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

[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 |u\rangle be the spin-up state of an electron, and let |d\rangle 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 |?\rangle, meaning it hasn't yet measured the spin. If the electron is spin-up, the device goes into state |U\rangle. If it is spin-down, the device goes into state |D\rangle. 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:

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

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

If that's an accurate description, then the Rules of Quantum Mechanics would say:
|?\rangle \otimes (\alpha |u \rangle + \beta |d\rangle) \Longrightarrow \alpha |U\rangle \otimes |u\rangle + \beta |D\rangle \otimes |d\rangle: If the composite state is one where the device is in state |?\rangle 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 |U\rangle and another state where the device is in state |D\rangle.

If the device were described by quantum mechanics, then you wouldn't get a definite result---either |U\rangle or |D\rangle---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 |U\rangle or |D\rangle---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 \alpha |u\rangle + \beta |d\rangle changes nondeterministically into either the state |u\rangle or the state |d\rangle. 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 \alpha |u\rangle + \beta |d\rangle changes nondeterministically into either the state |u\rangle or the state |d\rangle. 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. \alpha |u \rangle + \beta |d\rangle \Longrightarrow \alpha |u\rangle \otimes \beta |d\rangle
But then measurement apparatus as well can only change it's relative phase relationship between components, right? I.e. in expression |?\rangle \Longrightarrow \alpha |U\rangle \otimes \beta |D\rangle 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:

|?\rangle \otimes (\alpha |u \rangle + \beta |d\rangle) \Longrightarrow \alpha |U\rangle \otimes |u\rangle + \beta |D\rangle \otimes |d\rangle

Do I understand it right?

 

[PeterDonis]

Electron is quantized (discrete) unit.

This is not correct. A correct statement is that certain observables of an electron are quantized (i.e., have a discrete spectrum instead of a continuous spectrum) under certain conditions (for example, energy and angular momentum in bound states). That correct statement does not support the claims you are making.

 

[zonde]

This is not correct. A correct statement is that certain observables of an electron are quantized (i.e., have a discrete spectrum instead of a continuous spectrum) under certain conditions (for example, energy and angular momentum in bound states). That correct statement does not support the claims you are making.

How your statement that only certain observables under certain conditions have quantized spectrum makes the point that my statement is wrong?
It sounds like you are saying that in QM we can meaningfully talk about fractions of electrons, which is wrong of course.

 

[PeterDonis]

It sounds like you are saying that in QM we can meaningfully talk about fractions of electrons

No, I'm saying that you are making an incorrect assumption that there is a meaningful distinction between "an electron" and "a fraction of an electron", so that we can meaningfully ask whether an electron can be divided into smaller pieces. This would make sense if electrons were little billiard balls (or something equivalent), but they're not.

 

[zonde]

No, I'm saying that you are making an incorrect assumption that there is a meaningful distinction between "an electron" and "a fraction of an electron", so that we can meaningfully ask whether an electron can be divided into smaller pieces.

This is probably too philosophical for me but I will give it a try. As I see it if "an electron" is meaningful but "a fraction of an electron" is meaningless there is still meaningful distinction between "an electron" and "a fraction of an electron" (one is meaningful the other is not) even so we can't meaningfully talk about dividing electron into pieces.

 

[PeterDonis]

if "an electron" is meaningful but "a fraction of an electron" is meaningless

It depends on what you mean by "an electron". If you mean what you said in post #68, that an electron is "a quantized (discrete) unit", then no, "an electron" is not meaningful.

 

[zonde]

It depends on what you mean by "an electron". If you mean what you said in post #68, that an electron is "a quantized (discrete) unit", then no, "an electron" is not meaningful.

In first quantization "an electron" as a holder of observables is discrete unit.
In second quantization "an electron" as a basic unit in Fock states is quantized excitation of electron field.
I suppose it's meaningful enough.

 

[PeterDonis]

In first quantization "an electron" as a holder of observables is discrete unit.

I'm not sure what you mean by "a holder of observables". But in any case, first quantized theory doesn't work, so I'm not sure it counts as a valid model.

In second quantization "an electron" as a basic unit in Fock states is quantized excitation of electron field.

More precisely, the Fock states (eigenstates of the number operator) are a basis of the Hilbert space of the electron field. But that does not mean that all states of the electron field are Fock states; obviously that is false since the electron field can be in a state which is a superposition of multiple Fock states. So if "an electron" means "a Fock state", then not all states of the electron field are "electrons" in this sense, so "electron" is not a good term to use since there are lots of physical states, including states of the electron field in real materials, which are not "electrons". OTOH, if "an electron" means "a state of the electron field", then "electrons" are not quantized. Either way, saying "electrons are discrete units" doesn't, IMO, give a good description of the actual physics.

