Meaning of Wave Function Collapse

[rubi]

So the modes absorbed in first polarizer have to stay in the model, but for them to stay there they have to have some label from interaction with the second and third polarizer. And this labeling side effect seems rather artificial and detached from physical reality.

This makes no sense. The modes that are stuck in the first polarizer have no relation at all with the modes in the other polarizers. I don't know what you mean by "labeling side effect". There is nothing artificial in the model. It's absolute standard quantum physics and not at all detached from physical reality. We take tensor products of different systems and describe their interaction by unitary operators on the tensor product space. There's really nothing controversial about that.

 

[zonde]

This makes no sense. The modes that are stuck in the first polarizer have no relation at all with the modes in the other polarizers. I don't know what you mean by "labeling side effect". There is nothing artificial in the model. It's absolute standard quantum physics and not at all detached from physical reality. We take tensor products of different systems and describe their interaction by unitary operators on the tensor product space. There's really nothing controversial about that.

But the vector space has these dimensions associated with interaction history with polarizers. You are just adopting "n" as a sort of default state and "a" as a modified state. But "n" means that particular mode pointing in that direction has passed polarizer even if you take it as a default.
Or if it's not so then you have to give dual explanation for "n" dimension i.e. if vector points in "n" direction then associated mode either interacted with polarizer and passed it or it didn't interact with it at all.

 

[rubi]

But the vector space has these dimensions associated with interaction history with polarizers. You are just adopting "n" as a sort of default state and "a" as a modified state. But "n" means that particular mode pointing in that direction has passed polarizer even if you take it as a default.
Or if it's not so then you have to give dual explanation for "n" dimension i.e. if vector points in "n" direction then associated mode either interacted with polarizer and passed it or it didn't interact with it at all.

This is just a very basic model that allows you to effectively describe the transmission and absorption of photons due to the polarizers. The state just keeps track of which modes are present in the system. It has nothing to do with a history. Of course, you would normally start with a state containing only a photon, but that doesn't mean that this is somehow a "default state". As I said earlier, the model ignores all physical details and is just good enough to model the effect of the photon-phonon scattering on the polarization state of the photons due to the polarizer material, which is all you need here.

 

[zonde]

This is just a very basic model that allows you to effectively describe the transmission and absorption of photons due to the polarizers. The state just keeps track of which modes are present in the system.

But the model contains mode like $h \otimes a \otimes a \otimes a$. And it is meaningless.

 

[rubi]

But the model contains mode like $h \otimes a \otimes a \otimes a$. And it is meaningless.

How is it meaningless? It's a state that contains a phonon mode in each polarizer. This is the realistic situation, since in practice, no polarizer absorbs a mode completely. The idealized dynamics I gave cannot produce it from the $h\otimes n\otimes n\otimes n$ state, but you can easily include non-trivial absorption and transmission coefficients in the matrices and then photons will be partially absorbed in all polarizers, not just one of them. You can look at atyy's paper to see how it's done. (And by the way, this realistic situation can't be modeled by projections.)

 

[Carpe Physicum]

Sorry to post back in on what really is philosophy of science, but couldn't pass this up. Here's an article in advanced economics that illustrates a point I made earlier. https://www.physicsforums.com/insights/a-simplified-synthesis-of-financial-options-pricing/ I'm no mathematician, not even close, but this to me looks like an example of probability equations, including a reference to probability density. There's even pi in there. This looks suspiciously similar to equations I've seen in threads about QM. So how can we say the math is elegant in any way if similar math is used to discuss elementary particles and, ugg, calls and puts in stock markets? (There's nothing wrong with playing the stock market, but it's a tiny unimportant human activity compared to universal principles of elementary particles.) Seems to me one area of mathematical inquiry is, well, fooling itself. Or not. I don't know.

 

[Grinkle]

So how can we say the math is elegant in any way if similar math is used to discuss elementary particles and, ugg, calls and puts in stock markets?

That depends entirely on one's judgement-laden definition's of 'elegant' and 'similar' and 'in-any-way', does it not?

