Observing the observer

  • #1
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The relation between observer and observed is one of the controversial issues in quantum mechanics. In view of related discussions in other threads, let me summarize some statements by two of the most influential thinkers on the matter: John von Neumann and Eugene Wigner.


Von Neumann discusses the measurement problem in Chapters V and VI of his famous 1932 book. These two chapters are reprinted on pp. 549-647 of the reprint volume ''Quantum Theory and Measurement'' by Wheeler and Zurek, from which I take the page numbers (original page numbers are not given there).

He begins by contrasting process 1 (Measurement as orthogonal projection to an eigenstate of the operator R measured) and process 2 (the Schroedinger dynamics). His U denotes the density matrix, and is transformed to P^*UP by a measurement corresponding to the projection operator P, and by a unitary transform under the Schroedinger dynamics.

The discussion of process 1 assumes that R has discrete spectrum and that measurements produce exact eigenvalues of R (p.449) and are instantaneous (p.554), ''i.e., must be carried through in so short a time that the change of U given 2. is not yet noticeable''.

After a long thermodynamical interlude von Neumann introduces on p.622 the perception of the observer: ''at some time we must say: and this is perceived by the observer. That is, we must always divide the world into two parts, the one being the observed system, the other the observer. [...] The boundary between the two is arbitrary to a large extent. [...] experience only makes statements of this type: an observer has made a certain (subjective) observation; and never any like this: a physical quantity has a certain value.''

To prepare the derivation of the independence of the measuring process on where precisely this boundary is placed, von Neumann discusses the quantum description of the combination system+detector (detector is my short word for his ''measurement instrument''), culminating in the result on p.639 top characterizing the entanglement of system and detector (but the word entanglement was invented only a few years later by Schroedinger).

On p.641 it is assumed that the state of the observer is completely known (i.e., a pure state), and on p.645 enters the assumption that at some time before the measurement the density matrix of system+detector factors. Based on this, the proof of the boundary independence is completed on p.647.

In conclusion, von Neumann's analysis is based on five questionable assumptions:

1. The existence of process 1 as a real process.
But why should Nature respond to measurement differently than to everything else? Was there no state vector reduction before the first measurement was built, or before the first living being looked at something?

2. The assumption that measurement results are exact eigenvalues of the measured operator.
This is appropriate for the measurement of spin or helicity that have a simple rational spectrum but not for most real measurements, where the spectrum (though discrete) may consist of irrational numbers, which one can hardly claim to be exactly measurable.

3. The assumption that measurements are instantaneous.
The questionability of the instantaneity assumption is discussued by von Neumann himself and found harmless only in case of measurements that result in the mere emission of a light quantum (p.557).

4. The assumption that the state of the observer is pure.
Von Neumann notes on p.639 that in most cases, the states of two disjoint subsystems of a bigger system are not pure, but does not see that this essentially conflicts with his assumption.

5. The assumption that before the measurement, the density matrix of system+detector factors.
In view of the fact that the multi-particle (or field) Hamiltonian representing the dynamics of system+observer destroys separable states very quickly via decoherence, this is reasonable only if one assumes that the observer state is a thermal mixture in which details are averaged over, against assumption 4.
In addition, since system and detector are commonly composed of the same kind of indistinguishable particles, the separability assumption is in direct conflict with the (anti) symmetrization known to be necessary for all quantum systems composed of indistinguishable particles.


