Defining Determinism as a Consequence
of Properties of the Universe
Version date: June 23, 2008
We saw in "The Definition of Determinism Needs Updating" that the definition of traditional determinism lends itself to criticism because it contradicts some of nature's laws of evolution; this is the case, for example, for thermodynamic irreversibility and measures in quantum physics.
This text shows why the uniformity of some laws of the Universe compels us to extend the definition of determinism. Details and justification of its statements are in the book "Determinism Extended to Better Understand and Anticipate - A bridge between science and philosophy for Rational Thinking".
About the definition of determinism
Usually, a definition describes the meaning of a word. Such a descriptive definition being too restrictive for extended determinism, I use below a constructive definition allowing an infinite extension of this notion deduced from properties of laws of the Universe.
Uniformity of the laws of nature
A quick refresher about postulates of materialism and reality
§ In keeping with materialism, we postulate that reality (the Universe) exists independently of human representations, and that man can understand the Universe with a scientific approach.
§ The causal postulate (see details below) is a principle that governs – whether the subject is reality or its mental representation – the evolution from a cause to its consequence.
Properties of the laws of the Universe
We know that nature, as described by physical laws, is uniform. This uniformity of the Universe has fundamental consequences such as the conservation of momentum, of angular momentum, and of energy. Some characteristics of this uniformity are:
§ Space is homogenous and isotropic: it has the same properties at every point and in all directions.
The homogeneity and isotropy of the Universe shortly after the "Big Bang" were proven with an extreme precision by the discovery, in 1965, of the cosmic background radiation and its measure by the COBE (Cosmic Background Explorer) satellite and its successors: the energy density of the primitive Universe was the same at all its points, but quantum fluctuations occurred and still occur today. Inflation theory explains the extreme homogeneity measured at astronomical scale, and the presence of galaxies due to the fluctuations.
§ The Universe has fundamental constants, whose value is (and always was) the same everywhere and in all circumstances. Examples are:
· The speed of light in a vacuum, c;
· The electric charge of an electron, e, and its rest mass, me ;
· Planck's constant, h; etc.
§ The laws of physics are stable (invariant) when space or time vary. This property appears, for example, in astronomy: looking at a remote stellar object, for example at a distance of 1 billion light-years, shows the situation at that place one billion years ago; observations show that the physical laws that governed evolutions at that time were exactly the same as today.
Even when a law varies with time, there always is a stable law that describes or even explains the variation. Example: the radius of the Universe varies; this variation was noticed in 1927 when astronomers observed its expansion: the recession speed of distant galaxies increases with their distance, but remains the same in all directions. The radius of the Universe appeared to increase at a steady rate. Later, astronomers discovered that this rate of expansion varies too: the expansion speed accelerates. Finally, cosmologists discovered that at the very beginning of the Universe's existence, a very small fraction of a second after the Big Bang, its expansion speed was fabulously fast during a very short time, billions of times faster than the speed of light.
(The expansion speed of space is not limited by the speed of light, c, since it does not displace matter or energy.)
The scientific laws of the Universe are consistent (non-contradictory). They complement each other without ever contradicting each other. They respect the three fundamental laws of logic, formulated by induction from man's observations of nature.
§ Law of contradiction: a law of nature is true or false, but not both true and false; this law requires non-contradiction: no new law may be true if it contradicts an existing law without replacing it.
§ Law of excluded middle: a law of nature (whose text must be falsifiable, in accordance with critical rationalism, explained in the book) is either always true – and it has never been disproved - or false, if it has been disproved at least once; it can't be sometimes true and sometimes false, or have a probability of being true, or a probability of not being applicable in some special unexpected circumstances.
§ Principle of identity: a law (or a situation, or an evolution) is what it is, exactly what it is; it cannot be different from what it is.
Completeness of the laws of nature. (This is another expression of the causal postulate.)
§ Nature has all the laws required to account for all phenomena: this is Kant's postulate of complete determination.
· Nothing proves that all laws may be discovered, even given enough time, research personnel and talent. Nevertheless, our scientific knowledge makes progress and we have good reasons to continue engaging in research;
· In addition, all fields of truly scientific knowledge are based on axiomatic systems, with their a priori facts and deduction rules.
§ No phenomenon occurs without cause, or without respecting a stable law of nature; this excludes the possibility of transcendent or supernatural interventions.
