Insights Why the Quantum | A Response to Wheeler's 1986 Paper - Comments

[stevendaryl]

No, we have to interpret the complex coefficients of each term in the superposition as probability amplitudes for the measurement result described by that particular term to be observed when we make a measurement

If you describe the measurement process itself as a quantum-mechanical interaction, then what you will find is that the combination measured-system-plus-measuring-device-plus-environment will evolve into a superposition of a number of possibilities.

You have a particle that is in a superposition of, say, spin-up with amplitude $\alpha$ and spin-down with amplitude $\beta$. Then under unitary evolution, the whole shebang will evolve into a superposition of

1. The particle is spin-up and the measuring device measured spin-up and the environment is whatever is appropriate for a measuring device measuring spin-up.
2. The particle is spin-down and the measuring device measured spin-down and the environment is whatever is appropriate.

The amplitude for the first possibility will be $\alpha$ and the the amplitude for the second possibility will be $\beta$. You can interpret this as "there is a probability of $|\alpha|^2$ for the first possibility and a probability of $|\beta|^2$ of the second possibility. But to say that it requires another measurement of the measuring device before you can assign probabilities seems like it leads to an infinite regress.

 

[stevendaryl]

No, you have to say that, once the alternatives become macroscopically distinguishable, only one of the alternatives is real, and therefore you cannot describe the system as being in a superposition any more.

That's equivalent. You're interpreting "the system is a superposition of macroscopically distinguishable possibility with amplitudes given by Hamiltonian evolution" as "the system is either in one state or the other state, with probabilities given by the square of the amplitude".

If you don't treat macroscopic systems as different than microscopic systems, from the point of view of evolution, then the system will evolve into a superposition of macroscopically distinguishable alternatives. It's inevitable.

I'm talking about the implications of the minimal interpretation in which you try to maintain both (1) the claim that macroscopic systems evolve in the same way that microscopic systems do, and (2) the probabilities of measurement alternatives are given by the Born rule. It seems to me that there is no way to have both unless you interpret macroscopic superpositions as mixtures, essentially.

 

[vanhees71]

I think this is a misuse of the term "superposition". That term never means that "the system is either in this state or that state, with such-and-such probability". That is a "mixture".

The question is whether a superposition (defined as I just have) of macroscopically distinguishable states is even possible. The MWI says it is; a collapse interpretation says it isn't (collapse always removes all but one term in the superposition before that happens).

I couldn't agree more!

First of all you have to tell superposition of which vectors. Usually one takes an observable and decomposes the pure state, in terms of a normalized vector
$$|\Psi \rangle=\sum_a \Psi_a |a \rangle,$$
where $|a \rangle$ is a complete orthonormalized set of eigenvectors of the representing self-adjoint operator of the quantity measured. The state is then given by the statistical operator
$$\hat{\rho}=|\Psi \rangle \langle \Psi|.$$

Then it's of course wrong to say "the system is in a state where the observable $A$ takes all the possible values $a$ at the same time" (to make it clear again this sentence is WRONG, no matter how often it is repeated even in real textbooks, not only in popular writings!). The right thing to say is that for the quantum system prepared in this state the probability to find the value $a$ when you measure the observable $A$ is given by $P_a=|\Psi_a|^2=\langle a|\hat{\rho}|a \rangle$ (here for simplicity I assume the case that $\hat{A}$ is non-degenerate, i.e., I assume that all eigenspaces are one-dimensional).

Consequently this implies that the system has a determined value of the observable $A$ being $a$ if and only if $P_a=1$ and $P_{a'}=0$ for all $a' \neq a$. This implies that $|\Psi \rangle=|a \rangle$ and the state is $\hat{\rho}=|a \rangle \langle a|$.

If this is not the case, the observable $A$'s value is indetermined, and the probability to find any of the possible values $a$ is $P_a$. There's no other meaning (within the minimal statistical interpretation) than this, and as far as I know it's the meaning which is testable in the lab on doing measurements of $A$ on ensembles of equally prepared systems, using the usual statistical analysis to test probabilistic predictions.

Also the final statement is completely correct. If you say it's in any case in a state where $A$ has a determined value, but it's not known which value but you know there are probabilities $P_a$ for each value, then the correct association of a state, if no other information is given, is
$$\hat{\rho}'=\sum_a P_a |a \rangle \langle a|.$$
The thought-experimental realization is that Alice prepares an ensemble of systems providing Bob with the corresponding single systems. This means that Alice prepares each single member of the ensemble in a state described by the statistical operator $\hat{P}_a =|a \rangle \langle a|$ and she sends a fraction $P_a$ of single systems for each determined value $A$ to Bob. Of course $\hat{\rho}' \neq \hat{\rho}=|\Psi \rangle \langle \Psi|$. Although Bob cannot distinguish the two states by just measuring $A$, the states are different, and you can in principle find the difference by more fancy observations (see the excellent chapter on "state preparation and determination" in Ballentine's textbook).

