Clockwork After All Statistical

The ‘simple’ case we have analysed is representative of many others - in fact of all such as appear to evade the all-embracing principle of molecular statistics.

Clockworks made of real physical matter (in con- trast to imagination) are not true ‘clock-works’. The element of chance may be more or less reduced, the likelihood of the clock suddenly going altogether wrong may be infinitesimal, but it always remains in the background. Even in the motion of the celestial bodies irreversible frictional and thermal influences are not wanting. Thus the rotation of the earth is slowly diminished by tidal friction, and along with this reduction the moon gradually recedes from the earth, which. would not happen if the earth were a completely rigid rotating sphere.

Nevertheless the fact remains that ‘physical clock-works’ visibly display very prominent ‘order-from-order’ features - the type that aroused the physicist’s excitement when he encountered them in the organism. It seems likely that the 2 cases have after all something in common. It remains to be seen what this is and what is the striking difference which makes the case of the organism after all novel and unprecedented.

NERNST’S THEOREM

When does a physical system - any kind of association of atoms - display ‘dynamical law’ (in Planck’s meaning) or ‘clock-work features’? Quantum theory has a very short answer to this question, viz. at the absolute zero of temper- ature.

As zero temperature is approached the molecular disorder ceases to have any bearing on physical events. This fact was, by the way, not discovered by theory, but by carefully investigating chemical reactions over a wide range of temperatures and extrapolating the results to zero temper- ature - which cannot actually be reached. This is Walther Nernst’s famous ‘Heat Theorem’, which is sometimes, and not unduly, given the proud name of the ‘Third Law of Thermo- dynamics’ (the first being the energy principle, the second the en tropy principle).

Quantum theory provides the rational foundation of Nernst’s empirical law, and also enables us to estimate how closely a system must approach to the absolute zero in order to display an approximately ‘dynamical’ behaviour. What temperature is in any particular case already practically equivalent to zero?

Now you must not believe that this always has to be a very low temperature. Indeed, Nernst’s discovery was induced by the fact that even at room temperature entropy plays an astonishingly insignificant role in many chemical reactions. (Let me recall that entropy is a direct measure of molecular disorder, viz. its logarithm.)

What about a pendulum clock?

Its room temperature is practically equivalent to zero.

That is why it works ‘dynamically’.

It will continue to work as it does if you cool it (provided that you have removed all traces of oil!).

But it does not continue to work if you heat it above room temperature, for it will eventually melt.

The Relation Between Clockwork And Organism

Clockworks can functioning ‘dynamically’ because they are built of solids which are kept in shape by London-Heitler forces.

These forces are strong enough to elude the disorderly tendency of heat motion at ordinary temperature.

The organism also hinges on a solid as the aperiodic crystal forming the hereditary substance, largely withdrawn from the disorder of heat motion.

But please do not accuse me of calling the chromosome fibres just the ‘cogs of the organic machine’.

The most striking features are:

1. The curious distribution of the cogs in a many-celled organism

2. The single cog is not of coarse human make, but is the finest masterpiece ever achieved along the lines of the Lord’s quantum mechanics.