This chapter is about the meanings of the term free will, whether free will exists or not, whether determinism is universal or not, and whether quantum theory disproves determinism.
Section I. Free will and determinism
12.1. The various meanings of free will
12.2. The process of making a decision
12.3. Natural will and free will
12.4. Is free will predetermined?
12.5. Is nature deterministic?
12.6. The predetermined free will
Section II. Quantum theory and determinism
12.7. Quantum theory, classical determinism, and probabilistic determinism
12.8. The case of entangled particles
Section I. Free will and determinism
12.1. The various meanings of free will
Free will seems to be a simple term, yet in reality, it involves a complex concept and can mean different things to different persons [1-3]. This is because both the term free and the term will can be looked at from different points of view. Consequently, conclusions that are derived from this term are different, depending on its meaning. Consider some of its different meanings and their answers to the important question “Does free will exist?” in the following discussions:
FW1. Free will in the sense of the act of making a decision
A: Do we have free will?
B: Of course, we can do anything freely in this country, don’t we?
A: In a way, yes. But you have to obey the laws, the rules, the customs, and other regulations, so you can’t do everything you’d like to do, right?
B: Ok. I admit that’s true. So we don’t have free will all the time. But we still have free will to do anything we like when there aren’t any of those restrictions, don’t we?
A: I agree. But other than those restrictions, there’s something else too that can get in your way. Do you think that you have free will if you want to go shopping and decide to do so but can’t because you’re struck by sudden illness, obstructed by the accident on the way, or other things?
B: Well, I think that I still have free will. It is only that I can’t carry it out.
The free will that A and B are talking about is about the act of making a decision, and the criterion for being free will or not being free will is whether limitations exist that restrict or necessitate a change in the decision at the moment of making the decision. If the act of making a decision is without such limitations, then it is a free will; if such limitations exist, then it is not a free will. Obviously, free will by their definitions can occur only sometimes and under some circumstances: when there are no laws, rules, customs, etc. to restrict the choices or make a decision changing necessary. In many circumstances, when there are restrictions from or they have to alter their decision because of the laws, rules, customs, etc., they consider that they don’t have free will. And even if sometimes free will occurs, not all free will can be carried out; some of them will be futile.
Other people may disagree with A and B and think that to be called free will, the will must be carried out successfully too. That is, if limitations exist that necessitate a change in the decision even after the moment of making the decision, then it is not a free will because the already made decision needs to be changed. For them, if one wants to go shopping and decides to do so but can’t because of sudden illness, accident, or other things and has to change the decision, he/she does not have free will in that situation. In any case, the point here is not which criterion is correct; the point is that the criterion for whether the will is free will can be different for different people.
Anyway, the answer to whether free will in this sense exists is “yes”, but only sometimes.
FW2. Free will in the sense of the conscious perception of making a decision
C. I have read reports on free-will experiments, and they show that we don’t have free will.
D. What do you mean?
C. The experiments show that when you consciously make a decision, the perception that you are making the decision is just a mere reflection or report of an unconscious process that has already made the decision for you. Your conscious decision neither makes nor has any effect on the decision that is already made by the subconscious process. So the feeling that you freely make the decision or that you have free will is just an illusion*.
D. Interesting! I had been believing all along that when I consciously made a decision, the decision was being made from my conscious act at that moment.
(* That is the process of generation of a will may be all subconscious, and when the choice is made [a will is generated], a perception of “free will” will be generated [probably from an interaction between frontal and parietal areas] . Thus, the perception of “free will” is not the cause of the will but is the conscious awareness that the will has been generated. At present, there is a lot of evidence that this is the case [5-10], i.e., the perception of “free will” that we have is just an illusion that this feeling is the cause of the decision.)
The free will that C and D are talking about is about the conscious perception of making a decision, and the criterion for being free will or not being free will is whether the conscious perception is the cause of the decision. If the conscious perception is the cause, then it is free will. If not, then it is not free will.