 

[PeterDonis]

If you describe the measurement process itself as a quantum-mechanical interaction, then what you will find is that the combination measured-system-plus-measuring-device-plus-environment will evolve into a superposition of a number of possibilities.

Agreed.

You can interpret this as "there is a probability of $|\alpha|^2$ for the first possibility and a probability of $|\beta|^2$ of the second possibility.

And if you do that, then you are saying the system is not in the state "superposition of two possibilities". It's in either the "first possibility" state or the "second possibility" state, with the respective probabilities you give of being in each. And when you make predictions about the results of future measurements on the system, you will use one of those two states (whichever one actually gets observed when the measurement is made). You won't use the state "superposition of two possibilities".

That's equivalent. You're interpreting "the system is a superposition of macroscopically distinguishable possibility with amplitudes given by Hamiltonian evolution" as "the system is either in one state or the other state, with probabilities given by the square of the amplitude".

No, I'm not. Please read what I actually wrote. The words "you cannot describe the system as being in a superposition" are right there in what you quoted from me. "Cannot" does not mean "equivalent".

Again, if you say "the system is either in one state or the other state, with probabilities given by the square of the amplitude", then you are saying the system is not in a superposition. And I've tried to clarify what that means in the first part of this post.

 

[stevendaryl]

And if you do that, then you are saying the system is not in the state "superposition of two possibilities". It's in either the "first possibility" state or the "second possibility" state, with the respective probabilities you give of being in each. And when you make predictions about the results of future measurements on the system, you will use one of those two states (whichever one actually gets observed when the measurement is made). You won't use the state "superposition of two possibilities".

That's why I'm saying that I think there is something screwy about the minimal interpretation. If you don't have a wave function collapse, or something equivalent, then following a measurement you end up in an entangled state, not a state where measurement results have definite outcomes.

However, I think it is actually consistent (although weird, for a reason I'll get to in a second) to treat a superposition of macroscopically distinguishable states as a mixed state, where the amplitudes give the probabilities of the "true" state being this or that.

Mathematically, we can describe it this way: Let $j$ range over some coarse-grained partitioning of the state of the composite system, and let $\Pi_j$ be the corresponding projection operator. Then we can just declare that the probability of being in macro state $j$ given that the composite is initially in state $|\psi\rangle$ is:

$P_j(t) = \langle \psi| e^{iHt} \Pi_j e^{-iHt} |\psi\rangle$

So the macro state just nondeterministically changes from one state to another, with probabilities controlled by the microstate
$|\psi(t)\rangle = e^{-iHt} |\psi\rangle$

I think that's a consistent interpretation, although it's weird, in that the microstate affects the macrostate, but not vice-versa.

 

[stevendaryl]

Again, if you say "the system is either in one state or the other state, with probabilities given by the square of the amplitude", then you are saying the system is not in a superposition. And I've tried to clarify what that means in the first part of this post.

The distinction between superpositions and mixed states is mathematically described in terms of interference terms. But for macroscopically distinguishable states, the interference terms are completely negligible. So in practice, there is no detectable distinction.

 

[stevendaryl]

The distinction between superpositions and mixed states is mathematically described in terms of interference terms. But for macroscopically distinguishable states, the interference terms are completely negligible. So in practice, there is no detectable distinction.

To elaborate, a superposition of $\alpha |A\rangle + \beta |B\rangle$ corresponds to a density matrix $|\alpha|^2 |A\rangle\langle A| + \alpha^* \beta |B\rangle \langle A| + \beta^* \alpha |A\rangle\langle B| + |\beta|^2 |B\rangle \langle B|$

In contrast, the density matrix for the system is in state A with probability $|\alpha|^2$ and the system is in state B with probability $|\beta|^2$ is given by:
$|\alpha|^2 |A\rangle\langle A| + |\beta|^2 |B\rangle \langle B|$.

If $|A\rangle$ and $|B\rangle$ are macroscopically different, then the difference between these two density matrices is practically unobservable.

 

[PeterDonis]

That's why I'm saying that I think there is something screwy about the minimal interpretation.

I wouldn't say it's "screwy", just limited. In the minimal interpretation, when we say which state is "real" (as I did in previous posts), all we mean is that we are going to use that state to make predictions about future measurements on the system. We're not making any ontological claim about what state the system is "really" in; that is interpretation dependent. We're just describing the mathematical procedure for making predictions.

 

[PeterDonis]

If $|A\rangle$ and $|B\rangle$ are macroscopically different, then the difference between these two density matrices is practically unobservable.

Agreed. But that's not the issue I was trying to get at.

