Determinism, causality, locality and free will

Determinism is what we seek when we study the natural sciences. The principal laws of nature are described by Science as having a deterministic character: All scientific theories are based on the verified results of repeated tests and observations, and their mathematical formulations perform with precision for the benefit of successful scientific predictions.

Perceiving the world through our senses, there seems to occur in the natural processes a logical causal inference that we understand as being deterministic. The epistemology of science presupposes this classic deterministic model for any scientific experiment: - given the same initial conditions, each repetition of the same experiment will yield the same results. Mathematical deterministic equations produce determined results of a fixed type, and we are able to calculate this result because deterministic equations do not have random variables in their terms.

orbitals

A new epistemological way of understanding Nature is given by the assumption that the laws governing microphysics (individual atoms, electrons, photons etc.) cannot set predictions based on past causes and effects of what will happen next; they can only point out all the probabilities and reveal the chances of each one to take place.

The unpredictable behavior of the atom does not follow a strict causality (from point A to B to C), and we cannot infer anything with precision because these cause-effect links are broken. Because of this, the results of quantum mechanics calculations are not exactly deterministic ones.
If we measure a superposition of quantum states, we get as a result this or that state, depending on the odds. However, our measurement process is causal, because when we measure a quantum system in a superposition of states, coherence is destroyed and the whole system collapses/reduces to one state during the measurement, but not before it. The effect of the measurement occurs after its cause, you cannot change the outcome of an experiment that was done yesterday.

Despite the non-deterministic character of the atom, we can deterministically calculate the probability of a random event happening by employing the quantum formalism. The mathematics of probabilities has malleable equations, the workable results are not determined but balanced and flexible. 
Also, if the equations depended on chanciness or stochastic variables, the solutions would be random and meaningless.

On the other hand, whether we will be able to achieve any precision in order to predict anything past the quantum uncertainty postulate, the bottom line may lie at Nature's own fuzzy physical reality (space-time continuum alongside with single interactions between standing waves).

If all the historical data of a particle, from past to present, does not contain enough information to predict its future destination, and if this information is not contained in its last past moments (as in the classical differential equations), then where is it? After all, something must regulate the behavior of a particle. Some theories say that we cannot perceive the source of information controlling the particle behavior because it comes from the future. The information coming from the future could fill out deterministic gaps in the present. Moreover, the theory of Chaos explains why it might be unattainable or impossible to predict all the micro and macro events in real life (whether fundamental determinism exists or not).

All the repeated regularities patterns that we observe in Nature are combinations of (not reducible) components arranged in settings that spell out all these regularities. Combinations of numbers, words, letters, even the order of atoms form patterns that we recognize as regularities that can be reduced to a compressed state, where the randomly outspread components continue to bring meaning to us by means of new configurations, like compression codes. This information may be expressed in real numbers using digits, or in binary combinations of  0 and 1. Other information-words are comprised of letters in a certain order and can also be represented by symbols.

Any locality event, such as speaking some words or having a measurement done causes the localization of some information that was previously undefined increasing the amount of defined information stored in the Universe. The quantity of information never lessens, as information does not disappear. The amount of information stored in the Universe since the big bang is increasing, as a result of the realization of newly defined information from the indeterminate quantum nature source at every instant; emerging out of randomness to take its place in a measurement that will outline some pattern in the Universe. Prior to measurement, its pure and stochastic randomness has no meaning. For this to happen, a thinking construction in order to make sense is required. 

Measurements of quantum localizations give us more information about the random quantum states of reality. The continuous emergence of new information depends on the fact that the future is in fact truly undetermined, as seen in the quantum experiments, where the new information has the opportunity to come into existence, sometimes without a past causality, but with future effects. 

Physics information theory says that a particle is localized on the wave function whenever a new permanent information structure is created, the information that can be observed.

If the laws of the microworld are of an irreducibly probabilistic type, determinism must be false. These irreducible probabilities of the quantum realm are the foundations of every genuine objective event observed in our world.

Maybe one day we will be able to reach a sub-quantum theory in order to salvage the deterministic ontological status of the object we measure. This, if fundamental realism is true, and if the quantum objects hold well-defined properties and fixed real values, even when they are not being measured. We would need a "quantum plus-ultra" theory for a complete description of the many possible quantum states of a system, which are presently acknowledged via probabilistic epistemological statements only.

At this moment, the probabilities theory is the one that best describes the wave function. If we remove the uncertainty from the probabilities, what we get is a model for localized particles.

a quantum experiment

Free will

The deterministic model of classical mechanics events (that can foresee results and events in physics with the aid an accuracy mechanism), and the nondetermined probabilistic model of quantum mechanics (describing the inexact behavior atoms), both coexist at the same time in big objects comprised of many atoms. The combined pure and mixed quantum states of all the atoms of a large system go beyond the boundaries of quantum effects whenever classical determinism becomes evident. In Nature, we find both models working together: While some things are predetermined, others are not.

An exclusive deterministic model for humans would not produce us any opportunity for creativity or morality, while an entirely non-deterministic model contains no meaning, as randomness is not enough to explain the existence of free will.

Then why do we think that we have a behavioral choice? An answer to this question is that our sense of having a behavioral choice was carefully selected by evolution. A well-developed human sensation of having free will and to be able to select possible behaviors has a high survival value. People who, for some reason, lose the certainty that they can plan their alternatives and choose possible behaviors, tend to become fatalistic and stop fighting for survival. The belief in these free-will decisions is a necessary condition to have free will. When we plan the future and think about the possible actions to undertake, evolution makes us feel that our entire planning effort pays off, that we control what we do. If the efforts of our brains to model reality, predict the future and make good results possible cannot reach our sense of self and our will, fatalism and other self-destructive behaviors might set in. 

Thoughts are free and sometimes seem to come to mind from some unexplained origin, from an inspiration (word meaning in brought spirit), while our actions appear to stem from our own initiative. Thoughts and actions are capable of producing indeterminate options and therefore free will is not causal, a free action is possible without a cause. The analogy between an atom having its free will to pick one of the possible quantum leaps and the free will of a person to choose alternative behaviors is far too remote to be taken into consideration.

For either situation, the results are not predetermined, or else we cannot account for all factors influencing the outcome: a decision in the physical world is a fact that has future consequences without necessarily being causally connected to the past.

Philosophers should thoroughly discuss issues such as determinism, causality, and free will, while the scientists should struggle to prove that some of these philosophical answers are unfounded. Once a wrong philosophical answer is dismantled and destroyed by science, it no longer holds significance, and this problem disappears. This is so because Philosophy helps us to understand exactly what a scientific theory means, and which challenged philosophies that theory destroys. Hypotheses and philosophies are often cloudy and sometimes absurd, but it is up to Science to go for and sort it all out.