Monday, September 24, 2012

Karma-Quantum Interpretations-Bell's inequality

I'm thinking that I'll make short (ok, sorry, it's long for a blog post but short for the topic...) but more frequent post rather than wait for a well thought out parallels to come into my mind before writing these. These are kinda incomplete and thus unsatisfactory, so sorry!

Karma as according to the Buddhist interpretation, means that there is a cause and effect. Having a cause is not trivial. It means that things does not happen coincidentally, there is no randomness.
However, the Law of Karma is not deterministic either, there is some amount of choice that is possible. So the world that we live in is not totally random (chaos) not is it totally deterministic (total order). It is kinda like complexity theory. 

Well, this analogy is clear in our everyday life. We see things happen, we see there is a cause, by experience we know we have choices, sometimes, if we think out of the box, our choices seems unlimited. Just that sometimes, by classical ignorance we don't know all the causes, so when we meet our friend while we were out shopping alone, bham! Coincidence, we say. But is it really? 

We say that because we think with the centre of the universe to be ourselves. I know why I came to the shop at this particular time and place. And I know this friend there who I meet once a week in some class we take together. I didn't know he lives there and have some particular reason to come shopping at this particular time and place. 

His side of the picture is similar, most of us think: add these seemingly unrelated causes together and we get unexpected outcomes, it doesn't count as an effect. So it's random. By chance. However, if we de localize from ourselves, think in terms of full knowledge, we would not find it strange to bump into them. Whether we should add in a term that says, it's because of past karma that we are together in such and such place and situation that we would recognise each other when we meet again. I dunno. It's up to you. For me, it's the class we take together (we meet strangers all the time, the class give the condition for recognition) plus non-expectation due to incomplete knowledge that made the surprise meeting seems so special. To add in things like I must have known you in a past life, or God put us on collision course is not really helpful. 

Buddhism part done. Now for the Physics part.

Quantum Physics, commonly used to support the strange minds we have. Commonly misused. Too commonly. Why? Well for starters, what we call quantum physics is just a bunch of mathematics that can predict and explain the exact thing we see in experiments. Not just experiments, the very fact that transistors can be so small thus providing all the PC and mobile phone advances is due to quantum physics. So it's true. At least the maths is true so far. The Physical interpretation however, is insanely a lot.

From wikipedia (Might be wrong, as anyone can edit it, I've not checked it to be true yet too):
Local?Counterfactual definiteness?
Ensemble interpretationMax Born, 1926AgnosticNoYesAgnosticNoNoneNoNo
Copenhagen interpretationNiels BohrWerner Heisenberg, 1927NoNo1YesNoYes2NoneNoNo
de Broglie–Bohm theoryLouis de Broglie, 1927, David Bohm, 1952YesYes3Yes4YesNoNoneNoYes
von Neumann interpretationvon Neumann, 1932, WheelerWignerNoYesYesNoYesCausalNoNo
Quantum logicGarrett Birkhoff, 1936AgnosticAgnosticYes5NoNoInterpretational6AgnosticNo
Many-worlds interpretationHugh Everett, 1957YesYesNoNoNoNoneYesNo
Popper's interpretation[37]Karl Popper, 1957[38]NoYesYesYesNoNoneYesYes13
Time-symmetric theoriesYakir Aharonov, 1964YesYesYesYesNoNoYesNo
Stochastic interpretationEdward Nelson, 1966NoNoYesNoNoNoneNoNo
Many-minds interpretationH. Dieter Zeh, 1970YesYesNoNoNoInterpretational7YesNo
Consistent historiesRobert B. Griffiths, 1984Agnostic8Agnostic8NoNoNoInterpretational6YesNo
Objective collapse theoriesGhirardi–Rimini–Weber, 1986, Penrose interpretation, 1989NoYesYesNoYesNoneNoNo
Transactional interpretationJohn G. Cramer, 1986NoYesYesNoYes9NoneNoYes14
Relational interpretationCarlo Rovelli, 1994NoNoAgnostic10NoYes11Intrinsic12YesNo
There are at least 14 different interpretations. 
And I'm still reading up on some of it, so I can't give a one by one analysis of which interpretation is compatible with Buddhist Philosophy, or even give a parallel comparison. So here's just a brief one, the one I want to talk about is Bell's inequality. 

From the table that says deterministic? There are 4 yes, 7 no, and 3 agnostic. What it means is does the interpretation says there is intrinsic randomness in nature? The 7 "no deterministic" says there is intrinsic randomness. The 4 "yes deterministic" says we can recover classical beauty of deterministic world (which has caused some to believe we don't have free will) by this interpretation. The 3 "agnostic", I don't even know. Where's the middle path between order and chaos? Or is this making it too simple? Maybe the intrinsic randomness is required as a mechanism for free will to appear. I know too little right now to say more.

So let's go to more solid ground: Bell's inequality. Inspired by the intention to resolve one of the most famous interpretation clashes in quantum physics, (EPR paradox) this inequality was thought out and then experiments were tested. The violation of the inequality which is observed in experiments says something fundamental about our world. So even if there is another theory that replaces quantum later on, it also has to explain the violation of Bell's inequality. It's a fundamental aspect of our nature.

It is made to test one thing: quantum entanglement. In the quantum world, things do not have a definite value until it is measured (as per the conventional interpretation), when measured it has certain probability to appear as different outcomes, and we only see one. Measuring the same thing again and again, we get the statistics to verify the case of it's state. So it is intrinsically random, no hidden process to determine which values will appear for the same measurement. Einstein's view is that there is an intrinsic thing that is hidden away from us and therefore quantum physics is not complete, Bohr's view is that quantum physics is complete, so there is intrinsic randomness. Having not known how to test for hidden variables, it became an interpretation argument, not of interest to most physicist then.