 

[jambaugh]

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.

Primitive term in definition, not in explanation. Your description of the scientific method is all well and good, but two hypotheses with common predictions are empirically indistinguishable.

I think another way to say what I'm trying to say is this. We should not be calling "Many Worlds" or "Bhom's Pilot Waves" interpretations. They are rather Models akin to Maxwell's mechanical model or the geometric model of Einstein's GR. CI is the underlying interpretation, what the mathematical components mean operationally. You can build any explanatory scaffolding you like but in the words of King Arthur " It's only a model!"

JB

 

[zonde]

Primitive term in definition, not in explanation.

Definitions are part of explanation.

Your description of the scientific method is all well and good, but two hypotheses with common predictions are empirically indistinguishable.

If one hypothesis has made prediction before experiment that confirms that prediction but the second hypothesis is made after experiment then the first hypothesis is confirmed while the second one is not. Chronology is important.

I think another way to say what I'm trying to say is this. We should not be calling "Many Worlds" or "Bhom's Pilot Waves" interpretations. They are rather Models akin to Maxwell's mechanical model or the geometric model of Einstein's GR. CI is the underlying interpretation, what the mathematical components mean operationally. You can build any explanatory scaffolding you like but in the words of King Arthur " It's only a model!"

You are trying to change common terminology. This can only add confusion and won't add any new arguments to discussion.
All our scientific theories are models of reality.
What the mathematical components mean operationally are correspondence rules.
Interpretations are models that make the same predictions.

What I think you are trying to say is that we should be satisfied with phenomenological model and consider fundamental models as unimportant. If that's what you are trying to say then I somewhat can understand this position but I do not agree with it.

 

[jambaugh]

Definitions are part of explanation.

Are you kidding me? Of course they're a part, they're even an essential to explanation. And hence the base root of everything is your definitional primitives. In modern axiomatic mathematics you begin with undefined terms because (pure) mathematics is a conceptual construct. These terms are the foundation and their meaning comes from their use in the structure of the axioms and subsequent definitions. However in science we begin with operational primatives by which we can assert "if you do this then that will always occur."

If one hypothesis has made prediction before experiment that confirms that prediction but the second hypothesis is made after experiment then the first hypothesis is confirmed while the second one is not. Chronology is important.

Now you're just being silly. By that argument we should stick with the aether version of Lorentz relativity rather than Einstein's SR? Or for that matter, conspiring demons and deities since they "explain" everything and came first in our theories of the world. Chronology is irrelevant to truth or whether something is irrelevant to the truth. Go back to my prior post and try again.

You are trying to change common terminology. This can only add confusion and won't add any new arguments to discussion.
All our scientific theories are models of reality.
What the mathematical components mean operationally are correspondence rules.
Interpretations are models that make the same predictions.

I'm trying to enlighten you to the need to subdivide your concepts. The change in common terminology happened before I came onto the scene because there are two meanings (in science) to the word interpretation. Let's use whatever words you like but let's both use the same words in the same way.

First concept: What I call an interpretation is...
A system by which we translate the concepts, terms and symbols on paper into actions and observations in the laboratory. The correspondence rules to which you referred. Call this praxic interpretation. (praxic as in pragmatic, as in operational, as in positivistic).

Second concept: What I think you are calling an interpretation...
An ontological model (world picture) of what is going on beyond the praxic interpretation. A hypothesized state of the reality of objects as they are with objective properties as they are. Call this the ontic intepretation. But I call it a ontological model.

[For a reference these praxic vs ontic qualifiers, I got them from David R. Finkelstein, see his book Quantum Relativity.]

Perhaps you don't like my definitions above and you would like to rephrase them. I am after all trying to make a specific point and I may in point of fact be biased in my wording. Suggest what you like but can you not agree that the Orthodox CI is fundamentally different in nature from say Bohm's Pilot waves and Everetts MW in that it is a praxic interpretation* while these others are ontic interpetations. *(praxic interpretation plus a stronger assertion that we should refrain from any ontic interpretations hence its conflict with these others.)

What I think you are trying to say is that we should be satisfied with phenomenological model and consider fundamental models as unimportant. If that's what you are trying to say then I somewhat can understand this position but I do not agree with it.

That is not quite what I am saying. What we feel or want is irrelevant. Nature is as nature is. And the nature of our questing toward understanding things is that we observe things happen and construct mental models to "explain them". As we push deeper and deeper there must always be a level of praxic interpretation below the level of ontic interpretation to give it meaning in any scientific sense. Either it is perpetual chicken and egg and we never stop delving deeper or there is some level past which we cannot resolve. Maybe our current phenomonlogical wall can be pushed deeper but for now we cannot resolve any observables below the level of those in QM. (There are no probes that get us past Heisenberg's uncertainty principle).

