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Tuesday, November 10, 2020

Quantum interpretations and Buddhism Part 7: Interlude: A quantum game, Classical concepts in danger

 

Before going onto experiment no. 3, Bell's inequality violation, we need to settle a number of basic concepts relevant in foundational research of quantum mechanics in order to fully appreciate the importance of that experiment. Historically, before Bell came out with his inequality, these foundational concepts had been largely ignored by physicists. That's because they thought that no experiments could ever probe these foundational issues and they are considered as philosophy work to interpret these rather than physics’ work. Today, we can distinguish many of the interpretations based on these fundamental properties, three of them will be briefly introduced here. They are locality, counterfactual definiteness and freedom. See the table below for seeing which properties that various interpretations have. Don’t spend too much time on the table, don’t worry, it’s not meant to be understood, we’ll understand these later on.

Table from: https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#cite_note-61 

 

Interpre­tationYear pub­lishedAuthor(s)Determ­inistic?Ontic wave­function?Unique
history?
Hidden
variables
?
Collapsing
wave­functions
?
Observer
role?
Local
dyna­mics
?
Counter­factually
definite
?
Extant
universal
wave­function
?
Ensemble interpretation1926Max BornAgnosticNoYesAgnosticNoNoNoNoNo
Copenhagen interpretation1927Niels BohrWerner HeisenbergNoNo[a]YesNoYes[b]CausalYesNoNo
de Broglie–
Bohm theory
1927–
1952
Louis de BroglieDavid BohmYesYes[c]Yes[d]YesPhenomen­ologicalNoNoYesYes
Quantum logic1936Garrett BirkhoffAgnosticAgnosticYes[e]NoNoInterpre­tational[f]AgnosticNoNo
Time-
symmetric theories
1955Satosi WatanabeYesNoYesYesNoNoNo[54]NoYes
Many-worlds interpretation1957Hugh EverettYesYesNoNoNoNoYesIll-posedYes
Consciousness causes collapse1961–
1993
John von NeumannEugene WignerHenry StappNoYesYesNoYesCausalNoNoYes
Stochastic interpretation1966Edward NelsonNoNoYesYes[g]NoNoNoYes[g]No
Many-minds interpretation1970H. Dieter ZehYesYesNoNoNoInterpre­tational[h]YesIll-posedYes
Consistent histories1984Robert B. GriffithsNoNoNoNoNo[i]NoYesNoYes
Transactional interpretation1986John G. CramerNoYesYesNoYes[j]NoNo[k]YesNo
Objective collapse theories1986–
1989
Ghirardi–Rimini–Weber,
Penrose interpretation
NoYesYesNoYesNoNoNoNo
Relational interpretation1994Carlo RovelliNo[55]NoAgnostic[l]NoYes[m]Intrinsic[n]Yes[56]NoNo
QBism2010Christopher Fuchs, Ruediger SchackNoNo[o]Agnostic[p]NoYes[q]Intrinsic[r]YesNoNo

 

It is also the (faint) hope of some that as we know more about these fundamental properties and which ones does nature respect, we might be able to rule out some interpretations to finally arrive at the one true interpretation. Indeed, some work had been done to rule out interpretations which have a certain combination of these properties. And Bell's theorem was one of the first to do so. A bit of spoiler alert here, Bell's inequality violation means that nature is never simultaneously local (local dynamics in the table) and counterfactual definite. The more common name you might read is Bell's inequality ruled out local realism. As you can verify from the table above, there is no worthwhile interpretation which says yes to both locality and counterfactual definiteness. Unless you consider superdeterminism to be the true interpretation. I will explain what those are as you read on.

 

We had been talking about classical expectations of how the world should work versus quantum reality of how the world breaks classical expectations. In Bell's inequality, there are three main properties of how the world works are at play.

 

a. Locality (only nearby things affect each other at most at the speed of light),

b. Counterfactual definiteness, or realism (properties of objects exist before we measure them),

c. Freedom or free will, or no conspiracy or no superdeterminism (physical possibility of determining settings on measurement devices independently of the internal state of the physical system being measured. In other words, we are free to choose what to measure.)

 

If the world obeys all these three assumptions, then Bell's inequality cannot be violated. Yet experiments show that it is violated. Leading us to abandon one or more of these assumptions, depending on one's preference.

We can play a game using the classroom example below, based on Stern-Gerlach experiment to illustrate the parallels of the restriction rules to the three properties at play here.

