The End of Causality

Jonathan B. Marder

28/10/98

Did you ever wonder why flower petals form into such exquisite patterns and why snowflakes form in such perfect geometric shapes? Yet scientists tell us that the universe is winding down towards ever increasing disorder. Why the contradiction? The contradiction between science and "common sense" seems to be ever increasing. This is usually attributed to "strange" relativistic and quantum effects discovered in the twentieth century. The purpose of this short essay is to show that the roots of this problem go back to previous centuries - and you don't need to know quantum mechanics or relativity to understand it.

Causality

Patterns in nature reveal underlying cause. In the post-reformation age, scientists came to view patterns of change as a reflection of unseen physical forces driving change. This idea developed into a philosophy of causality which holds that any phenomenon can ultimately be exlained by determining the underlying mechanical processes. The word "cause" is a strange one. We sometimes use it in an objective sense, to mean the driving force behind some process of change. Alternatively, the word cause is sometimes used in a subjective sense to indicate an aspiration or a quest towards which people may work. Causality in science relates to the objective definition.

The laws of mechanics

Aristotle assumed that an unseen force must act on a moving body for movement to be maintained. Newton concluded that this was not so, and that a body would continue moving at constant velocity along a straight trajectory, carried by its own momentum. Acording to Newton's laws of motion, deviation from that trajectory is evidence for an external force. Newton's laws are the basis of our everyday understanding of the way objects move. They explain the motion of motor cars and cannonballs, and even of planetary orbits (taking account also of Newton's laws of gravity). However, in the realm of chemistry where one has to consider the behaviour of microscopic molecules, the orderly behaviour dictated by Newton's laws is buried in the chaotic interactions of immense numbers of particles.

Molecular mechanics

Democritus (5th century BCE) conceived of matter as particles moving around in a void. This is pretty close to our modern view which regards gases as molecules moving around randomly in empty space. During the 19th century, physicists like Maxwell and Boltzmann used Newton's mechanics to consider the random collisions of gas molecules with each other and the container walls. By this means then were able to derive the relationship pV /T = constant, where pressure p is determined by the impact of molecules against the container wall, V is the volume, and T (absolute temperature) is a measure of the average kinetic energy of the molecules.

The Gas Laws

The gas laws were established empirically during the 17th to 19th centuries, based on experiments measuring the properties of gases as elastic fluids. The three laws relate to a fixed mass of gas at constant temperature, pressure or volume.

Boyle's Law (Robert Boyle, 1662): pV remains constant at constant temperature.

Charles' Law (Jacques-Alexandre-Cesar Charles, 1787): V/T remains constant if the pressure remains constant.

Pressure Law (Joseph Louis Gay-Lussac, early 1800's): p/T is constant if volume remains constant.

The combined gas law which incoporates the three relationships above says that for a fixed mass of gas, pV/T=constant. This is exactly the same as the equation derived from first principals considering only the random motions and collisions of individual gas molecules.

Brownian Motion

A tiny particle (e.g. a smoke particle) suspended in air demonstrates random movements due to buffeting by the impact or air molecules. This is called Brownian motion and is visible under a microscope, an observation that supports the statistical mechanical view of gases as randomly moving and colliding particles. In one of his 4 famous scientific papers of 1905, Albert Einstein provided a mathematical description of Brownian motion using statistical mechanics. Einstein's considerations led to a deeper understanding of the movements of the unseen air molecules, and led to equations for diffusion.

Behaviour of individual molecules versus populations

The laws of diffusion and the gas laws provide a useful and definitive way of describing the behaviour of populations of molecules. Yet, the "obedience" of the population to those rules is no more than an expression of the totally random movements and collisions of individual molecules. There is no external cause or force which causes a group of gas molecules to spread out by diffusion. Furthermore, the work done by an expanding gas is an expression of the same random behaviour. This begs the question "do the individual molecules really behave randomly?" On the one hand, that was our starting hypothesis. On the other hand, that behaviour causes the population to behave non-randomly.

The above contradiction may in fact stem from two inherently contradictory world views, which are both incorporated in scientific theory.
  1. Newtons mechanics regards matter as inherently stable, following constant trajectories which only change in response to changes in external forces.
  2. Thermodynamics says that all matter has an inherent tendency to dissolve into disorder unless it is somehow held back.

