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None of his writings possesses more of this quality than his short classic What is Life? – which, as I now realize, must surely rank among the most influential of scientific writings in this century. It represents a powerful attempt to comprehend some of the genuine mysteries of life, made by a physicist whose own deep insights had done so much to change the way in which we understand what the world is made
Homo liber nulla de re minus quam de morte cogitat; et ejus sapientia non mortis sed vitae meditatio est. SPINOZA’S Ethics, Pt IV, Prop. 67 (There is nothing over which a free man ponders less than death; his wisdom is, to meditate not on death but on life.)
The arrangements of the atoms in the most vital parts of an organism and the interplay of these arrangements differ in a fundamental way from all those arrangements of atoms which physicists and chemists have hitherto made the object of their experimental and theoretical research.
Suppose that you could mark the molecules in a glass of water; then pour the contents of the glass into the ocean and stir the latter thoroughly so as to distribute the marked molecules uniformly throughout the seven seas; if then you took a glass of water anywhere out of the ocean, you would find in it about a hundred of your marked molecules.3
The king would naturally indicate a length comparable with that of his own body, knowing that anything else would be very inconvenient. With all his predilection for the Ångström unit, the physicist prefers to be told that his new suit will require six and a half yards of tweed – rather than sixty-five thousand millions of Ångströms of tweed.
Why must our bodies be so large compared with the atom?
Why should an organ like our brain, with the sensorial system attached to it, of necessity consist of an enormous number of atoms, in order that its physically changing state should be in close and intimate correspondence with a highly developed thought?
First, a physical organization, to be in close correspondence with thought (as my brain is with my thought) must be a very well-ordered organization, and that means that the events that happen within it must obey strict physical laws, at least to a very high degree of accuracy.
Only in the co-operation of an enormously large number of atoms do statistical laws begin to operate and control the behaviour of these assemblées with an accuracy increasing as the number of atoms involved increases. It is in that way that the events acquire truly orderly features.
But you must not think that they actually all turn parallel.
The orientation the field tends to produce is continually counteracted by the heat motion, which works for random orientation.
Though the single atoms change their orientation incessantly, they produce on the average (owing to their enormous number) a constant small preponderance of orientation in the direction of the field and proportional to it.
If the observed weak magnetization is really the outcome of rival tendencies, namely, the magnetic field, which aims at combing all the molecules parallel, and the heat motion, which makes for random orientation, then it ought to be possible to increase the magnetization by weakening the heat motion, that is to say, by lowering the temperature, instead of reinforcing the field.
Modern equipment even enables us, by lowering the temperature, to reduce the heat motion to such insignificance that the orientating tendency of the magnetic field can assert itself, if not completely, at least sufficiently to produce a substantial fraction of ‘complete magnetization’. In this case we no longer expect that double the field strength will double the magnetization, but that the latter will increase less and less with increasing field, approaching what is called ‘saturation’. This expectation too is quantitatively confirmed by experiment.
Notice that this behaviour entirely depends on the large numbers of molecules which co-operate in producing the observable magnetization. Otherwise, the latter would not be constant at all, but would, by fluctuating quite irregularly from one second to the next, bear witness to the vicissitudes of the contest between heat motion and field.
This example shows what funny and disorderly experience we should have if our senses were susceptible to the impact of a few molecules only.
But precisely in consequence of this, a plane separating two neighbouring slices will be crossed by more molecules coming from the left than in the opposite direction, simply because to the left there are more molecules engaged in random walk than there are to the right. And as long as that is so the balance will show up as a regular flow from left to right, until a uniform distribution is reached.
The smaller their number, the larger the quite haphazard deviations we must expect – and they can be observed under favourable circumstances.
In choosing lighter and lighter bodies and thinner and longer fibres – to make the balance susceptible to weaker and weaker forces – the limit was reached when the suspended body became noticeably susceptible to the impacts of the heat motion of the surrounding molecules and began to perform an incessant, irregular ‘dance’ about its equilibrium position, much like the trembling of the droplet in the second example.