Even once you've dropped the interference terms, you still will be switching density matrices once you know the actual measurement result. At that point, you aren't using $|\alpha|^2 |A\rangle\langle A| + |\beta|^2 |B\rangle \langle B|$ to predict future measurement results; you're using either $|A\rangle\langle A|$ or $|B\rangle \langle B|$. And the latter two states are not mixtures (nor are they superpositions).

 

[PeterDonis]

So the macro state just nondeterministically changes from one state to another

If you mean, this happens once when a measurement is made and its result is recorded, yes, I guess you could look at it this way.

If you mean, this is happening all the time and explains why measurement results on the system are probabilitistic, no, I don't think that works, because once you've measured the system to be in a particular eigenstate, you use that eigenstate as your starting point for future predictions, not the probabilistic mixture you were using before.

 

[stevendaryl]

If you mean, this happens once when a measurement is made and its result is recorded, yes, I guess you could look at it this way.

If you say that it only happens when you make a measurement would be treating measurements differently than other interactions. You could say, instead that it's true for every macroscopic state.

If you mean, this is happening all the time and explains why measurement results on the system are probabilitistic, no, I don't think that works, because once you've measured the system to be in a particular eigenstate, you use that eigenstate as your starting point for future predictions, not the probabilistic mixture you were using before.

That's what you would do if you're using the collapse hypothesis. If you are not assuming collapse, then you can't change the state based on what you observed.

However, in practice, this won't make any difference, because measurements are irreversible.

Suppose you start in state $|A\rangle$ and make a transition to either state $|B\rangle$ or $|C\rangle$ and then want to compute the probability that you end up in state $|D\rangle$.

If you don't assume collapse, then the probability is given by the following:

1. Let $\psi_{XY}$ be the probability amplitude for going from state $X$ to state $Y$.
2. We can write that as $\psi_{XY} = \sqrt{P_{XY}} e^{i \theta_{XY}}$, where $P_{XY} = |\psi_{XY}|^2$ is the probability of going from $X$ to $Y$ and $\theta_{XY}$ is the corresponding phase.

Then the probability to go from $A$ to $D$ is given by:

• $\psi_{AD} = \psi_{AB} \psi_{BD} + \psi_{AC} \psi_{CD} = \sqrt{P_{AB} P_{BD}} e^{i(\theta_{AB} + \theta_{BD})} + \sqrt{P_{AC} P_{CD}} e^{i(\theta_{AC} + \theta_{CD})}$
• $P_{AD} = P_{AB} P_{BD} + P_{AC}P_{CD} + IF$ where $IF$ is the interference term $2 \sqrt{P_{AB} P_{BD} P_{AC}P_{CD}} cos(\theta)$, where $\theta = \theta_{AB} + \theta_{BD} - \theta_{AC} - \theta_{CD}$

If instead you assume collapse, then you leave out the interference term. However, if states $B$ and $C$ are macroscopically distinguishable, then the interference term is essentially zero, anyway.

If $B$ is the state in which "I measured spin-up", and $C$ is the state in which "I measured spin-down", then there is no final macroscopically determinate state $D$ such that both $P_{BD}$ and $P_{CD}$ is significantly different from zero. In state $D$, either there will be a record of my having measured spin-up, or there will be a record of having measured spin-down. It's impossible (practically) that there could be a record of my measuring spin-up if I actually measured spin-down.

 

[PeterDonis]

If you say that it only happens when you make a measurement would be treating measurements differently than other interactions.

The "minimal" interpretation of QM, which is what I thought we were discussing, does treat measurements differently from other interactions. I thought that was the point you were repeatedly making in your discussion with @vanhees71.

If you are not assuming collapse, then you can't change the state based on what you observed.

Again, please read what I actually wrote. I didn't say the "real" state of the system changes. I only said the state you use to make predictions about future measurements you make on the system changes. That is true regardless of what interpretation you adopt.

Suppose you start in state $|A\rangle$ and make a transition to either state $|B\rangle$ or $|C\rangle$ and then want to compute the probability that you end up in state $|D\rangle$.

"Make a transition" is ambiguous. Do you measure the transition--do you observe either state $|B\rangle$ or $|C\rangle$? Or does no measurement take place, just a unitary evolution that assigns nonzero amplitudes to states $|B\rangle$ and $|C\rangle$?

If instead you assume collapse, then you leave out the interference term.

No, if you measure which intermediate state occurs, $|B\rangle$ or $|C\rangle$, then you leave out the interference term. Otherwise you don't.

For example, say $A$ is the state of a source that emits quanta that will pass through a double slit and then hit a detector screen; $B$ is the state of passing through the left slit; $C$ is the state of passing through the right slit; $D$ is the state of ending up at a particular location on the detector screen. If you measure which slit the quanta pass through, there is no interference; if you don't, there is. That is true whether or not you adopt a collapse interpretation; it's part of the basic math of QM.

In your example with spin up and spin down, you are measuring the spin, so there is no interference.