The answer to whether free will in this sense exists is “no” if the experiments’ findings are correct but is still debatable if the experiments’ findings are inconclusive.
FW3. Free will in the sense of the process of making a decision, with determinism of the process as the criterion
E. I believe in free will because I believe that nature is not deterministic and that there is no god, no fate, and no supernatural power to control our destiny (see reference 11 and “free will” in The Oxford English Dictionary). So everything, including our decisions, occurs freely, and we have free will.
F. I believe the opposite. I don’t believe in god, fate, or supernatural power, but I believe that nature is deterministic and that everything happens predictably with predetermined results. So, I believe that free will does not exist.
The free will that E and F are talking about is about the process of making a decision, and the criterion for being free will or not being free will is whether the process is deterministic or not deterministic. If it is deterministic, then free will does not and cannot occur, but if it is not, then free will occurs universally.
The answer to whether free will in this sense exists is debatable, depending on whether nature is deterministic (by itself, god, supernatural power, or something else) or not.
FW4. Free will in the sense of the process of making a decision, with interference on the process as the criterion
G. I believe we have free will most of the time.
H. Really? What are your reasons?
G. Well, most of the time, when we make a decision, the mind freely considers all the relevant factors and freely decides what it considers most suitable for it. As the process of making a decision occurs freely, it must be free will.
H. What are the relevant factors?
G. They are limiting factors like rules, laws, custom, and regulations; physical factors like your health, your strength, and even the traffic and the accident that may happen or the distance that you have to take into account if it involves travelling; your personal factors like your preferences, your goals, and your resources; and many other things.
H. Wow, I didn’t realize that we consider that many factors before we make a decision. But if the condition that the mind freely makes the decision renders the process of making a decision free will, then free will must occur all the time, not most of the time, because the mind always freely makes the decision, doesn’t it?
G. Not really, there are times that the mind doesn’t make the decision freely, such as when it is interfered with by psychoactive drugs, by brain injury, or by mental diseases such as encephalitis. Also, it is theoretically possible that someone can interfere with the process of decision making of another person’s mind with magnetic stimulations or other electromagnetic interference too.
H. Ah, I see. That’s why this kind of free will does not happen all the time.
The free will that G and H are talking about is about the process of making a decision, and the criterion for being free will or not being free will is whether the process occurs freely – without interference – or not. If it occurs freely, then free will occurs. If not, then free will does not occur.
The answer to whether free will in this sense exists is “yes”, most of the time, when there is nothing interfering with the process of making a decision.
These four points of view of free view and criteria to decide free view are just examples of how differently free will can be looked at and how different the criteria can be. Other people may even have other points of view and criteria. Evidently, therefore, free will has several different meanings and criteria. The answer to the questions about this term, such as “Does free will exist?” certainly depends on which meaning of “free will” and what criterion for “being free” are being used.
Because people use the term free will differently for a long time, it is unlikely that any meaning can be claimed to be the correct meaning of the term and will be accepted universally. Every meaning just reflects one aspect of free will, which has many aspects, and is equally correct. Thus, it depends on one’s intention what aspect of free will that one intends to discuss, and it should be clarified in the discussion to avoid confusion. In this theory, the discussion about “free will” will be about “free will” in the fourth sense (FW4): whether the process of making a decision is interfered with or not.
12.2. The process of making a decision
When we decide to do something, we consider many factors, both consciously and unconsciously, before we arrive at our decision. These factors can affect our decision in many ways, such as restrict, coerce, or attract our decision. Usually, several of them interact in our minds before the decision is finalized. These affecting factors are as follows:
- Physical factors, such as not having the required physical capability (to fly, to rescue a derailing train, to stop a natural disaster, etc.); being incapacitated by illness, injury, physiologic condition (exhaustion, sleepiness, hunger, etc.), or other conditions; being incarcerated by police, a criminal, an obstructing accident, etc.; or being too distant in space or time (to help a brother in a different country, to communicate with people in the next hundred years, etc.).