Imagine if you are a teacher, you have a class of students and you tell them you are going to subject them to a test. The test is a collective fail or success test. The main goal is for the class to behave as the experimental results described. So the students are given time and the materials to study and strategise amongst themselves. Once they are ready, one by one the students come to you, and you will ask many questions of the students, then record their answer. Your question is limited to asking x or z, and the answer is limited to up or down (left and right being relabelled to up or down). That's in direct analogy to the freedom of measuring in the x or z-axis and the particles either go up or down.

 

If you don't like the question being x or z, you can replace it with any yes-no questions with no fixed answer. Eg. Question one is: blue or not? Question two is: red or not? The answers are yes or no. The question does not refer to any specific object being red or blue, but just as an example of questions with only two possible answer but no fixed answer. To preserve close analogy with the experiment, we shall continue to use x, z as questions, up, down as answers. So the "magic" is not in the questions or answers but in their pattern.

 

There is no limit to how many questions you can ask any of the students, and part of the student strategy has to take that into account. After the test is done for the whole class and you had recorded their answers, you do the quantum analysis to see if they would obey the rules we found the experiments obey.

 

If the overall statistics differ too much from the quantum expectations, the whole class fails. So the students get very serious in their strategic planning. They found that it's simple to win the game or pass the test if they do not have any preconditioned answers to the questions but to just follow the quantum rules, so they ask you if they can decide on the answers on the spot. You detected intrinsic randomness at play here and you come out with rules that the student can or cannot do to satisfy classical thinking requirements. But you do not wish to reveal the true reason you set the rules, so you used the common exam reasons for the rules.

 

You control which questions you ask without letting them know beforehand, you can decide on the spur of the moment too. That's pretty obvious too in the test setting, students who know what will come out in the exam can score perfectly. The students cannot change their strategy halfway through. That's being unsure of their knowledge. They also cannot decide on the spur of the moment which answers they will give. That's like guessing in the exams. And they cannot communicate with each other once the game started. That's cheating in exams.

 

Try planning the strategy like the students, if you cannot pass the test, try dropping some of the rules which forbid things. See what kind of rules need to be abandoned to reproduce nature's results.

 

Here's a sample strategy, call it strategy A to get you started. Students pair up into groups of two, in each group we assign a definite answer for each student, and every group has the same strategy.

 

Student 1: Every time I meet z, I answer up. If I meet x, I answer down. I ignore the order of questioning.

 

Student 2: Every time I meet z, I answer down. If I meet x, I answer up. I ignore the order of questioning.

 

It's fairly straightforward to work out that this strategy will fail. The main goal of this exercise is to let you to appreciate the thought experiments physicists have to think when thinking about how to interpret quantum physics, and to see how classical thinking cannot reproduce quantum results.

 

In the classroom, each student is allowed to have their own piece of instructions on how to behave when encountering measurement. As quantum measurement can only reveal the probability distribution function after measuring many particles, there might be a need to coordinate what strategy the others will be using. When they are discussing, that's the silver atoms still in the preparation device. As the device activates, one by one the students come out, simulating the silver atoms coming out one by one.

 

So you as the teacher can in principle choose to have the student go through measurement x or z by asking the questions x or z, and the decision can be made at the spur of the moment. The student coming to the test one by one is parallel to the particles being measured one by one. The questions are measuring devices and having a choice in what to ask allows for freedom and building meaningful results.

 

The student as they leave their classmates, they cannot communicate with their classmates anymore. You told them it's to avoid cheating in the test, but the real reason is that's the rule of locality. Actually technically it is called the rule of no-signalling. No signalling in quantum setting means no communication faster than light. Why is faster than light relevant here? In principle, the first measurement the first particle (student) encounters do not have to be within the same lab. If we imagine that we have advanced technology, we can allow the particle to travel to the next galaxy, millions of light-years away before doing the measurement. So to communicate with the rest of the teammates back on Earth would require faster than light communication.

 

Another rule is, they cannot change their strategy. Having a strategy means that the properties of an object exist before we measure them. That's counterfactual definiteness. Counterfactual is what has not happened like the measurement has not happened, but the properties are definite. There is another common name for this called realism. That's because classical thinking insists upon the moon is there even if I am not watching it. That's pretty close to contextuality. And indeed it is, making the strategy fixed is non-contextuality. Objects answer does not change depending on the question you ask them. Certainly, the motion of a ball in free fall does not suddenly change depending on if I ask it what's the velocity or position that that point. And certainly, those properties exist before I even ask them. That's classical thinking. Having a strategy and not guessing it means you assume that the student must have the knowledge for the test instead of coming up with the answer on the spur. That's assuming that nature has definite properties even if you do not measure it.

