Kalama Sutta and Scientific method

 In Buddhism, there is this Kalama Sutta (AN 3.65) in which the Buddha told the people of Kalama village that there are ten specific sources which knowledge should not be immediately viewed as truthful without further investigation to avoid fallacies:

1.       by revelations,

2.       by traditions,

3.       by rumour, gossip, hearsay,

4.       by scriptures,

5.       by logical conjecture (alone),

6.       by it is a point of view or common sense,

7.       by having considered the reasons (philosophical dogmatism),

8.       by agreement with one’s own theories,

9.       by experts,

10.    by the thought “this monk is our teacher” (authority).

but when you know for yourselves that,

•       these qualities are skillful,

•       these qualities are blameless,

•       these qualities are praised by the wise,

•       these qualities, when adopted & carried out, lead to welfare & to happiness,

then you should enter & remain in them.

In science, theories must be verified and vetted by the experimental or observational data.

The Kalama sutta can be roughly divided into two categories of sources which are not reliable on their own, each of them has their parallels in the scientific endeavour. 

By Literature: The parallel in science would be the scientific papers and the masses of scientific knowledge and literature which had been gathered, including textbooks, lecture notes etc.

Revelations

Traditions

Rumour, gossip, hearsay

Scriptures

Experts

“This monk is our teacher”

By Logic: The parallel in science would be the mathematical derivation in physics, thought experiments, theoretical chemistry calculations, the logic of anatomy and physiology, simulations.

Logical conjecture

It is a point of view or common sense

Having considered the reasons

Agreement with one’s own theories

By Experiments: In science, this means spending billions to built expensive lab and equipment to detect Higgs boson and gravitational waves, basically all the experiments in science, clinical trials, actual lab work in chemistry, etc…

In Buddhism the term knows for yourselves is the one which one uses mindfulness to collect data first.

Then followed by clear awareness or clear comprehension or clearly knowing, whether or not the teachings are skillful, blameless, praised by the wise when adopted and carried out, lead to the welfare and to happiness. 

And if they are then entered and remain in them, or else just discard them.

This fits in with the process of experiments, first collect data, then analyse the data, do they fit into the hypothesis? If they do, adopt the hypothesis to become a theory. If they do not, abandon the hypothesis. The hypothesis is akin to the teachings of various religious teachers. The data is data of real life, by which we can judge if the teachings are skillful, blameless, praised by the wise when adopted and carried out, lead to the welfare and to happiness or do they not. 

Although this does seem like a good opportunity to market Buddhism as a science of the mind, there is resistance from scientists on accepting Buddhism as science. Namely that Buddhism does have some statements on how the world works which is not able to be verified or disproved by science yet. Chief amongst these are:

1. The existence of deities and other realms of rebirth beyond humans and animals.

2. The claim of rebirth happening to all beings. Even though there is evidence for rebirth, the number of scientifically trained people who are willing to look at it, and vouch for it is too little. Also, at the most the evidence for rebirth can only assure us that some people get reborn, it does not prove that everyone had been reborn countless times as what Buddhism claims. 

3. The law of kamma exist. This would be very hard to scientifically verify even if one has the power to look through past lives as the commonly accepted way to verify this is via wisdom arising. Unless the scientific method one day recognises wisdom as part of scientific tools, we have no hope of saying that the theory of kamma is scientifically valid. 

4. Supernormal powers exist, like the divine eye, ear etc. Although there are paranormal research going on, it’s still not yet accepted in mainstream science. 

One day perhaps in the future, wisdom arising from mindfulness gathering data can be seen as the analysis of data gathering in the scientific analysis. The bias towards insisting on physical objective ways of gathering data even when investigating non-physical stuff like the mind can be eliminated in favour of using the mind to investigate the mind (mindfulness of mind). And all these superpowers from the development of the mind are accepted as tools of science much like the telescope and microscopes were, then it’s possible one day to present Buddhism as part of scientific findings. However, given the existence of many other religions, the fact that scientists are humans with bias and the realisation that Buddhism will one day disappear from human knowledge, this future is not guaranteed to happen. 

One crucial difference between Buddhism and Science now is that Science no longer accept verification as a valid process for determining scientific findings as truth. Falsification is the rule of the day for scientific theories. Buddhism does accept verification to determine the truth. An analogy in Buddhism would be that we are deluded, thinking that a rope is a snake, thus fear arises. However, if we light a lamp of wisdom, we can see that a rope is merely a rope. Thus, even if the room goes back to darkness, we no longer have any fear. This is the verification which Buddhism approves and makes use of. And it’s so basic that all reasonable humans should also be able to accept verification of this kind. 

Quantum interpretations and Buddhism Part 11: Classical concepts

Now is the time to recap on what concepts are at stake in various quantum interpretations, and the comments involving Buddhism, whether Buddhism prefers an interpretation to have this or that quality. You’ll have familiarity with most of them by now after reviewing so many experiments.

 

I will mainly discuss the list on the table of comparisons taken from wikipedia. Table at the interlude: A quantum game.

 

Deterministic.

 

Meaning: results are not probabilistic in principle. In practice, quantum does look probabilistic (refer to Stern-Gerlach experiment), but with a certain interpretation, it can be transformed back into deterministic nature of things. This determinism is a bit softer than super-determinism, it just means we can in principle rule out intrinsic randomness. The choice is between determinism and intrinsic randomness.

 

Classical preference: deterministic. Many of the difficulties some classical thinking people have with quantum is the probabilistic results that we get from quantum. In classical theories, probability means we do not know the full picture, if we know everything that there is to know to determine the results of a roll of a dice, including wind speed, minor variation in gravity, the exact position and velocity of the dice, the exact rotational motion of the dice, the friction, heat loss etc, we can in principle calculate the result of a dice roll before it stops. The fault of probability in classical world is ignorance. In quantum, if we believe that the wavefunction is complete (Copenhagen like interpretations), then randomness is intrinsic, there’s no underlying mechanism which will guarantee this or that result, it’s not ignorance that we do not know, it’s nature that doesn’t have such values in it.

 

A Buddhist’s comment (basically me lah): On the one hand, we do not admit the existence of fatalism or fate, on the other hand, we don’t believe things happen for no reason. There was a heretical teacher back in Buddha’s time called Makkhali Gosala. Makkhali teaches the doctrine of fatalism. Everything is fixed, predetermined, there’s no role for effort in morality.

 

From sutta DN2, we get a glimpse of his teachings, which seems to include both fatalism and no causes.