In a contribution to a book with the title ''The Scientist Speculates''; reprinted on pp. 168-181 of the volume cited above, Wigner turns the cautious remarks of von Neumann about the possible involvement of the brain in quantum mechanics into a full-blown esoteric interpretation, complete with
-- the concept of consciousness as the actor in achieving a wave function collapse (''The preceding argument ofr the difference in the roles of inanimate observation tools and observers with a consciousness - hence for a violation of physical laws where consciousness plays a role - is entirely cogent so long as one accepts the tenets of orthodox quantum mechanics in all their consequences.'', p.178), and
-- a subjective interpretation of the state vector (as if quantum mechanics had nothing objective to say): ''The wave function is a convenient summary of that part of the past impressions which remain relevant for the probabilities of receiving the different impressions when interacting with the system at later times.'' (p.171)

He pays lip service to objectivity (''The information given by the wave function is communicable'', p.171) - without explaining why, when it is based on subjective impressions only. In his caricature of the real thing, the wave function turns into a separable state of system and observer already when ''his answer gives me the impression that he did [see the flash], the joint wave function of friend+object will change into one in which they even have separable wave functions''.

True to the title of the article collection, the scientist speculates - nothing more.


In a more serious article (reprinted on pp. 260-314 of the above reprint volume), Wigner recapitulates von Neumann's analysis (in much easier to read terms), repeating all his assumptions, but discussing its limitations in a bit more detail.
-- ''One has to admit, on the other hand, that (35) is a highly idealized description of the measurement. [...] The fact that the measurement is of finite duration introduces a more serious problem. [...] To which position at which time does the measurement then refer? This issue is unclear and is rarely discussed.'' (p.284)
-- ''for many if not most operators, this expression - or any other expression which might lead to that equation - contradicts some of the basic principles of quantum theory. What then are the limitations of measurability? Only quantities which commute with all additive conserved quantities are precisely measurable'' (p.298)

This leaves very little, since the Hamiltonian is additively conserved and commutes for most systems with hardly any of the traditionally measured variables. Moreover, if the Hamiltonian has irrational eigenvalues (which is the case with probability one), these cannot be exactly measured either.
 

Answers and Replies

  • #2
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To prepare the derivation of the independence of the measuring process on where precisely this boundary is placed, von Neumann discusses the quantum description of the combination system+detector (detector is my short word for his ''measurement instrument'')
FWIW, my view on this is that the inference of this independence, is actually a physical process too, and it takes place within the microstructure of observers.

So the situation we end up with is that the inference of the independens of the decomposition, is in fact only an EXPECTATION, living within another (usually much larger) observer.

I choose to see this "derivation of independence" rather as a process of emergence of the symmetry implied by observer invariance in the sense ot arbitraritiess of the boundary. But of course the only place for such a process to take place it relative to a yet another observer.

Usually the idealisation of "external observer" makes perfect sense if we are talking about subatomic systems, various detectors... all sitting inside a huge controlled laboratory. which monitors every details of the environment of the system+detector.

/Fredrik
 
  • #3
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A garden hose is expelling 10 gallons a minute un-observed.
Does the event of my looking upon the hose change, in any way, the water discharge?
No.
 
  • #4
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A garden hose is expelling 10 gallons a minute un-observed.
Does the event of my looking upon the hose change, in any way, the water discharge?
No.
Sure, Agreed. But this isn't the physical question.

It DOES change the ACTION of the gardener. The gardeners instant action depends on wether he has observed the running hose.

IMHO the question isn't what is and what doesn't make a difference when no observed. The only question an observer needs to ask, is how it's actions will be influenced by it's current information.

The action of the observer, is what makes the difference, and it's the only rational question he asks that has survival value.

/Fredrik
 
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Sure, Agreed. But this isn't the physical question.

It DOES change the ACTION of the gardener. The gardeners instant action depends on wether he has observed the running hose.

IMHO the question isn't what is and what doesn't make a difference when no observed. The only question an observer needs to ask, is how it's actions will be influenced by it's current information.

The action of the observer, is what makes the difference, and it's the only rational question he asks that has survival value.

/Fredrik

My point here is that the passive obsevation alone has no influence in that scenario.
 
  • #6
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My point here is that the passive obsevation alone has no influence in that scenario.
Influence what? It certainly influences the observers state. Which is exactly what the wavefunction/statevector is.

/Fredrik
 
  • #7
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This is my answer to queries from a different thread, but the topic better fits here.