 

Freedom is your own freedom to ask the questions. That is the experimental physicist freedom to choose which measurement to do first, in which order and to measure which beam. You told the students that if they know what questions will come out, they can cheat in the test. The same thing happens in nature. This is as if the universe is a conspiracy. It will somehow know what you as experimental physicist will choose and adjust so that the right silver atoms (or student) will go to the right experimental measurement at the right time to give the exact right answer so as to reproduce the experimental results. Therefore the alternative name of no conspiracy. In the test analogy, since there is no intrinsic randomness from the students having preset values, and the students already know what you will ask and their order of going for the test can be arranged to present the illusion of randomness to you.

 

A more scary thought is that if anything (including the universe) can know what you will choose, that means you have no real free will. No free will plus nature is deterministic, means there is nothing that is not fixed from the beginning of time. This is called superdeterminism.

 

Wait a minute, just now we said that nature can choose which atoms to present to you to keep up this conspiracy. Is that not a choice from nature, some sort of free will? Yet, there is no reason for the choice to be made in that instant, it can be fixed from the beginning, since everything can be predicted by nature, or nature already knows, so all possible conspiracy was already fixed back at the start. In that sense, nature also has no real choice. Super-determinism is pretty bad news for science as Anton Zeilinger has commented:

 

"We always implicitly assume the freedom of the experimentalist... This fundamental assumption is essential to doing science. If this were not true, then, I suggest, it would make no sense at all to ask nature questions in an experiment since then nature could determine what our questions are, and that could guide our questions such that we arrive at a false picture of nature."

 

You might ask for the difference between super determinism vs determinism. Determinism is more of due to cause and effect relationships in the physical equations. Technically for those who uphold the materialism/physicalism philosophy plus determinism, for them, how the mind works is fundamentally due to the physical laws of nature as well, so free will is an illusion. The philosophical technical term for this is hard determinism. Thus there is basically no difference between hard determinism and super determinism for them. For many who believe in true free will but also determinism like the Christians from the days of Newton to the discovery of quantum physics, for them, determinism does not extend to free will or domain of the soul. The technical philosophy term for this is compatibilism. So there is a difference between determinism of physical phenomenon and super determinism of everything. The Buddhist view on this issue will be discussed later on.

So to recap, the game/test is:

 

   Students take turns to go to the teacher.

   The teacher can ask each student as many questions as she likes, before testing the next student. The questions the teacher chooses can be freely chosen, not revealed to the students.

   Each student must have a guide, or an answer ready for any possible sequence of questions that the teacher asks, for all possible number of questions asked.

   Students once travelled to the teacher cannot communicate with the rest of the students on their interactions with the teacher.

   The goal is to simulate the experimental results without using quantum physics, only using reasonable classical assumptions.

 

Now let us do the exercise in the first experiment above. Hopefully, by now you had some break in between reading from there to here and had some time to think and ruminate on the strategies. Here is a step by step tutorial for that for those who are clueless or too lazy to do the exercise or those who simply wished to be spoon feed. Just kidding, I think writing this would be my first time analysing the problem in this framework as well. This is instructive in seeing the underlying reasons for deriving the Bell's inequality, to later see it's a violation as something amazing that nature throw at us.

Say we use the sampling strategy above and analyse why the teacher would fail the class in that case. When the teacher asks z first then x later, half of the students will give up to z, down to x, another half will give the opposite results. Overall, it seems to be half split into z, half split into x. It only superficially recreate a random result. It also fulfils the first picture below. If the teacher asks those who go up at z, the question z again, the students will give their previous fixed answer to z, the same answer. But grouping the students who give up to question z then seeing that they all go down at question x does not comply with how nature behaves. They are supposed to be half of those who answered up at z to go up at x and another half to go down at x. That's referring to the middle picture below. This strategy cannot also recreate the third picture below.

 

So the students had thought of all of these consequences and quickly discarded the sample strategy their teacher provided to get them started. They think of partitioning the students more. Partition into four people per group, each group with strategy as follows:

 

Student 1: answer up at z, up at x.

Student 2: answer down at z, up at x.

Student 3: answer up at z, down at x.

Student 4: answer down at z, down at x.

Ordering of questions does not matter to them.

 

They can recreate the second picture now while preserving the first picture. Still, they fail in the third picture. Those who answer up at z will be students 1 and 3. So the teacher need only to ask student 1 the question z again. And the results will still only be up. All student 1 in all groups will give the same answer thus the teacher fails them.

