Free will?

[LegionOnomaMoi]

This is not only dualistic, but mysticism.

And MWI is...? For most physicists (even proponents of the MWI), supporting the MWI means going beyond dualism, reductionism, physicalism, and perhaps even realism. It's the sort of theory that leads to the criticisms noted by the editor of Universe or Multiverse? (Cambridge University Press; 2007):

"Despite the growing popularity of the multiverse proposal, it must be admitted that many physicists remain deeply uncomfortable with it. The reason is clear: the idea is highly speculative and, from both a cosmological and a particle physics perspective, the reality of a multiverse is currently untestable. Indeed, it may always remain so, in the sense that astronomers may never be able to observe the other universes with telescopes a and particle physicists may never be able to observe the extra dimensions with their accelerators...
For these reasons, some physicists do not regard these ideas as coming under the purvey of science at all. Since our confidence in them is based on faith and aesthetic considerations (for example mathematical beauty) rather than experimental data, they regard them as having more in common with religion than science. This view has been expressed forcefully by commentators such as Sheldon Glashowm Martin Gardner and George Ellis, with widely differing metaphysical outlooks. Indeed, Paul Davies regards the concept of a multiverse as just as metaphysical as that of a Creator who fine-tuned a single universe for our existence. At the very least the notion of the multiverse requires us to extend our idea of what constitutes legitimate science.

In David Deutsch's contribution to Many Worlds? Everett, Quantum Theory, and Reality (Cambridgue University Press; 2010), he writes:
"I’ll start with a simple fact: in this room, in some nearby universes, Hugh Everett is here with us, celebrating. Perhaps he’s there, in that seat where Simon is. And therefore, in those universes, Simon is somewhere else."
You'll recall that Deutsch was one of two mainly responsible for popularizing a version of Everett's theory which became known as the many-worlds interpretation (or many-worlds theory) because of Dewitt and Deutsch.

 

[PolyHedral]

And MWI is...?

Sensible.

For most physicists (even proponents of the MWI), supporting the MWI means going beyond dualism, reductionism, physicalism, and perhaps even realism. It's the sort of theory that leads to the criticisms noted by the editor of Universe or Multiverse? (Cambridge University Press; 2007):

"The math points there" led us to believe in antiparticles... and oops, there they are. It also led us to believe that 4 extra types of quarks, and Higgs bosons existed, despite the fact we'd never observed them... and voila, we found them once we managed to take a good look. Of course, it's not a flawless method - we might've found two Higgs'.

In David Deutsch's contribution to Many Worlds? Everett, Quantum Theory, and Reality (Cambridgue University Press; 2010), he writes:
"I’ll start with a simple fact: in this room, in some nearby universes, Hugh Everett is here with us, celebrating. Perhaps he’s there, in that seat where Simon is. And therefore, in those universes, Simon is somewhere else."
You'll recall that Deutsch was one of two mainly responsible for popularizing a version of Everett's theory which became known as the many-worlds interpretation (or many-worlds theory) because of Dewitt and Deutsch.

Yes, that's a consequence of MWI. There's also a universe quite further away in which Simon never existed. There's also one (which has departed quite far from the Born statistics) where there are two Simons. Are you trying to suggest that this is wrong or ridiculous somehow? On what grounds?

The entire modern physics community would love you to explain what is still a mystery.

A general quantum state is a vector in complex Hilbert space (equivalent up to phase) and has a time evolution operator maps that vector space to itself. Observable quantities are represented by linear operators on that same space.

Now, the state on its own describes any entanglement (by way of [lack of] factorization into discrete components) or other quantum effects, so the only thing we need to metaphysically care about are the observable operators. (But this is a cheat as we'll see in a second.) Obviously, when we apply an operator, the quantum state can either be an eigenstate/in the spectrum of the operator, or it isn't. If it is, yay - that's the value we get, and the system doesn't change at all.

The metaphysics problems arise when it isn't an eigenstate. This means that the universe somehow chooses which of the eigenstates to deliver to our apparatus. (And subsequently, which eigenstate the system morphs into) How does it do that? The mechanism for doing so is, in almost all respects, a dragon in the garage - ineffable, unknowable, and unevidenced. We know only one thing about it - the result obeys the Born statistics. Furthermore, it's not clear what, exactly, counts as an observation - neither the mathematics, or the collapse postulate we've added in say anything.

MWI bypasses this problem entirely, by bringing to the fore the fact that the entire universe is a quantum system. This means that there is no "observables" as such - only quantum particle interactions, which never produce a collapse to a single eigenstate. What we're treating as observables is simply a consequence of treating some objects as classical, when they're really not. The explanation for why we never see a measured system spontaneously become unmeasured is simple - our apparatus has become entangled with the "observed" quantity. This quite neatly gets rid of any sort of dragon, and reveals the universe as a single semi-coherent wavefunction, just like any other composite system of objects.

So, I repeat: what's the problem?

 

[LegionOnomaMoi]

"The math points there" led us to believe in antiparticles... and oops, there they are. It also led us to believe that 4 extra types of quarks, and Higgs bosons existed, despite the fact we'd never observed them... and voila, we found them once we managed to take a good look. Of course, it's not a flawless method - we might've found two Higgs'.

"The math points there" got us nothing of the sort. Interpretations of the math did, and these were followed by interpretations of experimental results (determined to an unknown degree by the math itself).

Are you trying to suggest that this is wrong or ridiculous somehow? On what grounds?

I think it's wrong for the same reason Everett ended up with: it doesn't work. The logic it is based on is circular.

A general quantum state is a vector in complex Hilbert space (equivalent up to phase) and has a time evolution operator maps that vector space to itself.

You can't map a vector space to anything. That is, when we say something like "a function f mapping R to R ( or R->R)" we are saying nothing much at all. Because we have not described in what way this mapping works. There is no "general quantum state" either. Rather, in the standard formalization, "pure" quantum states are described by state vectors, such that each quantum system is attributed to, or said to "lie in" or "be in", a seperate space in H (i.e., distinct spaces in a complex vector space).

And most importantly, the "bra" and "ket" state-vectors are maps (or at least the "bra" is and the "ket" can be). The "bra" state-vector is a map from H to H*. However, in order get values associated with these "states", we do not use functions on the phase space but a linear Hermitian operator O on H. In other words, this:

Observable quantities are represented by linear operators on that same space.

is NOT true. We are not dealing with the same space, but rather a statistical operator or alternatively a normalized linear map from the observables to expectation values. And it is not over the complex numbers.

Obviously, when we apply an operator, the quantum state can either be an eigenstate/in the spectrum of the operator, or it isn't. If it is, yay - that's the value we get, and the system doesn't change at all.

Where are you getting the above from? The quantum state is not and is never equated with the eigenstate of the operator corresponding with any observables, whether or not we actually get an eigenstate of the operator corresponding to a measured observable. They are two fundamentally different things. The quantum formalisms representing the quantum state cannot ever be characterized by an eigenvalue. The operator ensures we will get particular observables with particular probabilities, independently of a wavefunction. That is, we do not obtain probabilities from Ψ(x), but only from the square of its absolute value and only after measurement.

We have only a quantum state to work with, and with that we cannot obtain anything meaningful (nor does any MWI, from the initial proposal of Everett to modern interpretations) change this. In order to get something, we have to introduce an entirely seperate formalism. So we simply state that Ψ is, we hope, a complete description of the state of the system. Fantastic, but useless. There is no information we can use here. For one thing, I can multiply this state vector with any arbitrary complex constant and somehow the "system" doesn't change. All we have done is call the system the phase space, but in doing so made it impossible to obtain any values or other information we can use. Something like Born's rule is necessary to give us anything meaningful. But any such formalism is entirely independent of the quantum system, was developed independently, and rests on circular assumptions and/or outright contradictions.

For Everett et al., this means that the operators used to tell us something about the quantum system are derived from an interpretation of that quantum system as it relates to physical reality to begin with.

The metaphysics problems arise when it isn't an eigenstate.

They don't. Because the eigenstates are eigenstates of an operator representing an observable, but as the actual quantum system allows infinitely many correct solutions (or infinitely many quantum states), the formalism developed to relate the quantum system to any observable at all are interpretation-laden and always involve the application of deterministic operators distinct from the quantum system itself.

This means that the universe somehow chooses which of the eigenstates to deliver to our apparatus.

Actually we care more about the eigenvalues, but that's not all that important. Again, there are infinitely many quantum states for any quantum system, but whether or not we get an eigenstate is defined not by the quantum system at all (nor the universe, not the apparati) but most fundamentally by operators meant to represent observables. These are distinct from the quantum system, regardless of what we measure, they are independent of the schroedinger equation, the wavefunction, and all the other mathematical representations fo the quantum system and its dynamics.

