Bit is It by Mikalai Birukou

About entanglement.

We, an external system, see two systems as being entangled because of confinement of their interaction. This confinement is key to having this quantum phenomena. Once we interact with one of the subsystems, so that result of interaction (or information we get) is related to the confined aspect, the entanglement breaks. Or, you can say that we start to be a part of tri-entanglement. It might be easy to visualise this using quantum computing schemes.

Entanglement is how we see two systems from the outside, while sub-systems' interaction is confined. It makes all reasoning simpler.

You see, if I give you just foundation for QM, which treats current imperfections, you may find it interesting, and move on. This foundation must produce hints for further development, that will be proved or disproved by experiments. And, in this essay, after all, we should try to dream like Wheeler did.

It seems to me that guys did the best job possible in forming mathematical framework for QM in 1900-1920's. They couldn't possibly do better, because they didn't have all experiments with particles of 1960's and later. But now, in 2010's, we may try to straighten things up, by placing QFT's concepts as a foundation, as a physical essence for QM's math. After all, everything is maid of particles seen at CERN.

Let's look at it conceptually.

Firstly, the OR sign in postulate #3 is a real OR for systems involved in the interaction. This way, when you assemble an interaction, which tells you which spin particle has, you will have one OR the other value. Remember, we have no special interactions here.

But, this OR does not apply to the external system! That is our interaction confinement. Information about interaction is not leaking without actual interaction with sub-systems. The OR, therefore, does not apply to external systems, till external system interacts with any of sub-systems. Pay a close attention to brackets in equations 5 & 6 of the essay. It is natural for us to assume brackets positions of 5, cause this is how information flows in our everyday life. But for quantum systems nature chooses 6!

You cannot make this up, that is why we needed an experiment to tell how OR sign should be related to external system. And that sums up entanglement phenomena.

From mathematical perspective, entanglement is a direct result of unitary evolution of a closed system. So, whichever element of theory gives you unitarity, that piece is responsible for entanglement. Interaction confinement postulate #4 gives unitarity here.

Check reference #9, where I go through steps of assembling usual QM math. Length of one essay cannot fit all details.

Check reference #9, where I go through steps of assembling usual QM math. Length of one essay cannot fit all details.

My last post in this thread was meant to be in the other thread.

Your point that unitary evolution implies entanglement is certainly correct, however, when you say 'when you assemble an interaction, which tells you which spin particle has, you will have one OR the other value', this isn't possible unitarily. In as much as your postulate 3 leads to the outcome of any interaction being a single, definite state rather than a superposition, it explicitly breaks unitarity. And even so, since a definite state in one basis is generally superposed in another, you are not out of hot water here; if you invoke postulate 3 to force the state of two electrons after interaction to be |00> or |11> rather than the superposition of both, then in the {|>,|->}-basis these will be superpositions of all basis vectors in general.

And I must admit that I find your notation in equations (5) and (6) to be rather confusing. I guess you mean to say that in equation (6) the additional system does not 'know' about the state of the original system, while in equation (5), it does; however, such knowledge only occurs through interaction, and thus, without having interacted with the original system, the outside system does not 'know' anything about it in both cases (as is shown by the fact that it does not change its state).

How would you, in your formalism, model an actual experiment? On the traditional view, you have some measurement apparatus that interacts with the system in such a way as to reflect the system's state in its own state after the interaction. So for instance, a {|0>,|1>}-detector is defined by the equations

[math]|r\rangle|0\rangle\to|"0"\rangle|0\rangle[/math]

[math]|r\rangle|1\rangle\to|"1"\rangle|1\rangle[/math]

where |r> is some ready state of the apparatus, and |"0"> resp. |"1"> is the state in which it indicates the measurement result 0 or 1 respectively.

Now, using such a measurement device, I can retell the story I told in my previous post, where each of Alice and Bob have both a {|0>,|1>} and a {|>,|->} measuring device (the latter of course working analogously to the above).

Now the measurement device, if I understand correctly, is your external system |Y>. What difference does it now make whether it works according to equation (5) or (6)? In both cases, it does not seem to change state---thus, it measures nothing, and knows nothing about the system. So, how would a measurement apparatus that changes its state according to the above definition interact in your picture? How would it, in particular, yield the observed perfect correlation across both bases? Certainly, if your framework is adequate, there should be a way to mathematically derive these correlations, just as I have done above for standard quantum mechanics; I'd be very grateful if you could show it to me.

