Observers

[The God]

It's oddly worded in the article - the limit is given by the inequality, above:

Bell's Inequality: in classical world, given three properties A, B, and C of any collection of countable things,
the number of them that possess A but not B, plus the number that possess B but not C, is equal to or greater than the number that possess A but not C.

That is a fact of the normal world. : that {A but not C} cannot be larger than the sum of the other two. {A & -B} + {B & -C} is therefore an upper limit on {A & -C}. That is the limit referred to.

As you can see, it holds in any collection of objects that either do or do not possess property B, communicate by cause and effect through space, and interact in ways that can be modeled in bi-valued logic (i.e. meaningful assertions of property possession are either true or false).

That limit is violated, in these quantum world measurements of entangled systems. {A & -C} is larger than {A & -B} + {B & -C}.

Dunno. Greater than the inequality allows, is the report.

So for couple of particles to be entangled one requires assessment of three properties (A, B, C), unless of course there is some other definition of finding out correlation and establishing violation of inequality.

Cat is dead, the other oft given example is that two photons are produced now due to conservation of angular momentum if one has clockwise angular momentum at the time of measurement then the other photon will be found with anti clockwise angular momentum when measured. So far no big deal both QMly and classically!

Now as I could figure out.....once the first photon angular momentum is measured, the second photon angular momentum is determined, but the second photon is in a state of superposition (QMly) before measurement, that means it could have any direction angular momentum (of course axis being same) if only local effects are to be considered, but on measurement it is found counter to its remote entangled partner whose measurement was earlier done. Surely the correlation for this direction is higher thus violating Bell's inequality.

 

[iceaura]

So for couple of particles to be entangled one requires assessment of three properties (A, B, C), unless of course there is some other definition of finding out correlation and establishing violation of inequality.

That's just a direct and experimentally available way of checking the theory, and eliminating some alternative explanations for the phenomena observed.

 

[arfa brane]

So we've explored entanglement and found out it's about:

1) particles interacting, except you can entangle parts of the vacuum.
2) measurement, except you don't have to measure anything. (Definitely not true in quantum computing, but see 1 above)
3) observers, except that particles are observers too, and you don't need particles.
4) nondistributive logic and a complex Hilbert space, neither of which are "physical".(?)

 

[The God]

That's just a direct and experimentally available way of checking the theory, and eliminating some alternative explanations for the phenomena observed.

Then what about the post #461 second part.

Two particles entanglement can be seen with the measurement of angular momentum, that's is only one property!

But yet to be measured angular momentum of entangled particle has multiple superposed states or degree of freedom (Arf, I am getting to your point) and ideally till measurement all states are locally equi-probable, but since the first particle has already given x direction of angular momentum so on measurement all other degrees of freedom (superposed states) would collapse except -x. That's non local higher correlation, a violation. Isn't it?

 

[arfa brane]

Is the fact that quantum logic is nondistributive, sufficient to derive Bell's inequalities?

Well, we want to 'encode' complementary degrees of freedom, in some ensemble, in terms of logical statements.
For instance, "If electron spin is measured in the x direction, then it will point in that direction or away from it".
Or just, "If spin is measured in the x direction, then it will be up or down". More succinctly, "x-spin up or x-spin down", where "x-spin" implies a measurement.

Ok so a complementary spin-degree of freedom is the y direction, so we write: " "x-spin up or x-spin down and y-spin up or y-spin down".
Now we have to make sure that deMorgan's Law doesn't apply, so we don't encode: "x-spin up and y-spin up", for instance. This would be like a coin that lands heads and tails.

So we need to modify the Boolean sense of and/or. Or just define meet-join relations over spin measurements in the x and y directions.

 

[iceaura]

Then what about the post #461 second part.

Two particles entanglement can be seen with the measurement of angular momentum, that's is only one property!

Quantum theory, including entanglement, describes many situations that do not involve violations of Bell's Inequality. That is ok.

 

[arfa brane]

Having the causal structure and locality built in, relativistic field theory offers a natural framework for investigating entanglement. Here we will consider the entanglement of the relativistic vacuum state, which as we shall shortly recall, has a role in both the Hawking black-hole radiation [2] and Unruh acceleration radiation effects [3].