The uncontrollable effect of the heat motion competes with the effect of the force to be measured and makes the single deflection observed insignificant. You have to multiply observations, in order to eliminate the effect of the Brownian movement of your instrument. This example is, I think, particularly illuminating in our present investigation. For our organs of sense, after all, are a kind of instrument. We can see how useless they would be if they became too sensitive.
Now, roughly speaking, this statistical law is quite general. The laws of physics and physical chemistry are inaccurate within a probable relative error of the order of 1/√n, where n is the number of molecules that co-operate to bring about that law – to produce its validity within such regions of space or time (or both) that matter, for some considerations or for some particular experiment. You see from this again that an organism must have a comparatively gross structure in order to enjoy the benefit of fairly accurate laws, both for its internal life and for its interplay with the external
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Thus we have come to the conclusion that an organism and all the biologically relevant processes that it experiences must have an extremely ‘many-atomic’ structure and must be safeguarded against haphazard, ‘single-atomic’ events attaining too great importance. That, the ‘naïve physicist’ tells us, is essential, so that the organism may, so to speak, have sufficiently accurate physical laws on which to draw for setting up its marvellously regular and well-ordered working.
As we shall presently see, incredibly small groups of atoms, much too small to display exact statistical laws, do play a dominating role in the very orderly and lawful events within a living organism. They have control of the observable large-scale features which the organism acquires in the course of its development, they determine important characteristics of its functioning; and in all this very sharp and very strict biological laws are displayed.
It is these chromosomes, or probably only an axial skeleton fibre of what we actually see under the microscope as the chromosome, that contain in some kind of code-script the entire pattern of the individual’s future development and of its functioning in the mature state. Every complete set of chromosomes contains the full code; so there are, as a rule, two copies of the latter in the fertilized egg cell, which forms the earliest stage of the future individual.
The chromosome structures are at the same time instrumental in bringing about the development they foreshadow. They are law-code and executive power – or, to use another simile, they are architect’s plan and builder’s craft – in one.
Thus, a body cell of mine is, on the average, only the 50th or 60th ‘descendant’ of the egg that was I.
The salient point is that each of the two ‘daughter cells’ gets a dowry of two further complete sets of chromosomes exactly similar to those of the parent cell. So all the body cells are exactly alike as regards their chromosome treasure.
Some time ago we were told in the newspapers that in his African campaign General Montgomery made a point of having every single soldier of his army meticulously informed of all his designs. If that is true (as it conceivably might be, considering the high intelligence and reliability of his troops) it provides an excellent analogy to our case, in which the corresponding fact certainly is literally true. The most surprising fact is the doubleness of the chromosome set, maintained throughout the mitotic divisions.
Cells with only one chromosome set are called haploid (from Greek , single). Thus the gametes are haploid, the ordinary body cells diploid (from Greek , double).
The issue was decided by a 50:50 chance in the meiosis taking place in my father’s body in November 1886 and producing the spermatozoon which a few days later was to be effective in begetting me. Exactly the same story could be repeated about chromosomes Nos. 1, 2, 3, …, 24 of my paternal set, and mutatis mutandis about every one of my maternal chromosomes. Moreover, all the 48 issues are entirely independent. Even if it were known that my paternal chromosome No. 5 came from my grandfather Josef Schrödinger, the No. 7 still stands an equal chance of being either also from him, or from his wife
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But actually it is the whole (four-dimensional) pattern of the ‘phenotype’, the visible and manifest nature of the individual, which is reproduced without appreciable change for generations, permanent within centuries – though not within tens of thousands of years – and borne at each transmission by the material structure of the nuclei of the two cells which unite to form the fertilized egg cell. That is a marvel – than which only one is greater; one that, if intimately connected with it, yet lies on a different plane. I mean the fact that we, whose total being is entirely based on a
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Selection has no effect – because the small, continuous variations are not inherited. They are obviously not based on the structure of the hereditary substance, they are accidental.