 

“Great king, there is no cause or condition for the corruption of sentient beings. Sentient beings are corrupted without cause or condition. There’s no cause or condition for the purification of sentient beings. Sentient beings are purified without cause or condition. One does not act of one’s own volition, one does not act of another’s volition, one does not act from a person’s volition. There is no power, no energy, no manly strength or vigor. All sentient beings, all living creatures, all beings, all souls lack control, power, and energy. Molded by destiny, circumstance, and nature, they experience pleasure and pain in the six classes of rebirth. There are 1.4 million main wombs, and 6,000, and 600. There are 500 deeds, and five, and three. There are deeds and half-deeds. There are 62 paths, 62 sub-eons, six classes of rebirth, and eight stages in a person’s life. There are 4,900 Ājīvaka ascetics, 4,900 wanderers, and 4,900 naked ascetics. There are 2,000 faculties, 3,000 hells, and 36 realms of dust. There are seven percipient embryos, seven non-percipient embryos, and seven embryos without attachments. There are seven gods, seven humans, and seven goblins. There are seven lakes, seven winds, 700 winds, seven cliffs, and 700 cliffs. There are seven dreams and 700 dreams. There are 8.4 million great eons through which the foolish and the astute transmigrate before making an end of suffering. And here there is no such thing as this: “By this precept or observance or mortification or spiritual life I shall force unripened deeds to bear their fruit, or eliminate old deeds by experiencing their results little by little,” for that cannot be. Pleasure and pain are allotted. Transmigration lasts only for a limited period, so there’s no increase or decrease, no getting better or worse. It’s like how, when you toss a ball of string, it rolls away unraveling. In the same way, after transmigrating the foolish and the astute will make an end of suffering.”

 

Here’s the Buddha’s critique on him, from the sutta AN1:319

 

“Mendicants, I do not see a single other person who acts for the hurt and unhappiness of the people, for the harm, hurt, and suffering of many people, of gods and humans like that silly man, Makkhali. Just as a trap set at the mouth of a river would bring harm, suffering, calamity, and disaster for many fish, so too that silly man, Makkhali, is a trap for humans, it seems to me. He has arisen in the world for the harm, suffering, calamity, and disaster of many beings.”

 

In practise terms, we should acknowledge that there are causes which we can built to attain to liberation from suffering, effort is important. Causes are important. So morality observance is not wasted, it is encouraged. The law of kamma does argue against suffering happening for no cause and against suffering is fated to happen. It gives hope in that in the present moment, we can plant good seeds to ripen to good results. The patterns from old kamma by itself doesn’t predetermine all future, the input from present moment is important too.

 

So in choosing between determinism and intrinsic randomness, it is a toss up. If we can be assured that this kind of determinism does not lead to superdeterminism (which is basically fatalism), it’s a better choice. If not, intrinsic randomness of quantum can be made to not contradict Buddhism. The results of individual experiments cannot be pointed to have one cause or another. To see this, refer to Stern-Gerlach experiment, same set up, that is same cause and conditions, different results of up and down for each identically prepared particles. Remember the exercise in ruling out hidden variables, there’s no underlying difference between one particle and the next already, if we believe that wavefunction is complete. So this seems to violate cause plus conditions equals results in kammic teaching. Yet, it allows for the future to have different paths even if the past is exactly the same.

 

Richard A. Muller in his book the Physics of Now, argues that physics cannot rule out free will based on quantum phenomenon. His work as an experimental physicists allowed him to analyse pions (one of the many subatomic particles in particle physics) in particle accelerators. Two pions he had observed interfere with each other, that shows that their wavefunctions are exactly the same. So same cause and condition. However, the pions disintegrated at different times, so different results. Thus it would seem that quantum rules out fatalism if we interpret wavefunction as the complete description of the quantum system. The price we pay is, we cannot point to a reason why this pion decay faster than that one. If we light up two dynamites, they explode at the same time, not so with two identically created pions which are born in the same instance.

 

Also, when quantum is decohered up to the Newtonian physics, this quantum randomness hardly shows up in the macroscopic realm, well except for the radioactive decay which is used in the popular example of Schrödinger's cat. So we cannot claim that there’s no cause for things based on mere acceptance of intrinsic quantum randomness. The results of quantum experiments are also pretty well defined to be in a range, eg. The spin result in Stern Gerlach is only up or down in the measurement axis. There’s no unpredictable thing like the electrons suddenly group together to become a dragon for no reason. So the cause-condition-result relationship can be restored, if we expand the definition of result to be quantum probabilistic range of result, and the probability distribution function is well defined and deterministic based on the experimental set up. For example, pion is created as cause and condition, result is, pion will decay. The time for the decay of pion matters not much.

 

Thus, there might be a stronger push to reject determinism.

 

Ontic wavefunction

 

Meaning: taking the wavefunction as a real physical, existing thing as opposed to just representing our knowledge. This is how Jim Baggott split up the various interpretations in his book Quantum reality.

 

Realist Proposition #3: The base concepts appearing in scientific theories represent the real properties and behaviours of real physical things. In quantum mechanics, the ‘base concept’ is the wavefunction.

 

Classical preference: classically, if the theory works and it has the base concepts in it, we take the base concept of the theory seriously as real. For example, General relativity. Spacetime is taken as dynamic and real entities due to our confidence in seeing the various predictions of general relativity being realized. We even built very expensive gravitational wave detectors to detect ripples in spacetime (that’s what gravitational waves are), and observed many events of gravitational waves via LIGO (Laser Interferometer Gravitational-Wave Observatory) from 2016 onwards. We know that spacetime is still a concept as loop quantum gravity denies that spacetime is fundamental, but build up from loops of quantum excitations of the Faraday lines of force of the gravitational field. Given that quantum uses wavefunction so extensively, some people think it’s really real out there.

 

A Buddhist’s comment: Well, the Buddha never mentioned wavefunctions as far as I know, so doesn’t really matters either way. Repeating the response in the motivation, the base concepts in classical theories just live in the heads of the physicists. Nature works as it is, the understanding of nature is also dependently arising, empty of inherent nature. This is how we can let go of even physics theories. Those who are more keen on practise may lean more towards seeing wavefunction as mere reflection of our knowledge rather than a real thing. As anything we deem real, we tend to attach to as we have the mistaken notion that real means permanent, reliable. As attachment causes suffering, we can save ourselves the trouble of suffering by not taking the reality of wavefunctions too seriously.

 

Unique History

 

Meaning: The world has a definite history, not split into many worlds, for the future or past. I suspect this category is created just for those few interpretations which goes wild into splitting worlds.

 

Classical preference: Yes, classically, we prefer to refer to history as unique.

 

A Buddhist’s comment: The past and future strictly speaking exist only in our minds. We can only have access to the present moment, the here and now. We remember the past (and due to light speed delay, we essentially see the past light cones reaching our eyes, but in practise we call it present), we can project the future. So having split past or split futures doesn’t really matter. However, the Buddha when he relates to his past lives didn’t change his story everytime, and he didn’t acknowledge a fixed future as the discussion on fatalism above shows. Thus the Buddhist philosophy of time also fits in growing box theory of time with the past is fixed, present exist, but future is free.