If you want to include the measuring devices and the environment in all of this, and you are measuring which intermediate state, $B$ or $C$, occurs (e.g., you are measuring spin up or spin down) before going on to state $D$, then the only source of "interference" terms comes from inaccuracy in the records left by the measuring devices--i.e., what you refer to here as being practically impossible:

It's impossible (practically) that there could be a record of my measuring spin-up if I actually measured spin-down.

But this is not the same as, for example, interference in the double slit experiment when you don't measure which slit the quanta go through.

 

[PeterDonis]

Suppose you start in state $|A\rangle$ and make a transition to either state $|B\rangle$ or $|C\rangle$ and then want to compute the probability that you end up in state $|D\rangle$.

Note also that you are implicitly assuming that this computation is made before the result of any measurement at the B/C stage is known. If there is a measurement at the B/C stage, and you know the result of that measurement, you just compute the probability $P_{BD}$ or $P_{CD}$, depending on which result was observed.

 

[bhobba]

So according to the minimal interpretation, there is no physical content to quantum mechanics in the absence of measurements. That's very different from Newtonian physics.

There is no physical content of any theory without measurements - if not you can't compare it to experiment so its not testable ie its not science.

The issue with QM is defining, using nothing but QM itself, what a measurement its. Great progress has been made in doing that - but some issues still remain eg some key theorems are still missing saying that it doesn't matter how you 'partition' a quantum system between what is doing the observing, what is being observed, and the environment, and any other thing you may come up with. If it can't be done or the theorem shows it depends crucially on that partition, then we have issues - I think they are probably resolvable - but current theory generally assumes you can do that. Then again in solving problems in mechanics such as balls rolling down inclined planes you make the same assumption and I do not think we have theorems for that either - however people generally do not seem to worry about it. It has long been my 'feeling' that some issues in QM people worry about are also present in other theories like probability and classical mechanics, however they are generally not worried about in those areas - except maybe by philosophers.

Thanks
Bill

 

[bhobba]

No idea what principles the "collapse postulate" contradicts. I don't understand the wave function as referring to something physically real.

It depends on your definition of the collapse postulate, and your view of the wave function. I know what Vanhees is getting at, and agree with him, but that will simply lead to a long thread that experience shows goes nowhere. We have had long threads about collapse and we (meaning the mentors) decided so as not to confuse anyone, it's when we know the outcome of an observation and that change in knowledge happens immediately. So please talk about it in that context. Its like the flipping of a coin in probability theory - we say nothing about what's going on during that flipping - but speak of the probability of an outcome.

The formalism of QM says nothing physically about what's going on during the observation - just about the probability of the outcome after it. We have speculations like MW, GRW, BM etc, but they are just that - speculations. The ensemble interpretation simply accepts the Born Rule as is with a frequentest type view of probability - it makes no assumption about what is going on during the observation, nor does it assume anybody needs to 'know' about it - so I will leave it up to you to decide if it has collapse or not. The general consensus is it doesn't.

Thabks
Bill

 

[bhobba]

Again, please read what I actually wrote. I didn't say the "real" state of the system changes. I only said the state you use to make predictions about future measurements you make on the system changes. That is true regardless of what interpretation you adopt.

Exactly. And the minimalist interpretation assumes only that. Of course when speaking about probabilities you have different views on that - Vanhees and myself take the Frequentest view - as many people in areas that apply probability do - but it is far from the only one. The frequentest view naturally leads to the Ensemble interpretation. As John Baez says much of the argument about QM interpretations is the same as arguments about what probability means:
http://math.ucr.edu/home/baez/bayes.html

Me and Vanhees do not ascribe to the Bayesian view - but really its just philosophy and in applying it makes no difference in practice - well most of the time anyway.

Thanks
Bill

 

[vanhees71]

The "minimal" interpretation of QM, which is what I thought we were discussing, does treat measurements differently from other interactions. I thought that was the point you were repeatedly making in your discussion with @vanhees71.

The problem in this discussion is that @stevendaryl claims that the interactions between an object and another object does not obey the general physical laws if the other object is used as a measurement apparatus to measure an observable on the first object. Now you also claim this. Is there some hope that one day one of you (or any other proponent of this hypothesis) could tell me what this difference may be?

For me it's an absurd idea since all our measurement devices from simple yard sticks to fancy detectors in the LHC are all constructed based on the known physical laws. There's no special law, e.g., in electrodynamics for calculating the effect of a coil in an electrical circuit, when this coil is used in an old-fashioned galvanometer to measure a current or voltage. It obeys the same laws as any other piece of matter containing electric charges and interacting with electromagnetic fields. On a microscopic level it behaves as predicted by QED (of coarse effectively here you can safely use classical electrodynamics as an excellent approximation).