So you're not talking about this at all?
Yes, I am talking about the topic discussed in this link, or rather about that the conventional treatment of the topic makes assumptions that are not warranted when this approach is applied to more than the most elementary situations.

To be specific, let me focus on one of the sources you refer to:
http://plato.stanford.edu/entries/qt-measurement/
Section 2 discusses von Neumann's views, the assumptions of which I had already summarized and commented in the opening post of this thread.

I consider the many worlds interpretation esoteric and irrelevant in view of the fact that the only universe that counts is the one we actually observe. I gave more detailed reasons in the section ''On the Many-Worlds-Interpretation'' of Chapter A4 of my theoretical physics FAQ at http://www.mat.univie.ac.at/~neum/physfaq/physics-faq.html#manyworlds


The reason I asked was because you don't really seem to be talking about the measurement I linked.You seem to be making four significant, unwarranted hypotheses that turn your argument into a straw-man.

The first is your hypothesis that a measurement be instantaneous. I have no idea about the original source, but it certainly wasn't required in the link I gave, nor is there any obvious reason why it should be so.
It is assumed both in von Neumann's treatment and in Wigner's treatment.
Otherwise the state reduction upon measurement doesn't make sense, since it interferes with the unitary dynamics in a formally uncontrollable way.

What is expected is just that the joint object - measuring device - environment* system undergoes unitary time evolution.
Only until it is observed by the superobserver. Then there should be a collapse, according to the Copenhagen interpretation which was the starting point of the discussion; see https://www.physicsforums.com/showthread.php?p=3125380#post3125380

The second is your hypothesis that the construction and reading of the measuring device must be practical. Again there was no such hypothesis in the link, nor any obvious reason why it should be so.
I don't assume that it must be practical (i.e., preparable by human beings); only that it must be physical (i.e., actually realized in the observable universe).

Anything else is science fiction, not physics.


Even if we wanted to consider the special case of a real-world measurement in a laboratory, we still don't even require distinguishing between all states of the device to be anything resembling feasible -- many device states will correspond to the same reading.
Yes, but the superobserver must still observe this fact.

The third is that the observer & measuring device must resemble a human and a real-life device we could call a measuring device. (or even that there must be an observer!)
I never assumed a human element. On the other hand, if the observer & measuring device does not resemble a hypothetical real-life device, how can one call it an observation or measuring device?

And that there must be an observer (and even a superobserver) was granted by you when you entered the discussion:
:confused: Accepting for the sake of argument it requires a hierarchy of superobservers, I really don't see why such a thing should be nonsensical.
Without that, the whole discussion would have been pointless.

The fourth one is the hypothesis that the measurement completely distinguishes the states of the object of study. While this is included in the link I mentioned, there is no obvious reason why it should be taken as a requirement.
As you say, it is the usual assumption under which these things are discussed. So it is legitimate to assume this as well.


In view of the above, I'd appreciate if you'd restate in reasonably precise terms what you are prepared to accept as assumptions, and what you consider the features to be explained on that basis.

Maybe you'd like to read Chapter A4 ''The interpretation of quantum mechanics'' of my theoretical physics FAQ at http://www.mat.univie.ac.at/~neum/physfaq/physics-faq.html#A4 before formulating your query.
 
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  • #8
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Hurkyl said:
Accepting for the sake of argument it requires a hierarchy of superobservers, I really don't see why such a thing should be nonsensical.
Without that, the whole discussion would have been pointless.
I actually agree with this but I'm not sure if it's for the same reason as yours.

As I see it, a conceptually major problem with the increasingly more complex superobserver picture, is that the deductive inference is encoded in some large physical structure that is not accesible to the original observer. It could not even be communicated give time since it's too much information for the original oberver to encode at one instant of time.

And we must not forget that it's the predictions of the the original observer we seek to understand (although of course, this observer is not uniqe).

Ignoring this unavoidable introduces non-local causation where the action of an observer depends on information that is unavailable in a way that I can't see as anything but irrational and lacking predictive value (even in the inductive sense).