 

So we are more comfortable with splitting the future rather than the past.

 

Hidden Variables

 

Meaning: The wavefunction is not a complete description of the quantum system, there are some other things (variables) which are hidden from us and experiments and might be still underlying the mechanism of quantum, but we do not know. Historically, the main motivation to posit hidden variables is to oppose intrinsic randomness and recover determinism. However, Stochastic interpretation is not deterministic yet have hidden variables, and many worlds and many mind interpretations are deterministic yet do not have hidden variables.

 

Classical preference: Yes for hidden variables, if only to avoid intrinsic randomness, and to be able to tell what happens under the hood, behind the quantum stage show.

 

A Buddhist’s comment: this seems like a good opportunity to insert the influence of mind on matter. We can even put kamma as a nice touch on how kammic actions, generated by the mind (intentions) can have physical effects in the world, not just mental results. However, there’s no reason to insist on it. The variables are hidden anyway, thus no way to test for it. 

 

Collapsing wavefunction

 

Meaning: That the interpretation admits the process of measurement collapses the wavefunction. This collapse is frown upon by many because it seems to imply two separate processes for quantum evolution

 

1.The deterministic, unitary, continuous time evolution of an isolated system (wavefunction) that obeys the Schrödinger equation (or a relativistic equivalent, i.e. the Dirac equation).

2.The probabilistic, non-unitary, non-local, discontinuous change brought about by observation and measurement, the collapse of wavefunction, which is only there to link the quantum formalism to observation.

 

Further problem includes that there’s nothing in the maths to tell us when and where does the collapse happens, usually called the measurement problem. A further problem is the irreversibility of the collapse.

 

Classical preference: Well, classically, we don’t have two separate process of evolution in the maths, so there’s profound discomfort if we don’t address what exactly is the collapse or get rid of it altogether. No clear choice. Most classical equations, however, are in principle reversible, so collapse of wavefunction is one of the weird non classical parts of quantum.

 

A Buddhist’s comment: This doesn’t really concern Buddhism. Irreversible, reversible, all part of impermanence.

 

Observer’s role

 

Meaning: do observers like humans play a fundamental role in the quantum interpretation? If not, physicists can be comfortable with a notion of reality which is independent of humans. If yes, then might the moon not be there when we are not looking? What role do we play if any in quantum interpretations?

 

Classical preference: Observer has no role. Reality shouldn’t be influenced just by observation.

 

A Buddhist’s comment: Just by studying quantum physics, we are participating in it. We cannot verify if reality is independent of observer as an observer. As highlighted in the motivation, an universe without sentient beings in there is metaphysics to us, as we are limited to observation from the vantage point of a sentient being. However, this is more of a tautology we would say the same to classical physics. Does observer play a fundamental role in quantum? Maybe, maybe not. Good if there is, then there can be more serious consideration to observe what does the observer do. In meditation, we call this mindfulness of the mind. Too often we don’t observe the observer. That’s where a lot of trouble starts.

 

Local dynamics

 

Meaning: is quantum local or nonlocal? Local here means only depends on surrounding phenomenon, limited by speed of light influences. Nonlocal here implies faster than light effect, in essence, more towards the spooky action at a distance. This is more towards the internal story of the interpretations. In practice, instrumentally, we use the term quantum non-locality to refer to quantum entanglement and it’s a real effect, but it is not signalling. Any interpretations which are non-local may utilise that wavefunction can literally transmit influences faster than light, but overall still have to somehow hide it from the experimenter to make sure that it cannot be used to send signals faster than light.

 

Classical preference: Local. This is not so much motivated by history, as Newtonian gravity is non-local, it acts instantaneously, only when gravity is explained by general relativity does it becomes local, so only from 1915 onward did classical physics fully embrace locality. Gravitational effects and gravitational waves travel at the speed of light, the maximum speed limit for information, mass, and matter. Quantum field theories, produced by combining quantum physics with special relativity is strictly local and highly successful, thus it also provides a strong incentive to prefer local interpretations by classically thinking physicists.

 

A Buddhist’s comment: Local or non local doesn’t really matter to Buddhists. There are many instances in the suttas where the devas and brahmas disappear from their realm and appear on earth to meet the Buddha. Depending on the nature of these beings, we might have claims that Buddhism allows for faster than light or not. However, the strongest motivation to disallow faster than light is the time travel conundrum. Since speed of light limits are not important or even hinted at in the suttas, there seems to be no reason for Buddhists to insist on locality, other than to adopt the concern of physicists.

 

Counterfactually definite

 

Meaning: Reality is there. There are definite properties of things we did not measure. Example, the Heisenberg uncertainty principle says that nature does not have 100% exact values for both position and momentum of a particle at the same time. Measuring one very accurately would make the other have much larger uncertainty. The same is true of Stern Gerlach experiments on spin. An electron does not have simultaneously a definite value for spin for both x-axis and z-axis. These are the experimental results which seem to show that unmeasured properties do not exist, rejecting counterfactual definiteness. We had also seen how Leggett’s inequality and Bell’s inequality together hit a strong nail on reality existing. Yet, some quantum interpretations still managed to recover this reality as part of the story of how quantum really works.

 

Classical preference: of course we prefer reality is there. The moon is still there even if no one is looking at it.

 

A Buddhist’s comment: It’s not hard for Buddhists to reject counterfactual definiteness. After all, the measurement is not done, why should we expect the properties to be underlying there in waiting? This is one of the strongest thing people identify intuitively when they read about quantum physics and then Buddhism or the other way around. Similar comments from the observer role can apply here too. We cannot verify if reality is independent of observer as an observer. We cannot say reality is there without measuring it. This is also a strong push for investigation by the Buddha. He asked us to come and see, investigate his words. He even showed a method to attain to the 4th Jhana, then develop the powers to recollect past lives to verify rebirth, the powers of divine eye to see the life, action, death, results of various beings to verify kamma. Thus Buddhism is not interested in metaphysics. And insisting on properties of things to be there without measuring it seems to be metaphysics. Of course, still, we believe that kamma and rebirth still works as usual even if we don’t develop those powers to directly verify it. Thus Buddhists do believe in counterfactual definiteness for these properties as well. Perhaps we are being too hasty in abandoning this concept?