Just as with the literal chicken and egg question there's a natural starting point (an egg is an egg whether it's a chicken egg or not...) there is a natural starting point in Science based on the scientific method. An act of observation is an act of observation whether it is consistent with one or many ontological interpretations or not. You can say EMW or BPW models "explain" quantum phenomena but they are of the "Gods and Demons" variety of explanation in that they are not testable. It is thus scientifically meaningless to say one or the other is true. If in future they become testable then they will be testable with a new set of operations in the lab/observatory. These new operations will be there first before the tests can be performed and you can again argue over the "interpretations" beyond their pragmatic meaning...

 

[stevendaryl]

There is a nice talk by Ron Garrett, an engineer who has worked for Jet Propulsion Lab and for Google.

He explains, informally, why he believes that single-world interpretations of QM are not consistent.

 

[stevendaryl]

There is a nice talk by Ron Garrett, an engineer who has worked for Jet Propulsion Lab and for Google.

He explains, informally, why he believes that single-world interpretations of QM are not consistent.

It's a very long talk, so let me just summarize the reasoning, and what he means by a "single-world interpretation".

The single-world interpretation of QM is basically Copenhagen. It treats observations as "real" but treats quantum states between measurements as merely calculational tools. His argument is that this is inconsistent because measurement results such as "Alice measured spin-up" are themselves ultimately just quantum facts, no different in principle from facts such as "the electron had spin-up before it was measured".

 

[LeandroMdO]

Since one may prove, by construction, that there exist single world hidden variable theories (such as Aaronson's flow model), it seems hard to justify speculation that single-world interpretations may be inconsistent. Either observers are describable within the mathematics of quantum mechanics (in which case they are also describable, or at least simulatable by the flow model or some other hidden variable model), or they aren't, in which case quantum mechanics itself is wrong regardless of interpretation.

 

[stevendaryl]

Since one may prove, by construction, that there exist single world hidden variable theories (such as Aaronson's flow model), it seems hard to justify speculation that single-world interpretations may be inconsistent. Either observers are describable within the mathematics of quantum mechanics (in which case they are also describable, or at least simulatable by the flow model or some other hidden variable model), or they aren't, in which case quantum mechanics itself is wrong regardless of interpretation.

Thanks for the link to Aaronson's paper. It's interesting, but I haven't completely studied it yet.

But the issue is not whether observers are describable within pure quantum mechanics, but whether observers with definite states are. In the quantum mechanics of a small number of particles, if a small subsystem is in a superposition of two states, and it interacts with a second small subsystem, then afterward, the composite system will be in a superposition.

Letting \Longrightarrow be interpreted as "evolves into" (after some specified amount of time T), then QM tells us:

If |u\rangle \otimes |\emptyset\rangle \Longrightarrow |u\rangle \otimes |U\rangle and |d\rangle \otimes |\emptyset\rangle \Longrightarrow |u\rangle \otimes |D\rangle then

(\alpha |u\rangle + \beta |d\rangle) \otimes |\emptyset\rangle \Longrightarrow \alpha |u\rangle \otimes |U\rangle + \beta \otimes |D\rangle

Informally, you have two systems, the system being measured, and the system doing the measurement. For simplicity, I'm assuming that the state being measured is a simple system with a two-state basis |u\rangle and |d\rangle, the eigenstates of an operator with two eigenvalues, spin-up and spin-down. I'm assuming that the second system is measuring the observable corresponding to that eigenvalue. To be a measurement device, the second system should evolve into a "pointer state" (either |U\rangle or |D\rangle) to indicate which value it measured.

If the measuring device is itself describable by QM, then if the initial state of the system to be measured is a superposition of eigenstates, then the composite system will evolve into a superposition of two possibilities: (1) the first system is in state |u\rangle and the second system is in state |U\rangle, or (2) the first system is in state |d\rangle and the second system is in state |D\rangle.

The final state is a "many-worlds" state, in that the measuring device is not in a definite measurement state.

To get a "single-world" from this, it seems to me that you need a second kind of dynamics (the hidden-variables of Aaronson, or Bohm) that selects one possibility out of the two possible measurement states.

 

[jambaugh]

Just reviewed the video and his statement that CI is "scientifically untenable because there just is no [physical] collapse" is the classic gross misunderstanding of CI.
In CI the collapse of the wave function is the collapse of our description of the system. CI exactly distinguishes the wave function from the material system. CI says "if you now assume you've made a specific measurement of the system then you must incorporate that assumption into your description of the system".