 

[Fra]

Sorry to post back in on what really is philosophy of science, but couldn't pass this up. Here's an article in advanced economics that illustrates a point I made earlier. https://www.physicsforums.com/insights/a-simplified-synthesis-of-financial-options-pricing/ I'm no mathematician, not even close, but this to me looks like an example of probability equations, including a reference to probability density. There's even pi in there. This looks suspiciously similar to equations I've seen in threads about QM. So how can we say the math is elegant in any way if similar math is used to discuss elementary particles and, ugg, calls and puts in stock markets? (There's nothing wrong with playing the stock market, but it's a tiny unimportant human activity compared to universal principles of elementary particles.) Seems to me one area of mathematical inquiry is, well, fooling itself. Or not. I don't know.

Don't underestimate the similarities between different complexity scales. The emergent rules of interaction on the market, as well as the population of players that survive, show striking conceptual similarities to emergent physical laws, and emergent population of elementary particles as you lower energy.

I think its a mistake often made by strong reductionists, to think that nothing important can be learned from studying complex system, such as economical systems. I think nothing could be more wrong. It may even be EASIER to learn from studying systems of intermediate complexity, than to probe deeper and deeper into matter.

Thus wether we find the mathematics to be similar it is not a coincidence. To find similar mathematics on these different scales are indeed beautiful.

I often think of particles as "players", their task is to gamble with their own integrity and try to survive. Those that survive populate the standard model, and their interaction rules would be stable in a "nash equilibrium" kind of sense.

Make sense?

/Fredrik

 

[Carpe Physicum]

Don't underestimate the similarities between different complexity scales. The emergent rules of interaction on the market, as well as the population of players that survive, show striking conceptual similarities to emergent physical laws, and emergent population of elementary particles as you lower energy.

I think its a mistake often made by strong reductionists, to think that nothing important can be learned from studying complex system, such as economical systems. I think nothing could be more wrong. It may even be EASIER to learn from studying systems of intermediate complexity, than to probe deeper and deeper into matter.

Thus wether we find the mathematics to be similar it is not a coincidence. To find similar mathematics on these different scales are indeed beautiful.

I often think of particles as "players", their task is to gamble with their own integrity and try to survive. Those that survive populate the standard model, and their interaction rules would be stable in a "nash equilibrium" kind of sense.

Make sense?

/Fredrik

Actually no. Human activity, being human, is temporary and negligible in the scheme of things. So to equate the mathematics describing trivial human activity and the grandness of the workings of the universe to me at least, and I admit I'm just a layman for whom Einstein and Bohr and in a different realm, Carl Sagan, are heros, is practically offensive. But maybe there's a way out. A friend on this forum pointed me to an interesting article that explained how confusion arises when epistemology and ontology in physics get mixed up. (I think he was saying that's one of the things the discussions about Einstein/Bohr debates bog down on.) The math of economics and experimental physics might be the math of epistemology. I.e. it's just a tool, not special in any grand sense, used to make sense of data, maybe even on a relatively deep level, and give clues to the underlying systems. And then there's another type of math used to address the ontology. Both are important of course so I don't mean to denigrate either - you need piano players and tuners both! OR is the current thinking that human activity, even macro activity such as playing the stock market, or raising chickens, or falling in love, really boils down to laws of nature discoverable by physicists? (And if that's the case, so be it.)

 

[Boing3000]

Actually no. Human activity, being human, is temporary and negligible in the scheme of things.

You need to use correct(useful) categorization. If an equation concern weasel and their "put" on food, would that make you "feel" better ?
The problem is about "scale" not of "personal taste". The "scheme of things" here being some agent driven by "force" to get some resource.

So to equate the mathematics describing trivial human activity and the grandness of the workings of the universe to me at least, and I admit I'm just a layman for whom Einstein and Bohr and in a different realm, Carl Sagan, are heros, is practically offensive.

What is offensive to me, is anthropocentrism, and to think that for some reason, a no-nonsense principle like "least action" (and beautiful, when expressed in math form) would not apply to human activity. Have you ever done some trekking ?

The math of economics and experimental physics might be the math of epistemology.