What does randomness really mean?

Randomness (lack of patterned behaviour) is not inherent to the system! It is a perception of the system. We can consider a gas as a large number of individual randomly-moving molecules, or as an elastic fluid substance with the properties summarized by the gas laws. The difference between the random and non-random viewpoint is one of perception, and has no basis in the properties of the gas. Thus, randomness cannot be considered an objective property of the whole system.

Does God play dice?

When Einstein stated "God doesn't play dice", he wasn't talking about the random movement of molecules, and especially not his statistical mechanical analysis of Brownian motion. He was talking about quantum mechanics (especially "Heisenberg's uncertainty principal") which describes the behaviour of subatomic particles in terms of statistics. Einstein firmly held that there must be causal mechanisms that determine the statistical distributions. Einstein would have said that molecular statistical mechanics was different, since it would be theoretically possible to track each individual molecule's movements and collisions, and explain its path in terms of classical mechanics. The dogma of quantum mechanics is that an equivalent analysis of subatomic particles is theoretically impossible.

But in the final analysis, the question may not even matter. Quantum mechanics has no need for the classical causal mechanism Einstein sought, and thermodynamics has no need for a classical analysis of individual molecular movements. In both cases, statistical considerations provide a perfectly adequate starting point.

The conceptual revolution

It is commonly accepted that physics went through an earthshaking paradigm shift as a result of quantum mechanical theory. A look back at the history of thermodynamics and statistical mechanics suggests a different interpretation. Thermodynamics came with a highly empirical pedigree, so had no problem dealing with statistical concepts. In contrast, quantum mechanics evolved from theoretical considerations in an intellectual environment, which (at first) regarded statistical variables as approximations alien to fundamental theory. Yet, it seems that the evolution of thermodynamic theory created problems which persist today as evidenced by the extreme difficulty most students and teachers have with explaining thermodynamic concepts like "entropy" and "free energy".

Thermodynamics made simple

Students of chemistry learn certain equations which enable one to predict the direction in which a chemical reaction will proceed. Since the free energy parameters central to the equations are basically determined from experimental measurements, the following tautological statement sums things up pretty accurately:-

"Chemical reactions tend to move the system from a less likely to a more likely state"

You can't get a much more statistical than that!

The cause of change

If you have read this far, you have just had a short lesson in thermodynamics. If you understood the lesson, you will realize that the cause of change in a process is not necessarily an external driving force, but sometimes an inherent tendency. If you look back to the paragraph on causality, "cause" is defined in both subjective and objective senses. "Inherent tendency" seems much closer to the subjective definition that equates cause with quest or aspiration. But ultimately, when it comes to deciding on which definition of cause best suits the science of thermodynamics, the tautological description of chemical reactions given above makes no distinction. Instead, the cause of change becomes an all encompassing concept which transcends any division of meaning.

Where from here?

Well it is already happening. While there is no need to belittle the tremendous achievements of quantum mechanics, certain areas related to statistical mechanics are also highly topical. Examples are information science (particularly regarding molecules as information carriers), control theory, complexity and chaos theory. The statistical approach enables us to calculate, predict and explain the changes we observe in ever increasingly complicated situations, without having to constantly look for hitherto undefined external causes.

An obvious candidate for our consideration is the process of biological evolution. The argument rages between the Darwinist position, that evolution just happens "randomly", and the counterposition that evolution is guided by forces we don't know and don't understand. The serious proponents of the latter position include a significant number of respectable physicists who find the idea of man evolving by chance as incredible. I basically take the Darwinist position.

Darwin's great insight was in realizing that evolution isn't a process directed towards some specific goal, but change away from a pre-existing situation. Random changes (e.g. mutations, genetic recombinations etc.) move organisms away from being direct clones of previous generations. Natural selection is the result of circumstances favouring certain directions of change above others. Thus, one can say that populations tend to evolve to more favoured forms! Alternatively, the survivors are the ones whose survival is favoured by circumstance! These statements are just as tautological as my earlier statement on the directionality of chemical reactions. Reducing things to tautologies suggests that these are truths which express underlying axioms. These fundamental axioms are expressed in chemistry, biology and whatever other complex systems we wish to consider.


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