§ A law is always respected; otherwise, it is not a law: in identical circumstances, consequences will always be identical, no phenomenon may "forget" to occur, or occur differently; in short, identical causes always produce identical effects.
However, when one cause produces a set of effects (the book provides several examples) and nature only retains one effect of the set, its choice may be random and we may only know in advance the probability each element has of being chosen.
Consequence: no law has a probability of being true or applicable; it is always applicable or it is not applicable.
Origin of the causal postulate
Some laws of physics describe evolutions of a system from an initial state to a final state. Their existence and stability when time or space vary suggest the postulate of causality: since the action of a given law on a given initial state is always followed by the same final state which depends only on the initial state and the law, reasoning by induction encourages us to postulate that this evolution is always governed by a principle, the causal postulate, which may be enunciated as follows:
In the Universe, whatever exists or happens has a cause and obeys laws.
This postulate is legitimate since it is verified by countless observations and is not contradicted by any. According to the definition of scientific truth of critical rationalism, this postulate may be considered a law of causality until proven wrong.
The existence of unexplained phenomena does not contradict this postulate; it encourages us to strive to find an explanation. It also encourages us to remain vigilant in case a new fact appears that cannot be accounted for by the law supposed to explain it, or that contradicts the law; we may have to alter the law or replace it. More details about the legitimacy of this postulate are in the book.
Definition of extended determinism
In accordance with the above, we will postulate the uniformity, stability, consistency and completeness of the laws of the Universe, and draw the following conclusion about the causal principle. Since every phenomenon has a cause, and the effect of that cause is uniform throughout space and stable in time, we shall define extended determinism as follows:
Extended determinism is the principle that governs the evolution from a cause to its consequences due to all applicable laws of nature.
We will first provide details about this definition; then we will justify it.
Details about this definition
The above definition of extended determinism must be complemented by:
1. The definition of traditional scientific determinism by a necessary and sufficient condition (the causal postulate), and a stability rule:
· Necessary condition: in the absence of the cause, the consequence does not happen; every observed situation was preceded by a cause, and nothing may exist without having been created;
· Sufficient condition: if the cause exists, its consequence happens inevitably.
Example: I hold a rock in my hand; if I let it go, it falls.
· Its fall is due to my act of letting it go, a necessary condition;
· If I let it go it falls, a sufficient condition.
This necessary and sufficient condition defines one of the principles of logic: the causal principle (also termed principle of causality or causal postulate).
· The necessary condition explains a consequence when one follows the flow of time backwards up to its cause.
· The sufficient condition enables the prediction of a consequence when one follows the flow of time from its cause toward the future… if causality implies predictability, which is not always the case, as the book shows.
The sufficient condition only implies that the cause will initiate the application of corresponding evolution law; but for some evolution laws it is impossible to predict the result before the evolution, or measure it after, with arbitrary precision.
Explaining (in the sense of causal understanding) and predicting justify the importance of determinism in rational thinking.
· Stability rule: the same cause always produces the same effect: the effect of a cause is reproducible. The physical laws whose action produces the consequence of a cause are stable; they are the same everywhere and at all times.
A consequence of this stability rule is that a stable situation never evolved and never will; it is its own cause and its own consequence! To observe an evolution after time t requires changing the definition of the observed system. In fact, the passing of time can only be observed when something changes; if nothing changes, time seems to stop.
2. Extensions and precisions provided below, such as: multiple consequences of a unique cause, random choice between multiple solutions, limited precision, etc.
Justification of this definition of extended determinism
We have already seen that the founding principles of extended determinism (the causal postulate, the stability rule, the consistency rule, and the completeness postulate) are justified by properties of the Universe, from which they were derived by induction and that no observation has ever contradicted. We shall now justify the uniqueness and the general scope of extended determinism implied by the definite article the before principle and the adjective all before applicable laws.
An in-depth exploration of the action of determinism brings up questions about the transitions from causes to consequences, such as:
§ Can a unique cause produce several consequences, and if it can, will they all be retained or only one? (Quantum physics provides an answer).
§ How do randomness and imprecision (observed, for example, in quantum physics) intervene in natural phenomena, and what are their relationships with determinism?
§ Does a deterministic process always produce a predictable outcome? (The book examines cases where the answer is no.)
