"Single-world interpretations.... cannot be self-consistent"

[Brage]

Observers in QM is something much more general than in normal usage - I added that refinement a bit later in my post.

Thanks
Bill

ok yes I understand what you mean then!

 

[bhobba]

ok yes I understand what you mean then!

The language used in QM is a BIG problem

Thanks
Bill

 

[Talisman]

Yes. Decoherence always involves entanglement, but not the vice versa.

Sorry for bumping an old thread, but can you help me understand when entanglement does not lead to decoherence? Would you say that in the state |0>|0> + |1>|1>, the first qubit exhibits decoherence when measured in the { |0> + |1>, |0> - |1> } basis?

 

[bhobba]

Sorry for bumping an old thread, but can you help me understand when entanglement does not lead to decoherence? Would you say that in the state |0>|0> + |1>|1>, the first qubit exhibits decoherence when measured in the { |0> + |1>, |0> - |1> } basis?

Do you understand what a mixed state is? Express it in terms of that and you will understand the answer. If you don't, and considering this is an I level thread then unfortunately it can't be answered at your level.

The answer is entangled systems, when you observe just one part exhibit the property of being in a mixed state so in that sense can be considered an example of decoherence. But decoherence has one other aspect - irreversibly which requires a more complex interaction/entanglement.

Thanks
Bill

 

[Demystifier]

Sorry for bumping an old thread, but can you help me understand when entanglement does not lead to decoherence? Would you say that in the state |0>|0> + |1>|1>, the first qubit exhibits decoherence when measured in the { |0> + |1>, |0> - |1> } basis?

The first qubit is in a mixed state, but that fact by itself is not decoherence. Decoherence will take place when the first qubit is measured, but that's because of the entanglement with the measuring apparatus.

 

[Talisman]

Thanks. I can see that the first qubit is in a mixed state, and so when it is measured, will exhibit decoherence. But I'm still missing something here. At what point should we consider the qubit to have been measured? For example, we can just say that the system evolves into |0>|0>|A> + |1>|1>|B>, right? And then once again, that fact by itself is not decoherence. Of course if I, the experimenter, am the measuring device, then I will see it "collapse" irreversibly into one state or the other. But that just seems to take us back to the fundamental question of what can be considered a measurement or collapse. Nonetheless, from my perspective as the experimenter, the system (apart from me) does continue to evolve in a reversible way. Which is why, I suppose, we require it be FAPP irreversible.

Does that sound about right?

 

[jambaugh]

They way I think about it is that decoherence is an increase in the system entropy. Whenever the system couples with another system it potentially becomes entangled with that system and, unless you expand your system definition, the system entropy increases. That system expansion is problematic when the other system is the environment (if your system entangles with light headed outward into the great beyond, there's little hope of manipulating that part of a meta-system). The coupling is irreversible and you get decoherence/entropy in the system.

You can even imagine that all entropy is exactly a system's entanglement with its environment and that the entropy of the "universe as a whole" is zero. It is only when we consider the universe subdivided into subsystems that we see positive entropy among those subsystems. However I don't think this last part is disprovable enough to have much scientific meaning. But taking it as an academic exercise it emphasizes the connection between entanglement, entropy, and decoherence.

 

[Talisman]

Thanks, that does clarify some things. In particular, in the state |0>|0> + |1>|1>, if we consider the second sub-system to be "the environment," and for whatever reason we cannot practically unentangle it, then it makes sense to consider the first particle as having decohered. But when it is explicitly written in the form above, and we are considering it as still part of the system under consideration, then it makes sense to say it isn't yet decoherent, because it is reversible.

So ultimately it comes down to practical definitions (hence, FAPP). There is no well-defined (or at least well-accepted) boundary beyond which it is fundamentally irreversible (which we already know as "the measurement problem"), and hence no well-defined boundary for decoherence.

 

[jambaugh]

@Talisman
Right, I find in contemplating this that I must constantly remind myself that many qualifiers we use do not refer to system observables. We must be very cautious when considering systems which we say are entangled, in superposition, coherent/decoherent, or having a specific entropy that we understand that these are really applied to our mode of system description, how we define the basis (eigen-basis of which observables), how we factor composite systems into components, and how thoroughly we have observed the system.