 

Extant universal wavefunction

 

Meaning: If we believe that quantum is complete, it is fundamental, it in principle describes the whole universe, then might not we combine quantum systems descriptions say one atom plus one atom becomes wavefunction describing two atoms, and combine all the way to compass the whole universe? Then we would have a wavefunction describing the whole universe, called universal wavefunction. If we believe in the axioms of quantum, then this wavefunction is complete, it contains all possible description of the universe. It follows the time-dependent Schrödinger equation, thus it is deterministic unless you’re into consciousness causes collapse or consistent histories. No collapse of wavefunction is possible because there’s nothing outside the universe to observe/ measure this wavefunction and collapse it, unless you’re into the consciousness causes collapse interpretation or Bohm’s pilot wave mechanics. It feels like every time I try to formulate a general statement some interpretations keeps getting in the way by being the exceptions.

 

Classical preference: Well, hard to say, there’s no wavefunction classically, but I am leaning more towards yes, if quantum is in principle fundamental and describing the small, then it should still be valid when combined to compass the whole universe.

 

A Buddhist’s comment: There are things outside of the universe. In sutta DN27:

 

There comes a time when, Vāseṭṭha, after a very long period has passed, this cosmos contracts. As the cosmos contracts, sentient beings are mostly headed for the realm of streaming radiance. There they are mind-made, feeding on rapture, self-luminous, moving through the sky, steadily glorious, and they remain like that for a very long time.

 

There comes a time when, after a very long period has passed, this cosmos expands. As the cosmos expands, sentient beings mostly pass away from that host of radiant deities and come back to this realm. Here they are mind-made, feeding on rapture, self-luminous, moving through the sky, steadily glorious, and they remain like that for a very long time.

 

 In sutta DN 1, there’s more details on the first being to be reborn back into the universe.

 

There comes a time when, after a very long period has passed, this cosmos expands. As it expands an empty mansion of Brahmā appears. Then a certain sentient being—due to the running out of their life-span or merit—passes away from that host of radiant deities and is reborn in that empty mansion of Brahmā. There they are mind-made, feeding on rapture, self-luminous, moving through the sky, steadily glorious, and they remain like that for a very long time.

 

But after staying there all alone for a long time, they become dissatisfied and anxious: ‘Oh, if only another being would come to this state of existence.’ Then other sentient beings—due to the running out of their life-span or merit—pass away from that host of radiant deities and are reborn in that empty mansion of Brahmā in company with that being. There they too are mind-made, feeding on rapture, self-luminous, moving through the sky, steadily glorious, and they remain like that for a very long time.

 

Now, the being who was reborn there first thinks: ‘I am Brahmā, the Great Brahmā, the Undefeated, the Champion, the Universal Seer, the Wielder of Power, the Lord God, the Maker, the Author, the Best, the Begetter, the Controller, the Father of those who have been born and those yet to be born. These beings were created by me! Why is that? Because first I thought:

 

“Oh, if only another being would come to this state of existence.” Such was my heart’s wish, and then these creatures came to this state of existence.’

 

And the beings who were reborn there later also think: ‘This must be Brahmā, the Great Brahmā, the Undefeated, the Champion, the Universal Seer, the Wielder of Power, the Lord God, the Maker, the Author, the Best, the Begetter, the Controller, the Father of those who have been born and those yet to be born. And we have been created by him. Why is that? Because we see that he was reborn here first, and we arrived later.’

 

And the being who was reborn first is more long-lived, beautiful, and illustrious than those who arrived later.

 

It’s possible that one of those beings passes away from that host and is reborn in this state of existence. Having done so, they go forth from the lay life to homelessness. By dint of keen, resolute, committed, and diligent effort, and right focus, they experience an immersion of the heart of such a kind that they recollect that past life, but no further.

 

They say: ‘He who is Brahmā—the Great Brahmā, the Undefeated, the Champion, the Universal Seer, the Wielder of Power, the Lord God, the Maker, the Author, the Best, the Begetter, the Controller, the Father of those who have been born and those yet to be born—is permanent, everlasting, eternal, imperishable, remaining the same for all eternity. We who were created by that Brahmā are impermanent, not lasting, short-lived, perishable, and have come to this state of existence. This is the first ground on which some ascetics and brahmins rely to assert that the self and the cosmos are partially eternal.

 

Thus, there’s no issue with universal wavefunction, the Brahms from the realm of streaming radiance (2nd Jhana Brahma realm) might act as the observer to collapse the wavefunction of the universe if need be. By the way, the above quote shows the Buddhist conception of how the ideal of a creator God comes to be.

 

Anyway this universal wavefunction along with the unique history are usually not a thorny issue that people argue about when they discuss preferences for interpretations, unless they have nothing much else to talk about.

 

Now that we have covered the relevant concepts, the classical preferences for them and a Buddhist’s comment about them, here’s some reflection. Buddhism is generally more open compared to classical thinking in accepting many strange features of various quantum interpretations. Buddhism is also less decisive in placing bets on what the “real” interpretation should look like or have certain properties, except for the clear rejection of superdeterminism.

 

Thus, from here we can dash out any hope of trying to use Buddhism as a guide to select interpretations. Still, certain interpretations will resonate with Buddhist concepts more strongly compared to others, but the preliminary analysis here seems to suggest that we do not place hope on advancing the physics interpretation cases via philosophical inputs from Buddhism. What about the payoff for Buddhists? We can still go through the interpretations and then Buddhists can realise that we cannot make simple statements like quantum supports Buddhist philosophical concepts. Many of the interpretations might not be relevant or resonate with Buddhist concepts and some might resonate strongly. It’s important to keep in mind that as interpretations, experiments had not yet been able to rule one or another out yet, and it’s a religion (personal preferences) for physicists to choose one over another based on which classical concepts they are more attached to.

Quantum interpretations and Buddhism Part 10: Experiment part 4 Delayed choice quantum eraser

 There is this thing called the delayed choice quantum eraser experiment which messes up our intuition of how cause and effect should work in time as well. 

Delayed choice quantum eraser is a delayed version of the quantum eraser. The quantum eraser[Experimental Realization of Wheeler’s Delayed-Choice Gedaken Experiment, Vincent Jacques, et al., Science 315, 966 (2007)] is a simple experiment. Prepare a laser, pass it through a beam splitter. In the picture of the photon, individual quanta of light, the beam splitter randomly allows the laser to either pass straight through, or to be reflected at 90 degrees downward.   Put a mirror at both paths to reconnect the paths to one point, at that point, either put a beam splitter back in to recombine the laser paths or do not. Have two detectors after that point to detect which paths did the photon go. Instead of naming the paths A and B, I use Arahant Path and Bodhisattva Path. 



If there is a beam splitter, we lose the information of which paths did the photons go. Light from both paths will come together to go to only one detector. If we take out the beam splitter, we get the information of which path did the photon went, if detector 1 clicks, we know it went by the Bodhisattva path, if detector 2 clicks, we know it went by the Arahant path. 