Let's consider a classical OR example. Imagine that you hide a coin in one of your hands behind the back. When you did so, interaction between hands and coin, or choice of hand happened. Now, I do not which choice happened. This is described by equation 5. Me, an external system does not have i-suffix, in 5, but the choice is fixed for me. And if coin's suffix says "right", any further interaction, like you showing me a hand with the coin will change my state accordingly, to "right" with 100%. This is a classical flow of information.

If it were quantum situation, or equation 6, although you chose the hand, this choice is already fixed, but only for you and a coin. My getting this information through interaction will be loaded with the choice "re-happening" for me. The system hand-coin will decohere for me. And notice that there are no good analogies, no good everyday words to describe this non-classical flow of information. This weirdness is the essence of entanglement, either in EPR, or in a double-slit experiment.

We can say that classical flow of info (equation 5) can be sufficiently described by REAL numbers, that are directly probabilities. But this calculus with real numbers has no room for choice "re-happening". A bit more room in math is needed, thus complex numbers are needed, with a prescription of obtaining real probabilities (0 to 1).

By the way, if we ask what sort of mechanics can drive info flow described by 6, in terms of something more common, which follows equation 5. May be, there are some hidden variables, for example. Variables are describable with real calculus, but it has no space to accommodate experimental results for Bell's theorem (Aspect's references). Thus, there is no use in trying to disassemble quantum info flow into less weird terms.

Hi Mikalai,

Thanks for the reply. I will have more questions later after a second reading of your essay.

Mikalai

"This weirdness is the essence of entanglement"

It is an indication that there is something wrong with the theory.

Whatever constitutes physical existence can only occur in one definitive physically existent state at a time, for the successor in the sequence to be able to exist, the predecessor must cease. And any cause/effect must function within physical rules which limit possible involvement. Assuming only direct cause, since everything is ultimately interrelated and therefore cause in the alternative context is meaningless. And that is because physical interaction cannot 'jump' physical circumstance, ie to be a possible cause it must be in a specific spatial relationship vis a vis the effect, and it must be in a specific relationship in the sequence order vis a vis the effect. Mentally, as I pointed out to Jochen, it is important to conceive of cause and effect, which are successive physical realities, as different rather than something which has changed in some way(s).

Because what is happening here is that we are failing to differentiate physical realities at the level at which they occur. That is, we are deeming what is actually a sequence of realities as one, &/or when considering what constitutes reality thereby confusing times of existence, ie what actually existed at the same time and was therefore a constituent of the same reality and what was cause and effect. Indeed, I doubt if we could in practice identify any given reality. The other important point being that measurement/sensing/whatever one wants to call it, has no effect on physical existence, that has already occurred.

So the principle remains the same at any level of conceptualisation. That is, we can deem St Paul's cathedral to be a reality, which it is not, or we can consider it in terms of how it exists which is a physically existent state at any given time, and any difference in that state is another state. The point being that existence is definitive, there is no indefiniteness or alteration involved in any actual physical reality. So we need to identify it and then make a proper estimate of what preceded it and what succeeded it. If we cannot, then we need to overcome that in some way. But not attribute physical existence with 'wierdness' because of our own failings.

Paul

Mikalai, but if you say that in the coin example, the choice has already been made after the interaction, then you're explicitly invoking hidden variables---those that determine what choice has been made (if there were no such variables, there's no sense in saying that the choice has already been made).

The problem really is that in order to solve the measurement problem, i.e. the question of why we never observe superpositions, your postulate 3 effectively says 'well let's get rid of the superpositions then'. But superpositions are critical for entanglement: without superpositions, you simply don't have it.