They definitively are. Ontological claims may be usefull to choose some direction for the "next step", but science is mostly concerned by epistemology (experimental verification).

I.e. it's just a tool, not special in any grand sense, used to make sense of data, maybe even on a relatively deep level, and give clues to the underlying systems.

It does, or it does not. "underlying" things are more treacherous that you think, and most definitely an excursion into the abyss (as Feynman beautifully explains)
Is the universe made "of field" or of little "strings" ? What if it does make any difference at all ? Even if the math turns out to have great deal of similarities ?

 

[richrf]

For the OP, I thought I might bring to his/her attention a new book by Adam Becker, called "What Is Real?"

The book traces the history of the foundational questions of Quantum Physics (which is what the OP addresses) as well as discussing in some depth the Bell Inequality Theorem and what it means in fairly layman's terms.

It is approaches the subject from many angles including the impact that philosophical positivism, political, and cultural biases had/has on quantum scientific research and how how alternative viewpoints that are explicitly and implicitly suppressed, specifically in the context of Bohmian Mechanics and Everett Many Worlds Interpretations.

The footnotes and bibliography are robust. Be forewarned, it does not put the scientific research culture in a very good light. In any case, it is very readable and once again raises the question, what is it precisely that we are talking about?

 

[jon4444]

For the OP, I thought I might bring to his/her attention a new book by Adam Becker, called "What Is Real?"

As someone also interested in the foundational questions, I found that book a disappointment. It did give interesting insight into research culture, but I felt it was rather weak on subject's like Bell's Inequality. (E.g., I had to go elsewhere to discover that experiments related to Bell's theorem involved a different type of entanglement than considered by Einstein, et. al. I still don't know if Bell's advances were due to him "discovering" this other form of entanglement or Einstein just missed the implications of entanglement with polariziation.)
Other major weakness was Becker's argument for why falsifiability shouldn't be a criteria for a scientific theory. After reading his book, I came away feeling more supporting of what I learned in school supporting Copenhagen Interpretation. Briefly, if there's no testable difference between explaining entanglement using retro-causality versus some form of non-locality, and over time differing explanations such as these haven't led anywhere constructive, then they have no explanatory power. What does "retro-causality" mean to us (who live in a world where we can't observe such a thing)--might as well resort to an explanation involving magical invisible unicorns.

 

[richrf]

As someone also interested in the foundational questions, I found that book a disappointment. It did give interesting insight into research culture, but I felt it was rather weak on subject's like Bell's Inequality. (E.g., I had to go elsewhere to discover that experiments related to Bell's theorem involved a different type of entanglement than considered by Einstein, et. al. I still don't know if Bell's advances were due to him "discovering" this other form of entanglement or Einstein just missed the implications of entanglement with polariziation.)
Other major weakness was Becker's argument for why falsifiability shouldn't be a criteria for a scientific theory. After reading his book, I came away feeling more supporting of what I learned in school supporting Copenhagen Interpretation. Briefly, if there's no testable difference between explaining entanglement using retro-causality versus some form of non-locality, and over time differing explanations such as these haven't led anywhere constructive, then they have no explanatory power. What does "retro-causality" mean to us (who live in a world where we can't observe such a thing)--might as well resort to an explanation involving magical invisible unicorns.

I may be incorrectly understanding your comment, but in regards to Bell's Theorem and polarization, I believe that the book described how it was papers written by Bohm that were the inspiration for Bell to use polarization as the backdrop for his theory to test non-locality. As the book explained, Einstein's primary objection to the completeness of Quantum Theory was that it undermined locality as demonstrated with EPR.

As for the Copenhagen Interpretation, Becker's main thrusts were that a) there was no such thing as there were serious disagreements among its advocates and b) the measurement problem is never addressed in any forthright manner, the problem being quite substantial and not peripheral to the interpretation as discussed in the book.

I found a good Youtube video of Becker at Google in which he summarizes his thoughts.

 

[Carpe Physicum]

For the OP, I thought I might bring to his/her attention a new book by Adam Becker, called "What Is Real?"