So far nothing seems to be puzzling. Yet, let us look deeper, is light behaving as particle of a single photon or as waves which travel both paths simultaneously? If light is behaving like a single photon, then the addition of the beam splitter at the end should further make it randomly either go through or reflected, thus both detectors should have the chance to click. Yet what is observed is that when the second beam splitter is inserted, only detector 1 clicks. Light is behaving like waves so that both paths matters and interference happens at the second beam splitter to make the path converge again and lose the information of which paths did the light took. Take out the beam splitter at the end, then we can see which path light took, detector 1 or 2 will randomly click, thus it behaves like a photon to us. 

So how light behaves depends on our action of whether to put in the beam splitter or not. Actually the more important thing is it depends on whether or not we know which path did the light took or was it erased. More complicated experiment[Multiparticle Interferometry and the superposition principle, Daniel M. Greenberger, Michael A. Horne, and Anton Zeilinger, Physics Today, pg 23-29 (August 1993)] shown below adds a polarization rotator (90o) at one of the paths and two polarisers after the end beam splitter shows that even through the polarisation rotator can allow us to tell which path did the photon took, the two polarisers (45o) after the beam splitters can erase that information, making light behave like waves and only trigger one of the detectors. If we try by any means to peek at or find out which path light took to the end, light would end up behaving like particles and trigger both detectors. 



Note that the second experimental set up did not actually erase the information but rather just scrambles it. The information can be there, but as long as no one can know it, light can behave like waves. It is potential information which can be known that matters. So if we have an omniscient person like the Buddha, even he could not know which path the photon took if the information is erased and inference happens so that only one detector clicks. If he tries to find out and found out which path the light took even by some supernatural psychic powers or special powers of a Buddha, then he would have changed the nature of light to particles and make two detector clicks randomly. 

Here is a bit more terminology to make you more familiar with the experiment before we go on further. Light behaves coherently with wave phenomenon of interference so that only one detector is triggered when information of which path it took is not available or erased. Light behaves like a particle, or photon, or decohered, or its wave function collapses to choose a path, randomly triggering either of the detectors, interference does not appear when information about which path it took becomes available, or not erased, even in principle. 

So now onto the delayed choice quantum eraser. It is the experimental set up such that the light has already passed through the beam splitter at the start then we decide if we want to know its path or erase that information. In the first experiment above, just decide to insert or not insert the end beam splitter after the laser light has passed through the start beam splitter and are on the way to the end beam splitter. The paths can be made super long, but of the same length to make them indistinguishable, and the decision to insert the end beam splitter or not can be linked to a quantum random number generator so that it is really last split second decision and at random. Our normal intuition tells us that light has to decide if it is going to be a particle or wave at the starting beam splitter. However, it turns out that the decision can be made even after that, while it is on its way along both paths as a wave or along one of them as a particle!

Other more complicated set ups[Delayed “Choice” Quantum Eraser, Yoon-Ho Kim, Rong Yu, Sergei P. Kulik and Yanhua Shih, Marlan O. Scully, Physical Review Letters, Volume 84, Number 1 (3rd January 2000)] involves splitting the light into entangled photons and letting one-half of the split photons to be detected first, then apply the decision to either erase the information or not to onto the second half of the photons, which by virtue of its entanglement would affect whether interference pattern appears at the detected first half of the photons. 

The box on the bottom right is the original experiment you had seen above. There’s an addition of entanglement generator, to get the separation of signal photon and idler photon. The signal photons are what we call the ones who end up clicking the detectors at 1 and 2. The idler photons are sent out to a longer path so that they click detector 3 and 4 at a much later time compared to 1 and 2. In principle, this time delay can be longer then a human lifespan, so no single human observer is special and required for the experiment. 

The clicks at the detectors are gathered with a computer which can count the coincidence and map which signal photon is matched with which idler photon. The choice of erasure is made before the idler photon reaches detector 3 and 4. If the beam splitter is removed, we have which-way information, and thus no interference pattern at 1 and 2. If it is inserted, we have erased the which-way information and thus interference pattern can emerge at 1 and 2. 

Note that this cannot be used to send messages back in time, or receive messages from the future because we need information from the second half of the photons to count the coincidence pattern of the signal photon to reveal whether or not it has the interference pattern depending on our delayed-choice on the idler photon. So when the signal photon hits the detectors, all the experimenters could see are random messes, regardless of what decision we make on the idler photon later on. This is true even if we always choose to put in the beam splitter and erase the which-way information. 

If this messes with your intuition, recall what does entangled photons do. They only show correlation when you compare measurement results from both sides. If you only have access to one side, you can only see random results. So for the case of if we always erase the information, we still do not immediately see interference pattern, but the detectors 1 and 2 keeps on clicking. Each of them is actually an interference pattern, it’s just overlapping interference pattern, we need to distinguish which detectors did the idler photon clicks in 3 and 4 to separate the signal photon out. If we had done the coincidence count right and group all the signal photons corresponding to idler photon clicking detector 3, that signal photon will only trigger one of the detectors 1 or 2, showing you the interference! 

In analogy to the perhaps more familiar spin entanglement you’ve some intuition about, this is like measuring entangled spin electrons. Each side measures in the same direction, and only sees a random up or down spin. It’s only when you bring them together and group which electron pairs correspond to which, do you see the correlation between each individual spins. 

If we choose not to put in the erasure, then comparing the idler and signal photons, there will be no pattern of interference which appears from the coincidence counting procedure highlighted earlier. So no magic here, only boring data analysis. 

Quantum interpretations and Buddhism Part 9: Interlude: Contextuality

 A special note on contextuality would be appropriate here. 

From Wikipedia, Quantum contextuality is a feature of the phenomenology of quantum mechanics whereby measurements of quantum observables cannot simply be thought of as revealing pre-existing values. Any attempt to do so in a realistic hidden-variable theory leads to values that are dependent upon the choice of the other observables which are simultaneously measured (the measurement context). 

After Bell, there are many different kinds of theorems and no-go things around. One of them is Kochen–Specker theorem. This works similar to Bell’s theorem, but in a more complicated scale, if you’re interested, you’re welcome to read it up on your own. Sufficient to say that this theorem rules out quantum interpretations involving hidden variables (wavefunction is not complete) which is not contextual. 

So measurement answers depend on the set of measurement being done, we cannot have pre-fixed answers for everything. Quantum non-locality of the entanglement types explored before can be considered as a special case of contextuality. 

Another interesting inequality is Leggett’s inequality. Leggett’s inequality violation is said to rule out counterfactual definiteness in hidden variable interpretations, whereas Bell’s inequality violation can only rule out the combined local reality hidden variable types. 

Leggett’s inequality is indeed violated by experiments, showing that quantum wins against a type of theories called crypto non-local hidden variable theories. Jim Baggott calls it somewhat halfway between strictly local and completely nonlocal. 

