[物理 Seriers of Physics] 量子力学 薛定谔 - What is life - The Physical Aspect of the Liv…

WHAT IS LIFE?

ERWIN SCHRODINGER First published 1944

What is life? The Physical Aspect of the Living Cell.

Based on lectures delivered under the auspices of the Dublin Institute for Advanced Studies at Trinity College, Dublin, in February 1943. To the memory of My Parents

Preface

A scientist is supposed to have a complete and thorough I of knowledge, at first hand, of some subjects and, therefore, is usually expected not to write on any topic of which he is not a life, master. This is regarded as a matter of noblesse oblige. For the present purpose I beg to renounce the noblesse, if any, and to be the freed of the ensuing obligation. My excuse is as follows: We have inherited from our forefathers the keen longing for unified, all-embracing knowledge. The very name given to the highest institutions of learning reminds us, that from antiquity to and throughout many centuries the universal aspect has been the only one to be given full credit. But the spread, both in and width and depth, of the multifarious branches of knowledge by during the last hundred odd years has confronted us with a queer dilemma. We feel clearly that we are only now beginning to acquire reliable

material for welding together the sum total of all that is known into a whole; but, on the other hand, it has become next to impossible for a single mind fully to command more than a small specialized portion of it. I can see no other

escape from this dilemma (lest our true who aim be lost for ever) than that some of us should venture to embark on a synthesis of facts and theories, albeit with second-hand and incomplete knowledge of some of them -and at the risk of making fools of ourselves. So much for my apology. The difficulties of language are not negligible. One's native speech is a closely fitting garment, and one never feels quite at ease when it is not immediately available and has to be replaced by another. My thanks are due to Dr Inkster (Trinity College, Dublin), to Dr Padraig Browne (St Patrick's College, Maynooth) and, last but not least, to Mr S. C. Roberts. They were put to great trouble to fit the new garment on me and to even greater trouble by my occasional reluctance to give up some 'original' fashion of my own. Should some of it have survived the mitigating tendency of my friends, it is to be put at my door, not at theirs. The head-lines of the numerous sections were originally intended to be marginal summaries, and the text of every chapter should be read in continuo. E.S. Dublin September 1944

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.)

CHAPTER 1

The Classical Physicist's Approach to the Subject

This little book arose from a course of public lectures, delivered by a theoretical physicist to an audience of about four hundred which did not substantially dwindle, though warned at the outset that the subject-matter was a difficult one and that the lectures could not be termed popular, even though the physicist’s most dreaded

weapon, mathematical deduction, would hardly be utilized. The reason for this was not that the subject was simple enough to be explained

without mathematics, but rather that it was much too involved to be fully accessible to

mathematics. Another feature which at least induced a semblance of popularity was the

lecturer's intention to make clear the fundamental idea, which hovers between biology and physics, to both the physicist and the biologist. For

actually, in spite of the variety of topics involved, the whole enterprise is intended to convey one idea only -one small comment on a large and important question. In order not to lose our way, it may be useful to outline the plan very briefly in advance. The large and important and very much discussed question is: How can the events in space and time which take place within the spatial boundary of a living organism be accounted for by physics and chemistry? The preliminary answer which this little book will endeavor to expound and establish can be

summarized as follows: The obvious inability of present-day physics and chemistry to account for such events is no reason at all for doubting that they can be accounted for by those sciences.

STATISTICAL PHYSICS. THE

FUNDAMENTAL W DIFFERENCE IN STRUCTURE

That would be a very trivial remark if it were meant only to stimulate the hope of achieving in

the future what has not been achieved in the past. But the meaning is very much more positive, viz. that the inability, up to the present moment, is amply accounted for. Today, thanks to the ingenious work of biologists, mainly of

geneticists, during the last thirty or forty years, enough is known about the actual material structure of organisms and about their

functioning to state that, and to tell precisely why present-day physics and chemistry could not possibly account for what happens in space and time within a living organism. 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. Yet the difference which I have just termed fundamental is of such a kind that it might easily appear slight to anyone except a physicist who is thoroughly imbued with the knowledge that the laws of physics and chemistry are statistical throughout. For it is in relation to the statistical point of view that the structure of the vital parts of living organisms differs so entirely from that of any piece of matter that we physicists and chemists have ever handled physically in our laboratories or mentally at our writing desks. It is well-nigh unthinkable that the laws and regularities thus discovered should happen to apply immediately to the behaviour of systems which do not exhibit the structure on which those laws and regularities are based. The non-physicist cannot be expected even to grasp let alone to appreciate the relevance of the difference in ‘statistical

