Determinism Extended
to Better Understand and Anticipate

A Bridge between Science and Philosophy
for Rational Thinking

Daniel MARTIN

Determinism Extended
to Better Understand and Anticipate

A Bridge between Science and Philosophy
for Rational Thinking

Version date: August 7, 2008

Daniel MARTIN

http://www.danielmartin.eu/emailaddress.htm

Purpose of this text

While reading a few books from well-known contemporary French philosophers, I appreciated their intelligence, their considerable philosophical knowledge, and their intellectual honesty. I also noticed, in a few places, small inaccuracies that implied two things: their scientific knowledge is one or two centuries behind the times; and their mostly literary culture has prevented them from acquiring as much experience of rigorous thinking as I expected they would have.

I therefore decided to offer them, in the above book, an update of scientific knowledge presented from a philosophical point of view; I also dedicate this contribution to intellectuals interested in rational thinking. It is organized using determinism and the causal postulate as a unifying thread, but I added to those two principles a number of philosophical clarifications based on recent scientific advances.

This text presents the ideas of the above book to help the reader decide if he wants to take time to read it. All scientific terms such as "eigenvalues" and "matter waves" are explained in the book; understanding them fully is not necessary in this introductory text.

Daniel MARTIN

Philosophical determinism

Definition

The traditional definition of determinism was published by the French mathematician, physicist and astronomer Pierre-Simon de Laplace in his book of 1814 "A Philosophical Essay on Probabilities":

"We should consider the present state of the Universe as the effect of its previous state and the cause of the state that will follow. An intelligence which, at a given time, would know all of the forces that govern nature and the respective states of all its beings – assuming it is vast enough to analyze that data – would grasp in the same formula the movements of the largest bodies of the Universe and those of its lightest atom; nothing would be uncertain for it, the future and the past alike would stand before its eyes."

(That intelligence is often called "Laplace's demon").

According to this founding text, philosophical determinism asserts that:

§ The future is completely determined by the present;

§ The future is completely predictable given perfect knowledge of the present;

§ Perfect knowledge of the present suffices to mentally reconstruct all of the past;

§ For each present situation there is a single causal chain (of events or situations) that starts infinitely far in the past and extends infinitely far in the future.

Philosophical determinism is contradicted by some facts

Philosophical determinism, which promises the possibility to predict all of the future and to mentally reconstruct all of the past, is contradicted by several phenomena of nature quoted in the book. Since a single counter-example suffices to contradict an assertive statement, here is one.

Radioactive decay (nuclear fission)

The atoms of a sample of uranium 238 will decay (decompose) spontaneously, without any cause other than passing time; an atom of uranium will decay into an atom of helium and an atom of thorium. The number of atoms of uranium 238 that decay per unit of time follows a known law: 50% of the atoms of a sample of arbitrary size will decay in a fixed amount of time T called "the half-life of uranium 238"; then half of the rest (one quarter) will decay during the next period of time T; then half of the rest (one eighth) will decay during the next period of time T, etc.

Natural (spontaneous) radioactive decay is attributed to the instability of the excitation energy of the neutrons and protons of a radioactive atom's nucleus. That energy varies spontaneously – a phenomenon deemed impossible in traditional deterministic physics, because it attributes an atom's decay to chance. Due to a tunnel effect, that excitation energy may sometimes exceed the potential energy that holds the nucleus together (known as the element's fission barrier), causing such a considerable deformation that the nucleus decays. The tunnel effect and its spontaneous nature can only be explained using the mathematical tools of quantum mechanics, which contradict traditional determinism by introducing spontaneous variations of energy levels and probabilities in the occurrence of an event.

Contrary to the promise of philosophical determinism to predict the future, it is impossible to know which atoms will decay during a given period of time, and when a given atom will decay. Radioactive decay follows a statistical law that applies to a population of atoms, but does not predict the evolution of a given atom.

Also, when a sample contains decayed atoms, it is impossible to know for any one of them at what time it decayed, which contradicts philosophical determinism as a principle for mentally reconstructing past events knowing the current situation.

