Einstein and "spooky actions"

[PolyHedral]

Good, I welcome that. Is there anything I can help to clarify my argument so that they can be clearer to you? Perhaps starting with this post? (or any other of your choosing)

http://www.religiousforums.com/forum/3320203-post134.html

Your distinction between classical and quantum logic appears meaningless. Quantum mechanics appears to work with exactly the same logic as anything else, merely using different objects to describe reality. It would be like drawing a distinction between the logic of the integers and of the fractions.

(It's not that hard to start from the classical ZF axioms and build Hilbert space. )

I think the moon is to massive too ignore classical physics.

Classical physics isn't some other theory that exists alongside QM. It's supposed to be an approximation of what QM looks like when it describes large, cool objects.

 

[idav]

Classical physics isn't some other theory that exists alongside QM. It's supposed to be an approximation of what QM looks like when it describes large, cool objects.

The moon keeps collapsing the wave function every time I look it!

 

[zaybu]

http://www.phy.duke.edu/undergradua...here-when-nobody-looks-physics-today-1985.pdf

Please read this and let me know what you think.

Thanks for the link.

One of the mistakes that Einstein made was to believe that measurement in A influence instantaneously measurement in B ( But there is no evidence that this is taking place). Of course having assumed that, he strongly argued, mainly with David Bohm, who was writing a textbook on QM, and with whom he had a lively correspondence, that this entails QM is operating under the assumption of some spooky action at a distance. The other mistake is that he doesn't apply the Uncertainty Principle correctly in the famous EPR paper. He also firmly believed that QM's claim - everything you can know about a particle resides in the wavefunction - is false and that QM is incomplete. He counters that with particles having hidden parameters.

The other mistake comes from the interpretation of Bell's theorem, which came later after Einstein. And on this I have argued in this thread that the mistake is not to recognize that its inequalities only apply to a classical system. If you have a quantum system understudy, its results will inevitably violate that inequality.

I've been trying to read up on quantum logic, it's formalism, and how it differs from classical logic. I'm well versed in classical logic having taken both math courses and a philosophy course in the subject, but can't seem to find any good info on quantum logic... I'm guessing it's a relatively new field. Anybody have any links for me?

http://plato.stanford.edu/entries/qt-quantlog/

From that link:

It is uncontroversial (though remarkable) that the formal apparatus of quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over by the “quantum logic” of projection operators on a Hilbert space.

 

[zaybu]

Your distinction between classical and quantum logic appears meaningless. Quantum mechanics appears to work with exactly the same logic as anything else, merely using different objects to describe reality. It would be like drawing a distinction between the logic of the integers and of the fractions.

(It's not that hard to start from the classical ZF axioms and build Hilbert space. )

For those unfamiliar with the subject try this link


Quantum Logic and Probability Theory (Stanford Encyclopedia of Philosophy)


Pay particular attention this:

It is uncontroversial (though remarkable) that the formal apparatus of quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over by the “quantum logic” of projection operators on a Hilbert space.

 

[Reptillian]

The moon keeps collapsing the wave function every time I look it!

It's the watched pot effect! Try waiting longer between looks.

 

[Reptillian]

Thanks for the link.

One of the mistakes that Einstein made was to believe that measurement in A influence instantaneously measurement in B ( But there is no evidence that this is taking place). Of course having assumed that, he strongly argued, mainly with David Bohm, who was writing a textbook on QM, and with whom he had a lively correspondence, that this entails QM is operating under the assumption of some spooky action at a distance. The other mistake is that he doesn't apply the Uncertainty Principle correctly in the famous EPR paper. He also firmly believed that QM's claim - everything you can know about a particle resides in the wavefunction - is false and that QM is incomplete. He counters that with particles having hidden parameters.

The other mistake comes from the interpretation of Bell's theorem, which came later after Einstein. And on this I have argued in this thread that the mistake is not to recognize that its inequalities only apply to a classical system. If you have a quantum system understudy, its results will inevitably violate that inequality.



Quantum Logic and Probability Theory (Stanford Encyclopedia of Philosophy)

From that link:

From your link " In this sense, then, quantum mechanics—or, at any rate, its mathematical framework—reduces to quantum logic and its attendant probability theory."

So if the mathematical framework was used to derive Bell's Inequalities, then doesn't that automatically make them compatible with quantum logic?

 

[zaybu]

From your link " In this sense, then, quantum mechanics—or, at any rate, its mathematical framework—reduces to quantum logic and its attendant probability theory."