MWI bypasses this problem entirely, by bringing to the fore the fact that the entire universe is a quantum system. This means that there is no "observables" as such

How do you bypass a problem by saying "here's the quantum system, here are the formalisms we use to determine anything at all about that system, these formalisms include a completely independent operatation which corresponds to observables, so we won't call them that any more". In otherwords, MWI retains the statistically developed operators which actually get us either an eigenvalue (a definite value) or some probability range. Any interpretation has to, because otherwise we don't have quantum mechanics. You don't "bypass" the problem of how an operator corresponding to observables (and not to the quantum system at all) does so by simply renaming them (and, fyi, that's not what is done in MWI).

What we're treating as observables is simply a consequence of treating some objects as classical, when they're really not.

No, we aren't. We're obtaining observables by representing the system and its dynamics using one set of formalisms, and then obtaining values or states which are the basis for all quantum mechanics using another, and that "other" (which is essential, and nobody from Everett onward has developed something which allows us to bypass it) is not related to the quantum system itself.

This quite neatly gets rid of any sort of dragon

Right. Except the one: the entirety of quantum mechanics. Because if the "universe" selects the observables, then we wouldn't need things like Hermitian operators, or any similar formalism which is required to say anything about any value we get.

So, I repeat: what's the problem?

Apparently, that you wish to adhere to an interpretation without knowing how your understanding of it conflicts with quantum mechanics and with any MWI. Or perhaps the problem is that I fail to understand how you can make statements like the following:

Ewww, dualism.

Guess what modern many-worlds interpretations are based on? Metaphysics, philosophy, interpretations of probability and in particular subjective probability, and perhaps most importantly things like quantum minds & quantum consciousness. In fact, the "universe is a quantum computer" is an approach found in deistic-like metaphysical and spiritual accounts of reality. The universe is essentially "God", the "mind" which has brought forth reality, and continually does so. Moreover, we (as conscious observers) are continually interacting with the "mind-universe" and thus intricately connected to the Creator, that consciousness which spawned reality and which continually does so, as do we (by "observations"). I've come across this type of view many times (Here's an example). But for someone who thinks that quantum mechanics isn't really all that important in understanding the brain, who regards dualism in the way you appear to, and who has consistently argued against things like "free will" and objected to metaphysical speculations about God, reality, consciousness, and quantum mechanics, your interpretation of the "many-worlds" approach reflects what one usually finds in esoteric blends of Eastern & Western spirituality. And if that's what you believe, fine. But it doesn't appear to be what you believe, so I don't understand how you can on the one hand seem to support the "shut up and calculate" approach to the copenhagen interpretation, yet call it a many-worlds interpretation simply because squish together the quantum system formalism with an entirely different formalism (which Everett did not do) used to get us results (i.e., to "shut up and calculate", we need this formalism) and refer to both as if they were indistinct, thereby contradicting every approach to quantum physics there is.

 

[LegionOnomaMoi]

I looked around to find the most comprehensive yet concise treatment or Everett, Decoherence, and the "measurment problem" which fit the following criteria:
1) It's both academic and freely available
2) It is sympathetic to (and in some sense supportive of) Everett.
3) It has the math, but not in any particularly difficult presentation.
4) It discusses clearly the break between "shut up and do the math" approach and Everett's solution (along with others).
5) It clearly lays out the difference between the formalisms behind measurement and systems (and "states"), and how descriptions of these frequently differ from the way actual experiments are conducted or what is found in specialist literature.
6) I don't agree with just about any part of it (probably the most important criterion).

I've probably linked to this before (I've lost track), but if I did it was probably in some other context for some other point. Here, it is to explain better than I seem to be able to how decoherence relates to quantum mechanics and to "the" MWI/Everett's solution, as well as how it does not. In fact, before getting into Everett (and the other) accounts of decoherehnce, the author introduces the section with: "Those readers inclined towards the so-called "shut up and calculate interpretation", therefore, can stop reading now."

Moreover, the author briefly but rather aptly addresses how the "right answers" relate to things like our knowledge of quarks, leptons, etc. In other words, what's the problem when the formalisms allow us to discover so much?
"The particle spectrum of a quantum field theory is determined by the dynamical features of the theory, and in general it is determined only approximately, and in a way that varies according to the contingent features of the regime which interests us. (In some situations, we analyse quantum chromodynamics in terms of quarks; in others, in terms of protons and neutrons; not only the masses and charges of the particles, but which particles we use in the first place, vary according to the energy levels at which the theory is analysed.)"
Although a vastly more intricate picture is behind this simple statement (i.e., some coherent and justifiable explanation of the relationship between predictions, mathematics, and what "particles" are "discovered", rather than simply described in different terms depending on the treatment), it at least addresses the issue. Finally, as stated in criterion 4, the issue of "eigenstates" and so forth is laid out.

Decoherence and its role in the modern measurement problem

 

[ThePainefulTruth]

Not too many of us suggest we have no free will in our everyday life.

However it does get kind of mystical when we wonder about what is happening, after a bout of idle mind, upstream from the underlying causes of our next thought.

Any thoughts anybody?
:human:

Free will, that is the freedom to be able to have thoughts independent from God and to exercise the choice to be moral/virtuous or not, I believe is the purpose for the universe.

How does a divine, omnipotent, omniscient, omnipresent God go about creating a creature capable of independent thought. Say abracadabra and poof, there's a man (or whatever) and then ask it, "what do you think of me, your God and creator? And if I created another one of your kind, how would you interact with it?" Does anyone really think that we would truly be ourselves with God watching over our shoulders?

The only way to to test us is to be able to put Him out of our minds so that we have no evidence that He even exists, which would require that we also have no evidence that He doesn't exist either. Once that's accomplished, both God and we know whether we would actually, say, kill our neighbor and take his stuff--or whatever example of immorality or virtue we can imagine.

 

[PolyHedral]

"The math points there" got us nothing of the sort. Interpretations of the math did, and these were followed by interpretations of experimental results (determined to an unknown degree by the math itself).

Well, sure, if you count working out what a "particle" looks in quantum field theory an "interpretation."

You can't map a vector space to anything. That is, when we say something like "a function f mapping R to R ( or R->R)" we are saying nothing much at all.

But we say a huge amount: we say it is a member of a well-defined and calculuable set. In doing so, we ascribe it a huge amount of properties. (Among other things, it allows us to make sure the workings are "type-safe" - e.g. we don't pass values which belong to the wrong sets into functions.)

There is no "general quantum state" either. Rather, in the standard formalization, "pure" quantum states are described by state vectors, such that each quantum system is attributed to, or said to "lie in" or "be in", a seperate space in H (i.e., distinct spaces in a complex vector space).

Pure quantum states are single vectors in Hilbert space. Superpositions of pure states are represented by linear combinations of basis states, but, of course adding any number of vectors yields a single vector.

As for the contents of Hilbert space, it is too small to contain the state space of every possible system, only any possible system. (At least, if I did the preliminary transfinite arithmetic right.)

And most importantly, the "bra" and "ket" state-vectors are maps (or at least the "bra" is and the "ket" can be). The "bra" state-vector is a map from H to H*.

The ket syntax is just another way to write a vector. The bra syntax is a mapping, i.e

, the bra state-vector is not. It's a member of H*. (I think. Depending on whether you interpret a transpose of a vector as a functor.)

However, in order get values associated with these "states", we do not use functions on the phase space but a linear Hermitian operator O on H. In other words, this: is NOT true.

Hermitian operators are functions, and in this case do operate on the phase space H. Also, which values are we talking about? As mentioned, state-vectors are values within a known set.

We are not dealing with the same space, but rather a statistical operator or alternatively a normalized linear map from the observables to expectation values. And it is not over the complex numbers.

You get your expected probabilities by rewriting your state-vector as a combination of the eigenvalues of your observable operator, and then absolute-squaring the coefficients. :sarcastic From there, calculating the expectation value is just a matter of normal statistics.

Where are you getting the above from? The quantum state is not and is never equated with the eigenstate of the operator corresponding with any observables, whether or not we actually get an eigenstate of the operator corresponding to a measured observable.

That's what collapse is. When you measure a superposition, you wind up with a value, and your system continues giving that value until sometihng else happens to it. Your state vector has changed from some combination of basis states into a single eigenstate. (Assuming your eigenvectors are your basis. Obviously it looks different if your statevectors aren't written in the basis for the operator you measured.)

That is, we do not obtain probabilities from Ψ(x), but only from the square of its absolute value and only after measurement.

We seem to have dropped the "predictive" part somewhere along the line.