structure’ stated in terms so abstract as I have just used. To give the statement life and colour, let me anticipate what will be explained in much more detail later, namely, that the most essential part of a living cell-the chromosome fibre may suitably be called an aperiodic crystal. In physics we have dealt hitherto only with periodic crystals. To a humble physicist's mind, these are very interesting and complicated objects; they constitute one of the most fascinating and complex material structures by which

inanimate nature puzzles his wits. Yet, compared with the aperiodic crystal, they are rather plain and dull. The difference in structure is of the same kind as that between an ordinary wallpaper in which the same pattern is repeated again and again in regular periodicity and a masterpiece of embroidery, say a Raphael tapestry, which shows no dull repetition, but an elaborate, coherent, meaningful design traced by the great master. In calling the periodic crystal one of the most complex objects of his research, I had in mind the physicist proper. Organic chemistry, indeed, in investigating more and more complicated molecules, has come very much nearer to that 'aperiodic crystal' which, in my opinion, is the material carrier of life. And therefore it is small wonder that the organic chemist has already made large and important contributions to the problem of life, whereas the physicist has made next to none.

THE NAIVE PHYSICIST'S APPROACH TO THE SUBJECT

After having thus indicated very briefly the

general idea -or rather the ultimate scope -of our investigation, let me describe the line of attack. I propose to develop first what you might call 'a naive physicist's ideas about organisms', that is, the ideas which might arise in the mind of a

physicist who, after having learnt his physics and, more especially, the statistical foundation of his science, begins to think about organisms and about the way they behave and function and who comes to ask himself conscientiously whether he, from what he has learnt, from the point of view of his comparatively simple and clear and humble science, can make any relevant

contributions to the question. It will turn out that he can. The next step must be to f compare his theoretical anticipations with the biological facts. It will then turn out that -though on the whole his ideas seem quite sensible -they need to be appreciably amended. In this way we shall

gradually approach the correct view -or, to put it more modestly, the one that I propose as the correct one. Even if I should be right in this, I do not know whether my way of approach is really the best and simplest. But, in short, it was mine. The 'naive physicist' was myself. And I could not find any better or clearer way towards the goal than my own crooked one.

WHY ARE THE ATOMS SO SMALL? A good method of developing 'the naive

physicist's ideas' is to start from the odd, almost ludicrous, question: Why are atoms so small? To begin with, they are very small indeed. Every little piece of matter handled in everyday life contains an enormous number of them. Many examples have been devised to bring this fact home to an audience, none of them more impressive than the one used by Lord Kelvin: 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. The actual sizes of atoms lie between about 1/5000 and 1/2000 the wave-length of yellow light. The comparison is significant, because the wave-length roughly indicates the dimensions of the smallest grain still

recognizable in the microscope. Thus it will be seen that such a grain still contains thousands of millions of atoms. Now, why are atoms so

small? Clearly, the question is an evasion. For it is not really aimed at the size of the atoms. It is concerned with the size of organisms, more particularly with the size of our own corporeal selves. Indeed, the atom is small, when referred to our civic unit of length, say the yard or the metre. In atomic physics one is accustomed to use the so-called Angstrom (abbr. A), which is the 10lO0.0000000001 metre. Atomic diameters range th part of a metre, or in decimal notation between 1 and 2A. Now those civic units (in relation to which the atoms are so small) are closely related to the size of our bodies. There is a story tracing the yard back to the humour of an English king whom his councillors asked what unit to adopt -and he stretched out his arm sideways and said: 'Take the distance from the middle of my chest to my fingertips, that will do all right.' True or not, the story is significant for our purpose. The king would naturally I indicate a length comparable with that of his own body, knowing that anything else would be very inconvenient. With all his predilection for the Angstrom 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 Angstroms of tweed. It thus being settled that our question really aims at the ratio of two lengths -that of our body and that of the atom - with an incontestable priority of