You can always "find" a contradiction in CI or any theory if you inconsistently interpret.

* CI says the wave function is not modeling physical system but a record of information about system behavior...
* QM describes how the wave function evolves dynamically and relates to system observables.
* CI says upon receiving updated information you update your wave function (collapse)
* CI is scientifically untenable because collapsing wave functions (when interpreted as physical objects (in contradiction to CI)) is bad [by various easy to generate means of demonstration].

I didn't see anything new or unique in his talk w.r.t. the physics or its interpretation.

 

[stevendaryl]

Just reviewed the video and his statement that CI is "scientifically untenable because there just is no [physical] collapse" is the classic gross misunderstanding of CI.
In CI the collapse of the wave function is the collapse of our description of the system.

I don't think that is a consistent interpretation, in light of Bell's theorem. I think that the video does a pretty good job of explaining why that doesn't work.

 

[Denis]

But the issue is not whether observers are describable within pure quantum mechanics, but whether observers with definite states are. ...
To get a "single-world" from this, it seems to me that you need a second kind of dynamics (the hidden-variables of Aaronson, or Bohm) that selects one possibility out of the two possible measurement states.

Yes, or you need a collapse, modifying QT, so that you have no longer pure QT, or you get the wave function for Schrödinger's cat. And to make the wave function for Schrödinger's cat compatible with the single cat you observe in a definite state, you need some other additional dynamics, which are not quantum.

But "why ... single-world interpretations of QM are not consistent" makes no sense, if adding the hidden variables makes everything ok, thus, consistent, given that you cannot make inconsistent things consistent adding something.

In the talk, from 4:20 to 4:50 he rejects realism, and claims that one can show that realism is not true. Which is wrong, given the realistic interpretations. And one can easily see where the proof goes wrong - when he rejects (without mentioning them) all the realistic interpretations for having FTL, and claims that FTL would lead to causal paradoxes, completely ignoring the forbidden possibility that FTL happens in a hidden preferred frame.

 

[Denis]

I don't think that is a consistent interpretation, in light of Bell's theorem. I think that the video does a pretty good job of explaining why that doesn't work.

CI is consistent.

You can simply take dBB theory and cut away the parts which are unobservable. That means, what remains from the Bohmian trajectory $q(t)$ is the classical trajectory $q_{classical}(t)$ of the classical part, and what remains from the Bohmian global wave function is the effective wave function of the quantum part
$$ \psi_{quantum}(q_{quantum}) = \psi_{Bohmian}(q_{quantum}, q_{classical}(t)).$$

Then, throw away this formula too (once it contains things which should not exist together) and add positivist reasoning that what is not observable does not exist, and you have the CI.

 

[stevendaryl]

CI is consistent.

You can simply take dBB theory and cut away the parts which are unobservable. That means, what remains from the Bohmian trajectory $q(t)$ is the classical trajectory $q_{classical}(t)$ of the classical part, and what remains from the Bohmian global wave function is the effective wave function of the quantum part
$$ \psi_{quantum}(q_{quantum}) = \psi_{Bohmian}(q_{quantum}, q_{classical}(t)).$$

Then, throw away this formula too (once it contains things which should not exist together) and add positivist reasoning that what is not observable does not exist, and you have the CI.

Very nice description of the relationship between Bohmian mechanics and Copenhagen. Is that original with you?

 

[jambaugh]

I don't think that is a consistent interpretation, in light of Bell's theorem. I think that the video does a pretty good job of explaining why that doesn't work.

See other posts but the problem with Bell's theorem only exists if you mistakenly (in absolute opposition to CI) reify the wave function. Bell's theorem negates the ANTI-Copenhagen interpretation of the wave function as a model of some physical reality... it supports CI. CI again asserts that the wave function is akin to a classic probability distribution, it is knowledge about how the random variables which are the system observables will behave. It is not the physical reality that is in superposition, it is the description (of how things have/will behave\d); It is not the physical reality that is entangled, it is the description; it is not the physical reality that collapses it is the description. If you're going to disagree with CI know what it is saying.

This does not negate the fact that assertions of superposition, entanglement, and collapse, of our descriptions have meaning w.r.t. the actuality of phenomena out there, it is just a necessarily oblique and indirect qualification of the actual since we do not and, by Bell, cannot have direct classical knowledge of the state of "out there" our knowledge must be acquired through observations which is why we start and end with our descriptions of those observations e.g. the wave functions or more general density operators. We are of necessity phenomenologists if we wish to remain empiricists.