- Non–physical factors, such as customs, rules, and laws of the society and other social institutions (school, business company, sport club, political party, organization, etc.); beliefs, precepts, and taboos (religious, superstitious, tribal, cultural, etc.); advice (medical, scientific, professional, etc.); situations (coercion from a criminal, threats of a looming danger, pressure from an approaching deadline, etc.); or not having enough capability (not having enough skill, not having enough wealth, not having enough clout, etc.).
- Personal factors: personal goals (how much happiness, fame, wealth, etc. are to be achieved), traits (preferences, dislikes, habits, etc.), and instincts (to survive, to avoid danger, to procreate, etc.).
- Consequences: possible good and bad effects of each choice on ourselves, our family, friends, loved ones, co-workers, nation, and other things that we concern (our pets, our plants, environment, humanity, etc.).
Therefore, when we wish to do or choose something, the above factors interact in our mind both consciously and unconsciously, and we automatically form various scenarios, determine their consequences, and compare their advantages and disadvantages (Figure 12.1) until the most desirable choice is found. Then our mind makes the decision to choose that choice [12,13] (Figure 12.2).
Figure 12.1 The Process of Decision Making
Figure 12.2 Natural Will
Thus, usually, the will to choose to do or not to do anything does not happen in our mind spontaneously and instantaneously but is the result of interactions of many factors and takes some time, from milliseconds to seconds, minutes, hours, days, or longer than that, depending on the situation. This kind of “will” happens naturally in normal condition, with the mind conscious, sane, and un-interfered with, so it is called “natural will” (Figure 12.2) in this theory.
There is another kind of “will” that happens in a condition that there is something interfering with the process of making a decision (Figure 12.3). These interfering conditions are:
– pathological conditions, such as encephalitis, temporal lobe seizure, post-ictal or post-concussion psychosis, etc.,
– pharmacologic effects, such as effects of alcohol, psychoactive drugs, toxic substances etc.,
– manipulated conditions, such as electrical or magnetic stimulations (which can theoretically interfere with mental processes to generate a will that is not originally intended by the mind).
Figure 12.3 Un-natural Will
In these conditions, the mind and/or the process that generates the “will” is interfered with. So this kind of “will” is called “unnatural will”.
12.3. Natural will and free will
In a normal condition, although many factors are involved in the generation of a will, as discussed above, the mind processes them freely (both consciously and unconsciously) before generating the will and, when finished, freely generates the will that it considers most suitable for it, all without interference on itself and the will-generation process. Even in a limiting situation (from one or more of the affecting factors in 12.2. above), in which the mind feels that it does not have the freedom to choose what it likes most and is compelled to choose something else, it always has the freedom to decide (both consciously and unconsciously) either to do or not to do as compelled – it always has the freedom to choose what it considers most suitable for it, weighing all the relevant factors. So, in the case of a natural will, the mind always has the freedom to decide; thus, a natural will is a free will in this sense. This is similar to Hallett M’s concept: “Free will might be considered to exist if a person’s brain is functioning normally without coercion.” . In this theory, this characteristic will be used to define free will.
Definition: Free will is the process of the mind to decide freely without interference on itself and its process of making a decision.
It does not matter whether there are limitations (from laws, rules, customs, etc.) on the decision or not; as long as the process of decision making occurs freely without interference, it is free will. Thus, in this sense, we always have free will, even if we have to decide according to the laws, rules, customs, etc. that we do not like. Also, it does not matter whether the conscious perception of making the decision is the cause of the decision or not; as long as the process of decision making occurs freely without interference, it is free will. Thus, in this sense, we always have free will, even if our decision is made unconsciously. Likewise, it does not matter whether the process of making a decision is deterministic by nature (or something else) or not; as long as the process of decision making occurs freely without interference, it is free will. Thus, in this sense, we always have free will, even if our decision is predetermined by nature (or something else).