The question I ask, and I think physics and measurement hteory should ask is:

1. Given this information; what is the optimal inference one can make?
2. How does one choose an action based on this expectation?
3. How does the inference machinery evolve in response to backreactions from environment as per the above.
4. How does such interacting inference systems behave? What selection principles appears and do they single out some of the actions we know from the standard model?

The notion of superobserver, is IMO an attempt to solve the lack of deductive power during the measurement, by trying to embed into another level of deductive power by making it larger. But this is IMHO missing the point of how decision making based upon incomplete information works.

/Fredrik
 
  • #9
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The question I ask, and I think physics and measurement theory should ask is:

1. Given this information; what is the optimal inference one can make?
The optimal inference given some quantum measurements is answered by quantum estimation theory; see, e.g.,
http://www.perimeterinstitute.ca/Events/Quantum_Estimation/Quantum_Estimation:_Theory_and_Practice/ [Broken]

Your other questions seem to me not well-posed enough to be answerable.



The notion of superobserver, is IMO an attempt to solve the lack of deductive power during the measurement, by trying to embed into another level of deductive power by making it larger. But this is IMHO missing the point of how decision making based upon incomplete information works.
I was assuming observers and superobservers only to show that the latter are nonsense.
(The assertion that a hierarchy of superobservers is nonsense prompted Hurkyl's query.)
 
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  • #10
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The optimal inference given some quantum measurements is answered by quantum estimation theory; see, e.g.,
http://www.perimeterinstitute.ca/Events/Quantum_Estimation/Quantum_Estimation:_Theory_and_Practice/ [Broken]
Thanks, but what I mean is (and this is an open question; so I don't expect the answer, I just stated what I think the questions are) not to ask what the optimal inference is, given that you assume quantum mechanics.

I am flipping the coin, and I seek a reconstruction of a new type of logic (generalizing Jaynes construction of the axioms) from different foundations where the optimal inference rules all actions and instead predicts quantum logic (or whatever that is replacing QM).

Just like one can argue how thermodynamics pretty much follows from classical inductive logic, I think a generalization imples QM (or what replaces it). Just like we today understand the structure of statistical mechanics and thermodynamics as almost following from an extension of logic (inductive reasoning, like JAynes put it), I think measurement theory will be understood similarly. Ie. quantum behaviour is there because it's selected by nature as more fit than classical inference (classical probability as opposed to transition amplitudes of QM)

Edit: While I disagree with ET JAynes, the IDEA is that his reasoning determines the axioms of inference, based on plausible and apparently rational assumptions. The resulting inference model, proves to be equivalent to kolmogorov axiomatic probability. But coming with a far and way more (IMHO) superior insigh into WHY we have these axioms and not some other ones.

Your other questions seem to me not well-posed enough to be answerable.
I agree they are not well posed measured relative to a mathematical problem, to compute or solve something. This is part of the real problem.

/Fredrik
 
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  • #11
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A garden hose is expelling 10 gallons a minute un-observed.
Does the event of my looking upon the hose change, in any way, the water discharge?
No.
so far as to propose that reality is created only when there is observed........
 
  • #12
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Influence what? It certainly influences the observers state. Which is exactly what the wavefunction/statevector is.
Even if the observed quantum system's wavefunction didn't change with the act of observation, the wavefunction of the composite system would however change. It's this that you mean?
Thank you.
 
  • #13
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After a long thermodynamical interlude von Neumann introduces on p.622 the perception of the observer: ''at some time we must say: and this is perceived by the observer. That is, we must always divide the world into two parts, the one being the observed system, the other the observer. [...] The boundary between the two is arbitrary to a large extent. [...] experience only makes statements of this type: an observer has made a certain (subjective) observation; and never any like this: a physical quantity has a certain value.''
I'm still with Bohr on this one... the measurement problem and observer / observed divides really aren't necessary. Basically, the idea is that the outcomes of experiments always depend on context or experimental setup. It simply doesn't make sense to talk about what's being measured (the observed) independent of your measuring device (the observer). And that's not as crazy as it might sound at first.

