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

[vanhees71]

I'm asking: What does it mean to measure something? Informally, I measured some property if I performed an action so that afterward, I know its value. That way of phrasing it sounds very solipsistic. Must there be a person around in order for quantum probabilities to be meaningful?

An alternative is to say that system A measures a property of system B if through interacting, the state of system A becomes correlated with that of system B and the alternative values of the property are macroscopically distinguishable. But that way of understanding it makes a macroscopic/microscopic distinction, which you claim not to be making.

That's again very easy. Measuring something means to compare the measured quantity with a unit which is defined by a real-world measuring procedure (or more precistely an equivalence class of measurement procedures; e.g., to measure the width of my office I can either use a simple yardstick or nowadays a laser rangefinder, but both measurements define the same quantity "length" of course).

Of course, on my opinion the probabilities of quantum theory do not need any human being to take note about the outcome of the measurement. I thought that's behind your insistence on the claim that QT necessarily implies that the universal physical laws do not hold for measurement devices.

Of coarse, I make this macroscopic-microscopic distinction, but I don't claim that there is a fundamental quantum-classical cut. The classical behavior of macroscopic objects, needed to make a measurement (this is one of the few things I think Bohr in fact got right), is however derivable from standard quantum theory in the minimal interpretation. It's based on using only averaged macroscopic observables of the macroscopic system, which are accurate enough to describe its behavior.

For measurement devices that's not different. Of course it has to interact with the measured object and gets entangled with this object in a way that a macroscopic pointer reading allows to uniquely read off the value of the measured observable.

 

[stevendaryl]

@vanhees71, can you at least admit that Newton's laws of motion do not mention measurements? But the axioms of the "minimalist interpretation" do mention measurements?

1. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
2. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma.
3. For every action there is an equal and opposite reaction.

None of those mention "measurement". I don't see how there is room to argue about that.

 

[stevendaryl]

That's again very easy. Measuring something means to compare the measured quantity with a unit which is defined by a real-world measuring procedure (or more precistely an equivalence class of measurement procedures; e.g., to measure the width of my office I can either use a simple yardstick or nowadays a laser rangefinder, but both measurements define the same quantity "length" of course).

Of course, on my opinion the probabilities of quantum theory do not need any human being to take note about the outcome of the measurement. I thought that's behind your insistence on the claim that QT necessarily implies that the universal physical laws do not hold for measurement devices.

Of coarse, I make this macroscopic-microscopic distinction, but I don't claim that there is a fundamental quantum-classical cut.

I don't really care about the quantum-classical cut, and I haven't mentioned that. But you now agree that the minimal interpretation treats macroscopic interactions differently than microscopic interactions? Surely, one electron scattering off another does not constitute a measurement?

 

[vanhees71]

No, any physical theory has to be able to model measurements. But the mathematical machinery of QM, the thing that makes predictions, does much more than that: it tells you, "when a measurement occurs, use the Born rule to calculate the probabilities of the possible outcomes". No other physical theory has a rule like that embedded in its mathematical machinery. Newton's Laws, to use the example you have been using, don't tell you "when a measurement occurs, use F = ma", for example. They just say "F = ma".

Quantum theory also simply says $\mathrm{i} \partial_t |\psi(t) \rangle=\hat{H} |\psi(t) \rangle$. This is as empty a mathematical phrase as $F=ma$ if you don't tell what it has to do with observables, i.e., measurable quantities. The only meaning of force, mass, and acceleration in Newtonian mechanics is through measurement procedures enabling you to measure these quantities. The same holds for state vectors: Together with eigenvectors of self-adjoint operators, representing the observables in the quantum formalism, its physical meaning is through the possibility to measure this observable on an ensemble of equally prepared systems (that's the difference to Newtonian physics indeed: you only make probabilistic statements which need an ensemble to be experimentally tested). The meaning is given by Born's rule, of course: $P(t,a)=|\langle a|\psi(t) \rangle|^2$ is the probability (distribution) to find the value $a$ when measuring the observable $A$, represented by the self-adjoint operator $\hat{A}$ and $|a \rangle$ being the eigenvector to the eigenvalue $a$ (assuming for simplicity non-degeneracy of the measured observable).

 

[vanhees71]

I don't really care about the quantum-classical cut, and I haven't mentioned that. But you now agree that the minimal interpretation treats macroscopic interactions differently than microscopic interactions? Surely, one electron scattering off another does not constitute a measurement?