Just started reading the book. Looks good. It's good to know too that the issue is actually a real one, not one of these "gee you're just a stupid layman suckered in by silly shows on TV".

 

[richrf]

Just started reading the book. Looks good. It's good to know too that the issue is actually a real one, not one of these "gee you're just a stupid layman suckered in by silly shows on TV".

For those who are interested in what precisely is quantum, the issue is very real. What is great about the book is the meticulous manner in which Becker walks through the history and documents with great precision the sequence of events which are rarely discussed our written about. I always had my suspicions but Becker provides the documentation.

Also, Becker does a great job of underscoring the issue of non-locality beginning with EPR and Bell's inspired solution to the problem together with a brilliant exposition of the Bell Theorem. The book is one part history, one part philosophy, one part physics and one part political thriller. A great read and a keeper.

 

[member 648030]

That is not right.
The quantum mechanical state "superposition of A and B" is different from the quantum mechanical state "It is A or B and we don't know which yet", and there is no classical analogy for the former.

From the point of view of the measure (which is what interests us), it is the exact same thing. It is clear that the example of money is only a "way" to explain, but the probability that a head or a cross comes out by throwing the coin, or measuring the spin up or down, is the same probability in the two cases.
Rather, the coin, in its "state" of launch is a rotating object subject to gravity that can be described with the classical equations etc etc. while a quantum state is neither more nor less than the wave function, or the wave vector of its state

 

[Boing3000]

but the probability that a head or a cross comes out by throwing the coin, or measuring the spin up or down, is the same probability in the two cases.

No it is not.
You've got a probability for one event for the coin (that you cannot entangled with another coin)
And you've got two events for entangled spin, that cannot be described classically.

 

[member 648030]

You have a 50% chance of getting head, and 50% chance of getting cross. After all, you have a 50% chance of getting spin up and 50% spin down. I see no difference

 

[Boing3000]

You have a 50% chance of getting head, and 50% chance of getting cross. After all, you have a 50% chance of getting spin up and 50% spin down. I see no difference

The difference is obviously the correlation between probabilities when both particles are measure along some axis. This correlation varies with the angle$\frac{1}{2}cos\theta$ That's what make entanglement different.

 

[Nugatory]

You have a 50% chance of getting head, and 50% chance of getting cross. After all, you have a 50% chance of getting spin up and 50% spin down. I see no difference

If you try measuring the spin on the horizontal axis instead, you will see the difference.

The state "it is spin-up or spin-down" will, when measured on the horizontal axis, give you spin-left 50% of the time and spin-right 50% of the time.

The state "superposition of spin-up and spin-down" will give you spin-left 100% of the time.

 

[member 648030]

The difference is obviously the correlation between probabilities when both particles are measure along some axis. This correlation varies with the angle$\frac{1}{2}cos\theta$ That's what make entanglement different.

but who is talking about "both" the particles? I am considering only one particle. It is more than enough that I am considering any X object that is in some X state

 

[member 648030]

If you try measuring the spin on the horizontal axis instead, you will see the difference.

The state "it is spin-up or spin-down" will, when measured on the horizontal axis, give you spin-left 50% of the time and spin-right 50% of the time.

The state "superposition of spin-up and spin-down" will give you spin-left 100% of the time.

Obviously a coin is not exactly an electron ...

 

[Boing3000]

but who is talking about "both" the particles?

I am, because one quantum state describe all there is to know of many entangled particles. And there is no classical counterpart for "coins"

I am considering only one particle. It is more than enough that I am considering any X object that is in some X state

No, it is not enough, a least in the context of quantum "object".
You post #57 about "coin" is irrelevant to "wave function collapse" for many reasons:
1) A coin is never in a superposition of head and cross, so there is no "Wave function collapse" that apply to coin.
2) QM superposition is not a "either or" but an "and"
3) "Wave function collapse" is in itself is not relevant for understanding QM. Evolution of state is.