So if the mathematical framework was used to derive Bell's Inequalities, then doesn't that automatically make them compatible with quantum logic?

No, and here's the reason:

In deriving his theorem, Bell used Boolean Algebra, which presupposed points in set theory. In classical physics, we need to have the position and momentum to know everything about the particle, and these are points in phase space. So set theory, points in set theory to represent position and momentum, and Boolean algebra is the right mathematical framework for classical physics. Call that classical logic. So from that, we can say that Bell's theorem is fine for any classical system.

But for a quantum system, we need to represent the state of a particle by a vector in Hilbert space, and observables by operators acting on those states, not points from set theory. This is a totally different framework than a classical system. Call that quantum logic. So Bell's theorem applied to a quantum system is not going to work. And that's why there are tons of papers published in scientific journals based on experiments on quantum systems that don't obey Bell's theorem.

 

[Curious George]

No, and here's the reason:

In deriving his theorem, Bell used Boolean Algebra, which presupposed points in set theory. In classical physics, we need to have the position and momentum to know everything about the particle, and these are points in phase space. So set theory, points in set theory to represent position and momentum, and Boolean algebra is the right mathematical framework for classical physics. Call that classical logic. So from that, we can say that Bell's theorem is fine for any classical system.

But for a quantum system, we need to represent the state of a particle by a vector in Hilbert space, and observables by operators acting on those states, not points from set theory. This is a totally different framework than a classical system. Call that quantum logic. So Bell's theorem applied to a quantum system is not going to work. And that's why there are tons of papers published in scientific journals based on experiments on quantum systems that don't obey Bell's theorem.

And why did Bell's theorem use Boolean Algebra?

 

[Reptillian]

Here's Bell's original paper: http://www.drchinese.com/David/Bell_Compact.pdf Please point out where he makes his assumption and mistake.

 

[zaybu]

And why did Bell's theorem use Boolean Algebra?

He's not around so we can't ask him. One possible guess is that he might not have realized that QM requires a different logic. You have to remember that back in the 50's-60's when this topic was discussed by people like Bohm, Bell and others, QM was not as well understood as today. They also believed then that the wavefunction was real. Most physicists don't take that position today. So our views on the subject is quite different than in those days.

 

[zaybu]

One more time: since no one has been capable of defeating my arguments, can I declare myself the winner of this debate?

 

[Reptillian]

Did you look at Bell's original paper in the link I sent? Where exactly did he make his assumption and mistakes?

 

[zaybu]

Did you look at Bell's original paper in the link I sent? Where exactly did he make his assumption and mistakes?

My apologies, I hadn't seen your post. Thanks for bring it up to my attention. I'm away for the weekend. Will answer in a few days.

 

[PolyHedral]

No, because you're talking nonsense.

In deriving his theorem, Bell used Boolean Algebra, which presupposed points in set theory.

Boolean algebra doesn't use points at all, as such. Boolean algebra is the language of expressions which are either true or false, and logical conjunctions of those. You may be thinking of "elementary" probability theory, which involves the evaluation of boolean functions (that is, functions which take some parameter and produce true or false) over some countable or continuum-sized set of other objects, e.g. in the question of "How many possible ways are there to toss a coin 20 times and get more than 10 heads?" the objects are series of coin tosses, and the function is the mathematical equivalent of, "Contains more than 10 heads."

In classical physics, we need to have the position and momentum to know everything about the particle, and these are points in phase space. So set theory, points in set theory to represent position and momentum, and Boolean algebra is the right mathematical framework for classical physics. Call that classical logic. So from that, we can say that Bell's theorem is fine for any classical system.

What does it mean to apply Bell's inequality to a classical system? The ineqaulity describes the outcome of random selections, which don't exist in classical mechanics.

But for a quantum system, we need to represent the state of a particle by a vector in Hilbert space, and observables by operators acting on those states, not points from set theory.

A Hilbert space is a set, as in set theory. In the case of a lone non-relativistic spin-zero particle, the space we do QM in is the space of all possible square-integrable functions. This has "points" in it, each of which represents a possible state of the particle.

This is a totally different framework than a classical system. Call that quantum logic. So Bell's theorem applied to a quantum system is not going to work. And that's why there are tons of papers published in scientific journals based on experiments on quantum systems that don't obey Bell's theorem.

Them not obeying Bell's theorem is the point - Bell's theorem is a result of local realism. No Bell inequality, no local realism, ergo, quantum mechanics is weird.

