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
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.
- 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.
- 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.
- 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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