 

[member 648030]

I am, because one quantum state describe all there is to know of many entangled particles. And there is no classical counterpart for "coins"

I see no reason to use the concept of entaglement for the superposition principle, nor for the collapse of the wave function. You can take the simple example of the hydrogen atom and you will have state overlap and collapse without entagled states

No, it is not enough, a least in the context of quantum "object".
You post #57 about "coin" is irrelevant to "wave function collapse" for many reasons:
1) A coin is never in a superposition of head and cross, so there is no "Wave function collapse" that apply to coin.

Obviously, money is a classic and not a quantum object, but under the probabilistic aspects the behavior is exactly the same

2) QM superposition not a "either or" but an "and"

the possible states are logically linked by "and" before the measurement. In fact it is said that they are "overlapped" in the sense that they coexist. But from the point of view of the result you can get a result "or" another result "or" another one etc. " But you can not get a result "and" another result

3) "Wave function collapse" is in itself is not relevant for understanding QM. Evolution of state is.

It is a pity that the collapse of the wave function is one of the fundamental principles of quantum mechanics(Heisenberg, Dirac, Born etc).
After the measurement, as you know, the wave function ceases to be an overlap of "possible" states.
For any observable, the wave function is initially some linear combination of the eigenbasis of that observable. When an observer, experimenter, etc ..measures the observable associated with the eigenbasis , the wave function collapses from the full to just one of the basis eigenstates
(But I do not think I have to explain the theory you already know perfectly)
Unless you consider the interpretation "to many worlds", where the wave function continues to evolve in all the possible worlds in which it can give a certain result, etc

 

[stevendaryl]

I see no reason to use the concept of entaglement for the superposition principle, nor for the collapse of the wave function. You can take the simple example of the hydrogen atom and you will have state overlap and collapse without entagled states

The concept of entanglement is an essential part of QM. It's inevitable. If you have two systems interacting, then their states will become entangled. If a $\pi^0$ particle decays into an electron-positron pair (I think that's an allowable decay) then the spins of the two particles will be entangled.

All that it means for systems to be entangled is for the composite system to be in a superposition of states that fails to factor into a product state. For example, for spin, the state $\frac{1}{\sqrt{2}} (|u\rangle |d\rangle - |d\rangle |u\rangle)$ is an entangled state.

 

[Boing3000]

I see no reason to use the concept of entaglement for the superposition principle, nor for the collapse of the wave function. You can take the simple example of the hydrogen atom and you will have state overlap and collapse without entagled states

The reason is not for the superposition of state, but the number of "object" they describe. There is no classical analog.

Obviously, money is a classic and not a quantum object, but under the probabilistic aspects the behavior is exactly the same

No, they are not exactly the same. The "behavior" for classic object don't exist. You are kind of "undoing" a pure abstract "probabilization" of a totally not random object, coin, money or whatever. You may call it "Collapse" if you want to, but it only concern you abstract description.
In QM "collapse" is not even a thing. It is a word that some interpretation use to describe when the application of the Born rule "change" the state of the object "for real". It is part of the broader measurement problem, and is not about "potential ignorance" being "undone"

the possible states are logically linked by "and" before the measurement.

Not in classical mechanic. A coin is never in two state, and no genuine behavior can be associated with an AND state.

In fact it is said that they are "overlapped" in the sense that they coexist. But from the point of view of the result you can get a result "or" another result "or" another one etc. " But you can not get a result "and" another result

The result in QM often spans an infinities of observable (angle for spin). It is definitelly finite in classical mechanics.
But the point that in QM object behave as OR between observation, and the value only exist after (or is created by) after observation.

It is a pity that the collapse of the wave function is one of the fundamental principles of quantum mechanics(Heisenberg, Dirac, Born etc).

It isn't. The application of the Born rule is somewhat special, but not synonymous to collapse. It is interpretation dependent.

After the measurement, as you know, the wave function ceases to be an overlap of "possible" states.

But that wave function will only be on a eigenvalue for that observable basis only. It may still contains "overlap" on some other observable basis.
That is also a different with a "classic" collapse.

Unless you consider the interpretation "to many worlds", where the wave function continues to evolve in all the possible worlds in which it can give a certain result, etc

Or one of the many others that don't mention collapse at all.