You could formulate this differently: if after the interaction, the choice has already been made, but is simply unknown to the external system, then the whole state can be described by a statistical mixture, for example 'either |0> or |1> with probability 1/2'. Mathematically, this is the density operator:

[math]\rho_1=\frac{1}{2}(|0\rangle\langle0| |1\rangle\langle1|)[/math]

But in ordinary quantum mechanics, the result is the pure state

[math]\rho_2=\frac{1}{2}(|0\rangle\langle0| |1\rangle\langle1| |0\rangle\langle1| |1\rangle\langle0|)[/math]

Now, the difference is that \rho_1 is diagonal, while \rho_2 is not. This means that I can do interference experiments that distinguish between the two. Since according to your postulate 3, I will always end up with a state of the form of \rho_1, i.e. one lacking any interference terms, I can never get the appropriate interference effects.

So the solution of the measurement problem offered by postulate 3 seems, to me, to overdo things: in throwing superpositions away---thus solving the problem of their unobservability---, it throws out most interesting quantum effects along with them. And I still can't see how postulate 4 is supposed to rectify this. Perhaps you could just tell me one thing: in your framework, what does measurement of the state |0> in the {|>,|->}-basis yield?

Paul,

"Weirdness", which is postulated due to experimental result, not due to someone's imagination is an indication that our everyday criterions, which we subconsciously take in with mothers milk, so to speak, are not adequate in describing physical fundamentals of this world.

It is just the same story, as it was with postulation of speed light constancy (experimental fact) in forming theory of Special Relativity, in early 1900's. One cannot explain speed constancy with anything. Its just is. And if you think, that due to this weirdness SR is wrong, I suggest you not to use GPS, as it uses SR in calculation, and not to use aviation as a whole, as the rely on GPS, and, therefore, on SR's calculations, etc.

Jochen,

I read essay a couple more times, and words "choice fixing" do not imply hidden variables. And it has been said explicitly, if there is ANY physical interaction or not. Do not assume. By the way, hidden variable constitute hidden, yet, physical interaction.

We may express equations 5 and 6 as a statement about nature of information. In 5, information about internal choice applies to the whole world, even though there were no physical interaction with that whole world. In 5 information is global phenomena. In 6, information about internal choice applies only to systems that physically interacted. In 6 information is a local phenomena. And nature chooses local information.

Now, superposition of states isn't something fundamental, but rather the fact that external system has no info about internal choice, and from the point of view of an external system, there is this superposition of possibilities, which resolves, or decoheres at interaction with a sub-system.

Mikalai, please understand that I'm just trying to reconstruct your arguments in language more familiar to me. To this end, you could greatly help me by answering my question: if I have a particle in state |0>, and measure it in the {|>,|->}-basis, what does your framework predict to happen? And how is this prediction arrived at?

As for superpositions, I can't see how they can't be fundamental: it is a basic element of the Hilbert space formalism (which you say derives from your postulates), and unitary evolution inevitably produces them.

Regarding hidden variables, if you mean to say something like 'an outside system attributes a superposed state to some interacting system, but the actual state is definite', which you seem to do in the last paragraph of your last post, then that's exactly a statement about hidden variables (and quite similar to the modal interpretations by van Fraassen, Kochen, Dieks etc.).

Hi Mikalai,

Under 7 you wrote:

"Applying Einstein's razor forces us to say that gravitational phenomena must

be a result of a Higgs mechanism as well.

For example, the closer the effective test particle to a massive body, the more it will be engaged into additional Higgs events, due to extra Higgs flying around given massive body, and the more dilated time of a test system will be. "

Well done!!

However don't you think that it is time to decide that the whole vacuum is filled with a dense system of energetic oscillating Higgs flying around and that all photon information is transferred by this Higgs system, able to influence the speed of light around massive objects like the earth?

See attachment.Attachment #1: 1_vacuum_lattice_and_particle_wave_duality.jpgAttachment #2: 1_dark_matter_BH_diluting_of_the_vacuum_lattice.jpg

Jochen,

I talked about superposition of entangled states. But if we are at the level with only two systems, lab and a qubit. Interaction with similarly prepared qubits leads statistics of 0's and 1's. Pure state qubit is such that info about its state hasn't leaked into environment of the lab before official "measuring" interaction, while statistical mixture is a case when some unintentional interaction between lab environment has already happened. Both of these states produce the same statistics, cause in a later case, second official "measurement" will lead the same info with 100%. Yet, only pure, untouched by lab environment state may be used to make entangled pair.