Socially, therefore, criminals who act by themselves (not under interference from psychoactive drugs, cerebral pathological conditions, magnetic stimulation, etc.), have free will in this sense – that they have the freedom to choose what they consider most suitable for them, weighing all the relevant factors and without interference on their decision making processes – and can justly be held responsible for their criminal acts. And it is the duty of the society to prevent future criminal acts by discouraging potential criminals with proper laws and punishments, which act as deterring factors (the non-physical factors in 12.2.b above) in the process of making a decision.
12.4. Is free will predetermined?
Is free will predetermined? If free will is not predetermined, it will not be known in advance by any means what it will be and will be unpredictable. This means that the will is not fixed either definitely or in some limited probability before we generate it. Yet, in reality, it seems that our wills are already fixed or limited before we produce them. When we go for shopping, we never or rarely buy things we do not want or need – we always buy similar things with similar color, style, brand, etc. to what we used to buy. Our family or our close friends may even know in advance what we will buy when we go out for shopping. So, our wills must already have been fixed definitely or in some limited probability even before we create them. This can similarly be said for other activities – eating, listening to music, talking, dressing, etc. A waiter in our favorite restaurant smiles knowingly when we seat ourselves and offers us our favorite menu. A music shopkeeper eagerly advises the new album that is of our favorite genre when we walk into his shop. Our close friend speaks aloud what we are about to say when we just move our lips. This kind of pre-fixed wills is true not only in wills that are related to our habits or preferences but also in other situations: a mother seeing her beloved child in danger is certain to decide to rescue her child, a woman offered a marriage from her loved boyfriend is likely to say yes, a man threatened with a danger that will end his life will definitely try to escape, etc. Thus, it is evident that our wills are not unlimitedly possible but already fixed definitely or in some limited probability by the nature of our minds: our preferences, our habits, our instincts, etc.: we are always restricted to decide in accordance with our preferences, our habits, our instincts, etc. And because our preferences, habits, instincts, etc. are limited, our decisions and our wills are limited. Thus, behaviorally, we do not have free will in the sense that it is not predetermined and is unlimited and unpredictable.
The next interesting question is whether this determinism is the fundamental nature of everything or just happens specifically in the case of free will. As discussed above, free will results from the free process of making a decision, which involves mental interactions between various mental processes weighing all the relevant factors. As mental interactions are physical processes (Theorem X), the mental process of generating a will is, in fact, a physical process. Therefore, if physical processes are deterministic, then the mental process of generating a will is also deterministic and the will is already predetermined. If the will is already predetermined, then the free will in the sense that it is not predetermined does not exist. But is a physical process deterministic – is nature deterministic?
12.5. Is nature deterministic?
Whether nature is deterministic or not depends on whether nature has order in her manifestations. If nature has order in her manifestations, then an event in nature will not take place haphazardly but will transpire according to some laws. The outcome or at least the probability of possible outcomes will always be predetermined by the initial state of the event and the governing laws, and it will always be predictable. If the governing laws yield definite results, definite outcomes are predetermined and predictable; if the governing laws yield probabilistic (or stochastic) results, probabilistic outcomes are predetermined and predictable.
For example, for a macroscopic object such as a rock that stays still on the ground, with no force acting upon it other than the exactly canceling forces between the gravitational force and the opposing force from the ground, the governing law (the laws of motion – first discovered by Newton and later, with more accuracy, by Einstein)* destines the stone to remain at the same position at the next second, minute, hour, day, and year and forever unless it is acted upon by some additional force. Thus, the future of the stone is already set by the initial state and the governing law and is predictable. In a quantum realm, events of a quantum object, such as an electron, may not occur with definite outcomes, yet they do not unfold haphazardly and are not completely unpredictable – they develop according to some laws and are probabilistically predictable. For example, an electron that is confined within a box with impenetrable walls, without any force acting upon it, the governing law (which, presently, is in the Schrödinger equation of quantum mechanics)* destines the electron to remain in the box, not anywhere else, indefinitely but with only a probabilistic position, not a definite position, in the box at any given time. Thus, the future of the electron is already set by the initial state and the governing law and is probabilistically predictable.
