Sir Arthur Stanley Eddington

“ But if there is annihilation of matter the life of the sun and the loss of mass continue far longer, and an extended track of evolution lies open before the sun; when it has got rid of three-quarters of its present mass it will have become a faint star like Krueger 60.
Our choice between the possible theories of subatomic energy only affects stellar evolution in one point—but it is the vital point. Unless we choose annihilation of matter, we cut the life of a star so short that there is no time for any significant evolution at all. ”

“ It will be seen that the star works the tap of subatomic energy just as an engine works the valve admitting heat into its cylinder; so that the pulsations of a star are started up like the pulsations of an engine. ”

“ THE AGE OF THE STARS WE have seen that spatially the scale of man is about midway between the atom and the star. I am tempted to make a similar comparison as regards time. The span of the life of a man comes perhaps midway in scale between the life of an excited atom (p. 74) and the life of a star. For those who insist on greater accuracy—though I would not like to claim accuracy for present estimates of the life of a star—I will modify this a little. As regards mass, man is rather too near to the atom and a stronger claimant for the midway position would be the hippopotamus. ”

“ At least we may peer gingerly round the corner, and perhaps we shall find there is nothing very formidable after all. Our object in diving into the interior is not merely to admire a fantastic world with conditions transcending ordinary experience; it is to get at the inner mechanism which makes stars behave as they do. If we are to understand the surface manifestations, [Pg 21] if we are to understand why ‘one star differeth from another star in glory’, we must go below—to the engine-room—to trace the beginning of the stream of heat and energy which pours out through the surface. ”

“ The nucleus is compared to the sun, and the electrons to the planets. Each kind of atom—each chemical element—has a different quorum of planet electrons. Our own solar system with eight planets might be compared especially with the atom of oxygen which has eight circulating electrons. In terrestrial physics we usually regard the girdle or crinoline of electrons as an essential part of the atom because we rarely meet with atoms incompletely dressed; when we do meet with an atom which has lost one or two electrons from its system, we call it an ‘ion’. ”

“ By Milne’s theory we can calculate the whole weight of the sun’s calcium chromosphere. Its mass is about 300 million tons. One scarcely expects to meet with such a trifling figure in astronomy. It is less than the tonnage handled by our English railways each year. I think that solar observers must feel rather hoaxed when they consider the labour that they have been induced to spend on this airy nothing. But science does not despise trifles. And astronomy can still be instructive even when, for once in a way, it descends to commonplace numbers. ”

“ You may wonder why, having said that the sun contains 2,000 quadrillion tons of energy at the most, I now assume that it contains just this amount. It is really only a verbal point depending on the scientific definition of energy. All mass is mass of something, and we now call that something ‘energy’ whether it is one of the familiar forms of energy or not. You will see in the next sentence that we do not assume that the energy is convertible into known forms, so that it is a terminology which commits us to nothing. ”

“ One suggestion for avoiding this dilemma is like the device of a novelist who brings his characters into such a mess that the only solution is to kill them off. We might assume that subatomic energy will never cease to be liberated until it has removed the whole mass—or at least conducted the star out of the white dwarf condition. But this scarcely meets the difficulty; the theory ought in some way to guard automatically against an impossible predicament, and not to rely on disconnected properties of matter to protect the actual stars from trouble. ”

“ We commonly use the method of spectrum analysis when we wish to determine which elements are present in a given mineral on the earth. It is equally trustworthy in examining the stars since it can make no difference whether the light we are studying comes from a body close at hand or has travelled to us for hundreds of years across space. But one limitation in stellar work must always be remembered. When the chemist is looking, say, for nitrogen in his mineral, he takes care to provide the conditions which according to his experience are necessary for the nitrogen spectrum to show itself. ”

“ When the guidance of theory is clear interest centres round the broad principles; when the theory is rudimentary, interest centres round technical details which are anxiously scrutinized as they appear to favour now one view now another. I have dealt mainly with two salient points—the problem of the source of a star’s energy and the change of mass which must occur if there is any evolution of faint stars from bright stars. I have shown how these appear to meet in the hypothesis of annihilation of matter. ”

“ The rash prophecy that knowledge of the composition of the heavenly bodies must be for ever beyond our reach has long been disproved; and the familiar elements, hydrogen, carbon, calcium, titanium, iron, and many others, can be recognized in the most distant parts of the universe. The thrill of this early discovery has now passed. But meanwhile stellar spectroscopy has greatly extended its scope; it is no longer chemical analysis, but physical analysis. When we meet an old acquaintance there is first the stage of recognition ”

