The entangled Universe ..

There has been a very interesting and permeating discussion going on about “Quantum Entanglement” and any imperceptible but conceptual connection it might have with “Pauli Exclusion Principle”. This has been started by Brian Cox so if you win over him you can come with “who started first?”.

I had started writing free-lancingly on various things of interest to me when I had a new-found interest about such conceptual bickering a year or two ago. I therefore had changed the name of my blog to “Various Musings of a Klong Meson”. Its the Klong meson that was my raison d’etre  for almost a decade when I had to give up on it. But it’s a blog where I started writing on everything I could interest myself about and since I had many blog sites over the time I merged them later and tried to copy these articles and now you can get almost all I have written at either this website mdashf.org or iphmdashf.org. Now it does not matter what was the name of the blog site, Various Musings, My Think Spot or Information Radar, they will all be found on these two. In transporting the files I lost some good work of the equation rendering which will take me some time to fix. Sometimes I take a hint from the “top posts” that are generated from copious statistics from readers. So I will try my best to fix some articles for their typeset, styling, better reading experience or rendering and especially editing and making correction of where I have kept in mind what I have found myself to be incorrect. Please keep reading more although I must apologize if you had a bad experience from any article due to its rendering issues or any incoherence because many ideas are scattered over 30 articles and its not my fault they can be really that extensive. All I can do is try to stream line it.

Here is then back to the main issue here that is “propping” in my mind. Since I am entangled more than the Universe’s tiny members and you must agree to it, I will try to keep it minimal.

Sean has written a really nice long article, extensively addressing the issue of Quantum Entanglement which now they call “Brian Cox rubbing a diamond” which is funny. I am not going to introduce who Sean is. But in the minimum he is a Professor of Theoretical Physics at Cal Tech and I came across his and other celebrated Physicists tweets on twitter. I was on twitter for insinuating on lesser mortals and for banging my celebrity drum and managed to write more than 3000 tweets in a short period although my following and follower list is not a disrespectful figure, following 5 and followed by 40. I had expected much much less.

I am not linking you to Sean Carroll’s blog site or his article. You should be able to find it. Sorry. I always try to write less. Lest I suffer from vicious incoherence.

But I have something in mind which I think is a kind of fallacy in Brian Cox thinking. While much is done for “popularization” of science and philosophy and science get too mixed up and its a really hard job to keep them apart here is what I think is the fallacy.

An entangled electron or any quantum particle is basically thought via a few electron system. It is for a special reason. In any case there must at-least be two electrons as far apart as possible for entanglement to be realized as a quantum mechanical “phenomena”,it  is greatly misunderstood and its implications unnecessarily blown up. [can there be self-entanglement?]

Entanglement refers to the connectedness of two quantum particles which can be infinitely away. This is the basic nature. If they were particles alone lack of “action at a distance” of Einstein [signal and interactions must traverse at or below speed of light] would mean there is no interaction instantaneously permeating to infinite distances. If they were waves alone they are bounded by their wave speed. So the unification of wave and particles is not sufficient to get past this constraint. What is then making these two wavy-particles interact from infinite distances?

I would think from my basic understanding that it is the indeterminacy aspects of quantum mechanics. That when these reality of particle nature and wave nature were unificated it permits their description through a statistical framework. That is we do not no more talk about well specified values for any physical variable and there is only a likelihood for interactions taking place, the amount of interaction through their energy, momentum .., the amount of these wavy-objects given by their cross-sections and so on.

Which means we also have uncertainty principle as a guiding constraint on these phenomena. If I know the first refered electron as a particle with energy E, it can only go as far below and above by an expectation value of this energy E with an uncertainty given by a standard deviation. The other variables then extend similar attributes of mathematical/statistical nature being objects of reality at the same time and they extend mutual conditions of uncertainty which are simple only in 3 particular cases but a little more detailed for any other variables-pairs. To think that these other variables [eg distance and time] do not extend a Heisenberg Uncertainty relation is a fallacy [which has afflicted the OPERA anomaly which is “greatly” dealt with in this website]. The other idea is energy is the expectation value of Hamiltonian Operator hence represents all the information of the system for any Physics implications. This is because Energy is defined as a Hilbert space function of all other variables such as configuration space x, phase space 4-momentum, spin space S/L/J and so on. The important thing to remember is there is no uniqueness of energy only in specific cases of the quantum-states and this is called degeneracy slightly different from splitting of the energy-state. Degeneracy: Many-one function, Many Hilbert space {x, 4-p, S/L/J …} map onto one energy E. Is splitting of E a mapping of same Hilbert space {x, 4-p, S/L/J …}  onto different energy values in a same-eigen-state?

In any case whether that point was any central to Brian Cox’s argument is a different route I think although important. What was centrally attempted to debunk in his argument was how meaningful it is really that rubbing something here would affect all the other objects [viz electrons here] in the Universe and unguarded this will be taken by swarming philosophers of the academia and lesser academia to relate it with Butterfly effect. So its become interesting and I would dwell on that but not on Pauli Exclusion Principle which I think was really unwarranted. As has been pointed out in a blog forwarded by Sean [Jon Butterworth] not only Fermions but also Bosons are quantum wavy-particles. Its for the reason of Pauli’s principle of exclusion the degeneracy of energy state was taken up.

The central point in my view is then how meaningful it is to talk about quantum entanglement?

I think the fallacy is when you relate one electron to every other electron in the Universe. In a mathematical way you can do, in a physical way you can’t. That means all electrons have the right to become a prime-minister. But they will not because they are all scattered across the Universe. But to be more clear and less philosophical it means no one electron is debarred from getting entangled with the first-refered electron. But not all of them will be entangled at the same time. For a special reason. They can not all be entangled. Whats the reason?

Energy.

The first-refered electron has a finite energy and it can’t be shared  with all other electrons. It can only be shared with a finite number of electrons. Each time it gets entangled with another electron it reduces its energy-line in its energy bank. A packet of energy is “released” or at-least necessary for entanglement with another. The probability of entanglement depends then on these two electrons. Lets say this probability is really small for two electrons A and B which are infinitely away. Lets say this is 1 part per billion probability. Of-course that the electron will be entangled with one very close is really high.

Now each time the electron A is entangled with another its a probability of 10^-9. Since energy will reduce for each entanglement it is clear that the probability of electron A getting entangled with two electrons will be like 10^-9 \times 10^-9 and so on.

The probability of entanglement with infinite electrons will be 10^{-9\times infinite}. Its an infinity on the power of the exponential. It makes a zero faster than any other function I know. And it is absolutely misleading to say ALL the other electrons will be entangled with this electron. What is better to say is “no one electron in the universe is disqualified from getting entangled with another electron because of its distance or any other physical attributes” They will not all be entangled at the same time. Even two electrons getting entangled is really unlikely although it has a meaning if we are sensitive to such a scale. Bringing in more electrons the probability will again die out as diminishingly as the small proportion for the first two. Brining in all other electrons will kill the whole game of connectedness.