Therefore, philosophical determinism cannot keep its promises to predict the future and mentally reconstruct the past: this principle is false in the case of radioactive decay. And since, according to critical rationalism explained in the book, a single counter-example suffices to disprove an assertion, we shall consider philosophical determinism erroneous, in spite of the fact that its definition is in some dictionaries.

Causality and determinism

Ever since man needs to understand the world around him and predict the evolution of situations, knowing determinism is important for rational thinking. And since philosophical determinism does not keep its promise to predict, we will delve into the issue of understanding and predicting on a less ambitious basis. We will start over from the causal postulate on which philosophical determinism is based, and ignore for the time being its promises to predict the future and reconstruct the past.

The causal postulate

Ever since man existed, he noticed links between situations and phenomena: a given situation, S, is always followed by phenomenon P. A natural process of induction made man assert a general postulate: "The same cause always produces the same effect". Reflecting on the conditions that governed the chains of events he observed, he inferred the following causal postulate stated below as a necessary and sufficient condition:

Definition of the causal postulate

§ Necessary condition: in the absence of the cause, the consequence does not happen; every observed situation or phenomenon was preceded by a cause, and nothing may exist without having been created.

§ Sufficient condition: if the cause exists, its consequence happens (it is certain).

However, that consequence is an evolution phenomenon, not a final outcome: we renounce the promise to predict the result of the evolution and retain only the postulate that it is initiated.

In some favorable cases, the causal postulate meets the need of rational thinking to understand and predict:

§ The necessary condition allows explaining a consequence by following the flow of time backwards up to its cause;

§ The sufficient condition allows predicting a consequence by following the flow of time forwards from its cause: the evolution is certainly initiated.

Scientific determinism

In order to better understand and predict, rational thinking requires an addition to the above causal postulate; it needs a rule that guarantees stability (reproducibility) in time and space.

Stability rule

The same cause always produces the same effect: the effect of a cause is reproducible. The physical laws consequences of a given cause are stable; they are the same everywhere and at all times.

Consequently, a stable situation never evolved and never will; it is its own cause and its own consequence! Taking into account an evolution after time t requires changing the definition of the observed system. In fact, the flow of time can only be observed when something changes; if nothing changes, time seems to stop. The stability rule is not trivial; one of its consequences is Newton's first law of motion, the law of inertia:

"The velocity vector of a body which is motionless or moves in a straight line at constant velocity will remain constant as long as no force acts on the body."

As far as determinism is concerned, this law implies that motion in a straight line at a constant velocity is a stable situation that will not evolve until a force is applied to the body; such a stable situation is its own cause and its own consequence!

The stability rule allows inducing a physical law of nature from a collection of cause-consequence sequences: after seeing the same cause-consequence sequence many times, I postulate that the same cause always produces the same consequence. We may now group the causal postulate and the stability rule to form a principle that governs all laws of nature describing a time evolution, the postulate of scientific determinism.

Definition of scientific determinism

The postulate of scientific determinism governs the time evolution of a situation due to laws of nature, in accordance with the causal postulate and the stability rule.

The deterministic nature of a law of the Universe does not entail the predictability of its results or their precision. Philosophers who believe the opposite are mistaken.

Scientific determinism and predicting

In the definitions of the causal postulate and of scientific determinism we renounced predicting evolution results. Since we know that a cause initiates the application of a law of nature, predicting an evolution result requires predicting the result of such a law.

Nature recognizes situations-causes and automatically initiates applicable laws each time, but it doesn't know the concept of result, a notion of interest only to humans. This remark allows us to eliminate right away a cause of unpredictability independent of nature: supernatural intervention. Obviously, if we admit that a supernatural intervention may initiate, prevent or alter an evolution, we renounce predicting its result. We will therefore postulate materialism; we will also assume that no intervention originating outside our Universe or independent of its laws is possible. The opposing doctrines of materialism and spiritualism are described and debated in Part 2 of this book, before Part 3 which is devoted to determinism.

Three types of reasons which prevent predicting the result of a deterministic law of evolution are: imprecision, complexity and chance.

Imprecision

Since the causal postulate and scientific determinism do not promise to predict a result, they do not promise to predict its precision either, when it is predictable; and this is regrettable since man often needs precise results.

