I Is Entanglement Properly Defined in Bohr's Idea of Complementarity?

[Lord Jestocost]

What lies beneath it all?

Physics cannot answer such questions because speculations about “Reality” shouldn’t be extended beyond the range of experiments. I think that corresponds to Bohr’s point of view. In “BOOJUMS ALL THE WAY THROUGH: Communicating Science in a Prosaic Age” Mermin puts Bohr view in the following way (Chapter 14 “The philosophical writings of Niels Bohr“):

“Typical quantum effects, Bohr notes, resist pictorial representations. Nor should this surprise us, since our ability to construct such representations or explanations in ordinary language was entirely developed in the course of coping with classical phenomena. Bohr repeatedly insists that we must therefore be content with a purely symbolic mathematical algorithm, which connects one classically specified set of conditions to another. This formalism offers no explanation in the customary sense, but by embracing all possible experimental arrangements it demonstrates the logical consistency of the entire scheme, which is all we can demand of it.“

 

[EPR]

As always in science, it's much easier to say how things are not, than how they are. Yet, it's human nature to enquire and question everything. This is how progress is made by our greatest minds. I am glad to be born in times when we know how certain things are not.

 

[sysprog]

As always in science, it's much easier to say how things are not, than how they are. Yet, it's human nature to enquire and question everything. This is how progress is made by our greatest minds. I am glad to be born in times when we know how certain things are not.

The difficulty of proving a negative comes to mind.

 

[EPR]

Can't prove a negative indeed. I don't find it reasonable to consider myself a 'robot' driven by purely mechanistic processes(which btw go back millions of years), so this(possibly outgoing) whole framework is outdated and patently false albeit still quite useful for technological purposes and progress.

It's dogma when a scientific or philosophical world view is still widely held in the face of overwhelming evidence to the contrary. Bohr was aware of what's coming and cryptically recommended to stay within the limits of what we can say about nature, not what and how nature is.

Let's see what assumptions go into the usual discussions of the complimentarity puzzle and paradox(and there are many):

1. That we experience the world directly. (false, we never do)
2. That the world of experience is a true representation of the world.(false)
3. Past success is a guarantee of future success of a model of the world. (false, google 'problem of induction')
4. That everything in nature can be reduced to interactions of the smallest particles.(false, lots of physics can't be reduced to 'particles', moreover my personal experience which, Corgito ergo sum is all that i have reliably, can't be reduced). We can't even begin to comprehend how something as unphysical as the human mind/our awareness/ can interact with the physical or attach itself to a physical brain and be carried around). Think physical/unphysical. In that respect human knowledge is in its infancy. It will probably take 15-20 lifetimes to understand some these issues that underlie the above paradox(complementarity).
5. That the Universe is fundamentally deterministic(false)
6. That the world is made of particles.(this in and of itself is also false, they are more truthfully represented as a set of relationships, e.g. in QFT)
7. ......

So the list of assumptions is almost endless and this open-ended list took us where we currently are.
80 years of fruitless endless debates and many thousands of papers with no resolution in sight... in a land of paradoxes. What happened and was revealed in those 80 or so years is there came further experimental confirmation, theorems and evidence that we are in serious error somewhere(see list of assumptions).

 

[sysprog]

Can't prove a negative indeed. I don't find it reasonable to consider myself a 'robot' driven by purely mechanistic processes(which btw go back millions of years), so this(possibly outgoing) whole framework is outdated and patently false albeit still quite useful for technological purposes and progress.

It's dogma when a scientific or philosophical world view is still widely held in the face of overwhelming evidence to the contrary. Bohr was aware of what's coming and cryptically recommended to stay within the limits of what we can say about nature, not what and how nature is.

Let's see what assumptions go into the usual discussions of the complimentarity puzzle and paradox(and there are many):

1. That we experience the world directly. (false, we never do)
2. That the world of experience is a true representation of the world.(false)
3. Past success is a guarantee of future success of a model of the world. (false, google 'problem of induction')
4. That everything in nature can be reduced to interactions of the smallest particles.(false, lots of physics can't be reduced to 'particles', moreover my personal experience which, Corgito ergo sum is all that i have reliably, can't be reduced). We can't even begin to comprehend how something as unphysical as the human mind/our awareness/ can interact with the physical or attach itself to a physical brain and be carried around). Think physical/unphysical. In that respect human knowledge is in its infancy. It will probably take 15-20 lifetimes to understand some these issues that underlie the above paradox(complementarity).
5. That the Universe is fundamentally deterministic(false)
6. That the world is made of particles.(this in and of itself is also false)
7. ......