Let's back up and start with the naive reality colors and sounds that we live in. In classical physics, we decided that not all of the properties we perceive are direct intrinsic properties of the objects we are perceiving. Redness, for example, is not an intrinsic property of my apple, but it is a result of wavelengths and reflections and all of that. We decided that intrinsically, everything out there was really just made of particles with location and momentum and charge - those were the basic intrinsic properties.

Moving to relativity... the concepts of location and mass etc had to be reconsidered. Unless you specify a frame of reference, these quantities are undefined. Length and mass are only intelligible subjectively, from a certain frame of reference. In this sense, you might even say that these properties are not intrinsic to things themselves, but that they are also extrinsic measurement-dependent properties. We still have rest mass and relative velocities with relativity though, so maybe this argument isn't the most convincing.

Enter QM. It turns out that even location and momentum cannot be the basic, persistent, properties of matter. Location and momentum inherently depend on the conditions of their measurement. They cannot be the intrinsic properties the world is made of.

QM casts out location and momentum as basic and puts them back on the same level as color. Is that really so counter-intuitive though? Okay, so particles with location and momentum and all of that good stuff are now only as real as tables and chairs, colors and sounds, and the meaning of my text. Isn't that what we wanted to begin with? Is it really so bad if all observables ( / properties) might be dependent on the conditions of their measurement?

Going back to color and sound again... consider the classic about a tree falling in the forest. Does it make a sound? Sound, as distinct from compression waves, is a certain type of perception. The existence of sound requires a few things... it requires a crashing tree, but it also requires a nearby person with working ears and a normal nervous system. Sound requires a complete experimental setup. It is nonexistent or meaningless in space or in a world of the deaf. Redness is meaningless in a world of the blind. The words I'm typing are meaningless without readers of English. Why should the properties of particles be any different? Why do we desperately need mass to be objective while happily accepting that colors and sounds are not?

By accepting that location and momentum might only be as real as colors and sounds, the measurement problem is avoided entirely.
 
  • #14
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The way the things are put somehow reveals how we all see this, and it does borderline to interpretational issues but to just respond shortly:

Even if the observed quantum system's wavefunction didn't change with the act of observation, the wavefunction of the composite system would however change. It's this that you mean?
Some distinguish between the observer and the measurement device - I don't.

The observer IS the "measurement device", or vice versa. The decomposition of the wavefunction encoding the observers knowledgea bout it's environment into; "system"+"measurement device"+"remainder" is strictly speaking completely arbitrary. It does not matter where you draw the boundaries as the system that's observers is nothing but the full system (what you call composite)

Consistency suggests that any decomposition must be equally valid.

So yes what I mean with just "the wavefunction" is the complete wavefunction. But I do not see it as a "composition". It's rather the DEcomposition in the first place that is ambigous and questionable.

There is no way the full function can not change during observation, unless of course, during the special case where the observes state is in perfect harmony with the environment. Then there is no collapse because "the collapse" conincides with the unitary evolution.

So the way I see it, the physical order of inference is not how to construct the wavefunction of a composite system from arbitrarily decomposed parts; it's rather how to decompose the full system into distinguishable parts in the first place.

So, in my view, the collapse is simply an "information update", except of course it doesn't follow classical logic, but a different logic. The "unitary evolution" just corresponds to the "self evolution" in absence of new information. When new information starts to be in perfect harmony with the prior one, there is no collapse anymore and any information updates coincides with the self evolution and merely circulates the same information.

Conceptually I think this is pretty clear. But taking this view seriously, do suggest that QM as it stands is merely an approximation of a more general inference. This is why these problems I think appear when people try to take QM as it stands as perfect, and extrapolate it to scenarious where we lack experimental confirmation. QM, is effectively only verified in the special case where there is massive assymmetry between observer (laboratory frame) and atomic world. If we're talking about system and observer of similar order of complexity, my understnading is that they mathematical structures simply fails to make sense. My conclusion then is that the structure of current QM, is not that last word.