No, I haven't said this. To the contrary I stated that macrscopic properties are emergent and derivable from quantum theory, using the universal physical laws of quantum theory.

I think we should end this discussion at this point since obviously we are not able to come to a conclusion anyway, and it's no longer of much use for any of the physics forum's readers.

 

[stevendaryl]

No, I haven't said this. To the contrary I stated that macrscopic properties are emergent and derivable from quantum theory, using the universal physical laws of quantum theory.

I don't see how that can possibly be. The issue is that you have to select a basis in order for quantum mechanics to have meaningful probabilities. So in a sense, there are no probabilities at the microscopic level, because microscopically, there is no basis selected. And since the laws of quantum mechanics (in the minimalist interpretation) only describe how probability amplitudes evolve, there would be no such thing as "universal physical laws" at the microscopic level, according to the minimalist interpretation. So there would be no way for macroscopic properties to be emergent from microscopic laws.

 

[PeterDonis]

Quantum theory also simply says $\mathrm{i} \partial_t |\psi(t) \rangle=\hat{H} |\psi(t) \rangle$.

No, it doesn't. It also says to use the Born rule to calculate probabilities when a measurement occurs. There is no such rule in Newtonian mechanics.

This is as empty a mathematical phrase as $F=ma$ if you don't tell what it has to do with observables, i.e., measurable quantities.

I agree that any physical theory has to tell you how to relate the mathematical symbols that appear in the theory to the quantities that are actually measured in experiments. But, again, QM, unlike any other physical theory, does much more than this.

 

[stevendaryl]

Quantum theory also simply says $\mathrm{i} \partial_t |\psi(t) \rangle=\hat{H} |\psi(t) \rangle$. This is as empty a mathematical phrase as $F=ma$ if you don't tell what it has to do with observables, i.e., measurable quantities.

They aren't comparable, at all. In the case of Newtonian mechanics, you have a description of how objects behave in the absence of any observers or measurements at all. Then to make the connection with observation/measurement, you only need to make the assumption that your measuring device is a particular system obeying Newton's laws. The fact that a spring scale measures mass follows from the assumptions that (1) the length of a spring is proportional to the force applied, and (2) the force on an object due to gravity is proportional to its mass. Together, these assumptions about a scale as a physical object imply that a scale will measure mass.

The contrast with the Hamiltonian dynamics of quantum mechanics is enormous.

Yes, you can describe the measurement device as a quantum-mechanical system. You can give it a Hamiltonian and describe how the measurement device interacts with the system being measured. But what that doesn't get you is:

1. The claim that a measurement of a property always gives an eigenvalue of the thing being measured.
2. The claim that the probabilities for the various outcomes is given by the square of the corresponding amplitudes in the decomposition of the state into eigenstates of the corresponding operator.

So if you want $\mathrm{i} \partial_t |\psi(t) \rangle=\hat{H} |\psi(t) \rangle$ to be the analog of Newton's laws, then it is clear that it doesn't work in the way that Newton's laws do. Without additional assumptions about measurements, you can't get any measurement results from that dynamical equation.

 

[vanhees71]

No, it doesn't. It also says to use the Born rule to calculate probabilities when a measurement occurs. There is no such rule in Newtonian mechanics.
I agree that any physical theory has to tell you how to relate the mathematical symbols that appear in the theory to the quantities that are actually measured in experiments. But, again, QM, unlike any other physical theory, does much more than this.

No, it precisely tells you about the meaning of the symbols used in the formalism. The probabilities according to Born's rule are the physics content of the theory, and as far as I can see the only physics content. It's probabilistic, and if QT is complete (which I don't know of course, because you can never know, whether any physical theory is complete in the sense that it describes right all of the possible observations of Nature), that's all there is.

The only difference is that Newtonian mechanics (and all of classical physics) is deterministic, i.e., the notion of state is different in the sense that knowing the exact state means to know the precise trajectory in phase space (which can be finite-dimensional as for point particle systems in classical mechanics of infinitely-dimensional as in the classical field theories) implies to precisely know the values of all possible observables of the system. In contradistinction to that QT is probabilistic, i.e., knowing the precise state of a system (i.e., being able to prepare it in a pure state) does not imply that all observables take determined values. It's even shown through the Heisenberg-Robertson uncertainty relation that you cannot prepare a state in which all observables take determined values, but that's the only difference.

As long as there is no deterministic (then necessarily non-local) theory that describes all phenomena, I fear we have to live with the probabilistic description of QT. Nature doesn't ask what we like to have but she is just as she is, and that's what physicists are aiming to figure out through more and more refined observations and mathematical models and theories.