This seems to imply that quantum interpretations without assuming hidden variables underneath the wavefunction (realism/ counterfactual definiteness) can stay in the non-signalling comfort of the non-local entanglement. However, once we insist on having realism, we need to seriously consider that the interpretation also has signalling of faster than light within its mechanics. And indeed this is what Bohm’s pilot wave interpretation does. The price of realism is high. 

Quantum interpretations and Buddhism Part 8: Experiment part 3 Bell's inequality

 

Bell's inequality is one of the significant milestones in the investigation of interpretations of quantum physics. Einstein didn't like many features of quantum physics, particularly the suggestion that there is no underlying physical value of an object before we measure it. Let's use Stern's Gerlach's experiment. The spin in x and z-axis are called non-commutative, and complementary. That is the spin of the silver atom cannot simultaneously have a fixed value for both x and z-axis. If you measure its value in the x-axis, it goes up, measure it in z, it forgot that it was supposed to go up in x, so if you measure in x again, you might get down. This should be clear from the previous exercise already and the rules which allow us to predict the quantum result.

 

There are other pairs of non-commutative observables, most famously position and momentum. If you measure the position of a particle very accurately, you hardly know anything about its momentum as the uncertainty in momentum grows large, and vice versa. This is unlike the classical assumption where one assumed that it's possible to measure position and momentum to unlimited accuracy simultaneously. We call the trade-off in uncertainty between these pairs as Heisenberg's uncertainty principle.

 

Niels Bohr and his gang developed the Copenhagen principle to interpret the uncertainty principle as there's no simultaneous exact value of position and momentum possible at one time. These qualities are complementary.

 

In 1935, Einstein, Podolsky and Rosen (EPR) challenged the orthodox Copenhagen interpretation. They reasoned that if it is possible to predict or measure the position and momentum of a particle at the same time, then the elements of reality exist before it was measured and they exist at the same time. Quantum physics being unable to provide the answer to their exact values at the same time is incomplete as a fundamental theory and something needs to be added (eg. hidden variables, pilot wave, many worlds?) to make the theory complete.

 

In effect, they do believe that reality should be counterfactual definite, that is we should have the ability to assume the existence of objects, and properties of objects, even when they have not been measured.

 

In the game analysis we had done, we had seen that if we relax this criterion, it's very easy to produce quantum results.

 

EPR proposed a thought experiment involving a pair of entangled particles. Say just two atoms bouncing off each other. One going left, we call it atom A, one going right, we call it atom B.

 

We measure the position of atom A, and momentum of atom B. By conservation of momentum or simple kinematics calculation, we can calculate the position of B, and momentum of A.

 

The need for such an elaborate two-particle system is because the uncertainty principle doesn't allow the simultaneous measuring of position and momentum of one particle at the same time to arbitrary precision. However, in this EPR proposal, we can measure the position of atom A to as much accuracy as we like, and momentum of B to as much accuracy as we like, so we circumvent the limits posed by the uncertainty principle.

 

EPR said that since we can know at the same time, the exact momentum of B (by measuring), and position of B (by calculation based on measurement of the position of A, clearly both momentum and position of atom B must exist and are elements of reality. Quantum physics being unable to tell us the results of momentum and position of B via the mathematical prediction calculation is therefore incomplete.

 

If the Copenhagen interpretation and uncertainty principle is right that both properties of position and momentum of a quantum system like an atom cannot exist to arbitrary precision, then something weird must happen. Somehow the measurement of the position of A at one side and momentum of B at the other side, makes the position of B to be uncertain due to the whole set up, regardless of how far atom A is from atom B. Einstein called it spooky action at a distance and his special relativity prohibits faster than light travel for information and mass, so he slams it down as unphysical, impossible, not worth considering. (A bit of spice adding to the story here.) Locality violation is not on the table to be considered.

 

Bohr didn't provide a good comeback to it. And for a long time, it was assumed that this discussion was metaphysics as seems hard to figure out the way to save uncertainty principle or locality. For indeed, say we do the experiment, we measured position of atom A first, we know the position of atom B to a very high accuracy. Quantum says the momentum of atom B is very uncertain, but we directly measured the momentum of atom B, there’s a definite value. Einstein says this value is definite, inherent property of atom B, not uncertain. Bohr would say that this is a mistaken way to interpret that exact value, momentum of atom B is uncertain, that value going more precise than the uncertainty principle allows is a meaningless, random value. Doing the experiment doesn’t seem to clarify who’s right and who’s wrong. So it’s regarded as metaphysics, not worth bothering with.

 

An analogy to spin, which you might be more familiar with now, is that two electrons are entangled with their spin would point the opposite of each other. If you measure electron A in the z-axis and get up, you know that electron B has spin down in z-axis for certain. Then the person at B measured the electron B in x-axis, she will certainly get either spin up or down in the x-axis. However, we know from previous exercise to discard the intuition of hidden variables that this means nothing. The electron B once having a value in z-axis has no definite value in x-axis, and this x-axis value is merely a reflection of a random measurement.

 

Then in 1964, came Bell's inequality which drags the EPR from metaphysics to become experimentally testable. 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 a 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 its 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?

 

Let’s go back to the teacher and students in the classroom. This time, the teacher tells the student that their goal is to violate this thing called Bell’s inequality. To make it more explicit and it's really simple maths, here's the CHSH inequality, a type of Bell’s inequality:

 

The system is that we have two rooms far far away from each other, in essence, they are located in different galaxies, no communication is possible because of the speed of light limiting the information transfer between the two rooms. We label the rooms: Arahant and Bodhisattva. The students are to come out in pairs of the classroom located in the middle and go to arahant room and bodhisattva room, one student each.

The students will be asked questions called 1 or 2. They have to answer either 1 or -1. Here's the labelling. The two rooms are A and B. The two questions are A_x or B_y with {x,y}∈{1,2} where 1 and 2 represent the two questions and {a_x or b_y}∈{−1,1} as the two possible answers, -1 representing no, 1 representing yes.

 

So we have the term: a₁(b₁+b₂)+a₂(b₁−b₂)=±2. This is self-evident, please substitute in the values to verify yourself. Note: in case you still don't get the notation, a₁ denotes the answer when we ask the Arahant room student the first question a₂ for the second question, it can be -1 or 1, and so on for b...

 

Of course, in one run 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 asking students), and average over it, so it's more of the average is bounded by this inequality. |S|= |<a₁b₁>+<a₁b₂>+<a₂b₁>−<a₂b₂>| ≤2 It's called the CHSH inequality, a type of Bell's inequality.

 

In table form, we can get possible values of say:

Questions asked	a1	a2	Separated by light years, student in B doesn’t know what student in A was asked, how student in A answered and vice versa.	Questions asked	b1	b2
A1	-1			B2		1
A2		1		B1	-1
A1	-1			B1	-1
A2		1		B2		1

 

S= |(-1)(-1)+(-1)(1)+(1)(-1)-(1)(1)|=2.