(*These laws and other current physical laws may change [mostly be refined] by new discoveries. This does not mean that there are no definite laws in the nature. It only means that we have not reached the true natural laws (i.e., the very laws that govern the events) yet, and the current laws may be just cruder forms of the true natural laws. Whether we can ever reach the true natural laws is disputable, but they absolutely exist. That all the current physical laws work excellently and consistently is the evidence that the true natural laws exist. Were there no true natural laws, the present laws, which are even cruder, would not work at all.)
Evidence that nature has order and that events in nature progress according to some laws are universal. From the trajectory of a falling apple to the revolutions of planets, stars, and galaxies, from the flow of direct current that lights a flashlight to the flow of alternating current that power our electrical devices/machines and light cities, and from the simple chemical reaction of oxygen and hydrogen to form water to the complex biochemical reactions that generate life, these events always follow some laws, and they can be predicted to a good accuracy by various laws of classical physics if all the involved parameters are known. For particles traveling near light-speed, such as cosmic particles or particles in powerful particle accelerators, or objects with tremendous mass and density, such as neutron stars or black holes, there is a lot of evidence that their events follow some laws that currently are the laws of the general and special relativity theories and can be likewise predicted to a high degree of accuracy. In the quantum realm, events such as those happen in a double-slit experiment, a quantum tunneling, and emission of atomic spectra have proved to follow some laws that currently are the laws in the quantum theory and thus can be predicted consistently, even though only probabilistically (or stochastically).** In more complex events such as in biology, the development of an embryo after a sperm fertilized an egg always follows some complex laws that lead to highly regulated events that are programmed to occur step by step at a scheduled pace, with various forms of embryo appear and then change into another form successively until a mature embryo of that specific species, not other species, is formed – all of these are predictable. Even behaviorally or psychologically, humans’ and animals’ behaviors and responses are stereotypical and follow certain rules, such as to survive, to satisfy bodily needs, to be happy, to avoid danger, and to procreate, and they can be predicted with some accuracy.
(** There is a misunderstanding in a lot of people that events in the Quantum Realm are indeterministic and unpredictable. This is not true. Events in the Quantum Realm do not occur haphazardly; they do occur according to some laws that currently are found to be the laws of quantum mechanics. Events in the Quantum Realm are probabilistically predictable by these laws. The obvious example is the outcome of the single-electron/photon double-slit interference experiments (the hallmark experiments of quantum mechanics): the probability distribution of where particles hit the screen are always the same and the whole pattern on the screen always come out the same, no matter where or when the experiments are done! And all of these are predictable. [See more discussion about this matter “Does quantum theory disprove determinism?” in Section II.])
That is why we can predict the revolutions of the earth, other planets, the sun, and the galaxies with definiteness from now to the very far future. (Even more obvious examples are that we can predict lunar eclipses, solar eclipses, when Shoemaker-Levy 9 would hit Jupiter, etc. very accurately, and that we could predict the path of New Horizon probe, then control and guide it for 9.5 years, past other planets and asteroids, to Pluto, 4.67 billion miles away, so precisely that it finally sent many spectacular photos back to us, who are moving very fast relative to it, accurately). That is why we can control and make use of electricity in various ways to facilitate our living, predictably. That is why we can make use of a lot of controlled chemical reactions to manufacture food, drugs, and many other things for our use, predictably. That is why we can do controlled experiments in powerful particle accelerators, can run predictable nuclear power plants, and can build and detonate predictable nuclear bombs. That is why we can make use of quantum phenomena and can build predictable and manageable electron microscopes, MRI scanners, laser devices, etc. That is why we can do controlled farming and harvest products at predictable times. That is why animals can predict each other behavior and thus can live together harmoniously. That is why our flows of thoughts, speeches, and acts are coherent and predictable. That is why our scheduled lives, our scheduled works, our scheduled traffics (air, train, bus, and others), and our regulated social interactions (holding conferences, playing games, driving on roads, etc.) as they are now are possible and predictable.***
(*** The word “predictable” in this paragraph means “predictable, at least probabilistically”, and the word “predict” is used in the similar sense. Definite predictability is not required here.)
