And I think this is sort of what one needs in the quest for unification.

Well, the quest for unification is not my quest. I guess my quest is just to be able to communicate (about physics), without too much appeal to authority.

I sort of get why preparation and measurement are closely related. For example, if I prepare atoms by shielding them and waiting long enough until they nearly all relaxed to their ground state, then I know that they are in their ground state. And because I know it, I can claim that I somehow measured it, because what else is measurement than knowing some specific properties. But ... I would prefer to measure properties which were there before I measured, and prepare states which will be there after I prepared.

 

[Couchyam]

My answer would be that preparation does not just determine the initial state, but also the Hamiltonian.

And in general, I guess that the failure to distinguish between preparation and measurement is responsible for some of the confusion with QM and its interpretation. Using measurement to emulate preparation seems so convenient and straightforward, just like an additional quantum symmetry. But you risk a totally unnecessary circularity in this way.

@gentzen: I'm not entirely sure if I understand the points you are making (about the Hamiltonian being determined by 'preparation', or the dichotomy between 'preparation' and 'measurement', or the nature of the 'circularity' that is risked by conflating the two.) Is the idea that it is hard to derive scientific meaning (or evaluate ethics) in experiments where there isn't a clear dichotomy between preparation and measurement, or are you saying something about the fundamental nature of Hamiltonians (to the extent that Hamiltonians are fundamental?) Consider for example an experiment in which, say half-way through, a completely random earthquake starts, jostling the apparatus: would the data be fundamentally useless because they weren't produced with the (intended) 'prepared' Hamiltonian, or could some kind of meaning be rescued at the end of the day if the bumps were measured precisely enough? (Would you interpret the 'bump measuring' apparatus as another necessary part of the preparation?)

@Fra: could you explain to me what you mean by a 'timeless Hamiltonian'? I would also much appreciate it if you could discuss what you meant by 'ANY "input" counts', or what it would mean to "freeze [a] process from a given observer".

 

[gentzen]

dichotomy between 'preparation' and 'measurement', or the nature of the 'circularity' that is risked by conflating the two

I don't think there is a dichotomy, or that the two are conflated. I think that measurement is presented as the special operation, and preparation is either ignored, or emulated by measurement.

I don't intent to talk about something complicated here. Just plain simple, if you prepare your experiment, call it preparation. Who cares whether you can make some interpretational dance and interpret it as a sort of measurement?

The circularity is also something very simple. Measurement has to store/register the new information somewhere. If you allow yourself the possibility to prepare a sufficient number of qubits in some well defined state (typically some ground state), then storing the new information there (even redundantly) is easy. But if you want to use measurement for preparing those qubits in a well defined state, then ... you risk to entangle yourself in circularity.

Is the idea that it is hard to derive scientific meaning (or evaluate ethics) in experiments where there isn't a clear dichotomy between preparation and measurement, or are you saying something about the fundamental nature of Hamiltonians (to the extent that Hamiltonians are fundamental?)

No, not at all. The idea is that preparation is (often) really simple, even in cases where it is a combination between knowing and ensuring certain things. Measurement is (often) more tricky.

 

[Fra]

I don't want to discuss too deeply into this, as that is impossible without getting offside...

@Fra: could you explain to me what you mean by a 'timeless Hamiltonian'? I would also much appreciate it if you could discuss what you meant by 'ANY "input" counts', or what it would mean to "freeze [a] process from a given observer".

The terms I used was not very formal, but

1) by timeless hamiltonian I essentially mean that the "laws of evolution" (which is often encoded as a hamiltonian) are fixed, non-dynamical and considered to be what they are becuase it's how nature is. This gives the paradigm that the initial conditions implies the future.

The opposite of this (which i prefer) implies that one should treat initial conditions and laws on more equal footing. See for example

Unification of the state with the dynamical law​

"We address the question of why particular laws were selected for the universe, by proposing a mechanism for laws to evolve. Normally in physical theories, timeless laws act on time-evolving states. We propose that this is an approximation, good on time scales shorter than cosmological scales, beyond which laws and states are merged into a single entity that evolves in time. Furthermore the approximate distinction between laws and states, when it does emerge, is dependent on the initial conditions. These ideas are illustrated in a simple matrix model. "
-- https://arxiv.org/abs/1201.2632

I would not bother with the explicit model in that paper(which I think is too simple), I think the important thing is the idea. He also dedicated books to argue. The purpose of the books are as I see it not to present the explicit model that solves this (this is an open issue), but the main objetive is to change the way many physicists thing of this. https://www.amazon.com/dp/1107074061/?tag=pfamazon01-20

2) But "any input" I mean any information that an agent makes inferences upon, makes use of both implicit and explicit informaiton, and it comes if different forms. The most obvious, explicit and most adjustable information can be encoded in a STATE. There are alot of background information, that we can fool ourselves with beeing just "mathematics", but I think it clearly biases our inferences (and any agents inferences), and this is not acceptable for me. The background information usually is chosen as well, but it's slower process. The LAW what deduces the future from the past (in the typical paradigm of a closeod system) is a very qualified piece of information. Where does this come from? A purist view of inference would expect this to follow from inference as well.