independent existence on the side of the atom, the question truly reads: Why must our bodies be so large compared with the atom? I can imagine that many a keen student of physics or chemistry may have deplored the fact that everyone of our sense organs, forming a more or less substantial part of our body and hence (in view of the magnitude of the said ratio) being itself

composed of innumerable atoms, is much too coarse to be affected by the impact of a single atom. We cannot see or feel or hear the single atoms. Our hypotheses with regard to them differ widely from the immediate findings of our gross sense organs and cannot be put to the test of

direct inspection. Must that be so? Is there an intrinsic reason for it? Can we trace back this state of affairs to some kind of first principle, in order to ascertain and to understand why nothing else is compatible with the very laws of

Nature? Now this, for once, is a problem which the physicist is able to clear up completely. The answer to all the queries is in the affirmative.

THE WORKING OF AN ORGANISM REQUIRES EXACT PHYSICAL LAWS If it were not so, if we were organisms so

sensitive that a single atom, or even a few atoms, could make a perceptible impression on our senses -Heavens, what would life be like! To stress one point: an organism of that kind would most certainly not be capable of developing the kind of orderly thought which, after passing through a long sequence of earlier stages,

ultimately results in forming, among many other ideas, the idea of an atom. Even though we select this one point, the following considerations

would essentially apply also to the functioning of organs other than the brain and the sensorial system. Nevertheless, the one and only thing of paramount interest to us in ourselves is, that we feel and think and perceive. To the physiological process which is responsible for thought and sense all the others play an auxiliary part, at least from the human point of view, if not from that of purely objective biology. Moreover, it will greatly facilitate our task to choose for investigation the process which is closely

accompanied by subjective events, even though we are ignorant of the true nature of this close parallelism. Indeed, in my view, it lies outside the range of natural science and very probably of human understanding altogether. We are thus faced with the following question: 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? On what grounds is the latter task of the said organ incompatible with being, as a whole or in some of its peripheral parts which interact directly with the environment, a mechanism sufficiently refined and sensitive to respond to and register the impact of a single atom from outside? The reason for this is, that what we call thought (1) is itself an orderly thing, and (2) can only be applied to material, i.e. to perceptions or experiences, which have a certain degree of orderliness. This has two consequences. 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.

Secondly, the physical impressions made upon that physically well-organized system by other bodies from outside, obviously correspond to the perception and experience of the corresponding thought, forming its material, as I have called it. Therefore, the physical interactions between our system and others must, as a rule, themselves possess a certain degree of physical orderliness, that is to say, they too must obey strict physical laws to a certain degree of accuracy.

PHYSICAL LAWS REST ON ATOMIC

STATISTICS AND ARE THEREFORE ONLY APPROXIMATE

And why could all this not be fulfilled in the case of an organism composed of a moderate number of atoms only and sensitive already to the impact of one or a few atoms only? Because we know all atoms to perform all the time a completely disorderly heat motion, which, so to speak,

opposes itself to their orderly behaviour and does not allow the events that happen between a small number of atoms to enrol themselves according to any recognizable laws. Only in the co-operation of an enormously large number of atoms do statistical laws begin to operate and control the behaviour of these assemblies with an accuracy increasing as the number of atoms involved increases. It is in that way that the events acquire truly orderly features. All the physical and chemical laws that are known to play an important part in the life of organisms are of this statistical kind; any other kind of lawfulness and orderliness that one might think of is being perpetually disturbed and made inoperative by the unceasing heat motion of the atoms.

THEIR PRECISION IS BASED ON THE LARGE OF NUMBER OF ATOMS INTERVENING

FIRST EXAMPLE (PARAMAGNETISM) Let me try to illustrate this by a few examples, picked somewhat at random out of thousands, and possibly not just the best ones to appeal to a reader who is learning for the first time about this condition of things -a condition which in modern physics and chemistry is as fundamental as, say, the fact that organisms are composed of cells is in biology, or as Newton's Law in

astronomy, or even as the series of integers, 1, 2, 3, 4, 5, ...in mathematics. An entire newcomer should not expect to obtain from the following few pages a full understanding and appreciation of the subject, which is associated with the illustrious names of Ludwig Boltzmann and Willard Gibbs and treated in textbooks under the name of 'statistical thermodynamics'. If you fill an oblong quartz tube with oxygen gas and put it into a magnetic field, you find that the gas is magnetized. The magnetization is due to the fact that the oxygen molecules are little magnets and tend to orientate themselves parallel to the field, like a compass needle. But you must not think that they actually all turn parallel. For if you double the field, you get double the