 

[member 648030]

No, they are not exactly the same. The "behavior" for classic object don't exist. You are kind of "undoing" a pure abstract "probabilization" of a totally not random object, coin, money or whatever. You may call it "Collapse" if you want to, but it only concern you abstract description.
In QM "collapse" is not even a thing. It is a word that some interpretation use to describe when the application of the Born rule "change" the state of the object "for real". It is part of the broader measurement problem, and is not about "potential ignorance" being "undone"

The fact that a state has a value and another value means, from the point of view of the experimenter, one of two things:
1. the state is defined, but we do not know it
2. they are co-present multiple states simultaneously.

The first interpretation leads to a possible theory of hidden variables (Einstein), which however has been shown to be erroneous

The second remains, which is counterintuitive, and also "illogical", as if one thing is black and white simultaneously. But that's how things work. For example, in Feynman's theory of "virtual paths", a particle simultaneously follows infinite trajectories, which is completely meaningless (from a classical point of view).

Now, a coin is certainly a classic and not a quantum object, so, to say that it is "head" and "cross" simultaneously does not really make sense. But its behavior from the experimental point of view, is completely identical to the collapse of the wave function, or whatever you want to call it (change of state etc.)
After all, Einstein himself, when he criticized the QM, said: "God does not play dice!". All right, he did not say "God does not play heads or tails", but I think the meaning was just that.

 

[sshai45]

I want to comment here a bit about the "study the math" rebukes I see: the trouble here is that the formalism itself is, or *seems*, not complete enough, in a rather basic way, that may go underappreciated depending on how one is coming at it. And that is this: it provides for two basic operations on the quantum state vector, one of which is deterministic (Schrodinger equation), the other probabilistic ("collapse" law). The trouble is, suppose you wanted to take this description and now program a computer - we'll forget about the difficulty of having enough computing power, just imagine an ideal, infinitely powerful one with unlimited processing power and unlimited memory - to simulate a universe that might be described by this theory. (E.g. imagine a really good computer game, that is based on quantum-simulating everything in its world up from the atomic level.) For the theory's mathematics to "make sense", this is the criterion in which I imagine it. And when you do this, you run straight up into a big problem:

How do you choose which dynamic law to apply to the state of this universe at any given time step?

The collapse law says "when a 'measurement' happens", but it does not provide a mathematical equation to decide when that is happening,i i.e. something digestible by a computer. "Measurement" is not a mathematical term. Figuring out when/how requires interpretation, and that means different programmers will program effectively different dynamics.

That's the problem. "Study the maths" does NOT solve it.

 

[Boing3000]

The fact that a state has a value and another value means, from the point of view of the experimenter, one of two things:
1. the state is defined, but we do not know it
2. they are co-present multiple states simultaneously.

No, that's not the concerns of the experimenter. In both cases the probabilities are the same.
That's a concern for the model, and in the model everything is known, and everything is predictable (which both your point 1 and 2 are correct).

The first interpretation leads to a possible theory of hidden variables (Einstein), which however has been shown to be erroneous

The "hidden variable" must be non-local, that much is proved. However the universe does it, you can always call it "a hidden variable". But those "values" can spans huge swats of space (that's how entanglement is of critical important)

The second remains, which is counterintuitive, and also "illogical", as if one thing is black and white simultaneously.

I see grey things all the time, I don't find it illogical. Counter-intuitive is much more appropriate, but as long as conversation law are there, I personally find everything logical.

But that's how things work. For example, in Feynman's theory of "virtual paths", a particle simultaneously follows infinite trajectories, which is completely meaningless (from a classical point of view).

From a classical perspective, I found it totally logical. If I had to go somewhere "blinded" without any "guidance", I would try every-possible way, and kept the most efficient ones. That's totally meaningful for me that nature "kind of" does it all the time.

Now, a coin is certainly a classic and not a quantum object, so, to say that it is "head" and "cross" simultaneously does not really make sense.

I agree, but then it still is kind of useful/meaningfull. If the coin is not "fair", it is more "head" than "cross", but still both...

But its behavior from the experimental point of view, is completely identical to the collapse of the wave function, or whatever you want to call it (change of state etc.)