Finally, the students get it. They partition themselves into groups of four again, with the same basic strategy as above, but here they have to take into account the ordering of questions.

If any questions ask z consecutively, keep answering the same answer as the previous z. Same case as with any consecutive question on x. If there is a switch of the question, say from z to x and back to z, then switch the original answer of z to the opposite of the original value. This holds even regardless of the number of x questions in between the two z questions. Each time there is a switch of questions, switch the answers back and forth. Same case for x, z, x questions.

Confident of their strategy, they rethink what would happen. As before, student 1 is asked z, x, then z again. This time, every student 1 in each group will give down to z. No one answers up. Still not recreating the third picture.

Then they preserve the same ordering rule but partitioned the students into groups of eight. Any leftovers (say 7 extra students) are welcomed to just fill the last group to however much leftover there is. Statistically, the leftovers do not matter as long as we have a lot of groups. If the classroom is not big enough, the students ask the classrooms next class and even the whole school and even neighbouring schools to make up the numbers.

Note: if you cannot follow this analysis, don’t worry, it’s not so important, it’s all my additional work, you might not encounter it in physics class. Just skim along for the theoretical payoff of which rules to break.

The strategy for the first few questions encountered is as in the table below.

 

Questions

Students

z

x

The first z after switch of question

1

up

up

up

2

up

up

down

3

up

down

up

4

up

down

down

5

down

up

up

6

down

up

down

7

down

down

up

8

down

down

down

 

Now the ordering rule reads, switch the latest answer of z to its opposite for subsequent switching of questions.

 

Now they think if the teacher asks only three questions maximum to each student, the teacher cannot detect any difference statistically from the quantum results. Unless another student points out, the teacher asks x, z, x.

 

Face-palming themselves after inviting so many students from neighbouring schools and yet still fail to come out with the winning strategy, the clever ones just try an update to groups of 16. This time, the x, z, x order are taken into account and the ordering rule also updates to the same for them, switch the latest answer of z or x to its opposite for subsequent switching of questions.

 

 

Questions

Students

z

x

The first z after switch of question

The first x after switching of question

1

up

up

up

up

2

up

up

up

down

3

up

up

down

up

4

up

up

down

down

5

up

down

up

up

6

up

down

up

down

7

up

down

down

up

8

up

down

down

down

9

down

up

up

up

10

down

up

up

down

11

down

up

down

up

12

down

up

down

down

13

down

down

up

up

14

down

down

up

down

15

down

down

down

up

16

down

down

down

down

 

Now as the group grows bigger, the number of clever students also increases. Another clever one pointed out that the teacher can ask more than three questions per student. We will fail then. The original group who thought of the ordering rule said that the ordering rule should take care of it.

"Really?" challenged the clever student. They rethink about it.

Say the teacher ask z,x,z,x,z,x. Six questions in that order.

The following table shows the results that the teacher would collect. One of the students quick with Microsoft Excel made a quick table.

 

 

Questions in order

Students

z

x

z

x

z

x

1

up

up

up

up

down

down

2

up

up

up

down

down

up

3

up

up

down

up

up

down

4

up

up

down

down

up

up

5

up

down

up

up

down

down

6

up

down

up

down

down

up

7

up

down

down

up

up

down

8

up

down

down

down

up

up

9

down

up

up

up

down

down

10

down

up

up

down

down

up

11

down

up

down

up

up

down

12

down

up

down

down

up

up

13

down

down

up

up

down

down

14

down

down

up

down

down

up

15

down

down

down

up

up

down

16

down

down

down

down

up

up

 

Let’s spend a moment reading this table. This is the expected outcome for one type of questioning the teacher may ask to one group of student. As we get many groups, the statistics can appear to still obey quantum rules, as long as the teacher only asks up to four questions.

 

Say the teacher is clever, she determined to only keep certain students which has the results of: down, up, up, up, for the first 4 questions, that is every student 9 in each group. On question 5, another z, all of the students answers down (opposite of the last z). this violates the quantum prediction already. Whereas in the quantum case, there would still be a split of ups and downs along z-axis from these groups of silver atoms.

 

At this point in the analysis, the students realise that they would need to continually double the size of the group to the maximum amount of questions the teacher can ask. We doubled from one student four times (two to the power of four) to get 16, and it can only fit the quantum case for up to four questions. Since the teacher told them that there is no limit to the number of questions that she can ask, they need an infinite amount of students to have an infinitely long strategy to win all the time.