There is a tendency to reify these concepts in the physical state sense because we know that they are physically meaningful and not "just in our heads" but this is where a proper operational interpretation of physics is necessary. When we assert that the meanings of our terms must derive from references to sets of operations we do in the laboratory/observatory then we understand that when we simply say system X has observable A of value alpha, we are asserting that a physical constraint or physical act of measurement has occurred. This is an active pragmatic interpretation and not an ontological one, and thereby qualifiers about the statements themselves gain physical meaning where none exists in the purely ontological interpretation.

For example if we are purely ontological as in the classical sense, then ascribing a probability distribution to our classical system is simply our admitting ignorance, though only partial ignorance about the systems singular state. Then also the entropy of that probability distribution should have no physical meaning... the second law of thermodynamics as derived from statistical mechanics is simply an assertion that over time our ignorance about a system in isolation (from us) must grow. This for obvious reasons doesn't sit well with the physics student and I recall my own despair at ever understanding this. Then when I studied QM it was even worse until my PhD thesis advisor set me straight. Once we give physical correspondence to our assertions about system observables (physical acts of observation which require physical interactions with the system), then qualifiers about our assertions themselves have more directly physical meaning.

This also is why you'll find me quite reactive in the various QM Interpretation discussions. The orthodox (CI) interpretation is a shift from ontic(object state based) to praxic (positivistic, operational, process based) interpretation and it resolves this as well as the mysteries of e.g. EPR in a less sexy but far more consistent way. But then again what would Star Trek episodes do without the MWI as a plot device!

There really is a great deal of philosophy in those PhD's we get... more than I ever imagined back in the day.

 

[stevendaryl]

This also is why you'll find me quite reactive in the various QM Interpretation discussions. The orthodox (CI) interpretation is a shift from ontic(object state based) to praxic (positivistic, operational, process based) interpretation and it resolves this as well as the mysteries of e.g. EPR in a less sexy but far more consistent way.

I guess my feeling about it is that the orthodox interpretation doesn't actually resolve any of the mysteries of quantum mechanics, but instead takes the point of view that you don't need to resolve them in order to get on with the task of doing physics.

 

[Talisman]

Thanks, that all makes sense.

If we say that entanglement causes decoherence only when it is irreversible "FAPP," then it seems we are indeed just kicking the can down the road.

 

[jambaugh]

I guess my feeling about it is that the orthodox interpretation doesn't actually resolve any of the mysteries of quantum mechanics, but instead takes the point of view that you don't need to resolve them in order to get on with the task of doing physics.

Realizing a "mystery" isn't really one is a form of resolution.

QM Mystery: "How do distant measurements of EPR pairs communicate FTL and even causally backward through time?"
Orthodox Resolution: "There's nothing in the physics that says they do and the only reason one might think they do is because one is trying to fit an additional classical objective state based interpretation on the quantum physics."

and to show it's not only about quantum theory:

Classical Mystery: "If two twins are traveling at appreciable speeds relative to each other each sees the other aging slower... but which one is actually slower?"
Relativity Resolution: "There is no mystery here but rather an ill posed question... the "which one is actually slower" part presupposes absolute time and simultaneity. Each twin is actually moving slower through time as defined by the other observer in the same sense that one twin on the pole and the other at 45deg lat each see the others "height" as shorter due to their relative vertical direction.

Note that with the aether based explanation for Lorentz transformations there really is a younger twin, the one moving faster relative to the aether but there's no physical way to tell which one that is. It too "resolves" the mystery but not in a way that has any physically observable meaning. Enter Occam, stage right, brandishing a razor.

Such explanations are of the "turtles all the way down" variety, IMNSHO.

 

[stevendaryl]

Realizing a "mystery" isn't really one is a form of resolution.

I'm claiming, on the contrary, that there really is a mystery, and the standard interpretation doesn't resolve it.

QM Mystery: "How do distant measurements of EPR pairs communicate FTL and even causally backward through time?"
Orthodox Resolution: "There's nothing in the physics that says they do and the only reason one might think they do is because one is trying to fit an additional classical objective state based interpretation on the quantum physics."