 

[Boing3000]

If it can't be done or the theorem shows it depends crucially on that partition, then we have issues - I think they are probably resolvable - but current theory generally assumes you can do that.

I thought it has been explained in this thread that the minimal interpretation exclude this assumption (of a possible derivation). By making measurement it axiomatic, any proof would be circular (within this interpretation).

Then again in solving problems in mechanics such as balls rolling down inclined planes you make the same assumption and I do not think we have theorems for that either - however people generally do not seem to worry about it.

I don't understand what you mean. There is absolutely no assumption made in classical mechanics. Measurement is not a special case, and actually does perturb the observed system (the actual source confusion with QM uncertainty principle). But those who care for those effects can use the same classical theory to get perfect/complete knowledge (up to precision) of the (very small) perturbation.

That's another reason why the claim that QM is complete is quite preposterous. "Measurement" of quanta, that Vanhees71 seems to deny the existence of, and instead only consider ensemble to be real (without bothering to define where those ensemble start or end), do something much more dramatic (picking of eigenvalue) that modify the state irreversibly in a huge manner.

Whatever how measurement do this "trick", it happens, on a event by event basis. Because every measurement, classic or quantum, is event base. But QM is incomplete because it need to process many event/measurement before it even can pretend to be "scientific" that is: verifiable.

(Also I will remind that QM have no clue about why the state of the apple move toward the state of the earth)

It has long been my 'feeling' that some issues in QM people worry about are also present in other theories like probability and classical mechanics, however they are generally not worried about in those areas - except maybe by philosophers.

I would be interested in such a discussion (maybe in another thread) about those "issues", my feeling is all the weirdness of classical theories a perfectly described by chaos...

 

[Boing3000]

The problem in this discussion is that @stevendaryl claims that the interactions between an object and another object does not obey the general physical laws if the other object is used as a measurement apparatus to measure an observable on the first object. Now you also claim this.

None of this claims have been made (quite the contrary). Instead you have denied that the "physical law" in question contains an explicit category difference between interaction and measurement. You are also denying that classical law does not need such a dichotomy.

 

[Lord Jestocost]

The problem in this discussion is that @stevendaryl claims that the interactions between an object and another object does not obey the general physical laws if the other object is used as a measurement apparatus to measure an observable on the first object. Now you also claim this. Is there some hope that one day one of you (or any other proponent of this hypothesis) could tell me what this difference may be?

For me it's an absurd idea since all our measurement devices from simple yard sticks to fancy detectors in the LHC are all constructed based on the known physical laws. There's no special law, e.g., in electrodynamics for calculating the effect of a coil in an electrical circuit, when this coil is used in an old-fashioned galvanometer to measure a current or voltage. It obeys the same laws as any other piece of matter containing electric charges and interacting with electromagnetic fields. On a microscopic level it behaves as predicted by QED (of coarse effectively here you can safely use classical electrodynamics as an excellent approximation).

Physical interactions between objects follow - so to speak - a law. As Jonathan Allday remarks in "Quantum Reality": "Any interaction between two quantum systems will entangle their states together. Consequently, the entanglement spreads like an infectious disease." Measurement-as-interaction doesn't work, or do I have missed some hidden ideas.

 

[vanhees71]

None of this claims have been made (quite the contrary). Instead you have denied that the "physical law" in question contains an explicit category difference between interaction and measurement. You are also denying that classical law does not need such a dichotomy.

Again for me this is the very statement, I don't buy. There is no difference between interaction and measurement. This is vaguely formulated, so maybe I understand you and other proponents of this claim in this thread in a wrong way. For me this says that you and others claim that there's a difference in the interaction of the measured object with the measurement apparatus and all other interactions. This doesn't make sense to me since the same physical laws apply to interactions no matter whether it's the interaction with a measurement apparatus or not. Neither in classical nor in quantum theory is any dichotomy in the applicability of the rules to measurement apparati and other objects. Measurement apparati are made of the same stuff as anything else, and also all physical laws apply to measurement devices as to any other object. That's all I'm claiming. This is also completely independent from which metaphysical additional interpretational ideas you follow on top of the postulates of the minimal statistical interpretation, which is, as its name says, the minimal set of postulates you need to make a physical theory out of the mathematical formalism used in quantum theory.