 

[zaybu]

Did you look at Bell's original paper in the link I sent? Where exactly did he make his assumption and mistakes?

No, because you're talking nonsense.

Boolean algebra doesn't use points at all, as such. Boolean algebra is the language of expressions which are either true or false, and logical conjunctions of those. You may be thinking of "elementary" probability theory, which involves the evaluation of boolean functions (that is, functions which take some parameter and produce true or false) over some countable or continuum-sized set of other objects, e.g. in the question of "How many possible ways are there to toss a coin 20 times and get more than 10 heads?" the objects are series of coin tosses, and the function is the mathematical equivalent of, "Contains more than 10 heads."


What does it mean to apply Bell's inequality to a classical system? The ineqaulity describes the outcome of random selections, which don't exist in classical mechanics.


A Hilbert space is a set, as in set theory. In the case of a lone non-relativistic spin-zero particle, the space we do QM in is the space of all possible square-integrable functions. This has "points" in it, each of which represents a possible state of the particle.


Them not obeying Bell's theorem is the point - Bell's theorem is a result of local realism. No Bell inequality, no local realism, ergo, quantum mechanics is weird.

I will reply to both of you, since the answer involves the same concepts.

Let me illustrate the differences between vectors in "ordinary" space, and vectors in a Hilbert space as used in QM.

There are certain similarities, obviously, since a Hilbert space is constructed analogous to ordinary space. And if they were exactly the same, then there wouldn't be any need to distinguish quantum physics from classical physics. You would have one happy family called physics. So it should come to mind why we distinguish quantum physics from classical physics.

In ordinary space, a vector is made of a line segment, with an arrow indicating direction. The line segment can be considered to be made of an infinite number of points and can be subdivided to any arbitrary size. If we look at position and momentum in classical physics, just looking at their magnitude, ignoring their direction for now, they can be represented by a point . Similarly for energy, which is a function of position and momentum, can take arbitrarily any value, and can be represented by points.

This is not the case for QM. Take for example, the hydrogen atom. The energy is quantized , and we talk about energy levels labelled by n=1,2,3... An electron can jump between any two levels, but it can't jump from n=1 to n=2.5 or 3.7 as these levels don't exist. These energy levels are represented by vectors in a Hilbert space. But these vectors cannot be reduced to points, and they cannot take any arbitrary value. It is in that sense that vectors in quantum physics are different than vectors in classical physics.


The second major difference is that in classical physics we don't distinguish between a state and an observable. If a particle has position x and momentum p, then the label x,p can represent either its state or the observables if we wish to measure them.

In QM, we make a distinction. For example, its momentum is represented by a ket Ip>, its dual vector by a bra <pI, but its observable in position space by an operator,

P &#8594; i(h-bar)d/dx, where i is the imaginary number,the square root of negative one, h-bar is the reduced Planck constant, followed by a derivative with respect to x, the position of the particle.

You can see that there is no equivalence in classical physics. That's why QM is developped along an entirely different mathematical framework.

In Bell's theorem, the derivation used is the ordinary framework of classical physics: ordinary vectors, points, etc. Its theoretical results will be satisfied by the experimental values of a classical system. But should you devise an experiment for a quantum system, its experimental results will violate Bell's theorem. But if you use the same mathematical framework in QM to work out the theoretical value of your experiment, your experimental results will agree with that theoretical value.

So, comparing the experimental values of a system understudy with Bell's theorem will only decide if the system you used is classical - in that case experimental and theoretical values agree; or it is a quantum system - in that case experimental and theoretical values disagree.

 

[Reptillian]

*Pulls Griffith's "Introduction to Quantum Mechanics" off the shelf and dusts it off*

I think we need to review and discuss all of chapter 3 and the afterword.

 

[Reptillian]

In Bell's theorem, the derivation used is the ordinary framework of classical physics: ordinary vectors, points, etc. Its theoretical results will be satisfied by the experimental values of a classical system. But should you devise an experiment for a quantum system, its experimental results will violate Bell's theorem. But if you use the same mathematical framework in QM to work out the theoretical value of your experiment, your experimental results will agree with that theoretical value.