We have only a quantum state to work with, and with that we cannot obtain anything meaningful (nor does any MWI, from the initial proposal of Everett to modern interpretations) change this. In order to get something, we have to introduce an entirely seperate formalism.

What is the quantum "state" we have to work with which is not the formalism? It's not as though we can actually look at what the universe is doing under the covers.

For one thing, I can multiply this state vector with any arbitrary complex constant and somehow the "system" doesn't change.

Just like the point of zero pontential energy is arbitarary, or the origin of the coodinate system is arbitarary - the scale of the state vectors is arbitarary and non-physical. So? Why must the scale affect the physical state?

All we have done is call the system the phase space, but in doing so made it impossible to obtain any values or other information we can use. Something like Born's rule is necessary to give us anything meaningful.

Once you write the system as a state-vector/wavefunction and choose your basis, that's enough for time-evolution. You don't need the Born rule except as a bridge between your system and a modelled-as-classical reality.

But any such formalism is entirely independent of the quantum system, was developed independently, and rests on circular assumptions and/or outright contradictions.

IOW, all of quantum mechanics is invalid logic? :sarcastic

Because the eigenstates are eigenstates of an operator representing an observable, but as the actual quantum system allows infinitely many correct solutions (or infinitely many quantum states), the formalism developed to relate the quantum system to any observable are interpretation-laden and always involve the application of operators distinct from the quantum system itself.

Infinitely many correct solutions to what? The wavefunction? Any system has a single state-vector at any given time, because of the normalization condition. (The fact that a state "vector" is really a function over dimensions of space and time is neither here or there.)

Again, there are infinite quantum states for any quantum system, but whether or not we get an eigenstate is defined not by the quantum system at all (nor the universe, not the apparati) but most fundamentally by operators meant to represent observables.

When a physical measurement is applied to a quantum system, the result produced is always an eigenstate of the operator corresponding to the measurement made. (Merely different ones, with different proportions, depending on original state.) That's the entire point of constructing observable quantities as operators in the first place.

These are distinct from the quantum system, regardless of what we measure, they are independent of the schroedinger equation, the wavefunction, and all the other mathematical representations fo the quantum system and its dynamics.

Except, as mentioned, they are predicted by the wavefunction's formulation.

You don't "bypass" the problem of how an operator corresponding to observables (and not to the quantum system at all) does so by simply renaming them (and, fyi, that's not what is done in MWI).

You do it by mkaing observables non-physical entities. The universe does not care what observables correspond to which operators, or even if there's a finite amount of operators - it just keeps on evolving.

We're obtaining observables by representing the system and its dynamics using one set of formalisms, and then obtaining values or states which are the basis for all quantum mechanics using another, and that "other" (which is essential, and nobody from Everett onward has developed something which allows us to bypass it) is not related to the quantum system itself.

What "other" formalism is there? As far as I've seen, there is exactly one formalism of non-relativistic quantum: the formulation of quantum state functions as vectors in projective Hilbert space.

Because if the "universe" selects the observables, then we wouldn't need things like Hermitian operators, or any similar formalism which is required to say anything about any value we get.

Unfortunately, I don't know what happens if you use an arbitarary operator as an observable. There may be mathematical reasons why there are only a finite number of operators availiable, in which case, ta-daa: the formalism tells us the observables availiable.

My issueis that QM does not tell us how the universe selects the eigenstate it does - hence getting rid of the problem by saying it doesn't.

n fact, the "universe is a quantum computer" is an approach found in deistic-like metaphysical and spiritual accounts of reality. The universe is essentially "God", the "mind" which has brought forth reality...

Minds are a strict subset of computable programs - the universe is distinctly not one, for it does not take in input or produce output.

Moreover, we (as conscious observers) are continually interacting with the "mind-universe" and thus intricately connected to the Creator, that consciousness which spawned reality and which continually does so, as do we (by "observations").

I diagree with that entirely, because I don't view minds as special. Which you should've really got from the "ewww, dualism" comment. As far as I'm concerned, minds are computations like any other. The universe doesn't recognise you as a distinct object (cause you're entangled with stuff) let alone your "mind" as a special, "other" thing that isn't just a bunch of fields interacting just like everywhere else. As far as humans being at all special is concerned...

 

[Skwim]

​

 

[LegionOnomaMoi]

I diagree with that entirely, because I don't view minds as special. Which you should've really got from the "ewww, dualism" comment.

Which is precisely why it is so strange to see you argue what you appear to think is some many-worlds interpretation but which has more in common with the Copenhagen consensus than anything else, yet at the same time talk about the universe in a way that one only finds in esoteric spiritual/theological interpretations of quantum mechanics (which you reject). Which leads me to wonder, apart from wikipedia, what exactly do you base your understanding of quantum mechanics and modern physics on? You have referred to very, very, little literature, and have disagreed with actual specialists writing specialest literature I have cited, yet with perhaps one exception you have relied entirely on wikipedia or other sources. Not that there is anything wrong with this per se, but when you start completely misconstruing what quantum mechanics involves, and disagreeing with peer-reviewed studies based on a wiki page, I do wonder where it is you are getting your information.

Pure quantum states are single vectors in Hilbert space. Superpositions of pure states are represented by linear combinations of basis states, but, of course adding any number of vectors yields a single vector.

Fantastic. Now, how do experiments in quantum mechanics work? That is, given the use of eigenspaces, eigenvectors, and eigenvalues in descriptions of the states of quantum systems, how are these determined based on anything that is related to quantum system dynamics?

As for the contents of Hilbert space, it is too small to contain the state space of every possible system, only any possible system. (At least, if I did the preliminary transfinite arithmetic right.)

It is not too small. Hilbert space is simply the extension of Euclidean infinite dimensional space over the complex numbers. So it is not only uncountably infinite, any complex vector space is necessarily in "Hilbert space", which is after all just the name given to the geometry of complex analysis.

Hermitian operators are functions, and in this case do operate on the phase space H.

"In order to associate states with values designating physical quantities, one then uses Hermitian linear operators O on H, rather than functions of phase-space points as is done in the case of classical mechanics, a fact which is intimately related to the remarks made in the opening of this chapter." from Entanglement, Information, and the Interpretation of Quantum Mechanics (The Frontiers Collection; Springer, 2009).

"The evolution of the pair of systems during these measurement-interactions must be described by some unitary operator,

Also, which values are we talking about? As mentioned, state-vectors are values within a known set.

See here: "Measurement in Quantum Mechanics: Decoherence and the Pointer Basis"

You get your expected probabilities by rewriting your state-vector as a combination of the eigenvalues of your observable operator, and then absolute-squaring the coefficients. :sarcastic From there, calculating the expectation value is just a matter of normal statistics.

"normal statistics" assumes that when I use frequency to create a statistical approach to some system such that I can say something about its states, I'm not simply "observing" one state out of some infinite number of others caused by the measurement process. If that were the case, then I'm no longer dealing with the same system, and I can't develop the rule. That's the difficulty with the MWI approach. It relies on statistical frequency, which is now part of the formalism, but it cannot derive it. Which means there is no basis for saying anything about any observable and all of QM is useless. After all, the entire formalism for prediction is built upon the assumption that repeated measurements with some quantum system can yield generalizable results, because these are, in some way, "observables" of the quantum system began with. In other words, I let some quantum system run, destroy it, see what I get, and repeat, assuming the whole time that the systems I disturb so that I can get something which I can somehow call a measurement is the same system I started out with and the final state is that of the entire system in some sense. Only if this is true can I continue to run such experiments and develop a formalism which allows me to describe the dynamics of a system I never see. If the measurement processs does not actually yield a singular state of the entire system, I have no justification for using my formalism. Which is what Everett and others realized. And so far, any MWI has yet to derive a justifiable approach to using the formalisms which dependend upon measuring the same system the experimenter started out with (not some split branch the universe delivered), there is no justification for the approach.

When you measure a superposition

Impossible.

you wind up with a value, and your system continues giving that value until sometihng else happens to it.

Wrong.

We seem to have dropped the "predictive" part somewhere along the line.

It's amazing how many times you display that emoticon, rather than cite something or refer to something in the actual literature. In any event, the "predictive part" disappears under the assumption of splitting branches. There is no longer any justification for the prediction, which is the result of formalisms designed under the assumption that this splitting did not occur.

What is the quantum "state" we have to work with which is not the formalism?