It is known that field observables at space-like separated points in vacuum are correlated. For massless fields in 3+1-D these correlations decay with the distance, L, between two points as 1/L^2. These correlations by themselves however do not imply the existence of quantum entanglement, because they can in principle arise as classical correlations. However, a number of studies provide evidence that the vacuum is indeed entangled [3, 4, 5]

2 Entropy, Correlations and Entanglement

We begin with a short review of the relation between entropy, correlations and entanglement. Consider a division of a system into two sets of commuting degrees of freedom whose combined Hilbert space can be described by the direct product of Hilbert spaces H1×H2. The operators O1 and O2 that act on H1 and H2, respectively and thus commute: [O1,O2] = 0. In a relativistic theory, the division of space to two space-like separated regions, implies by causality commutativity of local observables, and the above Hilbert space structure follows.

--https://arxiv.org/pdf/quant-ph/0212044.pdf

 

[iceaura]

Is the fact that quantum logic is nondistributive, sufficient to derive Bell's inequalities?

Bell's Inequality is a theorem in regular ol' two-valued logic, that holds in the classical and/or relativistic world.

 

[arfa brane]

Bell's Inequality is a theorem in regular ol' two-valued logic, that holds in the classical and/or relativistic world.

Indeed, but it seems you need to define three variables, and each has to have a binary probability (like heads or tails, gold or silver, shiny or dull, etc. in the case of coins). Then Bell's theorem depends only on a particular distribution of probabilities.

That you can derive the theorem with classical objects is as significant as being able to simulate a quantum algorithm on a classical computer.

 

[iceaura]

Indeed, but it seems you need to define three variables, and each has to have a binary probability (like heads or tails, gold or silver, shiny or dull, etc. in the case of coins). Then Bell's theorem depends only on a particular distribution of probabilities.

Bell's Inequality has nothing to do with probabilities, does not involve quantum or any other theory of Physics, and holds for all distributions of the properties involved. In classical world.

 

[arfa brane]

Bell's Inequality has nothing to do with probabilities,

You have a pair of objects, each with three binary-valued 'properties'. It does seem to have something to do with probabilities, or that's what these authors are saying at least:

Bell’s inequality refers to the correlation among measurement outcomes of the properties: call Psame(A, B) the probability that the properties A of the first object and B of the second are the same.

Under the conditions that three arbitrary two-valued properties A, B, C satisfy counterfactual definiteness and locality, and that Psame(X, X) = 1 for X = A, B.C (i.e. the two objects have same properties), the following inequality among correlations holds,

Psame(A, B) + Psame(A, C) + Psame(B, C) ≥ 1 (1)​

namely, a Bell inequality.

--http://www.johnboccio.com/research/quantum/notes/paper.pdf

Or are you saying probability is one way to derive an inequality, but isn't actually needed?

 

[The God]

I do not think Bell's inequality is ever violated. Despite 24 pages, not even single example of violation is put up here. Thankfully it is clear that Schrodinger's cat is not in two states dead or alive till we see. This wave function and superposed states concepts are being pushed too much like everything around Black Hole. Far from real representation of nature.

 

[arfa brane]

I do not think Bell's inequality is ever violated.

Good thing that physics is immune to what you think then.

Despite 24 pages, not even single example of violation is put up here.

So because you haven't seen it on sciforums, it can't be true?

This wave function and superposed states concepts are being pushed too much like everything around Black Hole. Far from real representation of nature.

Good thing you aren't doing any real research then.

 

[The God]

Good thing that physics is immune to what you think then.So because you haven't seen it on sciforums, it can't be true?Good thing you aren't doing any real research then.

Physics, aka study of nature, must be immune to what anyone thinks or pushes, but unfortunately it is not.

Even after 24 pages of repetitive stuff, at least one participant could have given one example of entanglement, none could give.

Schrodinger's cat failed and simple attempt by James (in line with general angular momentum conservation example) also failed.

I am doing research but I keep away from crap. The video of Sussy is pathetic as far as Physics content is concerned.

There are contradicting papers where authors claim no violation of inequality ever, violation of inequality even in macro world etc, but at the end just trust the nature it cannot keep you and me in superposed state of alive or dead, likewise the nature cannot keep an electron in superposed state of spinning or not spinning, spinning or counter spinning.

We must learn to appreciate that our models are great but pushing them beyond certain limits will give you Black Holes or absurdities like white holes or even further absurdities like entanglement as envisaged.


By the way, can you tell how the concept of entanglement came in, which nicety of the theory (or observation) leads to the conclusion of possibility of entanglement? Can you??

 

[arfa brane]

Try this site.

They reckon they have the qubits to entangle, if you want to try it yourself. That is, you can create your very own Bell states, I shit you not.
But then again it's only IBM.

 

[The God]

Try this site.

They reckon they have the qubits to entangle, if you want to try it yourself. That is, you can create your very own Bell states, I shit you not.
But then again it's only IBM.