So the list of assumptions is almost endless and this open-ended list took us where we currently are.
80 years of fruitless endless debates and many thousands of papers with no resolution in sight... in a land of paradoxes. What happened and was revealed in those 80 or so years is there came further experimental confirmation, theorems and evidence that we are in serious error somewhere(see list of assumptions).

I can't discuss the subject here, but I think you might like this article: https://en.wikipedia.org/wiki/Neutral_monism

 

[bhobba]

So the list of assumptions is almost endless and this open-ended list took us where we currently are.

Debatable would be a better description here. But if you want to discuss any of the things mentioned please start a new thread. But be careful, many of those are really questions in philosophy, not science. And of course we do not discuss philosophy here.

What happened and was revealed in those 80 or so years is there came further experimental confirmation, theorems and evidence that we are in serious error somewhere(see list of assumptions).

Sure, some errors were found eg Von-Neumann's no go theorem on hidden variables was false. But we have no evidence we are still in serious error anywhere - we may be as research progresses - but may not as well. You are falling for Feynman's trap and assuming things. Experiment is the rock bottom essence - any theory that conforms to that is fine. It does not depend on the way a person views the world, what they believe, what they find elegant etc. Some cases of reformulation of a theory supersedes previous theories. It's because its more general, easier to extend etc - but strictly speaking that does not disprove the previous theory - it simply makes life easier for physicists so becomes the accepted view. Within that limited paradigm you can discuss which view is better. Note however some theories like LET that fits that category virtually nobody uses, so on this forum we have banned discussing it - SR, having no unobservable aether is better suited for extension to QFT and GR. That does not preclude discussing genuine peer reviewed scientific theories like GLET,

Thanks
Bill

 

[EPR]

Sure, some errors were found eg Von-Neumann's no go theorem on hidden variables was false. But we have no evidence we are still in serious error anywhere - we may be as research progresses - but may not as well. You are falling for Feynman's trap and assuming things. Experiment is the rock bottom essence - any theory that conforms to that is fine. It does not depend on the way a person views the world, what they believe, what they find elegant etc.

I am not assuming anything, maybe you are.

Calling the deep foundational and conceptual problems a minor inconveniece is a gross understatement and misunderstanding.

It has been almost a century and quantum theory still lacks ontology(and for a reason). In fact, it's gotten ridden with more paradoxes. We now know quantum theory is correct and classical concepts outdated and wrong(although useful in a certain domain and perspective).

There is overwhelming evidence there is no coming back to the old concepts of immutable particles in time and space and afaik no research is being carried out in this direction.

 

[bhobba]

Calling the deep foundational and conceptual problems a minor inconveniece is a gross understatement and misunderstanding.

That there are foundational problems in QM is a matter of opinion. You are making an assumption there definitely is. That is not a universally held opinion. For example see:
https://www.amazon.com/dp/B008ABSSIW/?tag=pfamazon01-20.
Just a friendly bit of advice from a mentor, your personal opinions may not be universally accepted.

Thanks
Bill

 

[EPR]

All the approaches to unification get stuck in the question of what's fundamental(since matter, space and time aren't - they are context dependent in both QM, QFT and SR). There are no non-contextual 'particles' or properties as such.

I would refer everyone to my previous post:

Relativistic quantum fields and superpositions, brain(eyes + visual cortex), classical perception('particles'). Somewhere along the chain lies the measurement problem and the issue of Bohr's complimentarity(unobservable waves of probability and definite outcomes aka observable 'particles').

 

[Mentz114]

[..]
In fact, it's gotten ridden with more paradoxes.
[..]

That's interesting. Can you list them ?

 

[bhobba]

That's interesting. Can you list them ?

It's all interpretation and opinion dependent. For example the claim 'That everything in nature can be reduced to interactions of the smallest particles' is false, IMHO runs into what we know from QFT, where particles and fields are really the same thing. However fully fleshing it out requires a new thread. A lot of other claims are really philosophy in my opinion - but again it needs fleshing out. There is nothing wrong holding such views, and you can discuss them here (providing it's not really just philosophy), but saying it's definitely true is not really in the scientific spirit. As a mentor, unless it gets bad I would not consider it actionable, however its wise to keep in mind what the situation actually is. I find knowing about various different interpretations helpful in understanding claims like that made previously.

