I think, we go in circles here. It is very clear that physical theories are about describing measurements, i.e., quantative observations of Nature. What else should physics be about?stevendaryl said:That's my complaint about what you have said with regard to the minimalist interpretation. They make no sense to me. You have a theory whose assumptions explicitly mention measurement, and then you claim that there is nothing special about measurement. That seems like you're contradicting yourself.
Maybe there is a way to resolve the contradiction, but the minimal interpretation certainly doesn't.
vanhees71 said:Why should I do that, because I never claimed that this is the goal.
vanhees71 said:I think, we go in circles here. It is very clear that physical theories are about describing measurements
vanhees71 said:The measurement devices used are just made of ordinary matter and are thus described by standard quantum physics as any other lump of matter. That's all I'm saying
vanhees71 said:The basis chosen is dicated by the measured observable in the usual way (eigenstates of the corresponding self-adjoint operator representing this observable).
I'm too stupid to understand your demand. Sorry for that. Again: Physics is about observations of nature in a quantitative way, i.e., about measurements. All I'm saying is that measurement devices and the interactions of measured objects with them are following the universal natural laws discovered by physics, and these rules are quantum. It doesn't make sense to talk about physics at all if you don't talk about observations and measurements, because that's the topic of physics.stevendaryl said:Because if you are able to do that, that would demonstrate that the minimalist interpretation does not treat measurement different from other interactions. Nothing short of that would suffice.
That's a statement about properties of cats, and of course you can observe it and see, whether it's right or not. That cats very often land on their feet is even an interesting biomechanical issue and well investigated by physicists. I'm only totally unaware what this has to do with the interpretational issues of quantum theory.Suppose I have a law of physics that states that cats always land on their feet. Does that treat cats differently than other objects? Maybe, maybe not. To prove that it doesn't treat cats specially, you should be able to restate the laws in a way that doesn't mention cats, and the specific claim about cats should be derivable from that. If you can't do that, that means that your laws are treating cats specially.
Why should it treat measurements differently? Measurements are defined by a measurement apparatus, and the very construction of all measurement apparati I know use the known universal laws of physics. There is not difference whatsoever concerning the applicability of the physical laws to construct a measurement apparatus than any other technical gadget like a car or a smartphone (although particularly the latter also contains a lot of measurement apparati you can even use to do interesting measurements in physics classes).If you can't restate the minimalist interpretation in a way that doesn't mention measurement (or something equivalent) then to me, that's an indication that it treats measurements differently.
Sure, and Newtonian physics is as well about quantitative observations and thus measurements in nature. An in principle you are right, Newtonian mechanics also is in principle the sufficient basis to construct all the measurement devices you need to measure the quantities described by Newtonian physics (i.e., times, lengths, and masses; everything else is derived). Of course, the same physical laws are needed and the corresponding theory to define what's measurable (i.e., what are the observables) and at the same time are used to test this very theory. In this sense all experimental tests of physical theories are in fact consistency tests.You keep saying that all theories of physics treat measurement special in the same way, but that's absolutely false. Newtonian physics describes objects and their motion and the forces acting on them. Anything you want to say about measurement follows from Newton's laws plus the assumption that the measurement device is a particular physical system obeying Newton's laws.
That's simple: By measuring it. I think we just are unable to explain to each other what the issue is. Maybe it's better to leave it at that :-(.stevendaryl said:What makes something the "measured observable"?
vanhees71 said:I'm too stupid to understand your demand.
Sorry for that. Again: Physics is about observations of nature in a quantitative way, i.e., about measurements.
That's a statement about properties of cats, and of course you can observe it and see, whether it's right or not. That cats very often land on their feet is even an interesting biomechanical issue and well investigated by physicists. I'm only totally unaware what this has to do with the interpretational issues of quantum theory.
vanhees71 said:there's (a) no difference in the physical laws between situations where a measurement apparatus is used and where this is not the case and (b) that there's no difference between the physical laws concerning many-body systems making up measurement devices and any other quantum system, large or small.
vanhees71 said:Of course, to make a measurement we need a macroscopic device to be able to make a measurement. I've never claimed the contrary.
vanhees71 said:The only thing I'm saying is that the classical behavior of macroscopic observables does not contradict the fundamental laws of quantum theory but are well explained by standard (quantum!) statistical physics.
vanhees71 said:That's simple: By measuring it.
It is not possible to do physics without measurements, so any physical theory is about measurements. Your question doesn't make sense to begin with, and that's not philosophy but the simple definition of what physics is about.stevendaryl said:I'm asking a technical question: Is it possible to formulate the minimal interpretation of quantum mechanics in a way that does not mention measurement?
It's not different as with any other thery of physics, because physics is about measurements. Without measurements there's no physics.The answer seems to be no. That's very different from the case with every other theory of physics.
Of course are Newton's laws about measurements, because all of physics is about measurements. You start with the postulates about space and time, which implies that you talk about measurable quantities like the period of a pendulum or a planet orbiting the Sun and about distances and angles of bodies in space. Without at least these kinematical observables you cannot even start to state the postulates!Newton's laws are not formulated in terms of measurements. They make predictions about the results of measurements, which is all that you want for a theory to have empirical content.
What you stated is a prediction about the behavior of cats. You use (implicitly) the definition of "cat" and it's a statement about the mechanics of cats, which can be checked by observation. Of course, if you make a statement about something it's a statement about this entity. However, I don't see at all what this has to do with the foundations of quantum theory and particularly what this has to do with the existence of a classical-quantum cut (which you seem to insist on as vehemently as I deny any empirical foundation for its existence) or, for me even on the edge of esoterics, that a piece of matter cannot be described by the universal physical laws of nature only because it's used as a measurement device. Are you really claiming that a piece of wood changes to obey the known physical laws, only because I put some marks of it to use it as a yardstick? For me that would be utter nonsense.It shows that you are claiming two contradictory things. If my axioms mention cats, then either the axioms can be reformulated so that cats are not specifically mentioned, or else it's false to claim that they don't treat cats specially. If your axioms mention measurements, then either the axioms can be reformulated so that measurements are not explicitly mentioned, or it's false to claim that they don't treat measurements specially.
vanhees71 said:Why should it treat measurements differently?
vanhees71 said:It is not possible to do physics without measurements,
vanhees71 said:Of course are Newton's laws about measurements, because all of physics is about measurements.
vanhees71 said:It is not possible to do physics without measurements, so any physical theory is about measurements.
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).stevendaryl said: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.
vanhees71 said: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.
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).PeterDonis said: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".
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.stevendaryl said: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 said: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.
vanhees71 said:Quantum theory also simply says ##\mathrm{i} \partial_t |\psi(t) \rangle=\hat{H} |\psi(t) \rangle##.
vanhees71 said: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.
vanhees71 said: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.
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.PeterDonis said: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.
I can just use your sentence with a little change:stevendaryl said: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.
vanhees71 said: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.
vanhees71 said: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.
vanhees71 said: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.
vanhees71 said: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.
Lord Jestocost said: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
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).Lord Jestocost said: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.
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.stevendaryl said: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.
vanhees71 said:That's a problem only if you believe in the necessity of the collapse postulate, which is not necessary at all.
vanhees71 said: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).