There is no "the" formalism. There are two contradictory formalisms which are based on circular logic, contradicting assumptions, ignoring theory, or some other problem which has yet to be resolved (italics in original):
"It should now be clear that in quantum mechanics only probabilistic predictions are generally possible (the exception being if the state is an eigenstate of the relevant operator). But consider, for example, a wavefunction such as Ψ(x). The probabilities are obtained not from Ψ(x) itself, but from |Ψ(x)|^2, so that it is through |Ψ(x)|^2 that quantum mechanics makes contact with the physical world. So why not just work with |Ψ(x)|^2, and call that the quantum state? What’s the big deal?
The big deal is that if the fundamental thing is taken to be |Ψ(x)|^2, rather than Ψ(x), you absolutely won’t have quantum mechanics any longer!"
from G. E. Bowman's Essential Quantum Mechanics (Oxford University Press, 2008)

It's not as though we can actually look at what the universe is doing under the covers.

But the formalism we use assumes that we can. It further assumes that the states we get preclude any splitting.

Why must the scale affect the physical state?

If you can manipulate your mathematical model which is supposed to represent the physical state, then either the physical state has changed or you have made your model inaccurate.

You don't need the Born rule except as a bridge between your system and a modelled-as-classical reality.

So why did Everett use it?

IOW, all of quantum mechanics is invalid logic? :sarcastic

That's one popular interpretation, yes. More frequent is that it is flawed. But what is universal is the disagreement as to what the underlying logic and its relation to QM entails.

When a physical measurement is applied to a quantum system, the result produced is always an eigenstate of the operator corresponding to the measurement made.

It doesn't correspond to the "measurement made". It corresponds to a frequency approach to quantum systems which assumes that any MWI is wrong.

You do it by making observables non-physical entities.

Then they aren't observables.

What "other" formalism is there?

Plenty. See e.g., Non-Hermitian Quantum Mechanics or (even easier) the paper I linked to.

As far as I've seen, there is exactly one formalism of non-relativistic quantum: the formulation of quantum state functions as vectors in projective Hilbert space.

But you do realize that the above says nothing about what formalisms exist? It's like saying "As far as I've seen, there is exactly one formalism and it uses linear algebra" or better yet "it uses math"? Hilbert space is just that: a name given to a space used before quantum mechanics existed (Hilbert space, after all, was developed before quantum mechanics).

in which case, ta-daa: the formalism tells us the observables availiable.

It gives us the observables. It tells us next to nothing.

My issueis that QM does not tell us how the universe selects the eigenstate it does - hence getting rid of the problem by saying it doesn't.

Then you are getting rid of QM. See above.

Minds are a strict subset of computable programs - the universe is distinctly not one, for it does not take in input or produce output.

Hm.

 

[ThePainefulTruth]

(Ahem) I thought this worth repeating:

Free will, that is the freedom to be able to have thoughts independent from God and to exercise the choice to be moral/virtuous or not, I believe is the purpose for the universe.

How does a divine, omnipotent, omniscient, omnipresent God go about creating a creature capable of independent thought. Say abracadabra and poof, there's a man (or whatever) and then ask it, "what do you think of me, your God and creator? And if I created another one of your kind, how would you interact with it?" Does anyone really think that we would truly be ourselves with God watching over our shoulders?

The only way to to test us is to be able to put Him out of our minds so that we have no evidence that He even exists, which would require that we also have no evidence that He doesn't exist either. Once that's accomplished, both God and we know whether we would actually, say, kill our neighbor and take his stuff--or whatever example of immorality or virtue we can imagine.

 

[PolyHedral]

Free will, that is the freedom to be able to have thoughts independent from God and to exercise the choice to be moral/virtuous or not, I believe is the purpose for the universe.

Thoughts independent from the laws of physics are impossible, almost by definition. After all, there must be some rules that decide what "you" do - those rules must be part of the universe, since they interact with things in the universe, i.e. your body.

How does a divine, omnipotent, omniscient, omnipresent God go about creating a creature capable of independent thought.

Assuming God is genuinely omniscient, it's not possible. It would mean that God wasn't omniscient, which means he was never omniscient in the first place. (Because he couldn't see the future)

Say abracadabra and poof, there's a man (or whatever) and then ask it, "what do you think of me, your God and creator? And if I created another one of your kind, how would you interact with it?"

A true omniscient God will know both of the answers are probably false. They might not be lies, but they're almost certainly false.

Does anyone really think that we would truly be ourselves with God watching over our shoulders?

No, but that doesn't matter to God - He knows what you'd do if He wasn't watching anyway.

Once that's accomplished, both God and we know whether we would actually, say, kill our neighbor and take his stuff--or whatever example of immorality or virtue we can imagine.

But God already knows all of the circumstances were we would commit immoral acts, without having to hide Himself. That's what being omniscient means. It isn't just a perfect knowledge of the past and future - it's perfect knowledge of everything, including everyone, in all possible circumstances that could ever conceivably happen. (Including those that, with a cursory thought, could inconceivably happen. )

 

[PolyHedral]

Which is precisely why it is so strange to see you argue what you appear to think is some many-worlds interpretation but which has more in common with the Copenhagen consensus than anything else, yet at the same time talk about the universe in a way that one only finds in esoteric spiritual/theological interpretations of quantum mechanics (which you reject).

Considering I'm rejecting the collapse postule, i.e. the core of Copenhagen, as an illusion generated by how our minds are organized, I don't see how you get that idea.

Which leads me to wonder, apart from wikipedia, what exactly do you base your understanding of quantum mechanics and modern physics on?

While that's hardly relavent to how correct it is, it's mostly from Deutsch and Yudkowsky's series, I think. Also, later on, I pilfer from one of yours.

That is, given the use of eigenspaces, eigenvectors, and eigenvalues in descriptions of the states of quantum systems, how are these determined based on anything that is related to quantum system dynamics?

I don't understand the question. All of the eigen-things depend on the operator you're using as your view. (Apart from the eigenfunctions/eigenvectors of said operator, which are of course your wave function solutions.)

"In order to associate states with values designating physical quantities, one then uses Hermitian linear operators O on H, rather than functions of phase-space points as is done in the case of classical mechanics, a fact which is intimately related to the remarks made in the opening of this chapter."

Is

not a function? (I'm perhaps being slightly loose with what is and is not a function, but AFAIK, there's no other operation you can do on operators.)

It appears the standard theory fails: the final state that is assigned to the system is one that we never actually see when we perform the experiment. What we see is either

or

but quantum mechanics predicts something else entirely.

The author has skipped something in his analysis - he hasn't shown how the act of performing the experiment appears in the theory. It sounds akin to saying, in response to the development of the Dirac equation, "His theory fails! It produces too many answers!"

As such, he's ignored the "correct" and consistent answer - that quantum theory is correct, and the reason we never see the superposition is not because it's somehow disappeared, but because it spreads to include us.

See here: "Measurement in Quantum Mechanics: Decoherence and the Pointer Basis"

BTW, I notice that this paper agrees with my earlier argument that QM isn't counterfactually definite:
A basic postulate of quantum mechanics regarding measurement is that any measurement of the quantity A can only yield one of the eigenvalues, ais, but the result is not definite in the sense that different measurements for the quantum state |ψ> can yield different eigenvalues.

Also, re: measurement problem:
The entangled state describing the system-apparatus, as in (3) above should contain one-to-one correlations between the states of the system, {|ψSn}, and the states of the apparatus {|φAn}, so that a read out of the apparatus or meter states gives information about the states of the system.

A question: how do you read-out from the measuring apparatus? You observe it, using the apparatus that is your optic nerve, and we're back to square one! ...But we're not, because we know what an observation entails: the apparatus and the system being observed become entangled. Oh dear, now your optic nerve is in (entangled to) a superposition. By a similar chain of reasoning, your brain enters into a superposition.

...What was doing the observing again?

"normal statistics" assumes that when I use frequency to create a statistical approach to some system such that I can say something about its states, I'm not simply "observing" one state out of some infinite number of others caused by the measurement process.

Assuming you have a discrete series of probabilities, (p,q,r...) of a set of values (a,b,c...) being delivered, the statistics of which value is most likely is high-school level. It doesn't matter where those numbers came from or what they mean - that particular question and others can be answered with the same comparatively trivial process.

(Of course, it gets more complicated if there is a continous spectra and probability measure, but again, where those numbers mean and where they came from has no impact on questions like, "What is the most likely result?")

It relies on statistical frequency, which is now part of the formalism, but it cannot derive it. Which means there is no basis for saying anything about any observable and all of QM is useless.

MWI doesn't, technically, rely on statistical frequency, since it's possible to construct the wavefunction where all branches are equally real - however you are right that to get QM to link up to experimental data, you need the Born rule.

Although, what other rule would you use? Born himself said it's the only one availiable.

If the measurement processs does not actually yield a singular state of the entire system, I have no justification for using my formalism.

The measurement process does produce a singular state of the analyzed system - for every version of you.

And so far, any MWI has yet to derive a justifiable approach to using the formalisms which dependend upon measuring the same system the experimenter started out with (not some split branch the universe delivered), there is no justification for the approach.