Here are cases where the precision of the calculated or measured result of an evolution law may be considered inadequate by man.

Imprecision of the initial values of an evolution, or of a result's measure

An evolution law applies to variables. If those variables are known with insufficient precision, the calculated result may also be too imprecise. If a quantity is measured, that measure's precision may be inadequate.

Imprecision or non-convergence of calculations

If the calculations required by a formula or to solve an equation are not sufficiently precise, the result may be imprecise. This problem is serious, for example, when solving a system of equations requires inverting a matrix with thousands of rows and columns: inadequate precision may produce degeneracy, which makes calculating the inverse matrix impossible; it may also simply produce a result that is insufficiently precise.

When a physical phenomenon has a mathematical model, a computing algorithm in the model may sometimes be unable to provide its result, for example because it converges too slowly. Sometimes, the algorithm stops because a calculation is impossible: the book shows such a case in wave propagation.

Chaos

Sometimes a very small variation of a phenomenon's initial data, too small to be controlled, produces a considerable and unpredictable variation of the result of a phenomenon whose law is precise. This happens, for example, for the direction in which a pencil standing vertically on its tip will fall. It also happens when predicting the position, thousands of years ahead of time, of an asteroid whose motion is perturbed by the attraction of planets.

Chaos is a phenomenon that amplifies effects enough to switch from one solution of a mathematical model to another. It occurs, for example, in turbulent flows of liquids and in genetic evolution of species, often producing solutions grouped in the vicinity of particular points of phase space termed attractors. In practice, chaos limits the predictability horizon.

Quantum physics

The book quotes several laws of physics where nature limits precision. Examples:

§ When a corpuscle moves in a field of electromagnetic force, its position and velocity cannot be determined with an uncertainty better than half the width of the accompanying wave packet. No matter how fast a photograph is taken (in a thought experiment), the corpuscle will always appear fuzzy.

Worse still, the more precise the determination of position, the less precise that of velocity, and vice-versa.

§ Nature's precision refusal may cause quantum fluctuations. Example: at a point of void space between atoms or even between galaxies, energy may vary suddenly without any cause other than nature's refusal of its precision and stability. This energy variation ΔE may be all the greater that its duration ΔT is small: the product ΔE.Δt should always be less than a universal constant noted ½ä. On average, however, the energy at the fluctuation point remains constant: if nature "borrows" energy ΔE from surrounding empty space, it returns all of it less than Δt seconds later.

This phenomenon is far from negligible: a short while after the Big Bang when the Universe was born, it caused the formation of areas of high energy density that later became galaxies. From a predictability standpoint, it is impossible to predict where a fluctuation will occur, or when, or with what energy variation ΔE.

§ At atomic scale, nature allows superpositions of equation solutions. An atom may travel several trajectories simultaneously, producing interference fringes in Young's experiment, when it interferes with itself by going through two parallel slits several thousand atom diameters apart.

A molecule may be in several states at the same time. Example: quantum mechanics predicts that an ammonia molecule NH₃, whose shape is a tetrahedron, may have its nitrogen atom vertex on one side or the other of the plane of its 3 hydrogen atoms. It predicts that this plane (whose 3 hydrogen atoms are light) may spontaneously switch to the other side of the (heavy) nitrogen atom vertex because of tunnel effect, without any intervening physical force or absorption of a photon's energy. The hydrogen triangle may oscillate between the two symmetrical positions with a frequency in the range of centimetric wavelengths. This prediction of quantum mechanics is confirmed by radio astronomy observations, both in light absorption and emission by ammonia molecules of interstellar space.

When an experiment determines the state of an NH₃ molecule, nature chooses randomly which of the two symmetrical states it will reveal. Its choice is not completely random, it is an element of a predefined set of two elements called spectrum of eigenvalues of the experimental setup: natural randomness is limited to the choice of one of the values of the spectrum, all values of which are known precisely. In the case of the above ammonia molecule, nature chooses between two solutions, each with a certain predefined energy and shape.

§ Nature's refusal to satisfy man's need to know is spectacular in the non-separability phenomenon. The book quotes an experiment where two photons produced together (termed entangled photons) make up a single whole object even when the photons are 144 km apart: if one is absorbed, the other disappears immediately; the consequence is propagated from one to the other at infinite speed since they are part of the same initial object, which conserves its wholeness while it is deformed by the photons' motions.