Thanks
Bill

 

[Mentz114]

It's all interpretation and opinion dependent. For example the claim 'That everything in nature can be reduced to interactions of the smallest particles' is false, IMHO runs into what we know from QFT, where particles and fields are really the same thing. However fully fleshing it out requires a new thread. A lot of other claims are really philosophy in my opinion - but again it needs fleshing out. There is nothing wrong holding such views, and you can discuss them here (providing it's not really just philosophy), but saying it's definitely true is not really in the scientific spirit. As a mentor, unless it gets bad I would not consider it actionable, however its wise to keep in mind what the situation actually is. I find knowing about various different interpretations helpful in understanding claims like that made previously.

Thanks
Bill

Agreed.

I think the claim that 'QT has contradictions' is unsupported and there is no list.

 

[EPR]

That's interesting. Can you list them ?

You cut out and edited my post to remove the context but i will post it again here as conrext is crucial when discussing a cut out sentence.

It has been almost a century and quantum theory still lacks ontology(and for a reason). In fact, it's gotten ridden with more paradoxes. We now know quantum theory is correct and classical concepts outdated and wrong(although useful in a certain domain and perspective).

The paradoxes arise out of the lack of ontology. And the continued supporting evidence of standard quantum mechanics over classical mechanics post 1940(some new theorems and verifications have come about since giving further credence).
I stated earlier that i consider the Measurement Problem possibly the biggest mystery in science. But nobody is quoting that statement?

 

[bhobba]

The paradoxes arise out of the lack of ontology.

Ontology - the branch of metaphysics dealing with the nature of being. Being - existence. If QM has no existence then I do not know what theory does. Remember theories are not things that exist out there in the world, they are descriptions of things things that do. Now the nature of that existence is up for philosophical debate - but that is a question for a philosophy forum - not here.

Thanks
Bill

 

[Mentz114]

You cut out and edited my post to remove the context but i will post it again here as conrext is crucial when discussing a cut out sentence.

The paradoxes arise out of the lack of ontology. And the continued supporting evidence of standard quantum mechanics over classical mechanics post 1940(some new theorems and verifications have come about since giving further credence).
I stated earlier that i consider the Measurement Problem possibly the biggest mystery in science. But nobody is quoting that statement?

I do not agree that the MP is a mystery. The fact that QT only predicts probabilities means that QT ( ie unitary evolution) cannot predict the outcome of an experiment any more than a thermometer can meaure length. This only a problem if it is assumed ( incorrectly) that probability has any existence other than in our calculations.

 

[EPR]

I do not agree that the MP is a mystery. The fact that QT only predicts probabilities means that QT ( ie unitary evolution) cannot predict the outcome of an experiment any more than a thermometer can meaure length. This only a problem if it is assumed ( incorrectly) that probability has any existence other than in our calculations.

There are no particles.

This way of thinking(that particles have properties before measurement and we are just ignorant) is 19 century talk. You don't care what it is you are measuring right? As long as it produces results in agreement with the formalism made to reflect said behavior?

 

[Mentz114]

There are no particles.

This way of thinking(that particles have properties before measurement and we are just ignorant) is 19 century talk. You don't care what it is you are measuring right? As long as it produces results in agreement with the formalism made to reflect said behavior?

Even if the only particles that exist are the ones in our calculation then predicting results correctly means the theory is working. Assuming that this or that element in the calculation actually exists is speculative for anything that is below a certain size.

Which means that dialectic on this subject reduces to opinions about what exists and what does not.

 

[bhobba]

Which means that dialectic on this subject reduces to opinions about what exists and what does not.

And BM has a different take. This is one of the genuine issues with QM. Its difficult to say anything concrete about some things because there is an interpretation where its not true. I even fall for it on occasion such as when I explain entanglement. Once particles are entangled you can't speak about their individuality - but in BM you can - it really makes this 'semantically' difficult.

Thanks
Bill

 

[EPR]

BM is not taught in textbooks and due to its added 'baggage' is not part of any university curriculum.

Is it relativistically invariant?

 

[RUTA]

Bohr's answer, and even the answer I would give, is not at all satisfying even though I think its true. Its the very essence of quantum weirdness.:
https://arxiv.org/abs/0911.0695
You simply can't have other desirable properties without it.