That isn't resolving the mystery, it's ignoring it. I don't agree that SR is comparable. It may have seemed equally mysterious when it was proposed, but it was basically no longer considered mysterious 5 years later (except among a tiny group of dissenters). In contrast, it's been nearly 100 years since QM was proposed, and there is no consensus, even among the top physicists, as to what it really means. Ask Roger Penrose, or ask Sean Carroll, or ask Steven Weinberg about what's really going on in QM, and you'll get three different answers. That's really not the case with SR. With SR, the doubts are mostly (not 100%, but mostly) confined to newbies and crackpots.

Saying: "The state isn't actually objective" doesn't resolve the mystery. So it's not objective. What does that mean?

 

[stevendaryl]

SR messes with our intuitions about what is objective and what is not, but it does offer a substitute for those intuitions. Lengths and times are no longer objective, but depend on a frame of reference, but proper length and proper time are observer-independent. Anything expressed in the language of tensors is covariant; the components of the tensors may change when you change coordinates, but the tensors themselves can be understood as geometric objects that exist independent of coordinate systems.

What is the analogy when it comes to QM? The standard quantum "recipe" is very much observer-dependent: If you set up a system like this, and perform this type of measurement, you'll see this result with this probability. That is sort of similar to SR's operational definitions of things such as clock synchronization and distance measurements. But the difference (it seems to me) is that SR can be understood in terms of an objective reality that is independent of observers, and observer-dependent quantities are just particular "projections" of this shared reality. In QM, it's not clear what the shared reality is.

People often say that a physical quantity such as the component of a particle's spin along a particular axis simply doesn't have a value until measured. Okay, but what about after it is measured? Does it have a value then?

If you say it does, then it seems to me that you are assigning one type of physical interaction, a measurement, a role in making things "real" that is different from all other types of physical interaction. If you say it doesn't, then to me, you've got MWI, where nothing has definite values, not even measurements.

 

[jambaugh]

Yes, SR is still a classical theory and there is an objective reality behind it. My point was that the "mystery" in the twin "paradox" case was due to a failure of the thinker to wholly accept the relativity in the theory. QM is likewise a relativization, (word?) it however relativizes the objective state (in CI), that being relative to a choice of compatible observables. It is fundamentally different from classical theories, including SR so you won't find the same kind of loss of objective reality.

As to consensus among physicists CI is also referred to as the Orthodox interpretation. It still is the leading view: https://arxiv.org/abs/1301.1069
The "sexier" interpretations (EMW, BPW) get over-represented in discussion forums and Sci-Fi media. I would argue that Von Neumann's ensemble interpretation does not differ far from CI other than that there is a transition from classes of systems to sets of systems in the semantics.

Ask Roger Penrose, or ask Sean Carroll, or ask Steven Weinberg about what's really going on in QM, and you'll get three different answers.

That is exactly the type of "which twin is really older" question that begins with premises contrary to CI. Ask rather "what is actually happening" where "actually" means in the sense of actions and interactions between observer system and environment. You get the same answers when you ask what happens in the lab.

Note that all explanations/definitions/deductions start with unexplained/undefined/non-deduced primaries.

This debate over interpretations is a debate over the choice of primaries. The CI stops at the operational laboratory actions and observations. These are the primaries and all else is explained in terms of them.

Classical physics stops at the objective states and uses these to explain "what's really going on" during the laboratory actions but the states themselves are left unexplained (well we actually go in a circle the way dictionaries do with definitions, and explain states i.t.o. laboratory actions as well... until you get to Everettes worlds, Bhom's pilot waves, and the per-Einstein aether currents). This circularity is fine in classical physics because all acts of observations are commuting Maxwell demons. This is an implicit assumption in assuming objective states as one's primary and all actions are evolution flows on the manifold of possible states.

The SR analog is the pre-relativistic assumption that you can always fibrate space-time into a unique bundle of simultaneous spatial snapshots (fibers) over the base sequence of time. Once time is relativized you must shift to primaries of space-time event points. It's still objective/classical since the primaries, while changed, have not changed type.