Maybe we have to reformulate our claims, but I don't know, in which way I can reformulate mine. Perhaps I try to speculate what's the reason for our mutual misunderstanding. One that comes to my mind now is that it may be that you want to give an ontological meaning to the mathematical description used in physical theories, while I have an epistemic view. This concerns particularly the notion of "state" in both classical and quantum theory. In classical theory a state is given by a point in phase space (the "initial state"), in quantum theory it's the statistical operator (in the Heisenberg picture for a closed system it's time-independent). Both phase space in classical mechanics and the operators in Hilbert space are representing properties of observable facts about objects, described in an abstract mathematical way. The relation to physics is given by their relation to observations and measurements of appropriate observables. In classical physics the meaning is deterministic, i.e., all observables (i.e., quantifiable and objectively measurable properties) are always determined, and a probabilistic description is only necessary if we have not complete knowledge about the state of the system. In QT the description is explicitly probabilistic, and there's no other way within QT to describe systems. Due to the mathematically derivable uncertainty relation between incompatible observables it follows immediately that not all observables can be determine, no matter which state the system is in. That's the only profound difference between QT and classical theory: QT is indeterministic in the sense that necessarily not all observables can take definite values, while classical theory is deterministic since all observables always take a determined value.

 

[bhobba]

I thought it has been explained in this thread that the minimal interpretation exclude this assumption (of a possible derivation). By making measurement it axiomatic, any proof would be circular (within this interpretation).

There is an argument using what's called coarse gaining to derive the classical world from the quantum - as indeed you must have if it is to be a more fundamental theory than classical:
http://web.physics.ucsb.edu/~quniverse/papers/cop-ext2.pdf

Another way is using the path integral approach to easily explain the PLA from QM and hence classical mechanics. In fact Landau showed that and symmetry is basically all you need to derive classical mechanics, so in a sense all classical mechanics is, is QM in a certain limit - namely the limit where only stationary paths exist because that is the only case where a nearby path doesn't cancel out.

So it is not quite true that the minimalist interpretation doesn't allow one to be more precise about how the classical world emerges from the quantum. And once you do that it's possible to be more precise about exactly what a measurement is than an accepted primitive. But there are still issues with this approach even though a lot of progress has been made. Decoherent Histories for example tries to express QM in terms of histories, which are coarse grainings - the very thing used in deriving the classical world. But it is still an approach that is not totally developed. As an aside it was Feynmans view just before he died.

I would say in probability using the Kolmogerov axioms, event and its axioms is a primitive. From that abstract probability theory is derived. But you can derive things like the law of large numbers and likely other things that shed more light on exactly what this abstract thing probability is. I think the same with observation/measurement as an accepted primitive.

In QM the theory starts with measurement as primitives, leading to the minimalist interpretation, then sharpened up as it is developed. Approaches are around eg Quantum Darwinism, Decoherent Histories, Many Worlds, that try from the start to have the concept of measurement emerge from the theory - but issues still remain.

Thanks
Bill

 

[vanhees71]

Physical interactions between objects follow - so to speak - a law. As Jonathan Allday remarks in "Quantum Reality": "Any interaction between two quantum systems will entangle their states together. Consequently, the entanglement spreads like an infectious disease." Measurement-as-interaction doesn't work, or do I have missed some hidden ideas.

But how then is it possible that we construct all our measurement devices based on the known physical laws? Measurement always requires the interaction of the measured object with the measurement device, and in constructing our instruments we assume that this interaction follows the known rules. E.g., most photon detectors assume that in the photon-detector material the laws describing the photoelectric effect are due to quantum electrodynamics. The photon doesn't care whether the atom it hits and "frees" one of its electrons sits in a usual chunk of matter or whether it's part of a photodetector.

Also the very goal of a measurement is in fact to entangle the measured observable of the object with the pointer reasings of the measurment device, so that the pointer readings uniquely measure this observable.

Take the Stern-Gerlach experiment. The measured quantity is a component of the magnetic moment of the particle, and thus you let it run through an appropriately tuned inhomogeneous magnetic field (superimposed with a large practically homogeneous field which determines the direction of the measured component of the magnetic moment). Properly designed this leads to an entanglement of position and the to-be-measured component of the magnetic moment of the particle. The pointer observable here is the position of the particle, which can very easily measured by letting the particle interact with a screen. Using many equaly prepared particles you get a pattern on the screen whose intensity distribution gives the probability distribution for the various values the measured component of the magnetic moment can take. This setup is even simple enough that you can use it as a preparation procedure in the sense of a von Neumann filter measurement (with a careful design of the magnetic field you can make it even very close to an ideal one): You just absorb all the partial beams you don't want and keep only the one beam whose position refers to the wanted value of the component of the magnetic moment. This is all analyzed within quantum theory. Nowhere do I need special rules for interactions and nowhere do I need a classical approximation (although under the discussed conditions the WKB approximation is fully satisfactory).

 

[atyy]

But how then is it possible that we construct all our measurement devices based on the known physical laws? Measurement always requires the interaction of the measured object with the measurement device, and in constructing our instruments we assume that this interaction follows the known rules. E.g., most photon detectors assume that in the photon-detector material the laws describing the photoelectric effect are due to quantum electrodynamics.

Because the cut can be shifted. You can shift the cut, so that the measuring apparatus is quantum, but without a "classical" or "macroscopic" measuring apparatus to measure the quantum apparatus, quantum theory makes no predictions. In modern terminology, the quantum part of the apparatus is usually called an "ancilla".