§ How long can it take between a cause and its consequence?
Constructive definition of extended determinism
To take into account the answers to the above questions – and to many more that appear in an in-depth examination of the action of determinism – our approach will start with the definition of scientific determinism and build the definition of extended determinism by incorporating the various rules of evolution that appear when considering one by one the various laws of nature.
The theoretical justification of this approach was established by logicians who showed how an axiomatic system can be completed progressively, as new truths or deduction rules that cannot be deduced from existing axioms are discovered in the field structured by the axiomatic system. This subject is discussed in the book.
The practical justification of this approach is a consequence of it being part of the scientific method, which adds new laws to existing laws or replaces them, in the order in which discoveries are made. We thus add new evolution rules to extended determinism whenever new laws require such additions, carefully excluding redundancies and contradictions.
The manner in which the definition of extended determinism may be progressively completed is described in the book, where it requires about 200 pages. However, we can justify the definition of extended determinism now, as follows:
§ The uniqueness of the principle is a consequence of the progressive addition of all required evolution characteristics, while avoiding redundancies with existing characteristics.
§ The consequences of the above-mentioned consistency and completeness of the laws of nature are that in each situation of nature, one law applies, and only one; there is no situation where two distinct, contradictory, laws apply; neither can we find a case where evolution does not follow any law. In short, nature does not hesitate, does not contradict itself and does not conflict with itself.
The above statement requires rigorous enunciation of laws of extended determinism that describe how randomness and imprecision intervene in various circumstances; the book describes such laws, with their mathematical formulae.
In short, the uniqueness and completeness of extended determinism are consequences of its constructive definition, which includes a method for progressive extension without redundancy or inconsistency.
Remarks
The mental representation changes required to understand extended determinism are summarized in the short text "Up-to-date Mental Representation Methods".
The text "The Definition of Determinism Needs Updating", shows that extended determinism often contradicts Laplace's philosophical determinism ("the causal chain is unique and predictability is certain") [1]. We shall see in the extensions defined below that it excludes neither randomness nor imprecision, but considers them behavior laws with mathematical models for well-defined phenomena.
Scales of determinism
§ Since the Universe is uniform, determinism acts at all scales: if we postulate determinism at macroscopic scale, we must also postulate it at atomic scale. We will therefore state (and experiments will confirm) that the motion of a corpuscle:
· Is governed, at atomic scale, by the same laws as a motion at macroscopic scale (examples: electrostatic attraction following Coulomb's law and conservation of total energy, a motion described by the Schrödinger equation);
However, we shall see that a law that has considerable effects at atomic scale (such as de Broglie's law which associates a matter wave to a moving corpuscle), may have only negligible effects at macroscopic scale.
We shall also see that some phenomena revealed by mathematical properties at atomic scale have no correspondence at macroscopic scale, where such properties are not applicable.
· Is just as deterministic at atomic scale as it is at macroscopic scale, in keeping with the principle of correspondence.
However, since the Schrödinger equation has multiple solutions, we will have to extend determinism to permit – at least at atomic scale – several consequences of a single cause.
§ Depending on the phenomenon, we shall see that the scale of determinism is sometimes local, and sometimes global. For example, the macroscopic scale is global when compared with the atomic scale. The scale at which determinism governs a phenomenon (its cause or its effect) may vary considerably from a phenomenon to another.
In short, the concept of scale is a useful human abstraction tool; but we should not attribute to nature laws that depend on scale.
Below is a list of the most important extensions of traditional determinism that define extended determinism. Details and justifications are in the book.
§ At both macroscopic and atomic scale, a give cause may produce several consequences, sometimes an infinite number. Possible consequences make up a causal tree structure where each node represents an evolution stage and each branch an evolution from its situation node.
§ Determinism governs the evolution resulting from the initial cause; it does not guarantee that the result of this evolution may be predicted before or measured afterwards with arbitrary precision. Causality is always respected, but it does not guarantee the predictability of the result or the precision of its measure.
§ At each node, nature chooses the next evolution. This choice may be instantaneous or delayed. When it is delayed, several evolutions may occur simultaneously and exist together for a while, forming a superposition.
The sequence of branches traversed since an initial situation makes up a causal chain among all those possible in the causal tree.
§ Randomness does not affect the definition of situations: each state variable value results from a deterministic evolution, predicted for example by the Schrödinger equation.