 

The goal is to have a value of S above 2. That’s the violation of Bell’s inequality.

 

Before the class sends out the two students, the class can meet up and agree upon a strategy, then each pair of students are separated by a large distance or any way we restrict them not to communicate with each other, not even mind-reading. They each give one of two answers to each question, and we ask them often (easier with particles and light). Then we take their answers, collect them and they must satisfy this CHSH inequality.

 

The students discussed and came out with the ideal table of answers:

 

Questions asked	a1	a2	b1	b2
A1, B2	1			1
A2, B1		1	1
A1, B1	1		1
A2, B2		1		-1

 

S=4, A clear violation of Bell’s inequality to the maximum.

 

So for each pair of students going out, the one going into room arahant only have to answer 1, whatever the question is. The one going to the room Bodhisattva has to answer 1, except if they got the question B₂ and if they know that the question A₂ is going to be asked of student in room arahant. The main difficulty is, how would student B know what question student A got? They are too far apart, communication is not allowed. They cannot know the exact order questions they are going to get beforehand.

 

Say if students who goes into room B decide to go for random answering if they got the question B₂, on the faint hope that enough of the answer -1 will coincide with the question A₂. We expect 50% of it will, and 50% of it will not.

 

So let’s look at the statistics.

<a₁b₁> = 1

<a₂b₁> = 1

<a₁b₂> = 0

<a₂b₂> = 0

S=2

 

<a₁b₂> and <a₂b₂> are both zero because while a always are 1, b₂ take turns to alternate between 1 and -1, so it averages out to zero. Mere allowing for randomisation and denying counterfactual definiteness no longer works to simulate quantum results when the quantum system has two parts, not just one.

 

It seems that Bell's 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

 

1.There is realism, or counterfactual definiteness. The students have ready answers for each possible questions, so the random answering above is actually breaking this assumption already. These ready answers can be coordinated while they are in the classroom, for example, they synchronise their watches, and answer 1 if the minute hand is pointing to even number, and answer -1 if the minute hand is pointing to odd number. 

 

2.Parameter independence (or no signalling/locality), that is the answer to one room is independent of the question I ask the student in the other room. 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/ freedom) the teachers are free to choose to ask which questions and the students do not know the ordering of questions asked beforehand.

 

All three are perfectly reasonable in any classical system.

 

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

 

1.Most physicists say counterfactual definiteness is wrong, there is intrinsic randomness in nature or at least properties do not exist before being measured.

 

2.There are interpretations with locality 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 freedom being wrong, there is no point to science, life and the universe. Superdeterminism is a bleak interpretation.

 

Let’s go back to the game, and see if we relaxed one of the 3 rules, can the arahant and Bodhisattva room students conspire to win and violate CHSH inequality?

 

So to simulate that, say they decide to bring along their mobile phones to the questioning areas and text each other their questions and answers. Yet, this strategy breaks down if we wait until they are light years apart before questioning them, recording it, and wait for years to bring the two sides together for analysis. So for the time being, we pretend that the mobile phone is specially connected to wormholes and circumvent the speed of light no signalling limit. They easily attain their ideal scenario. S=4. We call it PR Box.

 

Actually this violation reaching to PR box is not reached by quantum particles. Quantum strangely enough only violates up to S=2.828… that means quantum non-locality is weird, but not the maximum weirdness possible. It’s this weird space of CHSH inequality violation that is non-local yet obeys no signalling. Thus the meaning of non-locality in quantum doesn’t mean faster than light signalling. We cannot use quantum entangled particles so far to send meaningful information faster than light. Quantum seems to be determined to act in a weird way, which violates our classical notion of locality, yet have a peaceful co-existence with special relativity.

 

This was a line of research which I was briefly involved in a small part during my undergraduate days. The researchers in Centre for Quantum Technologies in Singapore were searching for a physical principle to explain why quantum non-locality is limited as compared to the space of possible non-locality. So far, I do not think they have succeeded in getting a full limit, but many other insights into links between quantum and information theory arise from there and one of the interpretations involve rewriting the axioms of quantum to be a quantum information-theoretic inspired limits and derive the standard quantum physics from there.

 

The PR box example is actually the maximum non-locality that theoretical physics allows, bounded by no-signalling. So PR box still satisfy special relativity due to no signalling, however, they do not exist in the real physical world as it would violate several information-theoretic principles.

 

The PR box can be produced too if they know beforehand what questions they each are going to get, so no freedom of the questioner to ask questions. Yet, purely relaxing counterfactual definiteness cannot reproduce it. It’s because Bell’s theorem is not meant to test for purely that. We have another inequality called Leggett’s inequality to help with that (more on it later).

Puzzled by the strange behaviour of quantum, the students looked online to learn how entangled particles behave. Say using spin entangled electrons pairs, they both must have opposite spin, but whether they are spin up or down, it’s undecided until the moment they are measured. So if say electron A got measured to be spin up in z-axis, we know that electron B is spin down in z-axis immediately. With this correlation and suitable choice of angles of measuring the spin, experiments had shown that entangled particle pairs do violate Bell’s inequality, be it photon or electron. Like entangled photons (light) where we measure the polarisation angel, so the questions are actually polarisation settings which involve angles. The polarization of entangled photon pairs is correlated. A suitable choice of 3 angles across the 4 questions of A₁, A₂, B₁, B₂ allows for Bell’s inequality violation to the maximum for the quantum case. The different angles allow for more subtle distribution of probabilities to only ensure S goes to 2.828… and not more for the quantum case.

 

The students then try to simulate entangled particles without using an actual quantum entangled particle to see the inner mechanism inside it. The first idea they had was to use a rope to connect the students. Student pairs as they move to room A and B, they carry the rope along with them. When student A got question 2, student A will use Morse code to signal to student B both his answer and the question he receives, then student B can try to replicate quantum results.

 

The teachers then frown upon this method. She then spends some money from the school to actually make room A and room B to be far away. Say even send one student to Mars on the upcoming human landing on Mars mission. Now it takes several minutes for light to travel from Earth to Mars, and in that time, there’s no way for internal communication to happen between the two entangled particles. The rope idea is prevented by special relativity unless we really believe that entangled particles are like wormholes (which is one of the serious physics ideas floating out there, google ER=EPR), and that they do directly communicate with each other.

 

Quick note, even if entangled particles do internal communication, it’s hidden from us by the random results they produce in measurement. It’s due to this inherent randomness that we cannot use entanglement correlation to communicate faster than light. So any claims by anyone who only half-read some catchy popular science article title about quantum entanglement who says that with entanglement, we can communicate faster than light, you can just ask them to study quantum physics properly. Quantum non-locality is strictly within the bounds of no signalling. Don’t worry about it, it’s one of the first things undergraduate or graduates physics students try to do when first learning about it and we all failed and learnt that it is indeed due to the random outcomes of the measurement which renders entanglement as non-local yet non-signalling, a cool weird nature.