 

[vanhees71]

Well, the very fact that proponents of a quantum-classical cut always agree that the cut can shifted arbitrarily shows that the cut is as unnecessary as the aether in classical electromagnetics.

 

[PeterDonis]

the very fact that proponents of a quantum-classical cut always agree that the cut can shifted arbitrarily shows that the cut is as unnecessary as the aether in classical electromagnetics.

No, it doesn't, it shows that quantum mechanics as currently formulated is an incomplete theory. A cut is required to extract predictions from the theory, but the theory does not tell you where to put the cut; practically speaking, physicists put it wherever it works best in making predictions for a particular problem.

 

[atyy]

Well, the very fact that proponents of a quantum-classical cut always agree that the cut can shifted arbitrarily shows that the cut is as unnecessary as the aether in classical electromagnetics.

But you cannot shift it completely arbitrarily - it cannot be shifted such that the whole universe is quantum, unless perhaps one introduces hidden variables or MWI.

 

[vanhees71]

Hm, where do my experimental colleagues at CERN make some arbitrary cut when constructing their detectors?

 

[atyy]

Hm, where do my experimental colleagues at CERN make some arbitrary cut when constructing their detectors?

When they apply the Born rule :)

 

[PeterDonis]

where do my experimental colleagues at CERN make some arbitrary cut when constructing their detectors?

The cut isn't in the actual experimental devices; it's in the theory. As I said in post #176: "a cut is required to extract predictions from the theory". Extracting predictions from the theory is not the same as running experiments. And the fact that there is obviously no cut in the experimental devices, whereas you need one to extract predictions from the theory, is just another way of putting what I said in post #176, that QM as currently formulated is an incomplete theory.

 

[vanhees71]

But you cannot shift it completely arbitrarily - it cannot be shifted such that the whole universe is quantum, unless perhaps one introduces hidden variables or MWI.

That's true. The entire universe cannot be described quantum theortically within the minimal interpretation, because you cannot define what's observable about it, because for that you'd need to prepare many universes in the same initial state to investigate whether the probabilistic meaning of the state is correctly predicting its behavior.

 

[vanhees71]

The cut isn't in the actual experimental devices; it's in the theory. As I said in post #176: "a cut is required to extract predictions from the theory". Extracting predictions from the theory is not the same as running experiments. And the fact that there is obviously no cut in the experimental devices, whereas you need one to extract predictions from the theory, is just another way of putting what I said in post #176, that QM as currently formulated is an incomplete theory.

Hm, I don't need a cut to describe heavy-ion collisions and compare it to experiment. I just calculate the quantities, like dilepton invariant-mass and transverse-momentum spectra and compare them with the experimental results. Of course, these spectra are the collection of data from an ensemble ("the more statistics the better").

 

[atyy]

Hm, where do my experimental colleagues at CERN make some arbitrary cut when constructing their detectors?

Also, it must be admitted (von Neumann knew this, and it is discussed in the textbook by Wiseman and Milburn) the cut is not entirely arbitrary: https://arxiv.org/abs/quant-ph/9712044.

 

[vanhees71]

Ok, if the application of the Born rule is a cut, that's fine with me. But why should I call it a cut?

 

[atyy]

Ok, if the application of the Born rule is a cut, that's fine with me. But why should I call it a cut?

Because the point at which you decide to apply the Born rule comes from "outside" the quantum system - the initial quantum state and Schroedinger equation does not tell you when the Born rule is applied.

 

[vanhees71]

Also, it must be admitted (von Neumann knew this, and it is discussed in the textbook by Wiseman and Milburn) the cut is not entirely arbitrary: https://arxiv.org/abs/quant-ph/9712044.

I'd say von Neumann was very far away from a physical understanding of QT. His merit is in the proper mathematical formulation. His solipsistic Princeton Interpretation, however, is the worst flavor of the Copenhagen spirit ever.

I've to read the paper to comment it. As far as I see for usual measurements using a usual observable as a pointer there's really no problem with putting the cut anywhere, where a classical description is sensible.

 

[vanhees71]

Because the point at which you decide to apply the Born rule comes from "outside" the quantum system - the initial quantum state and Schroedinger equation does not tell you when the Born rule is applied.

No. Also Newton's equation of motion doesn't tell me when I look at the point particle I describe. Why should it?

 

[martinbn]

I thought that QT can make predictions without any cut. Say, if you smash these particles, then the probability to get those is so and so. No cut and a very spesific prediction. Or something along the lines a black hole will radiate and loose energy, no cut. Or is the cut somewhere implicit.

 

[atyy]

No. Also Newton's equation of motion doesn't tell me when I look at the point particle I describe. Why should it?

Because in classical mechanics the particle is there whether you look at it or not. In quantum mechanics, the formalism does not assign the particle a position until you look at it.