All the “that is why” in the previous paragraph will not be true if nature does not have order. There will be no governing laws. Events in nature will occur haphazardly, and their outcomes and future will not be predetermined either definitely or probabilistically. Nothing will be predictable. A still rock on the ground can suddenly disappear, shoot up into the sky, or change to a cloud (no laws of energy and mass conservation and no laws of motion). An electron can suddenly disappear into nothingness, change orbitals, or change into a proton (no laws of mass, energy, electrical charge, lepton, and baryon conservation), rendering stable atoms and everything else that consists of atoms impossible. Because there are no governing rules, parts of the body (the hand, heart, brain, etc.) can just teleport apart to other places, disappear, or change to something else, rendering life impossible. Nothing can hold together to form entities because there are no rules to hold them together; no reactions between things can occur because there are no rules to govern the reactions; there will be only chaos in the chaotic universe that has no rules. Evidently, the universe as it is now cannot exist if nature has no order. But the universe as it is now – in an orderly grand scale – does exist.
Therefore, it can be concluded that nature has order and that events in nature take place according to some laws. Their outcomes and future are predetermined definitely or at least probabilistically by their initial states and the governing laws. Thus, because nature has order, she is deterministic, at least probabilistically. Consequently, it follows that all physical processes, including the interactions of neural processes and thus of their mental processes, are deterministic, at least probabilistically, like nature. A free will, which is the result of interactions between involved mental processes, is thus predetermined (at least probabilistically). Therefore, fundamentally, free will in the sense that it is not predetermined by nature does not exist.
12.6. The predetermined free will
If free will is predetermined, where do the feelings that free will exists and that it is not predetermined come from?
As discussed above, when the mind decides to do something or choose something among several alternatives, it forms various scenarios, determines their consequences, and compares advantages and disadvantages based on its goals, its preferences, its beliefs, laws or restrictions, etc. of each consequence by using knowledge from its past experiences and related information from its memory until the most desirable choice is found, then the mind makes the decision to choose that choice. When the mind reflects back on this process, it will find that the decision is not predetermined because it does not have the decision in advance. The process of decision making by considering various factors has to be done in order to find the choice, and from its point of view, the process has been done entirely freely without any interference. The mind will thus conclude that it has free will, in the sense that is defined: the process of the mind to decide freely without interference on itself and its process of making a decision.
To be noted is that, from another point of view, the process of decision making flows naturally according to the laws of nature; we just call this natural flow of events deterministic. It is intrinsically deterministic – that is, it is deterministic in the process or is determined by the process itself, not extrinsically deterministic or determined by factors outside the process.
If free will does not exist, does it not mean that, when a criminal commits a crime, it is unavoidable, that he cannot control himself, and that he should not be held responsible for the crime?
First of all, it is true that a crime that happened was physically predetermined by nature. But we are not helpless to prevent future crime because we can manipulate the decision to commit a crime. The decision to commit a crime is the result of interactions of many factors. The most important ones are the psychological, physical, economic, and social background of the criminal, the deterring factors (laws, bond with family, peers, and society, and other factors), and the availability of means and opportunity to commit a crime. It is the duty of the society to increase the strength of the deterring factors, to decrease the strength of the compelling factors, and to restrict the availability of means and opportunity. Proper laws and punishments are means to increase the strength of the deterring factors. So, the punishment of a criminal is reasonable and necessary.