In QM under CI the primaries are changing type. The chicken and egg definition cycle of objects-observables, is stopped at observables because one notes there are more of them and they are more generally applicable than objects.

In the logic the set-inclusion lattice of subsets of states transitions to the quantum logic lattice of subspaces in Hilbert space. If you stick to only subspaces which are spans of a given orthogonal basis, you recover a classical logic lattice as a sub-lattice. You can embed classical descriptions in quantum. The thing is though, ALL the other subspaces have operational meaning. There are observables for these "states". There is more happening, more actions available, in a quantum logic lattice than can be expressed as a power set of a maximal set of primary states i.e. than can be expressed as point transitions between objective states. Quantum logic is a language of actions and it is a richer language than classical logic. This is why it is the natural place to start, the justification for actions are primary.

 

[stevendaryl]

Yes, SR is still a classical theory and there is an objective reality behind it. My point was that the "mystery" in the twin "paradox" case was due to a failure of the thinker to wholly accept the relativity in the theory.

And I'm saying that QM is not analogous.

As to consensus among physicists CI is also referred to as the Orthodox interpretation. It still is the leading view: https://arxiv.org/abs/1301.1069
The "sexier" interpretations (EMW, BPW) get over-represented in discussion forums and Sci-Fi media.

I would dispute that it is an interpretation at all. Instead, it is a "recipe" for getting predictions out of QM. That's why I said that the orthodox interpretation really amounts to saying that we don't care about what's going on "under the hood". Which is fine, as far as it goes. But saying you don't care about a question does not mean that you've answered the question, nor does it mean that you've proved the question to be ill-posed.

That is exactly the type of "which twin is really older" question that begins with premises contrary to CI.

I disagree. I don't think they are analogous.

In the logic the set-inclusion lattice of subsets of states transitions to the quantum logic lattice of subspaces in Hilbert space. If you stick to only subspaces which are spans of a given orthogonal basis, you recover a classical logic lattice as a sub-lattice. You can embed classical descriptions in quantum. The thing is though, ALL the other subspaces have operational meaning. There are observables for these "states". There is more happening, more actions available, in a quantum logic lattice than can be expressed as a power set of a maximal set of primary states i.e. than can be expressed as point transitions between objective states. Quantum logic is a language of actions and it is a richer language than classical logic. This is why it is the natural place to start, the justification for actions are primary.

I can't make any sense of what you wrote. If that's the solution to the mystery, then I still would claim that it's unresolved.

 

[stevendaryl]

As to consensus among physicists CI is also referred to as the Orthodox interpretation. It still is the leading view: https://arxiv.org/abs/1301.1069

I would say that that survey perfectly captures the muddled state of quantum interpretations. For example:

Question 5. The measurement

• A pseudo-problem 27%
• Solved by decoherence 15%
• Solved/will be solved in another way 39%
• A severe difficulty threatening quantum mechanics 24%
• None of the above 27%

If there were that kind of spread of opinions about SR, I would say that your comparisons with SR are apt.

 

[jambaugh]

I would dispute that it is an interpretation at all. Instead, it is a "recipe" for getting predictions out of QM. That's why I said that the orthodox interpretation really amounts to saying that we don't care about what's going on "under the hood".

No it says more, it says it is meaningless* to refer to "what's going on 'under the hood'" (between acts of observation) because that is, by definition unobservable. It is the same as the aether of unrelativity being fundamentally unobservable and thus meaningless*.

*Anyone can give personal meaning to a concept, like aether, pilot waves, demons, and deities. They are meaningless in a scientific context because there is no access to them. You can claim pilot waves or many worlds and I can claim leprechauns or bowling balls, if we both predict the same observable behavior our theories are not empirically distinguishable. They are at best, meaningful in the same sense as Maxwell's mechanical model, they might provide a conceptual scaffolding for organizing your description of the real physics... how observable entities behave.

So it is not just a question of sour grapes... to claim one doesn't care because one cannot reach them... it is a deeper question of the meaning of the "grapes" existing at all, (replace the fox and grapes with the "emperor's new clothes"... I put these alternative interpretations in the same story book as the taylors' claims about the invisible cloth.)