In quantum mechanics, there is a fundamental difficulty with applying the quantum state to the whole universe including the observer. In classical mechanics, there is no equivalent difficulty (there is a difficulty to include the whole universe from the singularities of GR, but that is different from needing to exclude the observer).

 

[martinbn]

In classical mechanics, there is no equivalent difficulty (there is a difficulty from the singularities of GR, but that is different from needing to exclude the observer).

Why is that? I mean the part in the parentheses.

 

[Demystifier]

I thought that QT can make predictions without any cut. Say, if you smash these particles, then the probability to get those is so and so. No cut and a very spesific prediction. Or something along the lines a black hole will radiate and loose energy, no cut. Or is the cut somewhere implicit.

Yes, the cut is implicit in your expression "to get". This really means "to observe" or "to measure by macroscopic apparatus", so you need a cut in order to distinginsh observers from non-observers or macroscopic from non-macroscopic.

 

[martinbn]

Yes, the cut is implicit in your expression "to get". This really means "to observe" or "to measure by macroscopic apparatus", so you need a cut in order to distinginsh observers from non-observers or macroscopic from non-macroscopic.

I don't get it. To make it specific let's look at the following. The probability that a photon will decay to a proton is zero. What measurement is needed to make this prediction?

 

[Demystifier]

I don't get it. To make it specific let's look at the following. The probability that a photon will decay to a proton is zero. What measurement is needed to make this prediction?

It's not a good example. Give me an example in which probability is neither zero nor one.

 

[martinbn]

I didn't mean that all predictions can be made without a cut. I said that the theory can make predictions without a cut.

 

[Demystifier]

Also Newton's equation of motion doesn't tell me when I look at the point particle I describe. Why should it?

Newton's equation is a statement of the form "position of the particle is such and such". It is not a statement of the form "When position of the particle is measured, then position of the particle is such and such".

But quantum mechanics is different. QM does not state that "probability of the position of the particle is such and such". It states that "When position of the particle is measured, then probability of the position of the particle is such and such".

 

[Demystifier]

I didn't mean that all predictions can be made without a cut. I said that the theory can make predictions without a cut.

But if some predictions cannot be made without a cut, then QM as a whole needs a cut.

Just as real numbers, as a whole, need Dedekind cuts, despite the fact that some real numbers (the rational ones) don't need Dedekind cuts.

 

[martinbn]

But if some predictions cannot be made without a cut, then QM as a whole needs a cut.

Yes, but somewhere above it was said that the theory cannot make predictions without a cut.

 

[Demystifier]

Yes, but somewhere above it was said that the theory cannot make predictions without a cut.

That statement, taken literally, was wrong. But it's clear (at least to me) that atyy wanted to say that the theory cannot make some of its predictions without a cut.

 

[bhobba]

that QM as currently formulated is an incomplete theory.

You could put it that way, and I would not argue it. However it depends on how you look at it. I prefer to say right now we have some unresolved issues - progress definitely has been made and research is ongoing. You can say observation is a primitive and all theories have primitives. I am not sure it does resolve it - but is it physics? To me it may be a bit semantic and what philosophers argue about. Personally I tend to side with Dirac and think all theories have issues and we just keep progressing and chipping away - it's very hard to predict where it will lead. I have posted it before, but just for completeness in case someone has not seen it see:
http://philsci-archive.pitt.edu/1614/1/Open_or_Closed-preprint.pdf

Thanks
Bill

 

[RUTA]

I didn't realize how close to this "minimalist interpretation" our interpretation was. We're saying the fundamental explanation for the QM correlations is conservation (of whatever) on average, not trial by trial. What we mean by "fundamental explanation" is that there is nothing deeper to explain this conservation principle. I just updated the arXiv version of the paper (will appear Mon -- I keep it updated at users.etown.edu/s/stuckeym/TsirelsonBound.pdf) which contains this:

Thus, we see explicitly in this result how quantum mechanics conforms statistically to a conservation principle without need of a `causal influence' or hidden variables acting on a trial-by-trial basis to account for that conservation. There are many attempts to add such classical mechanisms, but they are superfluous as far as the physics is concerned. The light postulate of special relativity is a good analogy for our proposed constraint. That is, ``the speed of light c is the same in all reference frames'' explains time dilation, length contraction, etc., but there is nothing to explain the light postulate. Likewise, ``conservation per no preferred reference frame'' (the most general form of our constraint) explains the Tsirelson bound, but there is nothing to explain that conservation principle (constraint).

That looks very similar to what the minimalist interpretation is calling an ensemble interpretation of the wave function. Further, the measured values proper are what contribute directly to this conversation. That is, whether or not there is some underlying or hidden "true" value of the angular momentum giving rise to what is measured is irrelevant, it is the actual measured values that account for the conservation.