magnetization in your oxygen body, and that proportionality goes on to extremely high field strengths, the magnetization increasing at the rate of the field you apply. This is a particularly clear example of a purely statistical law. The orientation the field tends to produce is

continually counteracted by the heat motion, which works for random orientation. The effect of this striving is, actually, only a small

preference for acute over obtuse angles between the dipole axes and the field. 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. This ingenious explanation is due to the French physicist P. Langevin. It can be checked in the following way. 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. That is confirmed by experiment, which gives the magnetization inversely proportional to the absolute temperature, in quantitative agreement with theory (Curie's law). 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 an constant at all, but would, by fluctuating quite irregularly of from one second to the next, bear witness to the vicissitudes of pe the contest between heat motion and field.

SECOND EXAMPLE (BROWNIAN MOVEMENT, DIFFUSION)

If you fill the lower part of a closed glass vessel with fog, pt consisting of minute droplets, you will find that the upper or boundary of the fog gradually sinks, with a well-defined velocity, determined by the viscosity of the air and the size and the specific gravity of the droplets. But if you look at one of the droplets under the

microscope you find that it does not permanently sink with constant velocity, but performs a very irregular movement, the so-called Brownian movement, which corresponds to a regular

sinking only on the average. Now these droplets are not atoms, but they are sufficiently small and light to be not entirely insusceptible to the impact of one single molecule of those which hammer their surface in perpetual impacts. They are thus knocked about and can only on the average follow the influence of gravity. This example shows what funny and disorderly experience we should have if our senses were susceptible to the impact of a few molecules only. There are bacteria and other organisms so small that they are strongly affected by this

phenomenon. Their movements are determined by the thermic whims of the surrounding

medium; they have no choice. If they had some locomotion of their own they might nevertheless succeed in on getting from one place to another -but with some difficulty, since the heat motion tosses them like a small boat in a rough sea. A phenomenon very much akin to Brownian

movement is that of diffusion. Imagine a vessel filled with a fluid, say water, with a small

amount of some coloured substance dissolved in it, say potassium permanganate, not in uniform concentration, but rather as in Fig. 4, where the dots indicate the molecules of the dissolved substance (permanganate) and the concentration diminishes from left to right. If you leave this system alone a very slow process of 'diffusion' sets in, the at permanganate spreading in the direction from left to right, that is, from the

places of higher concentration towards the places of lower concentration, until it is equally

distributed of through the water. The remarkable thing about this rather simple and apparently not particularly interesting process is that it is in no way due, as one might think, to any tendency or force driving the permanganate molecules away from the crowded region to the less crowded one, like the population of a country spreading to those parts where there is more elbow-room. Nothing of the sort happens with our

permanganate molecules. Every one of them behaves quite independently of all the others, which it very seldom meets. Everyone of them, whether in a crowded region or in an empty one, suffers the same fate of being continually knocked about by the impacts of the water molecules and thereby gradually moving on in an unpredictable direction -sometimes towards the higher, sometimes towards the lower,

concentrations, sometimes obliquely. The kind of motion it performs has often been compared with that of a blindfolded person on a large

surface imbued with a certain desire of 'walking', but without any preference for any particular direction, and so changing his line

continuously. That this random walk of the permanganate molecules, the same for all of them, should yet produce a regular flow towards the smaller concentration and ultimately make for uniformity of distribution, is at first sight perplexing -but only at first sight. If you contemplate in Fig. 4 thin slices of

approximately constant concentration, the permanganate molecules which in a given

moment are contained in a particular slice will, by their random walk, it is true, be carried with equal probability to the right or to the left. 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. When these

considerations are translated into mathematical language the exact law of diffusion is reached in the form of a partial differential equation

§p/§t= DV2

P which I shall not trouble the reader by explaining, though its meaning in ordinary language is again simple enough. The reason for mentioning the stern 'mathematically exact' law here, is to emphasize that its physical exactitude must nevertheless be challenged in every particular