 

[vanhees71]

They aren't comparable, at all. In the case of Newtonian mechanics, you have a description of how objects behave in the absence of any observers or measurements at all. Then to make the connection with observation/measurement, you only need to make the assumption that your measuring device is a particular system obeying Newton's laws. The fact that a spring scale measures mass follows from the assumptions that (1) the length of a spring is proportional to the force applied, and (2) the force on an object due to gravity is proportional to its mass. Together, these assumptions about a scale as a physical object imply that a scale will measure mass.

I can just use your sentence with a little change:

In the case of quantum mechanics, you have a description of how objects behave in the absence of any observers or measurements at all. It doesn't become wrong. The formalism precisely tells you how the state evolves with time, given the Hamiltonian of the system. If there's no interaction with a measurement apparatus this describes the system without measuring or observing it.

In Newtonian mechanics you also describe the state of the system without considering measurements as long as you choose not to include the interaction of the system with the measurement apparatus.

 

[stevendaryl]

I can just use your sentence with a little change:

In the case of quantum mechanics, you have a description of how objects behave in the absence of any observers or measurements at all. It doesn't become wrong. The formalism precisely tells you how the state evolves with time, given the Hamiltonian of the system. If there's no interaction with a measurement apparatus this describes the system without measuring or observing it.

In Newtonian mechanics you also describe the state of the system without considering measurements as long as you choose not to include the interaction of the system with the measurement apparatus.

Except that in your first paragraph, you completely left out probabilities.

 

[stevendaryl]

No, it precisely tells you about the meaning of the symbols used in the formalism. The probabilities according to Born's rule are the physics content of the theory, and as far as I can see the only physics content.

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.

 

[stevendaryl]

The only difference is that Newtonian mechanics (and all of classical physics) is deterministic, i.e., the notion of state is different in the sense that knowing the exact state means to know the precise trajectory in phase space (which can be finite-dimensional as for point particle systems in classical mechanics of infinitely-dimensional as in the classical field theories) implies to precisely know the values of all possible observables of the system. In contradistinction to that QT is probabilistic, i.e., knowing the precise state of a system (i.e., being able to prepare it in a pure state) does not imply that all observables take determined values. It's even shown through the Heisenberg-Robertson uncertainty relation that you cannot prepare a state in which all observables take determined values, but that's the only difference.

The only difference between ice cream and sand is that ice cream is cold and sweet and soft and sand is not. In other words, there is almost no similarity.

The notion of state in the minimalist interpretation of quantum mechanics is that it gives probabilities for measurement results. You can't then turn around and say that a measurement result is just another physical property like any other. No other interaction besides measurements results in probabilistic outcomes.

 

[stevendaryl]

It seems clear to me that quantum mechanics in the minimalist interpretation makes an essential distinction between measurements and other interactions. If you take $H |\psi\rangle = i \hbar \frac{\partial}{\partial t} |\psi\rangle$ as the equivalent of Newton's laws, then those laws don't describe the two most fundamental empirical facts about quantum mechanics: The fact that measurements result in eigenvalues of the thing being measured, and the the fact that the probabilities are given by the Born rule. Those are new elements that must be introduced into the physics to accommodate measurements.

That's very different from the case of pre-quantum physics. In pre-quantum physics, there are no additional physical laws needed to describe measurement. It is enough to model a measurement device or an observer as a physical system obeying the laws of physics. Then the properties of measurements follow from the rest of the laws of physics.

 

[Lord Jestocost]

Quantum theory also simply says i∂t|ψ(t)⟩=^H|ψ(t)⟩\mathrm{i} \partial_t |\psi(t) \rangle=\hat{H} |\psi(t) \rangle. This is as empty a mathematical phrase as F=maF=ma if you don't tell what it has to do with observables, i.e., measurable quantities.

In order to make clear that quantum mechanics and Newtonian mechanics aren't comparable in such a simple manner, let me quote Maximilian Schlosshauer/1/ more extensively:

“One way of identifying the root of the problem [the measurement problem] is to point to the apparent dual nature and description of measurement in quantum mechanics. On the one hand, measurement and its effect enter as a fundamental notion through one of the axioms of the theory. On the other hand, there’s nothing explicitly written into these axioms that would prevent us from setting aside the axiomatic notion of measurement and instead proceeding conceptually as we would do in classical physics. That is, we may model measurement as a physical interaction between two systems called “object” and “apparatus”—only that now, in lieu of particles and Newtonian trajectories, we’d be using quantum states and unitary evolution and entanglement-inducing Hamiltonians.