Two particles which are entangled are such that the two particles will give correlated (or anti-correlated) results when measured using the same measurements. Yet according to Bohr, the two particles has no intrinsic agreed upon values before the measurement, according to Einstein, they have! How to test it?

To make it more explicit and it's really simple maths, here's the CHSH inequality:

The system is that we have two parties: Alice and Bob. Or in Buddhist terms we can have an Arahant and a Bhikkhu. We ask them one of two different "yes-no" questions each day. Like "Blue or not?" and "Red or not?" (random questions, with no true-false value, since they can't lie and we need both yes-no answers) They can meet up and agree upon a strategy, then each are separated by a large distance or anyway we restrict them not to communicate with each other, not even mind-reading. They each give one of two answers to each questions, and we ask them often (easier with particles and light). Then we take their answers, collect them and they must satisfy this CHSH inequality.

Here's a bit more rigorous labelling. The two parties are \(A\) and \(B\). The two questions are \(A_{x} \text{ or } B_{y}\text{ with } \{x , y\}\in \{0,1\}\) where 0 and 1 represents the two questions and \( \{a_{x} \text{ or } b_{y}\} \in \{-1,1\}\) as the two possible answers, -1 representing no, 1 representing yes.

So we have the term: \( a_{0}(b_{0}+b_{1})+a_{1}(b_0-b_1)=\pm 2\). This is self evident, please substitute in the values to verify yourself. Note: in case you still don't get the notation, \(a_0\) denotes the answer when we ask the Arahant the first question \(a_1\) for the second question, it can be -1 or 1, and so on for \(b\)...

Of course, in one day of asking the question, we cannot get that term, we need to ask lots of times (with particles and light, it's much faster than one day per data), and average over it, so it's more of the average is bounded by this inequality. \(|S| =|<a_{0}b_{0}>+<a_0 b_{1}>+<a_{1}b_0>-<a_1 b_1>|\leq 2\) It's called the CHSH inequality, a type of Bell's inequality.

It seems that the inequality is obvious and cannot ever be violated, and it's trivial. Yet it was violated by entangled particles! We have skipped some few assumptions to arrive at the CHSH inequality, and here they are. The value for \(S\) must be less than 2 if we have 3 assumptions: (from my lecture notes in Quantum Measurement and Statistics)

  1.  There is outcome independence (or possibility of determinism) this is saying that there can be a more elementary process such that the outcomes of \(A\) and \(B\) are independent, such as the pre agreed upon strategy. Or saying that one parties' answer should be independent of the other's answer. 
  2. Parameter independence (or no signalling), that is the answer of one party is independent of the question I ask the other party. This is enforced by the no-communication between two parties (too far apart and so on...) Special relativity can be made to protect this assumption.
  3. Measurement independence (or free will), that is whatever fundamental physical process (or the choice of which strategies to use) that gives the output, cannot depend on the choice of questions I give. (especially if the strategy is agreed upon before I even know which questions to ask.) Lacking this, a God may control everything such that I'm not free to choose the measurements, just that I think I am free, so the violation can occur.

All three are perfectly reasonable in any classical system.

  1. The Arahant and Bhikkhu can list down say yes or no if asked this question or that... and made a long list, eg. I'll answer yes to question 1 for 3 times then no 4 times and then yes 2 times'll answer..... and it is deterministic.
  2. They are not allowed to communicate, or we can separate them so far that light has no time to travel between the asking of the question and answering for both parties. This is thus protected by Special relativity. (If faster than light communication is possible, then time travel would also be possible.)
  3. I'm free to ask any questions. (Some amount of free will).

Violation of Bell's inequality says that either one of the 3 above must be wrong.

  1. Most physicist says this is wrong, there is intrinsic randomness in nature.
  2. There are theories with this wrong, deterministic in nature, but since the signalling is hidden, no time travel or faster than light that we can use. Quite problematic and challenges Special relativity, not popular but still possible based on the violation of Bell's inequality alone.
  3. And if people vote for this wrong, there is no point to science, life and the universe. 
Phew, quite a lot for the Physics part, didn't really intended to make it so long. Well, what does karma says about this?
From a superficial look, it seems that 1 and 3 must be wrong, leaving us to think that Buddhism says  de Broglie–Bohm theory  (or the variants there) is right! 

However, that theory is still deterministic, and so to have the middle path between deterministic world and total randomness, we have two choices. Either to assert that free will comes with the mind somewhere when physics develops to biology develops to explain the neuroscience of the brain and therefore mind, humans and beings with mind have free will but others are deterministic, fundamentally.

Or to accept randomness from the start, with decoherence (transition into classical realm where classical deterministic world is the norm) with phenomena like radioactive decay remaining the quantum randomness that we can see. And one of these phenomena is using quantum to describe free will of the mind, some failure to do that by people... but this is a bit out of the usual experiences is it not? If our choices are totally random, we would be doomed from the start right? eating, drinking, not eating for days etc... but maybe our choices are like wavefunctions, with certain probability for each, and with each new out of the box idea, comes a new weightage for the choice and only when decision has to be made is the measurement that collapses the system into a single outcome be made? Or does the process of measurement is just shifting the weightage to one outcome?

Too many questions, too little answers, I've not think this through yet, so no idea for now!

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