Now, it is a philosophical issue whether we should punish a criminal, whose will is predetermined by nature. Physically, the fact is that if we select to punish a person only if the person’s will is not predetermined by nature, we will never punish anyone because free will in this sense does not exist, and we will never do anything to reciprocate or prevent crime. It is up to us to decide whether this is the right course to choose. Moreover, we should remember that free will can be looked at from other points of view. As discussed in the last paragraph of 12.3. above, a criminal who acts by him/herself (not under interference from psychoactive drugs, pathological cerebral conditions, magnetic stimulation, etc.) has free will in the sense that he/she has the freedom to choose what he/she considers most suitable for him/her, weighing all the relevant factors and without interference on their decision making processes. So, a criminal can justly be punished because, in this sense, he/she has free will. In conclusion, it is essential to remember that free will has several meanings, and it is up to us which meaning of free will is to be used as the basis of judgment.
If we do not have unlimited free will, what are we living for – what is the point of living?
This also seems to be a philosophical or psychological issue. Yet, from a physical point of view as stated before, we do have free will in the sense that we always have the freedom to decide what is most suitable for us for any situation; we only do not have free will in the sense that the decision is unlimited and not predetermined. Biologically, the free will in the former sense is enough for a being to live with satisfaction because it can decide what is most suitable for it. And it would not gain anything more even if it had the free will of the latter sense because it can choose what benefits it most already if it has the free will of the former sense. It might even be detrimental to have free will that is unlimited because if the mind had such unlimited free will, then it would be possible that it would decide to choose what is not most suitable for it or even what is harmful to it. Moreover, if such unlimited free will is possible universally, then animal decisions in general will become haphazard and their behaviors will become completely random and unpredictable. Chaos will ensue, and it will be difficult for animals to survive because interactions with other animals will become unpredictable and erratic. Animals actually benefit better from not having such unlimited free will than having it. And the same is true for us, humans.
Section II. Quantum theory and determinism
12.7. Quantum theory, classical determinism, and probabilistic determinism
If determinism means everything transpires according to some natural laws, not haphazardly, and can be predictable, then quantum theory does not disprove determinism. However, to be precise, although quantum theory does not disprove determinism that allows probabilistic prediction of events, it does disprove determinism that allows exact prediction of events, i.e., it disproves classical determinism. According to quantum theory, all quantum events, such as the future positions of an electron in a box, the scattering of electrons in a double-slit experiment, and the outcomes of spin measurement of entangled photons, do not occur with definite determinism but occur with probabilistic determinism according to certain quantum mechanics rules and can be probabilistically predicted with appropriate quantum mechanics formulae. That’s why the scattering patterns of all double-slit experiments, including single-electron double-slit experiments, always come out in the same pattern (pattern D, Figure 12.4) – the one pattern that is predicted by quantum mechanics – and never came out in other patterns (e.g. pattern E, F, G, or H in Figure 12.4).
Figure 12.4 Possible scattering patterns of double-slit experiment
(Theoretically, the pattern E, F, G, H, or other patterns in the double-slit experiments are possible, but the chance of their occurrences is very very extremely low – practically nil. That’s why they never came out in all laboratories that performed this experiment.)
12.8. The case of entangled quantum particles
Another quantum phenomenon that many people mistake as evidence that quantum theory disproves determinism is the outcomes of spin (or other quantum properties) measurement of entangled quantum particles. Let’s examine the essence of this kind of experiment again to see if it really disproves determinism.
Suppose two particles (such as photons or electron/positron), p1 and p2, were created in an entangled (singlet) state at the point O and sent out in opposite directions (Figure 12.5). Later, measurements are performed on the particles to determine their properties, such as spin.
Figure 12.5 Entangled particles
According to the quantum theory:
- If the spin of each particle is measured along the same certain axis, such as the z-axis, then the outcomes of both particles’ measurements will always be perfectly anti-correlated (as in Figure 12.5). That is, if one particle is measured and found to be spin-up, the other particle will be determined to be spin-down, and vice versa. So, the spin manifestation of entangled particles and its measurement outcome in this case are perfectly deterministic and perfectly predictable!