But randomness governs the choice of one evolution among all those that may follow a given initial situation.
§ Nature often allows only discrete (quantized) values for state variables, among which it chooses randomly that which will appear at human scale, for example during a measure.
§ Nature imposes precision limits when evaluating the values of state variables. Therefore, a position, a shape or a speed may be imprecise and appear fuzzy. That kind of imprecision is intrinsic; it bears no relationship with randomness: in that case, nature simply refuses to satisfy our mind's requirement for simplicity.
§ Some evolutions are irreversible; example: radioactive decay.
§ Some equations of physics are invariable when the direction of time changes, as if we viewed the film of events backwards; others are true only when time flows from present to future.
§ Natural has several conservation laws. Examples: conservation of angular momentum due to the isotropy of space; conservation of electric charge (cause: unknown).
However, measurable quantities such as energy are conserved in some circumstances and fluctuate in others; for each fluctuation, the location, the time and the amplitude are unpredictable.
§ Perfectly deterministic and reproducible processes or algorithms may produce results whose sequence is unpredictable. Example: the sequence of decimals of irrational numbers, whether considered one at a time, or 2, or 3, etc.
§ Deterministic processes may build, based on true axioms, undecidable propositions. Such a proposition is always true or always false, but it may not be proven based on the given axioms.
§ Darwinian evolution of species towards increasing complexity results from a chaotic thermodynamic phenomenon, whose determinism may produce multiple consequences of a given cause even at macroscopic scale.
§ In living beings, perfectly deterministic mechanisms may produce unpredictable behaviors, because the living beings selected by evolution benefit from this unpredictability.
Consequence: man has free will that lets him do what he wants to do; but he is not free to choose what he wants, because his desires are governed by determinism.
§ The global effect of many deterministic processes, similar or different but acting simultaneously, may be unpredictable, therefore non-deterministic.
§ Relativity shows that two distinct events A and B may be such that A precedes B or B precedes A, depending on the observer's location. The direction of the potential causal relationship between A and B is not always obvious!
§ Determinism may act at different scales, from the atomic scale to the infinite scale of astronomy. In the latter case, some properties obey non-separability, and the consequence of a cause may propagate instantaneously (yes, faster than light!) at any distance, for example 140 km.
§ Etc.
Mnemonic statements
The statements below do not prove anything and provide no new information. They are provided in this text simply because their conciseness may help some readers memorize fundamental properties of extended determinism.
General scope of extended determinism
Nature makes no
surprises;
all of its processes are governed by extended determinism.
We may be surprised by the discovery of a new law, but not by its existence or its scope, especially if we keep in mind that extended determinism has probabilistic aspects the book describes. The Nobel prizewinner Richard Feynman' opinion about nature's laws is:
"Nature has a great simplicity and therefore a great beauty."
Laws of nature and laws of a nation: an analogy
The causal principle which is the basis of extended determinism applies to all the laws of nature. This leads to the analogy below:
Extended
determinism governs the laws of nature
like a constitution governs the laws of a nation.
§ Extended determinism and a constitution are both sets of principles respected by all laws, except when men make mistakes.
§ Knowing the principles of extended determinism is useful in the same way as knowing the constitution; both types of knowledge enable understanding laws, their scope and limits, and predicting the evolution of some situations.
Contributions of extended determinism to our logical reasoning
§ A definition based on the laws of the Universe of the principles that govern transitions from causes to consequences;
§ A general scope, with no exceptions even in the fields of life sciences or human (illusory) free will;
§ A complete definition of randomness, of its role and intervention circumstances;
§ A clarification of the roles of complexity and undecidability in predictability;
§ Scientifically up-to-date materialistic arguments against spiritualism, etc.
Extended determinism is a bridge between science and philosophy that helps to better understand what is, and better anticipate what will be.
Appendix
[1] Philosophical (Laplacian) determinism
The fundamental hypothesis of philosophical determinism (the axiom of a single chain of events that starts infinitely far in the past and continues infinitely far in the future) is known as Laplace's determinism. In his book of 1814 "A Philosophical Essay on Probabilities", he wrote:
"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 state 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").
Therefore, philosophical determinism asserts:
§ That the future is completely determined;
§ That it is completely predictable given a perfect knowledge of the present.