/Fredrik
 
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I think that some confusion arises from too high expectations about the role played by quantum mechanics. Some people think that QM is an all-encompassing model of the world. Some even dream about writing the wavefunction of the entire universe comprising physical systems, observers, and everything else.

In my opinion, QM plays a more modest role. It is simply a mathematical model for specific experiments. You can apply QM (e.g., construct the Hilbert space) only after you've specified which experiment you want to describe. In each experiment there is a clear separation between observed physical system and the measuring apparatus. So, it is quite logical that QM's description of these two entities is very different. The system is described by the state vector in the Hilbert space, and the measuring apparatus is described by a Hermitian operator in the same Hilbert space.

Yes, you can decide to treat the "system+measuring device" as your new physical system, which is observed by somebody else. But then you've changed your original experimental setup: your physical system has changed and the measuring apparatus is different. So, the theoretical description should be changed as well. In QM you will need to construct a new Hilbert space, whose vectors and Hermitian operators are completely different from what you had before.

So, if you accept that QM is a mathematical model for specific experiments (rather than universal theory for the entire world), then the issue of "observing the observer" is not that controversial anymore.

Eugene.
 
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I think that some confusion arises from too high expectations about the role played by quantum mechanics. Some people think that QM is an all-encompassing model of the world. Some even dream about writing the wavefunction of the entire universe comprising physical systems, observers, and everything else.
*grrr* I've been told that QM in principle applies to everything.

And also I've been told decoherence doesn't put the quantum system under investigation into an either or state. system+environment in principle would be a new wavefunction in superposition, for isn't the environment also quantum mechanical too?
 
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*grrr* I've been told that QM in principle applies to everything.
Yes, quantum mechanics applies to everything. But a more precise statement is that quantum mechanics applies to any *experiment*. This does not diminish the value of QM at all, because everything we know about nature comes from experimental observations. The scientific principle teaches us that only those statements are meaningful, which can be verified by experimental means. This allows us to ignore various "tricky" questions, like "is there moon when nobody is looking?", "is there sound of the falling tree when nobody is listening?" or "does the electron pass through one slit or through two slits?" All these questions cannot be answered scientifically, because they do not permit an experimental check.

Eugene.
 
  • #18
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Oh ok! I must have muddled up what was said that made me think QM didn't apply to everything. Glad it's been clarified! Thanks. :)

Question: is what is said about the solutions to the Schrödinger equation the same as what can be applied to solutions to the Dirac equation, e.g. superposition of states?
 
  • #19
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Question: is what is said about the solutions to the Schrödinger equation the same as what can be applied to solutions to the Dirac equation, e.g. superposition of states?
My answer is "yes" and "no".

Yes, superposition of states occurs in relativistic quantum theory exactly as in the nonrelativistic theory.

No, Dirac equation is not about wavefunctions. So, it is not correct to consider Dirac equation as a relativistic analog of the Schrodinger equation. Dirac equation applies to quantum fields, which have no relationship to wavefunctions. They are two completely different beasts.

Eugene.
 
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  • #20
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There are different approaches to QFT or second quantization. And while indeed dirac equation is not a single component wavefunction, but a 4 component such (for one electron), that's furthermore second quantized (or if you prefer some other reconstruction) in QFT to account for the "em field" or multicple elctrons dep. ow you see it.

Anyway, I think it's better and cleaner to use the word "state vector", rather than associate to "wave"-function. The "wavefunction" is more the old word, coming from the wave-particle duality that mayve associates to the single component thing.

Then the conceptual points are quite similar. You have a "quantum STATE" (wether it's the state of a single componet probability amplitude, or the state of a multiple componetn amplitude, or the state of a FIELD) doesn't change the overall picture.

Then this quantum STATE has an expected univery evolution.
At each measurement the STATE is updated and the expectations is revised accordingly.