In MWI, you are "measuring" the same system the experimenter started out with - that is, you get yourself entangled with it. All the norman ontological assumptions about reality being consistent, repeatable and generalizable still hold - the problem is that they hold for weird Hilbert space vectors instead of the discrete, definite entities we conceived of because we exist at high scales and low energies. (compared to the Planck constant)

In any event, the "predictive part" disappears under the assumption of splitting branches.

It doesn't. It disappears under lack-of-Born-rule, which isn't quite synonymous. You have the Born probability measure across your multiverse, it's just an inelegant and arbitarary kludge. (However, less of a kludge than wavefunctions arbitararily "collapsing" at some undetermined scale.)

There is no longer any justification for the prediction, which is the result of formalisms designed under the assumption that this splitting did not occur.

In MWI+Born rule, the prediction is, "In x% of 'realities', we will find result foo..." which is still a useful prediction, and in agreement with experiment.

The big deal is that if the fundamental thing is taken to be |Ψ(x)|^2, rather than Ψ(x), you absolutely won’t have quantum mechanics any longer!"
from G. E. Bowman's Essential Quantum Mechanics (Oxford University Press, 2008)

Well, yeah: good luck constructing complex arithmetic and other field operators from real arithmetic.

But the formalism we use assumes that we can.

It explicitly says we can't, essentially since there's nothing we can use that will give us answers without invalidating some other previous answer and/or affecting the forward evolution of the system.

It further assumes that the states we get preclude any splitting.

I don't see what you mean by that. What do you mean by "splitting?"

If you can manipulate your mathematical model which is supposed to represent the physical state, then either the physical state has changed or you have made your model inaccurate.

So what's the physical meaning of zero potential energy?

So why did Everett use it?

Because he was trying to model observation?

That's one popular interpretation, yes. More frequent is that it is flawed. But what is universal is the disagreement as to what the underlying logic and its relation to QM entails.

Methinks they just want a more classical reality.

It doesn't correspond to the "measurement made". It corresponds to a frequency approach to quantum systems which assumes that any MWI is wrong.

I don't understand what you mean at all. The value you get back for measuring something, e.g. the momentum is a single real number.

Then they aren't observables.

I see what you're getting at, but I'm not sure what the most sensible relationship between observables and reality is. Clearly, they are observable - but since everything we think of as an observable reality is a conglomorate of quantum doodads, I'm not sure precisely what that means.

Plenty. See e.g., Non-Hermitian Quantum Mechanics or (even easier) the paper I linked to.

I'm not seeing anything about alternate formualisms in what I've read of it so far.

It gives us the observables. It tells us next to nothing.

The observables and corresponding operators are pretty important, considering that they also produce the conserved quantities and symmetries of the system.

Then you are getting rid of QM. See above.

It would seem to be the opposite. With no eigenvalue selection, there is no definite measurement, and so we never reach anything approaching classical mechanics. Oops.

Hm.

No scathing reply? Whatever should I do now?

 

[ThePainefulTruth]

Thoughts independent from the laws of physics are impossible, almost by definition. After all, there must be some rules that decide what "you" do.

"There must be some rules". Hardly definitive, much less something on which to base a claim to the impossible. It's impossible for God to be able to provide us with free will?

No, but that doesn't matter to God - He knows what you'd do if He wasn't watching anyway.

Even if He made it so that even we wouldn't know for sure what we'd decide until we did it? Is God omnipotent or not?

 

[LegionOnomaMoi]

Considering I'm rejecting the collapse postule, i.e. the core of Copenhagen, as an illusion generated by how our minds are organized, I don't see how you get that idea.

Because you hold on to the probabilistic interpretation (which is not really a part of most many-worlds interpretations in the way you have described quantum mechanics), and because unlike just about every MWI proponent (along with most working with quantum mechanics) you "don't see a problem" when it comes to the measurement problem. Finally, although your resolution to the "measurement problem" involves terms taken from the MWI, the actual formalism and explanation of it relies almost utterly on the "standard model" and the Copenhagen consensus. The description of "operators" you supply is & how it is related to the system by QM formalisms is mostly alien to modern physics, and belongs to a time during which the Copenhagen consensus ruled and the idea that the measurement problem was anything to worry about was not something one said without incurring the displeasure of one's colleagues. More specifically, where now the issue of using "observables" and the formalisms developed and applied independently of any actual quantum system are viewed as problematic (which wasn't not true while the Copenhagen interpretation ruled) is no longer a part of the decoherence framework of modern physics.

While that's hardly relavent to how correct it is

This is certainly true.

Deutsch and Yudkowsky's series

Yet unless Deutsch has radically changed his view since he wrote Fabric of the Cosmos, he is anti-reductionist, does not believe in any "impartial and infallible method" of logic, and argues that even "the idea that mathematics yields certainties is a myth too" (italics in original). Nor does his more recent work reflect your own on causality. Take, for example, his contribution to Many Worlds?: Everett, Quantum Theory, & Reality: "I should also mention time travel. I think that more work needs to be done on information flow round closed time-like curves. Because even if it turns out that we have to rule them out, how can we do that without understanding what causality means in the multiverse? And one thing we do know is that it means something different from what it means in spacetime." What you seem to rule out, he finds likely to be a real possibility. Additionally, his views on emergence are of the type which you seem to reject.

And Yudkowsky, as much as I have enjoyed some of his writing, is not a physicist. His background, actually, is somewhat similar to my own, although I do have some degrees (if memory serves, he does not) and have worked at a university lab doing grad research in the field he does. This is not to say that he is wrong (I can't recall reading anything he wrote on QM), but that whatever he has produced has at most as much behind it in terms of work in the field or expertise as any response I give. And I am not a specialist in physics, but rely on specialist literature.

Also, later on, I pilfer from one of yours.

(IMPORTANT! We don't call it "pilfering" we call it research. I steal from someone who stole from someone else so that someone can steal from me, but we call it "research" so that it sounds respectable).

I don't understand the question. All of the eigen-things depend on the operator you're using as your view

You wish, if I understand you correctly, to take the quantum formalisms describing the quantum "system" as is. However, the operators/functions which give us our observables were developed not through inference but through a frequentist approach to systems which precludes any splitting. In order for statistical probabilities to mean something such that over time we can say something about what some quantum system will do (such that we can apply something like Hermitian operators in order to get any "states" at all), we need to assume that this splitting does not occur. We assume that repeated measurements on a system prepared in such a way and then "measured" (destroyed) in such a way can, over time, tell us about the dynamics of that system. Given some specific specification on a quantum system, a frequency analysis tells us that we can use some "initial state" (which isn't really an initial state), apply some wavefunction which takes this state as input and which after "measurement" yields output (which we can't access), such that under the assumption we have developed model of quantum system dynamics by measuring the same system and how initial specifications correspond to final "measurements" of the same system yield particular states or probabilities. If we assume, on the other hand, that every measurement actually "splits" the universe in some sense such that the entire system is no longer present in the observer's/measurer's universe, then we cannot ever say that we have measured any "state". All of these states are based on the assumption that given specifications and particular measurements will cause the same system to respond in particular ways. If it does not, because whatever "state" we get is simply the result of a new branch, the functions developed to give us any measurements or values whatsoever are utterly useless.

The author has skipped something in his analysis - he hasn't shown how the act of performing the experiment appears in the theory. It sounds akin to saying, in response to the development of the Dirac equation, "His theory fails! It produces too many answers!"

Is

not a function?

It is only through measurement that we developed the formalisms to get any observables whatsoever. The above function was not only developed out of a statistical approach, but is only obtained after measurement.

BTW, I notice that this paper agrees with my earlier argument that QM isn't counterfactually definite:

The problem is how you interpret this. Counterfactual indefiniteness means that any "measurement" we get is meaningless. The "thing" or "entity" or "system" we are saying something about (some state of some quantum system or something about some subatomic "particle"), if it is counterfactually indefinite, cannot ever be described via measurement. Counterfactual indefiniteness implies that any measurement is meaningless. Again, it's like saying the moon is only there when you look, which means that anything you say about the moon's trajectory, mass, velocity, etc., is merely a consequence of you looking, and has nothing to do with whatever is actually "out there" and has nothing to do with "the moon".