“ I must premise that the heat of a gas is chiefly the energy of motion [Pg 12] of its particles hastening in all directions and tending to scatter apart. It is this which gives a gas its elasticity or expansive force; the elasticity of a gas is well known to every one through its practical application in a pneumatic tyre. Now imagine yourself at some point deep down in the star where you can look upwards towards the surface or downwards towards the centre. Wherever you are, a certain condition of balance must be reached ”

“ Although the X-rays are left to your imagination, the photograph at any rate shows the process of ionization which is so important in the stellar interior—the freeing of electrons from the atoms by the incidence of X-rays. You notice that it is just a chance whether the X-ray ionizes an atom when it meets it. There are trillions of atoms lying about (of which the photograph takes no notice) ; but, nevertheless, the X-rays travel a long way before meeting the atom which they choose to operate on. ”

“ There is no earthly reason why a perfect gas should not have a density far exceeding iron. Or it would be more accurate to say, the reason why it should not is earthly and does not apply to the stars.
The sun’s material, in spite of being denser than water, really is a perfect gas. It sounds incredible, but it must be so. The feature of a true gas is that there is plenty of room between the separate particles—a gas contains very little substance and lots of emptiness. ”

“ The Story of Algol
This is a detective story, which we might call ‘The Missing Word and the False Clue’.
In astronomy, unlike many sciences, we cannot handle and probe the objects of our study; we have to wait passively and receive and decode the messages that they send to us. The whole of our information about the stars comes to us along rays of light; we watch and try to understand their signals. There are some stars which seem to be sending us a regular series of dots and dashes—like the intermittent light from a lighthouse. ”

“ Since neither one thing nor the other happens and the star remains practically unchanged for hundreds of years, we must infer that the two tendencies just balance. At each point the elasticity of the gas must be just enough to balance the weight of the layers above; and since it is the heat which furnishes the elasticity, this requirement settles how much heat the gas must have. And so we find the degree of heat or temperature at each point. ”

“ The one reason for thinking that the real truth cannot be so very far away is that in the interior of a star, if anywhere, the problem of matter is reduced to its utmost simplicity; and the astronomer is engaged on what is essentially a less ambitious problem than that of the terrestrial physicist to whom matter always appears in the guise [Pg 40] of electron systems of the most complex organization. ”

“ Perhaps she has hidden in the star something novel which will upset all your ideas.’ But I think that science would never have achieved much progress if it had always imagined unknown obstacles hidden round every corner. ”

“ But the alternative is to leave the stars in sleepy uniformity with no prospect of development or change until their lives come to an end. Something is needed to galvanize the scene into that activity, whether of progress or decay, in which we have so long believed. Rather desperately we seize on the one visible chance. The petrified system wakes. The ultimate particles one by one yield up their energy and pass out of existence. ”

“ Our views of stellar energy are likely to be affected on one crucial point. Hitherto we have usually supposed that the very high temperature in the interior of a star is one of the essential conditions for liberation of subatomic energy, and that a reasonably high density is also important. Theoretically it would seem almost incredible that the building up of higher elements or the annihilation of protons and electrons could proceed with any degree of vigour in regions where encounters are rare and there is no high temperature or intense radiation to wake the atoms from apathy ”

“ Let us consider the factor which hinders the leakage—the turning back of the ether-waves by their encounters with atoms and electrons. If we were dealing with light waves we should call this obstruction to their passage ‘opacity’, and we may conveniently use the same term for obstruction to X-rays.
We soon realize that the material of the star must be decidedly opaque. The quantity of radiation in the interior is so great that unless it were very severely confined the leakage would be much greater than the amount which we observe coming out of the stars. ”

“ The phrase ‘annihilation of matter’ sounds like something supernatural. We do not yet know whether it can occur naturally or not, but there is no obvious obstacle. The ultimate constituents of matter are minute positive charges and negative charges which we may picture as centres of opposite kinds of strain in the ether. If these could be persuaded to run together they would cancel out, leaving nothing except a splash in the ether which spreads out as an electromagnetic wave carrying off the energy released by the undoing of the strain. The amount of this energy is amazingly large ”

“ Astrophysicists are not likely to repeat this achievement; they cannot discover new elements if there aren’t any. The unknown source of the two rings close together on the right of the photograph (a bright ring and a fainter ring) has been called nebulium. But nebulium is not a new element. It is some quite familiar element which we cannot identify because it has lost several of its electrons. An atom which has lost an electron is like a friend who has shaved off his moustache; his old acquaintances do not recognize him. We shall recognize nebulium some day. ”