The extra issues of QFT has IMO more to do which what spaces really is - in terms of a measurement theory. QFT as it stands relies on the same QM.

There is a quantum state in a hilbert space.
There is a unitary evolution.
There are measurements.

The quantum state is simply the representation of the state of information about the system. Wether it's a field, single component wave funtion, or multiple component wavefunctions, depends just on the particular system and does not acceft the basic structure of quantum mechanics as it stands. In either cases there is a hilbert space. They are just given different names, fock spaces etc. But in the end the whole construction is supposed to simply be a hilbert space of the new system (many particle/second quantized fields etc etc).

But exactly how this will be in when full unification is seen remains open I think. But regarding current formalism, the "quantum mechanics parts" of QFT, is no different than the non-relativistic one. The difference lies more in the system, spacetime etc.

/Fredrik
 
  • #21
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Basically, the idea is that the outcomes of experiments always depend on context or experimental setup. It simply doesn't make sense to talk about what's being measured (the observed) independent of your measuring device (the observer).
How do you interpret Born's rule in the light of your statement above?
It is a statement about measurement results independent of context.
 
  • #22
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Yes, quantum mechanics applies to everything. But a more precise statement is that quantum mechanics applies to any *experiment*.
No. QM applies, e.g., to the nuclear processes deep inside the sun, although we can't make any experiments about it. We can only check some consequences about what is radiated to the earth or to a satellite.
 
  • #23
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I think it's better and cleaner to use the word "state vector", rather than associate to "wave"-function.
It is better mainly since there are many quantum systems (e.g., arrays of qubits)
that have state vectors but no wave function.

The "wavefunction" is more the old word, coming from the wave-particle duality that maybe associates to the single component thing.
The term wave function is not old-fashioned. It is fully appropriate (and used) when a particle or multiparticle system is duscussed in the position or momentum representation.
And _only_ then.
 
  • #24
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No. QM applies, e.g., to the nuclear processes deep inside the sun, although we can't make any experiments about it. We can only check some consequences about what is radiated to the earth or to a satellite.
OK, perhaps *experiment* was not the right word as it implies some possibility to tweak the measured system. Then call it *observation* and my logic applies.

For example, the physical system is a couple of nuclei inside the sun and a neutrino emitted as the nuclei join together. The measuring apparatus is the detector on Earth. Quantum mechanics applies. The important thing is that there is a clear separation between the physical system and the observer. This separation is reflected in the QM formalism which treats one part of this duo as a state vector and the other part as a Hermitian operator.

It is also true that we can apply QM to things that we can see only indirectly. For example, the same couple of nuclei inside the sun is ultimately responsible for the light emitted from the sun's surface and captured on Earth. In principle, it is possible to build a full quantum-mechanical model of the sun with all nuclear reactions happening inside, pressure, temperature, radiation, etc. Then the mentioned couple of nuclei will be a part of a huge quantum-mechanical state describing the sun.

Eugene.
 
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  • #25
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The term wave function is not old-fashioned. It is fully appropriate (and used) when a particle or multiparticle system is duscussed in the position or momentum representation.And _only_ then.
Ok, that's true.

What I meant, is that IMHO, it's more clean to think also also of the x-p case as simply an abstract state space. And that the "wavefunction" is just a state vector. That way it becomes more transparent. Using different words for the same abstraction doesn't help seeing a coherent picture.

All else, is IMO, simply a matter of how the distingusiahble states in the state space is "indexed" and normalized; and how this index can be built in different ways and continuums with integration measures, discrete structures etc. And how different ways to encode the total information can be dual to each other.

I have some other views to this indexing process, and how it's inferred by the observer; rather than put in by hand when defining the problem, which is why I personally prefer to make such distinction as clear as possible.

In this sense the dirac or schrödinger equation are still of the same "form"; only the index space is different of course; one is a simple position/momentum, the other involves components and/or field parameters.

/Fredrik
 

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