What we would then intuitively expect—and perhaps even demand—is that when it’s all said and done, measurement-as-axiom and measurement-as-interaction should turn out to be equivalent, mutually compatible ways of getting to the same final result. But quantum mechanics does not seem to grant us such simple pleasures. Measurement-as-axiom tells us that the post-measurement quantum state of the system will be an eigenstate of the operator corresponding to the measured observable, and that the corresponding eigenvalue represents the outcome of the measurement. Measurement-as-interaction, by contrast, leads to an entangled quantum state for the composite system-plus-apparatus. The system has been sucked into a vortex of entanglement and no longer has its own quantum state. On top of that, the entangled state fails to indicate any particular measurement outcome.


So we’re not only presented with two apparently mutually inconsistent ways of describing measurement in quantum mechanics, but each species leaves its own bad taste in our mouth.”

/1/ M. Schlosshauer (ed.), Elegance and Enigma, The Quantum Interviews, Springer-Verlag Berlin Heidelberg 2011, pp. 141-142

 

[stevendaryl]

In order to make clear that quantum mechanics and Newtonian mechanics aren't comparable in such a simple manner, let me quote Maximilian Schlosshauer/1/ more extensively:

“One way of identifying the root of the problem [the measurement problem] is to point to the apparent dual nature and description of measurement in quantum mechanics. On the one hand, measurement and its effect enter as a fundamental notion through one of the axioms of the theory. On the other hand, there’s nothing explicitly written into these axioms that would prevent us from setting aside the axiomatic notion of measurement and instead proceeding conceptually as we would do in classical physics. That is, we may model measurement as a physical interaction between two systems called “object” and “apparatus”—only that now, in lieu of particles and Newtonian trajectories, we’d be using quantum states and unitary evolution and entanglement-inducing Hamiltonians.


What we would then intuitively expect—and perhaps even demand—is that when it’s all said and done, measurement-as-axiom and measurement-as-interaction should turn out to be equivalent, mutually compatible ways of getting to the same final result. But quantum mechanics does not seem to grant us such simple pleasures. Measurement-as-axiom tells us that the post-measurement quantum state of the system will be an eigenstate of the operator corresponding to the measured observable, and that the corresponding eigenvalue represents the outcome of the measurement. Measurement-as-interaction, by contrast, leads to an entangled quantum state for the composite system-plus-apparatus. The system has been sucked into a vortex of entanglement and no longer has its own quantum state. On top of that, the entangled state fails to indicate any particular measurement outcome.


So we’re not only presented with two apparently mutually inconsistent ways of describing measurement in quantum mechanics, but each species leaves its own bad taste in our mouth.”

/1/ M. Schlosshauer (ed.), Elegance and Enigma, The Quantum Interviews, Springer-Verlag Berlin Heidelberg 2011, pp. 141-142

Exactly!

 

[vanhees71]

What we would then intuitively expect—and perhaps even demand—is that when it’s all said and done, measurement-as-axiom and measurement-as-interaction should turn out to be equivalent, mutually compatible ways of getting to the same final result. But quantum mechanics does not seem to grant us such simple pleasures. Measurement-as-axiom tells us that the post-measurement quantum state of the system will be an eigenstate of the operator corresponding to the measured observable, and that the corresponding eigenvalue represents the outcome of the measurement. Measurement-as-interaction, by contrast, leads to an entangled quantum state for the composite system-plus-apparatus. The system has been sucked into a vortex of entanglement and no longer has its own quantum state. On top of that, the entangled state fails to indicate any particular measurement outcome.

That's a problem only if you believe in the necessity of the collapse postulate, which is not necessary at all. It even contradicts fundamental principles (relativistic spacetime structure) and it's almost always not what happens in real experiments. Of course, in some simple cases you can perform von Neumann filter measurements, but this also is within the realm of "measurement-as-interaction" as anything else, as far as quantum theory is considered complete (and today there's nothing known pointing to some incompleteness at all).

 

[vanhees71]

It seems clear to me that quantum mechanics in the minimalist interpretation makes an essential distinction between measurements and other interactions. If you take $H |\psi\rangle = i \hbar \frac{\partial}{\partial t} |\psi\rangle$ as the equivalent of Newton's laws, then those laws don't describe the two most fundamental empirical facts about quantum mechanics: The fact that measurements result in eigenvalues of the thing being measured, and the the fact that the probabilities are given by the Born rule. Those are new elements that must be introduced into the physics to accommodate measurements.