 

Throwing their hands in the air, they cried foul to the teacher and explained their findings.

 

Now putting yourself back as the teacher, you look to see the analogy with the silver atoms. You ask yourself how many measurements of alternative switch do you need to do on the silver atoms to completely verify that there is no classical strategy like above to reproduce the experiment? A quick guide in the number of silver atoms there are in 108 g of silver, the weight of one mole of silver is the Avogadro's number, that is 6.02*1023. How many doubling of twos is that number? It's seventy nine. 279 would just be slightly bigger than Avogadro's number. So just do the alternate measurements eighty times, if you plan to use up all 108g of silver in the Stern-Gerlach experiment to completely verify that there is no way nature can conspire with such strategy.

 

Now I am not aware that any experimentalist had done this yet, but it's a good paper to write if you are one and happen to have all the equipment at hand! Of course, this will be very technically challenging as it entails measuring to about one or two atoms of silver at the last few stages of measurement. Not to mention all the losses that would occur at the process of heating the atoms to become a beam, controlling the beam to be one atom at a time, doing in in vacuum to avoid air pushing the silver atoms out of the path and so on.

 

Here’s a disclaimer. the weakness of this analysis includes: The students have rigid rules of grouping, like the same number of students to every group and their own rule that every group has the same strategy. They can relax these requirements and also find more clever ways of putting if-then statements to their answers, instead of just a simple switch to opposite. So this does by no means show that it’s impossible for the ensemble interpretation of quantum to be ruled out. However, there are other reasons to rule the ensemble interpretation as defunct. We shall go back and focus on the rule-breaking.

 

Suffice to say that theoretically speaking, we should abandon one of the rules which we had set up previously for the students to pass the test. To choose which rules to abandon and the subsequent strategy which the students are free to employ are part of the work of interpretation of quantum. Nature is not classical, but just how not classical it needs to be? In particular, which part of classical should nature abandon to behave like quantum? You might also read somewhere else that says the same thing in different words: Just how weird quantum needs to be? Which weirdness are you comfortable with? That's pretty much how people choose their interpretations.

 

So knowing that different students in the class will have different preferences for which weirdness they are comfortable with, you divided the class into three unequal groups. One is allowed to break locality, the second allowed to break counterfactual definiteness and the third allowed to break freedom. You explain a bit of what these concepts are and which rules the tie in to and let the students pick their own group. Technically this case is not the experiment studied by the Bell's inequality violation, so it's more of a tutorial case for you to get familiar with how physicists do fundamental quantum research.

 

Once the sorting is done, each group works out their solution to your test, taking full advantage of the one rule they can break. Let us visit them brainstorming one by one. Don't worry, the workings are much shorter than what we had done above.

 

  1. Locality violation, or Non-locality.

This allows the student coming up to communicate with the rest of the classmates as he answers the questions. He can tell the rest what questions he received, but it's not useful as it's not guaranteed that the teacher will use the same ordering of questions on the next person. He can communicate how many questions he got in total, but it's again not useful as the teacher can always increase the number of questions for the next person. He can tell the classmates what he answered, but everyone already knows what he will answer to all possible combination of answers if the strategy is long enough. Overall, relaxing this rule does not help.

 

This is perhaps not so surprising as back in 1922 when the Stern-Gerlach experiment was performed, no one was concerned about locality violation from this experiment. We need a minimum of two particles and two measurements to possibly test for locality violation. That's what Bell's inequality violation experiment uses. It's called quantum entangled particles.

 

 

  1. Counterfactual definiteness violation, or no fixed answers, or answers does not exist before we ask the questions.

 

This allows the student to go out with just a small list of instructions, like a computer programme, which can easily replicate quantum results. The instructions are as follows. Each student has only to remember two bits of information, or in colloquial terms, two things. That is there are two memory slots, each capable of storing one of two states. In computer language, it would be 0 or 1. We can relabel them to any two-valued labels like x or z, up or down.

 

When they go for the test both memory slots are empty. The teacher asks the question of either x or z. The student stored the questions ask in the first slot. The answer the student gives depends on a few factors.

 

If the first slot was empty beforehand and just got a new value, and the second slot is also empty, the answer is a random selection of 50% chance up or 50% chance down. Store the answer in the second slot memory.

 

If the first slot was not empty, compare the question to the first slot. If the question is the same, use the same answer in the second slot memory. This ensures that if the teacher asks z, z in a row, the second z will get the same answer as the first z.

 

If the question is different from the first slot, discard the second memory and do the random selection again and store the new value in the second slot memory. Also, update the first slot to the latest question.