We should expect a definite observed mutation to be caused by a change in a definite region in one of the chromosomes.
For exactly half of the offspring exhibit the mutant character and half the normal
The fact that two individuals may be exactly alike in their outward appearance, yet differ in their inheritance, is so important that an exact differentiation is desirable.
The danger factor for an incestuously bred child is thus 1:16. In the same way the danger
The anti-selective effect of the modern mass slaughter of the healthy youth of all nations is hardly outweighed by the consideration that in more primitive conditions war may have had a positive value in letting the fittest tribe survive.
If a spontaneous mutation is a small step in the development of the species, we get the impression that some change is ‘tried out’ in rather a haphazard fashion at the risk of its being injurious, in which case it is automatically eliminated. This brings out one very important point. In order to be suitable material for the work of natural selection, mutations must be rare events, as they actually are. If they were so frequent that there was a considerable chance of, say, a dozen of different mutations occurring in the same individual, the injurious ones would, as a rule, predominate over the
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An analogy might be sought in the working of a large manufacturing plant in a factory. For developing better methods, innovations, even if as yet unproved, must be tried out. But in order to ascertain whether the innovations improve or decrease the output, it is essential that they should be introduced one at a time, while all the other parts of the mechanism are kept constant.
The percentage of mutations in the offspring, the so-called mutation rate, can be increased to a high multiple of the small natural mutation rate by irradiating the parents with X-rays or γ-rays.
The experiments on X-ray-produced mutations give the impression that every particular ‘transition’, say from the normal individual to a particular mutant, or conversely, has its individual ‘X-ray coefficient’, indicating the percentage of the offspring which turns out to have mutated in that particular way, when a unit dosage of X-ray has been applied to the parents, before the offspring was engendered.
Mutation is thus not an accumulated effect, brought about by consecutive small portions of radiation reinforcing each other. It must consist in some single event occurring in one chromosome during irradiation. What kind of event?
There are plenty of occasions in modern life when a human being has to be exposed to X-rays. The direct dangers involved, as burns, X-ray cancer, sterilization, are well known, and protection by lead screens, lead-loaded aprons, etc., is provided, especially for nurses and doctors who have to handle the rays regularly. The point is, that even when these imminent dangers to the individual are successfully warded off, there appears to be the indirect danger of small detrimental mutations being produced in the germ cells – mutations of the kind envisaged when we spoke of the unfavourable results
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To put it drastically, though perhaps a little naively, the injuriousness of a marriage between first cousins might very well be increased by the fact that their grandmother had served for a long period as an X-ray nurse. It is not a point that need worry any individual personally. But any possibility of gradually infecting the human race with unwanted latent mutations ought to be a matter of concern to the community.
How can we, from the point of view of statistical physics, reconcile the facts that the gene structure seems to involve only a comparatively small number of atoms (of the order of 1,000 and possibly much less), and that nevertheless it displays a most regular and lawful activity – with a durability or permanence that borders upon the miraculous?
In the light of present knowledge, the mechanism of heredity is closely related to, nay, founded on, the very basis of quantum theory. This
The Heitler–London theory involves the most subtle and intricate conceptions of the latest development of quantum theory (called ‘quantum mechanics’ or ‘wave mechanics’).
a number of atomic nuclei, including their bodyguards of electrons, when they find themselves close to each other, forming ‘a system’, are unable by their very nature to adopt any arbitrary configuration we might think of.
The transition from one of these configurations to another is a quantum jump. If the second one has the greater energy (‘is a higher level’), the system must be supplied from outside with at least the difference of the two energies to make the transition possible. To a lower level it can change spontaneously, spending the surplus of energy in radiation.
Atoms in such a state form a molecule. The point to stress here is, that the molecule will of necessity have a certain stability; the configuration cannot change, unless at least the energy difference, necessary to ‘lift’ it to the next higher level, is supplied from outside. Hence this level difference, which is a well-defined quantity, determines quantitatively the degree of stability of the molecule.