In quantum physics, many human wishes of result prediction, precision or stability are denied by nature.

Relativity and causality

The book describes in detail a property of space-time, due to the speed of light, which compels one to reflect on the definition of the causality which governs the transition from one event to another. In certain specific cases, two events A and B may be seen by some observers in the order A then B, and by others in the order B then A! The first group of observers will know that A occurred before B, and will draw consequences different from observers of the second group, who will see B appear before A.

Complexity

The overall effect of many perfectly deterministic phenomena may be unpredictable, even if each phenomenon is simple and its result is predictable. Example: consider a small closed container which holds billions of identical molecules of a liquid or a gas. Since these molecules have a temperature above absolute zero, they keep moving; their kinetic energy results from their temperature. Their agitation makes them bounce into each other and against the container's inner surface, their motion obeying well-known deterministic laws. In spite of their deterministic motions, it is impossible to know the position and velocity at a given time t of all molecules, because there are too many; therefore, it is impossible to calculate (predict) the position and velocity one second later of one particular molecule, because in the mean time it has bounced thousands of times against other moving molecules and against the inner surface.

This impossibility is very general: the combined effect of many deterministic phenomena with predictable individual evolutions is an unpredictable evolution, whether these phenomena are of the same type or not. From a philosophical point of view, we can assert that the complexity of a phenomenon with deterministic components generally produces an unpredictable evolution.

In theory that unpredictability does not exist, but in practice it does. It does not affect nature, which never hesitates or predicts the future, but it prevents man from predicting what nature will do. And nature's unpredictability grows with the number of simultaneous phenomena, their diversity, and the number of their interactions.

Actually, interactions between phenomena also impact their determinism. An evolution whose result impacts the initial conditions of another evolution impacts its stability rule, therefore also the reproducibility of its determinism, which hinders even more the prediction of its result.

That is why even though the most complex phenomena (the phenomena of living beings, of man's psyche, and of human society) are based only on predictable deterministic evolutions, their results are generally so unpredictable that man is under the impression that nature does anything. We shall come back to this issue below.

Chance

From a philosophical point of view we should stop believing in chance as a principle of unpredictable behavior of nature. The Schrödinger equation, whose results are probabilistic matter waves, is deterministic in the traditional sense, and so is Newton's second law of motion, which is also based on energy conservation: a given initial situation always produces the same result, which is sometimes a set of results instead of a single result. No unpredictability there, nature is never unorthodox: in a given situation its reaction is always the same.

Man must get used to the fact that some situations produce multiple consequences: either several laws of evolution acting in parallel, each producing a single result; or a single law of evolution producing multiple results. And when man wants to know the result of evolution (for example using a measuring device), nature chooses one randomly among those resulting from the initial situation and displays it.

Nature's choosing process follows a simple rule governed by a form of determinism that applies to a set of alternatives instead of applying to a single alternative: if a given experiment is iterated a large number of times, each possible alternative appears the same number of times. This set determinism also governs other phenomena; example: radioactive decay of uranium 238, where determinism governs the proportion of decaying atoms per unit of time, not the choice of a particular atom that will decay.

Similarly, there is no randomness in the position, the velocity or the energy of a corpuscle, there is indetermination, a refusal of nature to grant us the possibility of infinite precision which would make us feel comfortable; and this refusal is due to the wavelike nature of each corpuscle.

The unpredictability associated with local energy fluctuations is not due to chance, either. It is a consequence of Heisenberg's uncertainty principle, which states that during a short time interval Δt an energy is not defined with an uncertainty less than ΔE, where ΔE.Δt ≥ ½ä. Those fluctuations only embody a refusal of precision on the part of nature, a refusal which only lasts for a short while and does not alter the average local energy. We should accept the existence of those fluctuations like we accept the imprecision on the position of a moving corpuscle, located "somewhere" in its wave packet: in none of those cases does nature act randomly by doing anything. Other examples of nature's limited precision are given in the book in sections that describe chaotic phenomena.

Conclusions

§ Randomnes