That's very different from the case of pre-quantum physics. In pre-quantum physics, there are no additional physical laws needed to describe measurement. It is enough to model a measurement device or an observer as a physical system obeying the laws of physics. Then the properties of measurements follow from the rest of the laws of physics.

Of course, besides the dynamical laws there are kinematical laws (you have to formulate first). I thought, the quantum postulates of the minimal interpretation are well-known enough, as we have discussed this over and over in the past. Obviously that's not the case. So here are the kinematical postulates again.

(1) A quantum system is defined by an Hilbert space and a realization of an algebra of observables.
(2) Observables are represented by self-adjoint operators, densely defined on Hilbert space (which implies that their (generalized) eigenstates form a complete set). The possible values of the so represented observables are given by the spectrum of these operators.
(3) States are represented by a self-adjoint positive semi definite operator $\hat{\rho}$.
(4) The probability for finding an observable $A$ to have the value $a$ in the spectrum of its representing operator $\hat{A}$ is given by
$$P(a|\hat{\rho})=\sum_{\beta} \langle a,\beta|\hat{\rho}|a,\beta \rangle.$$
Here, $\beta$ for each $a$ label the orthonormalized eigenvectors of $\hat{A}$ with eigenvalue $a$ (of course $\beta$ can also be continuous, but that's only a mathematical detail, unimportant for our discussion).

As in classical physics also in quantum physics measurements are not described by theory but done in the lab. Of course, the measurement devices are constructed based on knowledge about the known laws of physics. How else should you be able to construct them?

 

[stevendaryl]

That's a problem only if you believe in the necessity of the collapse postulate, which is not necessary at all.

I don't see how there is any physical content to the minimal interpretation without the collapse hypothesis. You measure an electron's spin relative to the z-axis. You find it's spin-up. Does that mean that your measurement device is in the state of "having measured a spin-up electron", or not?

I assume that it does mean that. Then you have a contradiction. On the one hand, you computed the state of the measurement device using quantum mechanics, and you found that it's entangled, and has no state of its own, but that the entire system is in a superposition of "the electron is spin-up and the measurement device measured spin-up and the environment is whatever is appropriate for a measurement device that measured spin-up" and "the electron is spin-down and all that entails". On the other hand, you see that the measurement device is in a particular state---having measured a spin-up electron. The wave function corresponding to that state is a different state than the wave function corresponding to the entangled state. You have a contradiction.

If you want to say that measuring the electron to have spin-up doesn't imply anything about the state of the measurement device, then it seems to me that you've abandoned the whole point of measurement, which is to give information about the world.

 

[stevendaryl]

Of course, besides the dynamical laws there are kinematical laws (you have to formulate first). I thought, the quantum postulates of the minimal interpretation are well-known enough, as we have discussed this over and over in the past. Obviously that's not the case. So here are the kinematical postulates again.

(1) A quantum system is defined by an Hilbert space and a realization of an algebra of observables.
(2) Observables are represented by self-adjoint operators, densely defined on Hilbert space (which implies that their (generalized) eigenstates form a complete set). The possible values of the so represented observables are given by the spectrum of these operators.
(3) States are represented by a self-adjoint positive semi definite operator $\hat{\rho}$.
(4) The probability for finding an observable $A$ to have the value $a$ in the spectrum of its representing operator $\hat{A}$ is given by
$$P(a|\hat{\rho})=\sum_{\beta} \langle a,\beta|\hat{\rho}|a,\beta \rangle.$$
Here, $\beta$ for each $a$ label the orthonormalized eigenvectors of $\hat{A}$ with eigenvalue $a$ (of course $\beta$ can also be continuous, but that's only a mathematical detail, unimportant for our discussion).

Yes, assumption number (4) makes a distinction between observations and other interactions. It's right there in the postulates. Yet you deny that it makes such a distinction. It really seems that you believe contradictory things.

 

[vanhees71]

I give up. Obviously we have a very different perception by the meaning of the word "distinction". For me observations take place via the usual physical laws. There's nothing special about them. Obviously for you there is some distinction, I'm not able to comprehend. You don't tell me what this distinction might be, but just state it about axioms where I don't even mention measurements. Usually one doesn't even mention measurments in the formulation of Newton's laws either, because what a measurement is is not within the axioms but given by what observers do in the lab.

 

[stevendaryl]

I give up.