 

[LegionOnomaMoi]

A question: how do you read-out from the measuring apparatus? You observe it

It's far more complicated. The apparatus just give me some number. Unless I have the formalism which describes the system dynamics and the way in which observables correspond to these, I have nothing from my read-out. "In quantum mechanics, wave functions evolve according to the Schrödinger equation which is linear and deterministic and this evolution is unitary in nature. Unitary evolutions ensure that eigenvalues are preserved. There is no way that some terms of the density matrix can vanish in the course of a unitary evolution." In other words, Schroedinger's equation and the formalism behind "standard" QM is self-contradictory. Decoherence approaches now do not seek to isolate any quantum system so that any "measurement" can yield it's states, but attempt to infer things about the system by seeing under what conditions quantum "processes" are no longer measureable/observable. Simplistically, rather than try to "observe" the system (destroying it to get some "measurement" values), decoherence approaches in general preserve the quantum state, and seeing what is or is not involved in its coherence. But this again creates a problem for any MWI approach, as we cannot say much about splitting branches from a system we don't have any data about until after it splits.

Assuming you have a discrete series of probabilities

We don't.

Although, what other rule would you use?

Good question. If we have only a wavefunction, and no way of using Born's rule or something like it, then we have no quantum mechanics. This is the major problem facing "relative state" (MWI) approaches to quantum theory.

In MWI, you are "measuring" the same system the experimenter started out with

But the values obtained by that measurement are only obtained via an assumption that MWI rejects.

You have the Born probability measure across your multiverse, it's just an inelegant and arbitarary kludge.

It's circular logic. We get a probability only by assuming that particular results (which, if some MWI is correct, are not the result of the system's dynamics but of something else like the entire universe) can tell us over repeated experiments what this type of system does given some type of interaction/measurement. All that disappears under any MWI, because whatever values we obtain to build up some frequency analysis yielding something like the Born rule is invalid. It assumes that we are running similiar systems and interacting/destroying these in similar ways such that the resulting measurements of such a system can (over repeated trials) tell us how the system works in response to some specific interaction (even if only probabilistically). Any MWI assumes that we aren't actually getting "measurements" from a system but that we are "splitting" the universe such that we only observe one particular state. However, there is no logic behind the state that we get once we assume an MWI is correct.
(However, less of a kludge than wavefunctions arbitararily "collapsing" at some undetermined scale.)

Well, yeah: good luck constructing complex arithmetic and other field operators from real arithmetic.

I don't think you got the point there.

I don't see what you mean by that. What do you mean by "splitting?"

Whatever state we get is not the result of "destroying" or "interfering" with an entire system which remains in the "observer's" universe, such that over time probabilistic dynamics can be assumed, but that instead whenever we try to "reconstruct" a quantum system's dynamics by using a frequency approach to post-interference "observations" we are not observing e.g., patterns (in e.g., a version of the double-slit experiment) from that system, but any and every "spot" which we detect is somehow related to a "selected state" of some system in some way we do not know.

So what's the physical meaning of zero potential energy?

How does this relate to the question?

I'm not seeing anything about alternate formualisms in what I've read of it so far.

What would you consider "alternate"?

The observables and corresponding operators are pretty important, considering that they also produce the conserved quantities and symmetries of the system.

"Produce" is an apt term.

 

[PolyHedral]

Because you hold on to the probabilistic interpretation (which is not really a part of most many-worlds interpretations in the way you have described quantum mechanics),

I don't really see what you mean by that. Probability isn't really part of the ontology of the wavefunction.

and because unlike just about every MWI proponent (along with most working with quantum mechanics) you "don't see a problem" when it comes to the measurement problem.

Essentially, because the concept of measurement at all is an illusion spawned by the mechanics of entanglement.

The description of "operators" you supply is & how it is related to the system by QM formalisms is mostly alien to modern physics, and belongs to a time during which the Copenhagen consensus ruled and the idea that the measurement problem was anything to worry about was not something one said without incurring the displeasure of one's colleagues.

I'm explaining what a measurement operator is, while also noting its ontologically inaccurate. I don't see the inconsistency.

What you seem to rule out, he finds likely to be a real possibility.

It is known that across the multiverse, the concept of causality disappears entirely. But in any single state of the universe, there's an ontologically defined "history." (Except, like the future, it's fuzzy.)

(IMPORTANT! We don't call it "pilfering" we call it research. I steal from someone who stole from someone else so that someone can steal from me, but we call it "research" so that it sounds respectable).

[youtube]UQHaGhC7C2E[/youtube]
Tom Lehrer - Lobachevsky - YouTube

However, the operators/functions which give us our observables were developed not through inference but through a frequentist approach to systems which precludes any splitting.

But they will be produced by any other interpretation of the statistics involved. I therefore can't see how constructing the operators precludes the universe splitting.

apply some wavefunction which takes this state as input...

This may be a source of confusion. The wavefunction is the state we have.

...such that under the assumption we have developed model of quantum system dynamics by measuring the same system and how initial specifications correspond to final "measurements" of the same system yield particular states or probabilities.

Remember that due to the indistinguishableness of quantum particles, I can construct one system an arbitarary number of times, anywhere in time and space. Just like flipping 1 coin 1000 times produces the same results as flipping 1000 coins at once, constructing 1000 instances of a quantum system should - and does - produce the same statistics as constructing and measuring the same quantum system 1000 times sequentially.

In the electron diffraction experiment, you are not firing 1000 electrons at the screen one at a time. You are taking 1000 measurements of one electron hitting the screen.

If we assume, on the other hand, that every measurement actually "splits" the universe in some sense such that the entire system is no longer present in the observer's/measurer's universe, then we cannot ever say that we have measured any "state".

So what did the splitting?

The above function was not only developed out of a statistical approach, but is only obtained after measurement.

I don't know what you mean by saying that it was obtained "after measurement." Do I not have a correct position (for instance) operator... until after I have measured a system's position?

The "thing" or "entity" or "system" we are saying something about (some state of some quantum system or something about some subatomic "particle"), if it is counterfactually indefinite, cannot ever be described via measurement. Counterfactual indefiniteness implies that any measurement is meaningless.

These two statements say slightly different things. It is shown in the experiment that the system cannot be completely described by any theorectical measurement. But it can be described by an aggregate of measurements, which is essentially what QM produces.

Again, it's like saying the moon is only there when you look, which means that anything you say about the moon's trajectory, mass, velocity, etc., is merely a consequence of you looking, and has nothing to do with whatever is actually "out there" and has nothing to do with "the moon".

Reember why "I think therefore I am" still works even if I'm the Matrix. It might not be what I think is doing the thinking, but something must be. Similarly, there must be something generating the image of the Moon, even if it isn't the nice Newtonian body we thought it was.

It's far more complicated. The apparatus just give me some number.

How do you get the number? You observe the apparatus.

In other words, Schroedinger's equation and the formalism behind "standard" QM is self-contradictory.

Which is why I reject the collapse postulate.

We don't.

How can we not have a discrete set of probabilities if we are interested in the probability of a particle's spin?

Good question. If we have only a wavefunction, and no way of using Born's rule or something like it, then we have no quantum mechanics. This is the major problem facing "relative state" (MWI) approaches to quantum theory.

The Born "rule" seems to actually fall out of the bra-ket syntax. <k|k> is a positive real number for all complex k, if I did the math right.

All that disappears under any MWI, because whatever values we obtain to build up some frequency analysis yielding something like the Born rule is invalid. It assumes that we are running similiar systems and interacting/destroying these in similar ways...

This isn't an assumption - it's demonstrated by the fact that particles are indistinguishable.

Any MWI assumes that we aren't actually getting "measurements" from a system but that we are "splitting" the universe such that we only observe one particular state. However, there is no logic behind the state that we get once we assume an MWI is correct.

There's no logic in any other interpretation without the Born rule.

(However, less of a kludge than wavefunctions arbitararily "collapsing" at some undetermined scale.)

I don't think you got the point there.

|psi^2| is a real number. The point of the wavefunction being a complex number is that complex arithmetic works differently than real arithmetc. You can't use |psi^2| as your fundamental object because you need that complex number behaviour.

Whatever state we get is not the result of "destroying" or "interfering" with an entire system which remains in the "observer's" universe, such that over time probabilistic dynamics can be assumed, but that instead whenever we try to "reconstruct" a quantum system's dynamics by using a frequency approach to post-interference "observations" we are not observing e.g., patterns (in e.g., a version of the double-slit experiment) from that system, but any and every "spot" which we detect is somehow related to a "selected state" of some system in some way we do not know.

But we do know why we that spot on the screen - someone must.

How does this relate to the question?

The scale of the vector in Hilbert space has the same physical meaning as the potential energy zero line - none. They are arbitarary.

 

[LegionOnomaMoi]

These are the most fundamental issues (IMO):

Remember that due to the indistinguishableness of quantum particles, I can construct one system an arbitarary number of times, anywhere in time and space. Just like flipping 1 coin 1000 times produces the same results as flipping 1000 coins at once, constructing 1000 instances of a quantum system should - and does - produce the same statistics as constructing and measuring the same quantum system 1000 times sequentially.