 

[stevendaryl]

No it says more, it says it is meaningless* to refer to "what's going on 'under the hood'" (between acts of observation) because that is, by definition unobservable. It is the same as the aether of unrelativity being fundamentally unobservable and thus meaningless*.

I think that point of view is nonsense. An observation is a particular kind of interaction. To say that the only thing that is real are those interactions that count as observations is hopelessly solipsistic, in my opinion.

 

[stevendaryl]

So it is not just a question of sour grapes... to claim one doesn't care because one cannot reach them... it is a deeper question of the meaning of the "grapes" existing at all, (replace the fox and grapes with the "emperor's new clothes"... I put these alternative interpretations in the same story book as the taylors' claims about the invisible cloth.)

No, it's not any deeper. It's just a pretense of being deeper.

 

[jambaugh]

I think that point of view is nonsense. An observation is a particular kind of interaction. To say that the only thing that is real are those interactions that count as observations is hopelessly solipsistic, in my opinion.

The interactions need not themselves be observables, they need to be definable in terms of changes they make on observables.

If you claim interaction A is occurring and I claim no, interaction B is occurring and if no-where is there an observable that will be distinct depending on which case is true then it is meaningless in a scientific discussion to say either is truer than the other. You, for example cannot empirically disprove those fringe who believe in an aether. The claimed interaction between aether and clock and between aether and measuring rod, make that interaction meaningless in terms of distinguishable observations. If I were to go on about how the aether really really is there, and that's really what's going on under the hood of SR you'd shower me with far more derision than I'm feeling from you now. But nowhere could you disprove my claim because my claim is meaningless when it comes to actual changes in empirical behavior vs Einstein's version.

No, it's not any deeper. It's just a pretense of being deeper.

Is to, is to! (We can do that all day until the mods shut us down. How about some point beyond the claim.)

So let me ask you then, which is right, Bohm's Pilot waves, or Everett's Many Worlds? Both "explain" as you think of it, both make no further prediction about what we will see in the lab or observatory than is made by CI. If I create the Baugh's Many Worlds of Pilot Waves Through the Superluminal Aether with Supervising Pixies, interpretation, how can you distinguish my absurdity from theirs?

 

[Boing3000]

You, for example cannot empirically disprove those fringe who believe in an aether.

I am under the impression that science works the other way around. So let's keep the burden of proof where it belongs.

So let me ask you then, which is right, Bohm's Pilot waves, or Everett's Many Worlds?

All are. Copenhagen also. They don't go on to prove anything. For that they would need to make a distinguishable claim (experimentally verifiable)
And claiming the CI solve "a problem" by ignoring it is fine ... I suppose. But I think it is clearly closing the door to many paths of investigation. And I personally find it strange that wishful ignorance should enter the scientific method on no other ground that "a problem" is too tough to brake.

how can you distinguish my absurdity from theirs?

From my limited layman's knowledge, BM pilot wave is quite deterministic. So it could be possible to prepare a system where all the outcome would be identical. So I suppose there is no harm trying that ?
As for other interpretations, I suppose they have not been invented just to fill layman's literature (or forums), but also to distinguish themselves about possible experiment outcome. CI is quite different in that regard.

 

[zonde]

they [interactions] need to be definable in terms of changes they make on observables.

You are putting cart before the horse. Observations (even more, statistical properties of many similar observations) can't be primitive terms in explanation.
Scientific method works by formulating hypothesis (explanation), then deriving predictions from hypothesis and then testing predictions against observations.

 

[forcefield]

People often say that a physical quantity such as the component of a particle's spin along a particular axis simply doesn't have a value until measured. Okay, but what about after it is measured? Does it have a value then?

If you say it does, then it seems to me that you are assigning one type of physical interaction, a measurement, a role in making things "real" that is different from all other types of physical interaction. If you say it doesn't, then to me, you've got MWI, where nothing has definite values, not even measurements.

Well, if we take the analogue of flipping a coin, then I'd say that QM measurement is analogous to flipping the coin and looking at the result (value) is just trivial.