Quantum mechanics makes an experimental prediction. Hidden variable proponents suggest that quantum mechanics is correct, but incomplete in that some other information besides the wavefunction is needed to fully describe the state of a particle. They did this to salvage the idea that particles have well defined properties regardless of whether we measure them or not. Bell showed that such an idea is incompatible with the initial quantum mechanical prediction. He used the mathematics of quantum mechanics to derive this result. If there is some extra (local) hidden variable, then you simply cannot reproduce the initial result using the mathematics of quantum mechanics. If we insist on realism, then we have to abandon locality. Either that, or nature is both real and local and quantum mechanics is just plain wrong...but experiment doesn't favor this option.

So the response to Einstein's question "Do you really believe that the moon isn't there when nobody's looking?" seems to be "It may be there when we're not looking; but if so, then we can't separate it from the rest of the universe."

 

[idav]

Either that, or nature is both real and local and quantum mechanics is just plain wrong...but experiment doesn't favor this option.

The experiments show that both are actually true which lends to QM not being wrong but incomplete. Take for example a photon being both a wave and a particle. People like to argue that the photon is in no way a particle but that it is only a wave all that exists is some wave hologram illusion type reality.

 

[zaybu]

. He (Bell) used the mathematics of quantum mechanics to derive this result. "

Susskind has derived Bell's theorem using only Venn's diagram, ignoring the whole mathematical apparatus of QM. Go figure.

So the response to Einstein's question "Do you really believe that the moon isn't there when nobody's looking?" seems to be "It may be there when we're not looking; but if so, then we can't separate it from the rest of the universe."

You can put a detector that will register the photons bouncing off the moon. You don't need humans to do the observation. The reality is that we are always being observed.

 

[Mr Spinkles]

One more time: since no one has been capable of defeating my arguments, can I declare myself the winner of this debate?

Since you are not capable of realizing and admitting instances when you are definitely shown to be wrong, you have disqualified yourself from this debate, as I explained here. Therefore, you are free to declare yourself whatever you like, and no one will care.

For the benefit of everyone else, here are some points that should help clarify some things:

(1) A consequence of QM is that a measurement over here can have an instant effect on another measurement occurring very far away. This is, by definition, "nonlocality" and it has been demonstrated by experiments.

(2) However, this "quantum nonlocality" is of a special kind. You can't control how your measurement turns out, and therefore you can't control how the other distant person's measurement turns out, either. In other words, this is a statistical effect, not a strictly deterministic or causal effect. Because of this, quantum nonlocality does not violate Special Relativity, which prohibits faster-than-light causal influences. It is worth distinguishing nonlocality as it occurs in QM from other kinds of nonlocality. For example, a faster-than-light force transmitting a casual influence, or a faster-than-light communication transmitting information, would violate Special Relativity. Sometimes people call all of these things "nonlocality" even though they are distinct, and this can cause confusion.

(3) In order to escape the straightforward QM interpretation of (1), you have to do some work. You might claim that QM makes correct statistical predictions, but really underneath it all everything is a deterministic clockwork (classical). So, for example, you might suppose that by some mechanism unknown to physicists ("hidden variables"), each particle in an entangled pair actually has a well-defined spin (up or down) as soon as they are separated from each other, before anyone does any measuring. If this were true, then QM would still give correct statistical predictions. But the QM interpretation in (1) would be wrong: my measurement over here would NOT actually affect your measurement way over there, in any way. IOW, there wouldn't be ANY kind of nonlocality, not even the weak "quantum" kind described in (2).

(4) Bell showed, in a nutshell, that supposing QM is incomplete and we adopt the seemingly reasonable alternative in (3), we get predictions which are in conflict with experiments. In other words, the alternative in (3) is wrong. The only way to save it is to modify it by: (a) assuming instantaneous influences can occur between distant particles, i.e. nonlocality; or (b) assume that QM is at least partially correct, in that particles really do follow statistical rules not just in appearance but in actuality--IOW the entangled pair discussed in (3) really didn't have definite spins (up or down) before measurement. Or you could assume both (a) and (b). Finally, you could give up on this alternative altogether and just accept QM as described in (1).

(5) Most physicists feel that since alternatives to QM still require weird assumptions or consequences in order to be compatible with experiment, we may as well just accept QM and the straightforward interpretation of experiments as described in (1).

For what it's worth: I'm a PhD candidate in physics with 2 grad courses and 1 undergrad course in QM, I've watched all the videos and read all the refs. posted by zaybu, I also checked my QM textbooks, and Legion and I consulted a number of peer-reviewed papers from Science, Nature, PNAS etc. I know from experience what my profs. and fellow students would say. This doesn't in and of itself make me right; again take it for what it's worth.