This may be a source of confusion. The wavefunction is the state we have.
I don't really see what you mean by that. Probability isn't really part of the ontology of the wavefunction.

In the electron diffraction experiment, you are not firing 1000 electrons at the screen one at a time. You are taking 1000 measurements of one electron hitting the screen.

Everything about measurements and many-worlds is irrelevant if something as basic as the difference between the states of the system and the wavefunction is not realized. Under no interpretation of QM is the wavefunction the "state we have". It's a function (the relationship between the so-called "generalized wavefunction" and quantum systems is still not a matter of "states"). Like all functions, it takes input and produces output. When a system is transcribed into QM formalism (a wavefunction) &#936;(x), the variables x form a set which is supposed to be characteristic (i.e., represent in some sense) the prepared quantum system. In other words, the actual wavefunction which is the "quantum system" is only the system because the argument of the function is intended to relate to the specifications/preparation of some specific quantum system. We do not get anything with a wavefunction unless we can independently talk about characteristics of the prepared system itself, such that the wave function can do what functions do: mapping.

More importantly, this

How can we not have a discrete set of probabilities if we are interested in the probability of a particle's spin?

Is fundamentally contrary to Everett's position (see here). There is no "particle". Reality itself is nonlocal and we get into violations of all causality in this world (as Everett's relative state was not a "many-worlds" interpretation). In the Copenhagen interpretation, we have "particles" like electrons and photons. In Everett and modern decoherence approaches, we have to throw out most of QM as it has been understood along with causality. The quantum world isn't accessible by QM as it was performed for most of its history, because the measurement process and the development of probabilities that certain "systems" prepared in certain ways would yield certain results is abandoned as hopelessly circular and both theoretically and empirically invalid. For example, as I have repeatedly said (and linked you to entire studies) macroscopic systems and actual implementation of Wheeler's delayed choice experiment have showed that all the "weirdness" of quantum mechanics can be empirically observed in this world. Not "splitting" branches of reality, but one fundamentally nonlocal reality which we cannot ever really access and can instead only observe the conditions under which "classical" reality can or cannot be observed.

If you wish to support the idea that QM demonstrates "measurments" are just some "splitting" of classical reality, then you have to deal with the experimental evidence which allows us to show the same system in multiple states at the same time, or macroscopic systems in superposition states. For example:

REALLY!!? "Quantum systems exhibit particle- or wavelike behavior depending on the experimental apparatus they are confronted by. This wave-particle duality is at the heart of quantum mechanics. Its paradoxical nature is best captured in the delayed-choice thought experiment, in which a photon is forced to choose a behavior before the observer decides what to measure. Here, we report on a quantum delayed-choice experiment in which both particle and wave behaviors are investigated simultaneously. The genuinely quantum nature of the photon&#8217;s behavior is certified via nonlocality, which here replaces the delayed choice of the observer in the original experiment. We observed strong nonlocal correlations, which show that the photon must simultaneously behave both as a particle and as a wave." A Quantum Delayed-Choice Experiment

Or

"In as far as [Schrödinger's cat] designates the quantum superposition of two macroscopically distinct states of a highly complex object, the molecules in our new experimental series are among the fattest Schrödinger cats realized to date. Schrödinger reasoned whether it is possible to bring a cat into a superposition state of being 'dead' and 'alive'. In our experiment, the superposition consists of having all 430 atoms simultaneously 'in the left arm' and 'in the right arm' of our interferometer, that is, two possibilities that are macroscopically distinct. The path separation is about two orders of magnitude larger than the size of the molecules."

from "Quantum interference of large organic molecules"

Now, if "classical" reality emerges from quantum reality by "splitting" branches of reality, how is it that we can experimentally demonstrate what has always been integral (if ignored) to QM itself: the nonlocal nature of reality. That is, according to a "splitting universe"-type theory, the "measurement means a selection of some branch. Here, we have two experiments among many others that can detect what they shouldn't (two "branches" which the measurement should have "selected" from to create one observation).

I'm explaining what a measurement operator is, while also noting its ontologically inaccurate. I don't see the inconsistency.

See here: Naive realism about operators

It is known that across the multiverse, the concept of causality disappears entirely. But in any single state of the universe, there's an ontologically defined "history." (Except, like the future, it's fuzzy.)

Which explains why we can get contradicting measurments of the same system or observe superposition in one macroscopic system (and one reality)? How?

[youtube]UQHaGhC7C2E[/youtube]
Tom Lehrer - Lobachevsky - YouTube

I've seen that before. It's brilliant, and I'd forgotten it, so I owe you again.

But they will be produced by any other interpretation of the statistics involved. I therefore can't see how constructing the operators precludes the universe splitting.

Because the operators are constructed indepedently of the wavefunction and under the assumption of a "collapse". No relative state theory or MWI has managed to find another explanation without this assumption.

I don't know what you mean by saying that it was obtained "after measurement." Do I not have a correct position (for instance) operator... until after I have measured a system's position?

That's correct. Or, perhaps a better way of putting it, you have nothing at all until after you measure the system, and if modern decoherence approaches and Everett are correct, you didn't have anything to begin with either.

Reember why "I think therefore I am" still works even if I'm the Matrix.

I read Descartes but I don't see the relevancy:

Although the actual phrase cogito ergo sum does not appear in the Meditatio II, the argument does. It is an argument against the impossibility of epistemology and absolute skepticism. Descartes addresses this possibility by asking whether some God (aliquis Deus) or something/someone (quocun) is capable of constructing a universe of experience and perception so completely false that nothing whatsoever could be known. He answers this by turning skepticism on itself: "Haud dubie igitur ego etiam sum, si me fallit/At any rate I, at least, consequently am, if [as] I am deceived."

This is merely the starting point, however. Having established (at least as far as he is concerned) that absolute skepticism inevitably falls on its own sword, Descartes proceeds from the one thing he believes cannot be doubted, as the act of doubting requires a cognizer to doubt, and moves on from there to other truths one can glean from cognitive and perceptual faculties.

 

[ThePainefulTruth]

Thoughts independent from the laws of physics are impossible, almost by definition.

The minute our human (sentient) brains became fully self-aware, we acquired the ability to override the decisions our nature might lead us to, like murdering your neighbor and taking his wife and stuff.

Assuming God is genuinely omniscient, it's not possible. It would mean that God wasn't omniscient, which means he was never omniscient in the first place. (Because he couldn't see the future)

If God can't put something outside His power when He wants to, He wouldn't be omnipotent. To say so is to declare God's power to be limited.

No, but that doesn't matter to God - He knows what you'd do if He wasn't watching anyway.

Not if He wanted to create you to be so, if He is truly omnipotent. Where do all these omni's come from anyway.

But God already knows all of the circumstances were we would commit immoral acts, without having to hide Himself.

If God already knows, why not create us in our respective heaven or hell with the memories of what He knows we would have done, and bypass all this tribulation in the universe.

That's what being omniscient means. It isn't just a perfect knowledge of the past and future - it's perfect knowledge of everything, including everyone, in all possible circumstances that could ever conceivably happen. (Including those that, with a cursory thought, could inconceivably happen. )

Ditto my last response. This is a test which requires one thing, free will. Otherwise, without free will, we're just sock puppets--just mortal angels. Which is another thing, if God is all those omnis (which I'm not disputing), whyfore angels?

 

[PolyHedral]

The minute our human (sentient) brains became fully self-aware, we acquired the ability to override the decisions our nature might lead us to, like murdering your neighbor and taking his wife and stuff.

Oh, sure, we can consider and reject bad ideas. But that's in our nature.

If God can't put something outside His power when He wants to, He wouldn't be omnipotent. To say so is to declare God's power to be limited.

And therefore omnipotence is a logically incoherent concept.

Not if He wanted to create you to be so, if He is truly omnipotent. Where do all these omni's come from anyway.

You were the one who posited that God is omnipotent/scient.

If God already knows, why not create us in our respective heaven or hell with the memories of what He knows we would have done, and bypass all this tribulation in the universe.

Your hypothesis, you answer.

 

[PolyHedral]

Like all functions, it takes input and produces output. When a system is transcribed into QM formalism (a wavefunction) &#936;(x), the variables x form a set which is supposed to be characteristic (i.e., represent in some sense) the prepared quantum system.

When formulating the WF as &#936;(x,y,z,t), the input variables aren't characteristic of the system at all - they are coodinates of time and space. It is, depending on how you look at it, either &#936; itself or the value &#936;(x,y,z,t) which characterisizes the system.

In other words, the actual wavefunction which is the "quantum system" is only the system because the argument of the function is intended to relate to the specifications/preparation of some specific quantum system. We do not get anything with a wavefunction unless we can independently talk about characteristics of the prepared system itself, such that the wave function can do what functions do: mapping.