 

Example. The student comes up, got the question x. He randomly selects up as the answer. The next question is x. He gives the same answer up. The next question is z, he forgets about question x, updates his first slot with z, selects random results, say down and also updates the second slot. The next question is x, he updates the first slot with x, select random results, say down and updates the second slot with the new answer. And so on.

 

That's all that is needed to replicate quantum results. The crucial freedom here is that the answers do not have to exist before the question is asked. And if no question is asked, eg. on consecutive questioning of z, z, there is no meaning to ask if the teacher had asked x instead of z as the second question, what would the answer be? Since x was not asked on the second question, it is counterfactual, and there is no definite answer to that question.

 

This way, each student can have a finite, small list of instructions on what to do for all questions, so the number of questions asks does not matter. The number of students required does not matter as the strategy does not depend on that. Well, as long as it's enough to do a statistical analysis. Students can pass the test with 100% certainty.

 

Contextuality is not really apparent here and is better tested via other means.

 

  1. Freedom violation or cheat mode enabled.

 

It's a bit tricky to detail how the students can win with this. It entails placing restrictions. So the students know beforehand that the teacher cannot possibly ask an infinite amount of questions. They already know the maximum amount of questions which the teacher will come out with. It's never infinity. And they can know which sets of questions the teacher will ask for the first student and the second one and so on. They can then arrange for the student who prepared their strategy just up to the maximum amount of questions the teacher will ask that student to.

 

Eg. if the teacher will ask 10 questions to the first student, the first student who goes out only needs to prepare until 10 possibilities. Normally, the students also do not know which x, z ordering of the questions will come out and the student has to prepare their answer for 2^10, or 1024 possible sets of questions. One set can read all 10 x, another can be x,z alternate, another can be z, x, x, z, x, x, z, x, z, x. Each question can have 2^10 possible answers too. Like all 10 ups, or up, up, down, down, up, down, up, up, up, up. So it's 1,048,576 possible answers.

 

We simplified the possibilities in the analysis before relaxing the rules by using for all question x, answer up etc. It selects a narrow range from all these possibilities, with the advantage that the student can have fixed answers up to infinite questions. Also, the quantum results already ruled out most of the possible answers. Like for consecutive x, x, we can only have either up, up or down, down, not up, down or down, up. That's half of the possible results gone with one of the quantum rules. We just have to replicate that by ruling out impossible results.

 

But now, we know exactly which of the 1024 sets of question ordering the teacher will ask, as this is a conspiracy. So we only need to prepare the first student for a minor selection of the 1024 possible answers left to give to be consistent with quantum results. We can also prepare all others to fit in with the first student to get quantum statistics overall, tricking the teacher.

 

There is just one tiny detail left to address. The teacher also selects the number of students. So what if the teacher asks more questions than there are enough students to answer to provide the quantum statistics for? Then it's the fault of the teacher for not allowing enough students to participate or asking too many questions. The teacher cannot conclude anything without enough data.

Wait, this last bit of information does seemingly destroy our reasoning that nature is not classical above. There is no point doing 80 measurements of alternative directions if we do not provide more than one mole of Silver atoms to get the statistics. Adding up more silver atoms allows for nature to cheat on us. Not adding means we do not have enough data to conclude that nature can be fundamentally classical.

 

The solution to this conundrum is to realise that to be paranoid about nature betraying us is actually assuming the conspiracy theory. Look at the word cheat on us in the previous paragraph. If nature is fair and classical, we should already get deviation from quantum results way before having to do 80 measurements in a row. Which is probably why no one bothered to do this experiment. If nature cheats on us anyway, there is no way we can ever know. That makes the last assumption, no freedom, or super-determinism fall into the category of unfalsifiable interpretation.

 

Now, satisfied with the results of our analysis, most people conclude that nature is counterfactual indeterminate as you can imagine superdeterminism is not popular with people. Historically, superdeterminism is not considered until Bell's inequality is shown to be violated. Thus, it would be interesting to explore how do some of the interpretations can still retain counterfactual definiteness. We will discuss their explanation of these experiments when we get to them.

 

So many people are quite comfortable to say quantum experiments tell us that nature does not exist until you observe them from throwing out counterfactual definiteness, or realism. Yet, this is deliberately excluding that interpretation which still retains realism. Strange, is it not, that even this seemingly fundamental part of what almost everyone thinks what quantum is, turns out to be not necessarily true.

 

Next up, we will talk more on Locality and Bell's inequality violation.

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