So there is no mystery why there is no result for the coin or for the "spin" before "measurement".

 

[Jilang]

Except for entangled pairs!

 

[stevendaryl]

Well, if we take the analogue of flipping a coin, then I'd say that QM measurement is analogous to flipping the coin and looking at the result (value) is just trivial.

So there is no mystery why there is no result for the coin or for the "spin" before "measurement".

That's treating measurement as fundamentally different from other interactions. But why is it different? A measuring device just relies on the same electromagnetic forces that most other interactions involve.

 

[forcefield]

That's treating measurement as fundamentally different from other interactions.

What do you mean ? I am considering the measurement to consist of the whole experimental configuration.

I think we are getting off topic here.

 

[stevendaryl]

What do you mean ? I am considering the measurement to consist of the whole experimental configuration.

I mean that if you take the approach that a system doesn't have a value for a property until that property is measured, then that seems to be giving a role to measurement that is different from the role of any other measurement.

I think we are getting off topic here.

To me, it seems exactly what the thread is about---whether single-world interpretations are consistent. The reason for thinking that maybe they aren't consistent is because if you treat a measurement process as just like other types of interactions, then measurement would not result in a single unique value any more than any other interaction does.

 

[forcefield]

I mean that if you take the approach that a system doesn't have a value for a property until that property is measured, then that seems to be giving a role to measurement that is different from the role of any other measurement.

I can't make sense of that.

To me, it seems exactly what the thread is about---whether single-world interpretations are consistent. The reason for thinking that maybe they aren't consistent is because if you treat a measurement process as just like other types of interactions, then measurement would not result in a single unique value any more than any other interaction does.

Then I would say that there is something wrong in the logic that does not lead to single unique values.

 

[stevendaryl]

I can't make sense of that.

Let me illustrate by an (oversimplified) example.

Let [itex]|u\rangle[/itex] be the spin-up state of an electron, and let [itex]|d\rangle[/itex] be the spin-down state (relative to the z-axis, say). Now, consider a measuring device that attempts to measure the spin of an electron. It starts off in the state [itex]|?\rangle[/itex], meaning it hasn't yet measured the spin. If the electron is spin-up, the device goes into state [itex]|U\rangle[/itex]. If it is spin-down, the device goes into state [itex]|D\rangle[/itex]. You can imagine that the device has two lights, one labeled "U" and one labeled "D", and one or the other lights turns on.

Then we would describe this as:

• [itex]|?\rangle \otimes |u\rangle \Longrightarrow |U\rangle \otimes |u\rangle[/itex] (where [itex]\Longrightarrow[/itex] means "evolves into"). In words: if the composite state is one where the device is in state [itex]|?\rangle[/itex] and the electron is in state [itex]|u\rangle[/itex], then the composite system evolves into the state where the device is in state [itex]|U\rangle[/itex].

• [itex]|?\rangle \otimes |d\rangle \Longrightarrow |D\rangle \otimes |d\rangle[/itex] If the composite state is one where the device is in state [itex]|?\rangle[/itex] and the electron is in state [itex]|d\rangle[/itex], then the composite system evolves into the state where the device is in state [itex]|D\rangle[/itex].

If that's an accurate description, then the Rules of Quantum Mechanics would say:
[itex]|?\rangle \otimes (\alpha |u \rangle + \beta |d\rangle) \Longrightarrow \alpha |U\rangle \otimes |u\rangle + \beta |D\rangle \otimes |d\rangle[/itex]: If the composite state is one where the device is in state [itex]|?\rangle[/itex] and the electron is in a superposition of spin-up and spin-down, then the composite system evolves into a state that is a superposition of one where the device is in state [itex]|U\rangle[/itex] and another state where the device is in state [itex]|D\rangle[/itex].

If the device were described by quantum mechanics, then you wouldn't get a definite result---either [itex]|U\rangle[/itex] or [itex]|D\rangle[/itex]---you would get a superposition of possibilities. That's what Many-Worlds says happens.