Pl answer the following.

can you tell how the concept of entanglement came in, which nicety of the theory (or observation) leads to the conclusion of possibility of entanglement?

 

[iceaura]

You have a pair of objects, each with three binary-valued 'properties'. It does seem to have something to do with probabilities, or that's what these authors are saying at least:

You do not have "a pair" of objects, but thousands of them, in these tests of Bell's Inequality in quantum world.

You are mistaking a test of Bell's Inequality in quantum world, for a derivation of it.
You are mistaking the "measurement outcomes" - the things to which Bell's Inequality would apply, which are not probabilities but actual instrument readings - for the theoretical basis of the predictions of these outcomes, which involves probabilities in QED.

The statement of the Inequality is clear, I handed it to you above, and it has nothing to do with probabilities. Again:

Bell's Inequality: in classical world, given three properties A, B, and C of any collection of countable things,
the number of them that possess A but not B, plus the number that possess B but not C, is equal to or greater than the number that possess A but not C.

If you don't like my wording, I posted the Wiki link. Many others are available on the net.

It has to do with counting definite physical properties objects actually possess with a probability of one - in the case of the paper slips: you are holding them in your hand, registering the possession of the properties, and counting them.

People checking the Inequality are counting measurement outcomes, not probabilities.

I do not think Bell's inequality is ever violated.

You are wrong. Quantum theory predicts it will be violated in certain circumstances involving quantum level interactions, and every time anyone has checked it has been. Hundreds of times. Post 441 provides a link to a recent one - devoted not to once again ascertaining the violation, which is taken for granted now, but to constraining one category of the proposed explanations for the violation. Post 441 also provides a Wiki link which provides you with dozens of references to related reports of experiment, all agreeing that the Inequality is violated exactly as predicted by QED.

 

[arfa brane]

It has to do with counting definite physical properties objects actually possess with a probability of one - in the case of the paper slips: you are holding them in your hand, registering the possession of the properties, and counting them.

People checking the Inequality are counting measurement outcomes, not probabilities.

So what you're saying is when Bell's inequalities "appear" in QED measurements, it isn't because quantum states are complex probability amplitudes? The states aren't probabilistic once you measure them, or something?

Without repeating that Bell's theorem is not about quantum states, but applies to any experiment with instrument readings, is it just then that Bell's theorem applies because quantum states are measured.
And you seem to be implying that measurement isn't probabilistic, although it is statistical. You're drawing a line between statistics and probability that I'm having trouble seeing.

 

[The God]

People checking the Inequality are counting measurement outcomes, not probabilities.

You are wrong. Quantum theory predicts it will be violated in certain circumstances involving quantum level interactions, and every time anyone has checked it has been. Hundreds of times. Post 441 provides a link to a recent one - devoted not to once again ascertaining the violation, which is taken for granted now, but to constraining one category of the proposed explanations for the violation. Post 441 also provides a Wiki link which provides you with dozens of references to related reports of experiment, all agreeing that the Inequality is violated exactly as predicted by QED.

Ok, they are checking the measurement outcome..but hold on...

I will post the standard well known example, see if you agree with me on that...

Two entangled photons are created, the spin of photon one is measured and say it is clockwise with respect to some axis, now the entanglement supporters argument is that when the spin of the second photon is measured it will be counter clockwise.

The natural question is what will be the outcome of second measurement if the first measurement never took place?

As I understand as per QM it could have been any direction, but since first measurement took place, all other directions possibility vanished and only counter direction to the first measurement remained. That surely violates Bell's inequality, and gives an impression that information regarding first measurement was transmitted to second d photon instantly, distance notwithstanding.

 

[iceaura]

So what you're saying is when Bell's inequalities "appear" in QED measurements, it isn't because quantum states are complex probability amplitudes? The states aren't probabilistic once you measure them, or something?

Example: The spin on some axis is measured as up or down. If it is measured up, the probability that it is down is zero (barring error) until further notice.

And you seem to be implying that measurement isn't probabilistic, although it is statistical. You're drawing a line between statistics and probability that I'm having trouble seeing.

? People measure the spin of an electron on some axis, they get a measurement (up or down), they record this information. What's the problem?

As I understand as per QM it could have been any direction, but since first measurement took place, all other directions possibility vanished and only counter direction to the first measurement remained. That surely violates Bell's inequality, and gives an impression that information regarding first measurement was transmitted to second d photon instantly, distance notwithstanding.

So far no violation of Bell's Inequality has appeared in your example.
To transmit information instantaneously violates Relatively Theory. People are searching for some other explanation.