The function

describes the probability of the particle being found in position (x,y,z,t). This is not directly related to any characteristic of the system, since many functions will produce the same value for a given tuple. (Although no two distinct functions will produce the same value for all tuples - that makes them the same function.) IOW, the arguments do not relate to the system's structure - the structure of the function relates to the system's structure.

There is no "particle".

There is a thing called spin, though, even if it's just a part of the structure of the equations.

Reality itself is nonlocal and we get into violations of all causality in this world (as Everett's relative state was not a "many-worlds" interpretation).

How can we get causality violation when nothing travels faster than light, ever? The Wheeler double-slit variant, despite first appearances, is entirely local.

For example, as I have repeatedly said (and linked you to entire studies) macroscopic systems and actual implementation of Wheeler's delayed choice experiment have showed that all the "weirdness" of quantum mechanics can be empirically observed in this world. Not "splitting" branches of reality, but one fundamentally nonlocal reality which we cannot ever really access and can instead only observe the conditions under which "classical" reality can or cannot be observed.

Wheeler's experiment is only non-local if you try to squeeze in a decision being made before/after the screen is moved. That's nonsense. It's nonsense speficially because the quantum thing you are firing through the double-slits is not a billiard-ball particle, or a classical wave. It is a quantum thing. It doesn't need to decide - it just excites your detector.

If you wish to support the idea that QM demonstrates "measurments" are just some "splitting" of classical reality, then you have to deal with the experimental evidence which allows us to show the same system in multiple states at the same time, or macroscopic systems in superposition states.

If a superposition exists, it hasn't been measured.

Now, if "classical" reality emerges from quantum reality by "splitting" branches of reality,

Classical reality emerges from quantum by a combination of law of really large numbers, entanglement and decoherence.

See here: Naive realism about operators

Operators don't correspond to ontologically reals things. Isn't that what I said?

Which explains why we can get contradicting measurments of the same system or observe superposition in one macroscopic system (and one reality)? How?

Like I said, fuzzy.

I've seen that before. It's brilliant, and I'd forgotten it, so I owe you again.

I'm writing a novel ATM exploring the effects of memes. I am vey inclined to include a Vladviostock telephone directory at the back and a note: "First person who can tell me why this is here gets $50."

Because the operators are constructed indepedently of the wavefunction and under the assumption of a "collapse". No relative state theory or MWI has managed to find another explanation without this assumption.

In MWI, you can interpret the collapse not as a WF vanishing, but as a conditional probability. "You've become entangled with this object. Given you are in state x, now what?"

That's correct. Or, perhaps a better way of putting it, you have nothing at all until after you measure the system, and if modern decoherence approaches and Everett are correct, you didn't have anything to begin with either.

But I have this operator, right here on the page!

I read Descartes but I don't see the relevancy:

It was in the next sentence.

 

[LegionOnomaMoi]

When formulating the WF as &#936;(x,y,z,t),

Where is that done? Ever? I've seen Dirac's notation (probably the most common), Feynmann's, vector representations, and others, but never anything using coordinates. In fact, using psi to "characterize" the system "is in contrast to the classical description of state which for a system of particles is represented by the coordinates {q1, q2, q3, . . .} and momenta {p1, p2, p3, ...}." (Bell's Theorem and Quantum Realism). Likewise, "Classically, the space of particle joint position&#8211;momentum states, phase space, is a six-dimensional manifold of points; in quantum mechanics, states can be associated only with finite areas, for which the product of the variances of these quantities are less than half the quantum of action h, in an analogous space." (Entanglement, Information, and the Interpretation of Quantum Mechanics; italics in original). In Dirac's notation, kets represent the state as an abstract vector space unique to that system which spans some subspace of H.

the input variables aren't characteristic of the system at all - they are coodinates of time and space.

"Each state of a microscopic system A is represented by a vector in an abstract Hilbert space HA and the physical observables of this system are associated to the hermitian (self-adjoint) operaters in HA." from Exploring the Quantum (Oxford Graudate Texts). Where's time in all of this?

"As stated above, the description of the state and its evolution does not constitute the entire quantum formalism. The wave function provides only a formal description and does not by itself make contact with the properties of the system. Using only the wave function and its evolution, we cannot make predictions about the typical systems in which we are interested, such as the electrons in an atom, the conduction electrons of a metal, and photons of light. The connection of the wave function to any physical properties is made through the rules of measurement. Because the physical properties in quantum theory are defined through measurement, or observation, they are referred to as &#8216;observables&#8217;. The quantum formalism represents the observables by Hermitian operators on the system Hilbert space." (Bell's Theorem and Quantum Realism)

It is, depending on how you look at it, either &#936; itself or the value &#936;(x,y,z,t) which characterisizes the system.

Where are you getting these variables from? Do you think the wave function tells us anything about time evolution of any quantum system?

There is a thing called spin, though, even if it's just a part of the structure of the equations.

There's things called waves, even if it's only in the math.

How can we get causality violation when nothing travels faster than light, ever?

Because there is not sufficient evidence to support this. I went through some dozen or so studies already in this thread, and ended a lengthy discussion of the literature here:

An example of another, simpler (and perhaps more realistic from an experimental and theoretical standpoint) approach is that found in Jensen's "On using Greenberger-Horne-Zeilinger three-particle states for superluminal communication" (found in AIP Conference Proceedings vol. 1208). Here the entangled states of photons are argued to allow sender and receiver to transmit information nonlocally, and therefore faster than the speed of light.

In summary:

1) It is by no means the case that superluminal or nonlocal causation has shown to be impossible. Quite the contrary.

2) Other studies have been published, and will almost certainly continue to be, which argue that superluminal transmission or nonlocal causation is impossible. However, it must be understood that a central component of these "proofs" is certain assumptions which are not supported by either theoretical or experimental results. Rather, they are aesthetically and/or philosophically motivated.

3) What "entanglement" means is so much of an issue that certain physicists argue all of QM must be either considered incomplete or re-formulated.

4) The relationship between SR and GR is not that of the latter making any finding of the former irrelevant, and in fact the relationship between classical mechanics and modern physics is still a matter of some debate.

I then later linked to papers on the demonstration that QM is inconsistent with causality.

The Wheeler double-slit variant, despite first appearances, is entirely local.

It isn't. More importantly, the detection of macroscopic systems in two places at the same time is hardly local. Yet we have so many Schroedinger kittens to deal with now. Here's about the best consise statement on the nonlocality of quantum systems (italics in original): Quantum mechanics has forced us to radically reevaluate our notion of the locality of states. While interactions continue to be local also in the quantum theory (i.e., quantum mechanics is still a local theory), the states that can be generated by these local interactions are distinctly nonlocal." The only sense in which QM is "local" is in the sense that it deals with systems in space, but as these systems are described as fundamentally spread out in multiple regions of space (and have been detected, even beyond the so-called classical limit, as existing in such regions in such a way), to say that the experimental realizations of Wheeler's delayed choice experiment or the superposition of macroscopic systems somehow support "local causality" or "locality" period has been almost indefensible theoretically from the start, and is now experimentally without support. Which, again, is why the foremost association of physicists in the US can publish a volume of their proceedings (i.e., a selected presentation which is then re-written, reviewed, and accepted for publication in a major component of physics scholarship) which contains a paper on the incompatibility of QM and causality. Period. Thanks to the "just take the math as is" approach, it's entirely possible to show that quantum systems violate superluminal restrictions, can be entirely acausal in this reality, can exist in multiple places at once in this reality, and can be dected in multiple differnt states at the same time and in this reality. Not some "multiverse". I linked you to two fully accessible studies with plenty of references to previous work in this field you can access without cost (which, alas, is not generally true).

Wheeler's experiment is

utterly irrelevant. Because it is no longer a thought-experiment. It's now empirical. More importantly, we now have "quantum teleportation" and other such violations of superluminal restrictions and causality. All without some "many-worlds" splitting.

If a superposition exists, it hasn't been measured.

Insofar as measurment is at all meaningful in physics, it has.

Classical reality emerges from quantum by a combination of law of really large numbers, entanglement and decoherence.

The "law of really large numbers" assumes a probabilistic framework which precludes any MWI.

Operators don't correspond to ontologically reals things. Isn't that what I said?

They are all we observe, and exist independently of the wave function formalism.

In MWI, you can interpret the collapse not as a WF vanishing, but as a conditional probability.

Which is irrelevant, as the wave function tells us nothing about anything. See the quote above from Bell's Theorem and Quantum Realism (the second one).

It was in the next sentence.

Do you think the universe is conscious and is capable of self-determining states of being through mental causation? Because that was the point of Descartes argument. Not a quantum computer, but consciousness.