Thanks
Bill

I’m confused by something in that paper. They write:

In this work we have shown that classical probability theory and quantum theory – the only two probability theories for which we have empirical evidences — are special in a way that they fulfill three reasonable axioms on the systems’ information carrying capacity, on the notion of locality and on the reversibility of transformations. The two theories can be separated if one restricts the transformations between the pure states to be continuous. An interesting finding is that quantum theory is the only non-classical probability theory that can exhibit entanglement without conflicting one or more axioms. Therefore – to use Schro ̈dinger’s words – entanglement is not only “the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought”, but also the one that enforces the departure from a broad class of more general probabilistic theories.

So, axiom 3 (Reversibility) alone distinguishes classical probability theory (CPT) and quantum theory, but they also write that:

As we will see later, taking the latter choice, it will follow from axiom 1 alone that the state space must contain entangled states.

So, from this statement and the fact that axiom 3 alone distinguishes CPT from QT, I infer that classical probability theory contains entangled states. But, that is at odds with entanglement as “the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought”.

What am I missing?

 

[bhobba]

What am I missing?

I think you may have picked up a logical issue with the paper - at least a badly expressed idea. It says 'An interesting finding is that quantum theory is the only non-classical probability theory that can exhibit entanglement without conflicting one or more axioms.'

It has not ruled out entanglement in classical probability theory - but for the life of me I can't think of how classical probability theory can have entanglement. It has me beat. In fact the following paper states it outright:
http://staff.utia.cas.cz/swart/lecture_notes/qua17_04_05.pdf
' In classical probability, entangled states do not exist'

Thanks for your careful reading - I should have spotted it - but didn't.

Someone else may be able to disentangle (pun intended) the intent - but I can't see it at the moment.

Thanks
Bill

 

[RUTA]

I think you may have picked up a logical issue with the paper - at least a badly expressed idea. It says 'An interesting finding is that quantum theory is the only non-classical probability theory that can exhibit entanglement without conflicting one or more axioms.'

It has not ruled out entanglement in classical probability theory - but for the life of me I can't think of how classical probability theory can have entanglement. It has me beat. In fact the following paper states it outright:
http://staff.utia.cas.cz/swart/lecture_notes/qua17_04_05.pdf
' In classical probability, entangled states do not exist'

Thanks for your careful reading - I should have spotted it - but didn't.

Someone else may be able to disentangle (pun intended) the intent - but I can't see it at the moment.

Thanks
Bill

I just emailed Professor Dakic, perhaps someone in his group will clarify their use of the terminology in that paper. I'll let you know what they say :-)

 

[RUTA]

I just emailed Professor Dakic, perhaps someone in his group will clarify their use of the terminology in that paper. I'll let you know what they say :-)

Here is Dakic's reply:

the sentence in question: "As we will see later, taking the latter choice, it will follow from axiom 1 alone that the state space must contain entangled states." refers to the previous: ...also called “generalized bit”. So, the logic is that any 1 bit-system obeying Axiom 1 is either: a) discrete (and in this case only classical bit is a consistent solution) or b) continuous (such as real, quantum or some general bit). In the latter case, entanglement is the necessary feature. The only counter-example to this is the classical bit and consequently classical probability theory. They do not exhibit entanglement.

Here is the entire paragraph, so that his reply makes more sense:

In logical terms axiom 1 means the following. We can think of two basis states as two binary propositions about an individual system, such as (1) “The outcome of measurement A is +1” and (2) “The outcome of measurement A is -1”. An alternative choice for the pair of propositions can be propositions about joint properties of two systems, such as (1’) “The outcomes of measurement A on the first system and of B on the second system are correlated” (i.e. either both +1 or both -1) and (2’) “The outcomes of measurement A on the first system and of B on the second system are anticorrelated”. The two choices for the pair of propositions correspond to two choices of basis states which each can be used to span the full state space of an abstract elementary system (also called “generalized bit”). As we will see later, taking the latter choice, it will follow from axiom 1 alone that the state space must contain entangled states.

So, yes, trivially the discrete (classical bit) option is an "entangled state" in the sense of the "alternative choice for the pair of propositions about joint probabilities," i.e., the outcomes are either correlated or anti-correlated. But, since there is no continuous mapping between such basis states in the classical case, there is no entanglement proper, as is well known. Thus, strictly speaking, I would say axiom 1 and axiom 3 are both required for entanglement. Maybe I'm missing something. What to the mathemagicians say?