“ However, even in the depths of space the breaking-up of the atom continues; because there is always starlight passing across space, and some of the light-waves are quite powerful enough to wrench a first or second electron away from the calcium atom. It is one of the most curious discoveries of modern physics that when a light-wave is attenuated by spreading, what it really suffers from is laziness rather than actual loss of power. What is weakened is not the power but the probability that it will display the power. ”

“ But there are in the universe exceptional regions with temperature not far removed from the absolute zero, where the physical properties of matter acquire great complexity; the ions surround themselves with complete electron systems and become the atoms of terrestrial experience. Our earth is one of these chilly places and here the strangest complications can arise. ”

“ The main store of energy in a star cannot be used for radiation unless the matter composing the star is being annihilated.
It is possible that the star may have a long enough life without raiding the main energy store. A small part of the store can be released by a process less drastic than annihilation of matter, and this might be sufficient to keep the sun burning for 10,000,000,000 years or so, which is perhaps as long as we can reasonably require. The less drastic process is transmutation of the elements. Thus we have reached a point where a choice lies open before us ”

“ You remember the ether waves inside the star. These are trying to escape outwards and they exert a pressure on the matter which is caging them in. This outward force, if it is sufficiently powerful to be worth considering in comparison with other forces, must be taken into account in any study of the equilibrium or stability of the star. Now in all small globes this force is quite trivial; but its importance increases with the mass of the globe, and it is calculated that at just about the above mass it reaches equal status with the other forces governing the equilibrium of the star. ”

“ Do stars in the Andromeda nebula run their course in less time than their light takes to reach us?
It is one thing to feel a limitation of time-scale irksome, ruling out ideas and explanations which are otherwise plausible and attractive; it is another thing to produce definite evidence against the time-scale. I do not think that astronomers had in their own territory any weapon for a direct attack on the Helmholtz-Kelvin hypothesis until the Cepheid variables supplied one. ”

“ It is more than 100,000 times the mass of the calcium chromosphere. The sun would have to blow off its chromosphere and form an entirely fresh one every five minutes in order to get rid of as much mass in this way as it loses by radiation. It is obvious from solar observation that there is no such outrush of material. To put it another way—in order to halve the time-scale of evolution stated above it would be necessary that a billion atoms should escape each second through each square centimetre of the sun’s surface. ”

“ The only important release of energy by transmutation occurs at the very beginning of the evolution of the elements.
We must start with hydrogen. The hydrogen atom consists simply of a positive and negative charge, a proton for the nucleus plus a planet electron. Let us call its mass 1. Four hydrogen atoms will make a helium atom. If the mass of the helium atom were exactly 4, that would show that all the energy of the hydrogen atoms remained in the helium atom. But actually the mass is 3·97; so that energy of mass a 0·03 must have escaped during the formation of helium from hydrogen. ”

“ For the time being the sun is comfortably settled in its present state, the amount of energy radiated being just balanced by the subatomic energy liberated inside it. Ultimately, however, it must move on. The moving on, or evolution, is continuous, but for convenience of explanation we shall speak of it as though it occurred in steps. Two possible motives for change can be imagined, (1) the supply of subatomic energy might fall off by exhaustion and no longer balance the radiation, and (2) the sun is slowly becoming a star of smaller mass. ”

“ The architect can work out the stresses inside the piers of his building; he does not need to bore holes in them. Likewise the astronomer can work out the stress or pressure at points inside the sun without boring a hole. Perhaps it is more surprising that the temperature can be found by pure calculation. It is natural that you should feel rather sceptical about our claim that we know how hot it is in the very middle of a star—and you may be still more sceptical when I divulge the actual figures! ”

“ No source of energy is of any avail unless it liberates heat in the deep interior of the star. The crux of the problem is not merely the provision for radiation but the maintenance of the internal heat which keeps the gravitating mass from collapsing. You will remember how in the first lecture we had to assign a certain amount of heat at each point in the stellar interior in order to keep the star in balance. But the internal heat is continually running away towards the cooler outside and then escaping into space as the star’s radiation. ”

“ We may look forward to a time when the supply of subatomic energy fails and there is nothing to maintain the high temperature; then on cooling down, the material will return to the normal density of terrestrial solids. The star must, therefore, expand, and in order to regain a density a thousandfold less the radius must expand tenfold. Energy will be required in order to force out the material against gravity. Where is this energy to come from? An ordinary star has not enough heat energy inside it to be able to expand against gravitation to this extent ”