In QM superposition IS a thing of "reality". Negative probability and interference ALSO.
But classically there is nothing that change in the coin state on "collapse". It is never in superposition.

After all, Einstein himself, when he criticized the QM, said: "God does not play dice!". All right, he did not say "God does not play heads or tails", but I think the meaning was just that.

That's kind of unrelated. I think he just didn't like the stochastic only nature of the wavefunction.

 

[member 648030]

The concept of entanglement is an essential part of QM. It's inevitable. If you have two systems interacting, then their states will become entangled. If a $\pi^0$ particle decays into an electron-positron pair (I think that's an allowable decay) then the spins of the two particles will be entangled.

All that it means for systems to be entangled is for the composite system to be in a superposition of states that fails to factor into a product state. For example, for spin, the state $\frac{1}{\sqrt{2}} (|u\rangle |d\rangle - |d\rangle |u\rangle)$ is an entangled state.

It is not necessary to invoke entaglement
In fact, in general, I can represent any quantum state as a vector in a Hilbert space.
$| \psi\rangle=\sum_ {i = 1} ^ \infty c_i |\psi_i\rangle$
where $|\psi\rangle$ can be, for example, the wave function of a particle in a potential hole.
(or a hydrogen atom, to be more realistic)
As you can see, the $|\psi\rangle$ is not an entagled state at all, but rather the overlap of an infinite series of self-states by some operator (eg Energy)

 

[stevendaryl]

It is not necessary to invoke entaglement

In fact, in general, I can represent any quantum state as a vector in a Hilbert space.
$| \psi\rangle=\sum_ {i = 1} ^ \infty c_i |\psi_i\rangle$
where $|\psi\rangle$ can be, for example, the wave function of a particle in a potential hole.
(or a hydrogen atom, to be more realistic)
As you can see, the $|\psi\rangle$ is not an entagled state at all, but rather the overlap of an infinite series of self-states by some operator (eg Energy)

How you write it doesn't change whether it's entangled. The fact is that if you have a pair of particles that are in a superposition of

1. One state in which the first particle has spin-up and the other particle has spin-down
2. A second state in which the first particle has spin-down and the other particle has spin-up

then the spins of the two particles are entangled. Whether you write it as a product state or not doesn't change this.

Measuring the spin of one particle immediately tells you the spin state of the other particle, and vice-versa. But neither particle has a definite spin state prior to measurement.

 

[stevendaryl]

Now, a coin is certainly a classic and not a quantum object, so, to say that it is "head" and "cross" simultaneously does not really make sense. But its behavior from the experimental point of view, is completely identical to the collapse of the wave function, or whatever you want to call it (change of state etc.)

No, they aren't the same, from an experimental point of view. That's the whole point of Bell's inequality, to show that there are testable differences between quantum uncertainty and classical uncertainty.

 

[member 648030]

How you write it doesn't change whether it's entangled. The fact is that if you have a pair of particles that are in a superposition .

I do not see a pair of particles, let alone entagled. If you prefer, put the electron in a potential hole, or in any potential V. I still do not see two particles. Besides, I'm not interested in spin but only at energy levels. I still do not understand what entaglement has to do with it.

 

[member 648030]

No, they aren't the same, from an experimental point of view. That's the whole point of Bell's inequality, to show that there are testable differences between quantum uncertainty and classical uncertainty.

Suppose an apparatus similar to that of the Stern-Gerlach experiment. Suppose that you count from a beam of electrons those that have spin up (where the axis is chosen arbitrarily) and those with spin down. How many electrons will you count with spin up and how many with spin down? Or rather, the question is: how likely is (in your opinion) to find a spin up and to find a spin down. If you made a bet with a large sum where would you put it: on spin up or down?

 

[member 648030]

No, that's not the concerns of the experimenter. In both cases the probabilities are the same.
That's a concern for the model, and in the model everything is known, and everything is predictable (which both your point 1 and 2 are correct).

So in a quantum state measure, you are 100% sure to get a certain result, just like, knowing the initial conditions of a cannonball, can you predict exactly where it ends?