3) By freeze I meant effectively a perturbative approach, where you take any existing state of hte observer as fixed, and perturb from there, it is quite obvious that the differential state is going to be simpler and more linear mathematics, just like you can taylor expand any function. So the "present" becomes the "background". But on larger time scales the background must evolve somehow. Until we understand this batter, we can simply say we have a different "effective theory" at any point in this abstract space. But it's the relation and how they flow into each other as part of physical interactions (NOT just flowing into each other on the theorists noteblock) that I find the challenge to understand.

/Fredrik

 

[vanhees71]

I do not understand the term "after the magnet" in the above. I believe this goes to the fundamental disagreement in much of this discussion. Is this temporal? Spatial?

Both. You have an Ag atom moving through the magnet in a finite time, and behind the magnet you have an entanglement between position and spin component, i.e., when selecting only Ag atoms in one of the corresponding spatial regions you find them to have a definite spin component ("up" or "down", depending on which region you choose).

 

[vanhees71]

What I mean is that the Hamiltonian is (conventionally understood as) a 'definite operator', as opposed to an operator-valued random number generator, or a wave function over a space of operators (or part of some larger wave function of the universe.) It might change over time, and it might be impossible to measure its components exactly, but at every instant it has (in principle) a well-defined value. If a formulation of quantum mechanics existed in which the Hamiltonian wasn't definite, the authors of the theory would need to explain the exact nature of its indefiniteness very carefully (possibly by appealing to a more fundamental mechanism for time evolution.) There may be some way for a Hamiltonian to 'emerge' from a wave function that either lacked inherent dynamics or was described by some completely strange-looking but unitary 'super-Hamiltonian', but that would mark a departure from the conventional picture.

What's deterministic in quantum dynamics is the evolution of the probabilities, and that's indeed described by the Hamiltonian. Concerning the observables it's indeed in a sense a random-number generator (as far as we know a perfect one, i.e., it's not somehow deterministic in a hidden way). The Hamiltonian in standard QT doesn't "emerge from a wave function" but is given for the system under investigation to determine the time evolution of the wave function from the initial wave function (given by the "preparation of the system"). In this sentence you can everywhere write "statistical operator" instead of "wave function" to cover the most general case of states.

 

[LittleSchwinger]

What I mean is that the Hamiltonian is (conventionally understood as) a 'definite operator', as opposed to an operator-valued random number generator

Such a concept wouldn't make much sense.

In QM you have your algebra of observables and then per Gleason's theorem (or Busch's if you take POVMs) quantum states, i.e. statistical operators, can be derived as probability assignments to the observables.

Thus they do take values probabilistically, but having the operator itself be random wouldn't make much physical sense. In a lab we know if we are measuring $S_{x}$ or $S_{z}$, based on the orientation of the Stern-Gerlach magnets for example, that doesn't fluctuate.

 

[gentzen]

I do not understand the term "after the magnet" in the above. I believe this goes to the fundamental disagreement in much of this discussion. Is this temporal? Spatial?

Both. You have an Ag atom moving through the magnet in a finite time,

But in this specific experiment, you have no control over when an Ag atom reaches the magnet (and can't measure it either), so I think that for this specific experimental arrangement, "Spatial" is the better answer. There could be similar experiments where control and knowledge about time is relevant. But one lesson from QT is that you have to focus on your specific actually performed experiment, and not on some other experiment which you could have performed instead.

and behind the magnet you have an entanglement between position and spin component, i.e., when selecting only Ag atoms in one of the corresponding spatial regions you find them to have a definite spin component ("up" or "down", depending on which region you choose).

You see, in this specific experiment, you choose a spatial region. That is my argument for why "Spatial" should be the answer.

 

[gentzen]

Thus they do take values probabilistically, but having the operator itself be random wouldn't make much physical sense.

Bell-tests are often arranged in a way that depending on some random element, something macroscopically different is done. This would be reflected in a time dependent Hamiltonian, if the used quantum description were "sufficiently complete". But since the outcome of this random element will be known in the analysis of the measurement results, it is unclear whether saying that the Hamiltonian was random makes physical sense.