 

Experimentally, Bell’s inequality violation has been tested on entangled particles, with the distance between the two particles as far away as 18km apart, using fibre optics to send the light to another lab far far away. With super fast switching, they managed to ask the entangled photons questions far faster than it is possible for them to coordinate their answers via some secret communication. Assuming no superluminal communication between them.

 

Well, ok, no rope, so what’s so strange about correlation anyway? Classically, we have the example of the Bertlmann’s socks. John Bell wrote about his friend Dr. Bertlmann as a person who couldn’t be bothered to wear matching socks so he takes the first two he has and wear them. So on any given day, if you see the first foot he comes into the room as pink socks, you can be sure that the other sock is not pink. Nothing strange here. So what’s the difference with entanglement?

 

The main difference is, before measurement, the entangled particles can be either pink or not pink, we do not know. There’s the probabilistic part of quantum which comes in again. We call it superposition of the states of pink and not pink. For photons, it can be superposition of polarisation in the horizontal and vertical axis, for electron spin, it can be superposition of up and down spin in z-axis. Any legitimate quantum states can be superpositioned together as long as they had not been measured, and thus retain their coherence, and as long as these quantum states are commutable (can be measured together).

 

In Copenhagen picture, the entangled particles acts as one quantum system. It doesn’t matter how far away in space they are, once the measurement is one, the collapse of the wavefunction happens and then once photon in A shows a result, we know immediately the exact value of photon B. Before measurement, there was no sure answer. This happens no matter if photon A is at the distance of half a universe away from photon B.

 

This type of correlation is not found at all in the classical world. The students were not convinced. They tried to gather a pink and a red sock they have to put into a bin. Then a student blindfold himself, select the two socks from the bin, switch it around and hand them over to the student pairs who will go to room A and B, one sock each. The students put the socks into their pocket, not looking at it, and only take it out to see it and try to answer based on their correlation, if one has red, we know the other has pink immediately. The pink and red colour can be mapped to a strategy to answer 1 or -1 to specific questions. This is not the same thing as real quantum entanglement, they didn’t perform better at the game. They have counterfactual definiteness. Before asking the students what colour the socks are, we know the socks already have a predetermined colour. With predetermined answers, we cannot expect b₂ to have the ability to change answers based on different questions of A₁ or A₂. Thus no hope of producing quantum or PR box-like correlation. 

 

The teacher finally felt that the students are ready for a simple Bell’s inequality derivation. She selected three students up, each student having a label of an angle: x:0 degrees, y:135 degrees and z:45 degrees. Each student is given a coin to flip. There are only two possible results each, heads or tails. Refer to the table below for all possible coin flip results:

 

0 means tails, 1 means head. The bar above means we want the tails result. So the table shows us that we can group those with x heads and y tails (xy̅) as case 5 and 6, case 3 and 7 are part of the group of y heads and z tails (yz̅). And finally, the grouping of x heads and z tails (xz̅) are case 5 and 7. It’s obvious that the following equation is trivially true. The number of xy̅ plus the number of yz̅ is greater than or equal to the number of xz̅ cases. This is called Bell’s inequality.

 

Quantum results violate this inequality, the angles above are used in actual quantum experiments to obtain the violation. In quantum calculations, the number of measurements in xy̅ basis and yz̅ basis can be lower than the number of cases in xz̅ basis. Experiment sides with quantum.

 

To translate this to CHSH, the questions that were given to the students can have a combination of two of the three angles. So the question in room arahant can be 0 degrees (x), and the question asked in room bodhisattva can be 135 degrees:y, followed by Room A asks y, Room B ask z, Room A asks x again, Room B asks z. Notice that Room A only asks between x and y, and Room B only asks between y and z, so it fits with only two questions per room. A₁ =x,  A₂=B₁=y, B₂=z.

 

Each of run the experiment can only explore two of the three angles. The heads or tails, 0 or 1 corresponds to the student’s 1 and -1 answer. As the table shows for the coin settings, the implicit assumption is that there’s counterfactual definiteness. Even if the experiment didn’t ask about z, we assumed that there’s a ready value for them. So any hidden variable which is local and counterfactual definite cannot violate Bell’s inequality. For quantum interpretations which deny counterfactual definiteness, they have no issues with violating Bell’s inequality.

 Back to EPR, Einstein lost, Bohr won, although they both didn't know it because they died before Bell's test was put to the experiment. 

Quantum entanglement was revealed to be a real effect of nature and since then it has been utilised in at least 3 major useful experiments and technologies.

1. Quantum computers. Replacing the bits (0 or 1) in classical computer with qubits (quantum bits), which you can think of as a spin, which has continuous rotation possible for its internal state, capable of going into superposition of up and down states at the same time, and having the capability to be entangled, quantum computers can do much better than classical computers in some problems. The most famous one is factoring large numbers which is the main reason why our passwords are secure. Classical computers would take millions of years to crack such a code, but quantum computers can do it in minutes. Thus with the rise of quantum computers, we need…

 

2. Quantum cryptography. This is the encoding between two parties such that if there’s an eavesdropper, we would know by the laws of physics that the line is not secured and we can abandon our quantum key encryption. There’s some proposal to replace the classical internet with quantum internet to avoid quantum computer hacking into our accounts.
3. Quantum teleportation. This has less practical usage, but still is a marvellous show of the possibility of quantum technologies. The thing which is teleported is actually only quantum information. The sending and receiving side both have to have the materials ready and entangled beforehand. The quantum object to be teleported has to be coherent (no wavefunction collapse) to interact with the prepared entangled bunch of particles at the sending end. Then the object to be teleported is destroyed by allowing it to interact with the sending entangled particles, we do some measurements, collect some classical information about the measurement, then send it at the speed of light to the receiving end. The receiving end has only the previously entangled particles, now no longer entangled due to the other end having interacted with measurements. They wait patiently for the classical data to arrive before they can do some manipulation to transform the receiving end stuffs into the quantum information of the thing we teleported. If they randomly try to manipulate the receiving end stuffs, the process is likely to fail. The classical data sent is not the same even if we teleport the exact same thing because of quantum inherent randomness involved in the measurement process. The impractical side is that large objects like human bodies are never observed to be in quantum coherence, too much interference with the environment which causes the wavefunction to collapse. And if we want to quantum teleport a living being, it’s basically to kill it on the sending side and recover it on the receiving side. It’s not known if the mind would follow, does it count as death and rebirth in the same body but different place? Or maybe some other beings get reborn into the new body?