 

[forcefield]

If the device were described by quantum mechanics, then you wouldn't get a definite result---either [itex]|U\rangle[/itex] or [itex]|D\rangle[/itex]---you would get a superposition of possibilities. That's what Many-Worlds says happens.

Yeah well I don't buy that. I'm pretty sure Bohr didn't agree with that either.

 

[stevendaryl]

Yeah well I don't buy that. I'm pretty sure Bohr didn't agree with that either.

There is no buying or not buying. The issue is how to explain the appearance of single values for measurements in a way that is consistent with the Rules of Quantum Mechanics. Bohr simply said that QM applies to the microscopic world, while classical physics (objects have definite locations and velocities at all times) applies to macroscopic objects. But the question is whether that's actually consistent. If macroscopic objects are just made up of microscopic objects, then how can macroscopic objects behave differently than microscopic objects. How does the common-sensical world that we are familiar with arise from the Rules of Quantum Mechanics? Or does it?

Saying "I don't buy that" is not really an answer.

 

[zonde]

Electron is quantized (discrete) unit. It is unclear then what is the meaning of ##\alpha |u \rangle + \beta |d\rangle## after measuring apparatus when ##|u \rangle## and ##|d\rangle## components appear at spatially different outputs. If we say that ##|\alpha|^2## and ##|\beta|^2## are probabilities then there should be collapse i.e. ##\alpha |u \rangle + \beta |d\rangle## physically changes to ##|u \rangle## or ##|d\rangle## (and later detectors simply finds out in which output electron ended up).
But If we say that ##|\alpha|^2## and ##|\beta|^2## are something else than probabilities then how we can claim that electron is quantized?
I would say that MWI is just a way how to claim that electron is sort of quantized (in different worlds) and at the same time give meaning to superpositions of spatially separate components.

 

[stevendaryl]

Electron is quantized (discrete) unit. It is unclear then what is the meaning of ##\alpha |u \rangle + \beta |d\rangle## after measuring apparatus when ##|u \rangle## and ##|d\rangle## components appear at spatially different outputs. If we say that ##|\alpha|^2## and ##|\beta|^2## are probabilities then there should be collapse i.e. ##\alpha |u \rangle + \beta |d\rangle## physically changes to ##|u \rangle## or ##|d\rangle## (and later detectors simply finds out in which output electron ended up).

I'm not sure exactly what you're talking about, but there is no process in quantum mechanics by which a state [itex]\alpha |u\rangle + \beta |d\rangle[/itex] changes nondeterministically into either the state [itex]|u\rangle[/itex] or the state [itex]|d\rangle[/itex]. If the measuring device is itself governed by the laws of quantum mechanics, you're never going to get a unique result. A way out is to say that measurement is a special kind of process that selects one possibility out of a superposition (with probabilities given by the square of the amplitudes), but that seems to be treating a measurement device in a way that doesn't actually follow from the way that electrons, protons, etc., behave.

 

[zonde]

I'm not sure exactly what you're talking about, but there is no process in quantum mechanics by which a state [itex]\alpha |u\rangle + \beta |d\rangle[/itex] changes nondeterministically into either the state [itex]|u\rangle[/itex] or the state [itex]|d\rangle[/itex]. If the measuring device is itself governed by the laws of quantum mechanics, you're never going to get a unique result.

So you say that in quantum mechanics electron can only change it's relative phase relationship between components as a result of interaction i.e. [itex]\alpha |u \rangle + \beta |d\rangle \Longrightarrow \alpha |u\rangle \otimes \beta |d\rangle[/itex]
But then measurement apparatus as well can only change it's relative phase relationship between components, right? I.e. in expression [itex]|?\rangle \Longrightarrow \alpha |U\rangle \otimes \beta |D\rangle[/itex] state ##|?\rangle## just means different relative phase relationship between ##\alpha |U\rangle## and ##\beta |D\rangle## components.
I am referring to this expression of yours:

[itex]|?\rangle \otimes (\alpha |u \rangle + \beta |d\rangle) \Longrightarrow \alpha |U\rangle \otimes |u\rangle + \beta |D\rangle \otimes |d\rangle[/itex]

Do I understand it right?