- If the spin of each particle is measured along different axes, quantum theory predicts that the probability that both particles will be found to have opposite spins (one spin-up, the other spin-down) relative to their measurement axes is (1+cosθ)/2, where θ is the angle between the chosen axes [14,15]. For example, at θ = 0 (parallel axes), the probability is 1 (which is the case in Figure 12.5 above); at θ = π/2 (perpendicular axes), the probability is 0.5; and at θ = π (anti-parallel axes), the probability is 0 (i.e., the probability that first particle is spin-up relative to the Z-axis while the second particle is spin-down relative to the (-Z)-axis, or that both particles are spin-up relative to the Z-axis, is 0 – this can never happen). This probability prediction has been found by experiments to be true for all pairs of measurement angles, not just the three angle pairs in the preceding examples. Thus, once one particle is measured to be spin-up relative to a certain axis, the other particle is determined to be spin-down relative to another certain axis with some definite probability that is predicted by quantum theory. This indicates that, like the case in 1., the manifestations of spins (and other characteristics, likewise) of entangled quantum particles and their measurement outcomes are probabilistically deterministic and probabilistically predictable – they are not absolutely non-deterministic and are not absolutely unpredictable.
- The quantum predictions and the classical predictions for spin measurements when the angles are 0, π /2, and π are the same. However, the quantum predictions for spin measurements in other pairs of angles are in conflicts with classical predictions (or predictions on the assumption that spin values exists by themselves or by some hidden variables before the measurement , which is called the hidden variable theory). Bell (1964) proved mathematically that, in a certain setting, measurement outcomes predicted by any hidden variable theory will satisfy a certain inequality  (which is now called Bell’s inequality and is in various forms) but that measurement outcomes predicted by quantum theory will violate this inequality. After that, many experiments were set up to check whether the outcomes of measurements of spin (or other quantum properties) of entangled quantum particles satisfy this inequality or not. If they satisfy the inequality, then the hidden variable theory is correct – which means that spin or other quantum properties exist in quantum particles by themselves or by some hidden variables even before any measurements are made. If not, then the hidden variable theory is incorrect – which means that spin or other quantum properties do not exist in quantum particles before any measurements are made and that they come to exist in both particles only when the measurements are made on either particle. So far, these experiments (which now commonly called EPR [Einstein-Poldalsky-Rosen] experiments) have found that Bell’s inequality were violated (i.e., not satisfied), which means that the hidden variable theory is not correct. Additionally, these experiments found that the measurement results were very close to those predicted by quantum theory , which substantiates that quantum theory is correct. Therefore, at this point, it must be emphasized that these experiments do not prove that quantum particle spins (or other quantum properties) are unpredictable; they only prove that the predictions based on hidden variable theory are wrong and that the predictions based on quantum theory are correct. Thus, contrary to the widespread misunderstandings, these experiments do not disprove determinism. Quite the opposite, these experiments attest that quantum predictions are correct, which means that quantum particle spins (and other quantum properties) are indeed determined (by some unknown laws)# and predictable (by quantum theory)!
#(These unknown laws may involve effects that are faster than light-speed – or spooky action at the distance, in Einstein’s words – because, when the spin of one entangled quantum particle is measured to be in some state, the spin of the other entangled quantum particle will instantly get into some certain state too, no matter how far apart the two particles are. Again, the probability of the state that the second particle will get into is not totally random and unpredictable but probabilistically determined by these unknown laws and probabilistically predictable by quantum theory.)
In summary, if all kinds of determinism are false, then everything will transpire haphazardly, not according to any natural laws, and will be totally unpredictable – that is nothing, not even quantum events, is predictable. But, so far, the quantum theory has been verified by a multitude of experiments to be true – it predicts quantum events correctly. So, the quantum theory itself verifies that absolute indeterminism – that all kinds of determinism are false and that everything is totally unpredictable – is not true. Everything, including quantum phenomena, is at least probabilistically determined and probabilistically predictable.
We should be thankful that nature has order
and is deterministic,
because, if she were not so,
there would not be everything that we see around us,
there would not be our houses, our friends, our families,
and there would not be us.
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Keywords: free will, natural will, unnatural will, predetermined free will, determinism, classical determinism, probabilistic determinism, quantum indeterminacy