I think that's appropriate, because what you're defending is just indefensible. You have an interpretation that makes an essential difference between observations and other kinds of interaction. It has no physical content without that distinction. Yet you're denying that it makes such a distinction. It seems like a contradiction.

 

[stevendaryl]

There's nothing special about them.

Then why is there an axiom that only applies to observations/measurements? (Axiom 4)

What you're saying just seems like a contradiction.

 

[vanhees71]

Axiom 4 doesn't claim anything about the specialty of observations in contradistinction to any other interaction. It just tells the meaning of the formal objects of the theory when applied to real-world phenomena. That's what's necessarily done in all theories, including classical mechanics. There you also start from abstract objects like points on a fibre bundle representing spacetime when dealing with Newtonian mechanics or a affine Minkowski space when dealing with special relativistic mechanics. The relation to the observations is, admittedly, more direct in this case, and you don't have to deal with probabilities necessarily to begin with, but neither in quantum theory nor in classical physics is anything special about observations or measurement. In both cases the interaction between measurement device and measured object follows the general laws of nature as discovered by physics.

 

[stevendaryl]

Axiom 4 doesn't claim anything about the specialty of observations in contradistinction to any other interaction

That seems completely wrong. Other interactions don't have the property that the interaction results in an eigenvalue of some operator, with some particular probability.

If you treat an observation as an ordinary interaction, then what you get from an observation is that the observer becomes entangled with the thing observed. Nothing nondeterministic happens, and there is no eigenvalue selected.

Now, you could at this point say that you interpret "The measuring device is entangled with the system being measured" as "The measuring device is either in this macroscopic state or that macroscopic state, with the probabilities given by the square of the amplitudes for the different possibilities in the entangled wave function." But if you do that, then you are making a rule that applies to measuring devices, or to macroscopic systems that does not apply to microscopic systems.

It's not true in general that a superposition of two states means "the system is either in this state or that state, with such-and-such probability". It's only true if it's a superposition of macroscopically distinguishable states.

 

[Lord Jestocost]

That's a problem only if you believe in the necessity of the collapse postulate, which is not necessary at all. It even contradicts fundamental principles (relativistic spacetime structure) and it's almost always not what happens in real experiments.

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

 

[PeterDonis]

It's not true in general that a superposition of two states means "the system is either in this state or that state, with such-and-such probability". It's only true if it's a superposition of macroscopically distinguishable states.

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).

 

[stevendaryl]

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".

I'm disagreeing with that. In the case where you have a superposition of macroscopically distinguishable alternatives, it DOES mean that.

If the state of the universe starts off as a pure state, then it will evolve into another pure state. If in the history of the universe, we perform measurements, then that pure state will involve a superposition of some states in which the measurement yielded this result, and some states in which the measurement result yielded that result. If we are to give a probabilistic interpretation to this situation, we have to give probabilities to elements of a superposition.

[edit]I'm talking here about a minimalist interpretation, in which there is no collapse hypothesis. If you have no collapse hypothesis, and you still want to preserve the probabilistic predictions of QM, I think you have to say that a superposition of macroscopically distinguishable alternatives implies that one of the alternatives is real, and which one is purely probabilistic.

 

[PeterDonis]

If we are to give a probabilistic interpretation to this situation, we have to give probabilities to elements of a superposition.

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. That is not the same as saying that the superposition itself--the state with all the terms in it, each with its amplitude--is a state in which each term has some probability of being real. A superposition is a state in which all of the terms are real. If we are trying to describe a situation where only one of the states is real, we just don't know which, that's a mixture, not a superposition.

I'm talking here about a minimalist interpretation, in which there is no collapse hypothesis.

No, but, as you have been insisting all along, there is still a distinction between states that are "macroscopically distinguishable" and states that aren't.

I think you have to say that a superposition of macroscopically distinguishable alternatives implies that one of the alternatives is real, and which one is purely probabilistic.

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. You have to apply the Born rule to calculate the probabilities of each alternative being real, and then you treat the actual state of the system as being the eigenstate corresponding to whichever alternative is measured to be real.

 

[vanhees71]

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

The instantaneous-collapse postulate obviously contradicts Einstein causality.

I'm also not sure whether it's clear what you mean by "something physically real". The wave function has a clear probabilistic meaning, referring to the expected statistics when doing measurements in ensembles of correspondingly prepared quantum systems. So it has a real meaning in the sense that you can observe, what it predicts, namely the statistics for the outcome of observations on ensembles of equally prepared quantum systems.