The second part is here: Freundlich's Inaugural, Part 2
The Educational Value of the Study of Astronomy
Astronomy has so far found only very limited acknowledgement at the Universities of Great Britain. Only very few of the English Universities had, until a few years ago, a chair of Astronomy, or maintained research at an Observatory; Scotland is, in this respect, definitely further advanced; for now in three out of the four Scottish Universities Astronomy is represented.
This reluctance in admitting Astronomy into the academic circle is, to a certain extent, conditioned by the relatively low educational value that so far has been attached to the teaching of natural science. This attitude was intelligible as long as man's understanding of Nature was very restricted. As long as his attitude towards Nature was governed by fear and superstition, and science was not sufficiently advanced to outline clearly man's position in the Universe, the educational value of Astronomy remained limited.
The aim of education has always been to transmit all experience and knowledge, thought to be valuable, from one generation to the following younger one. In its earliest phases education was based on those branches of human activities which concerned chiefly the relation of man to man and of man to society. We need not go further back than, say, 1000 years to realise that to teach reading and writing and to transmit the most fundamental rules of decency meant at that time education. In its rudiments human education does not differ fundamentally from that which all higher developed animals try to transmit to their young ones. When the structure of human society became more complex, when clearly defined frames of civilisations and cultures had been formed, education, which included the introduction of the young generation into the various mystic rites, became correspondingly complex.
The true educational value, immanent in the teaching of natural science, could only emerge when science reached a level in understanding the complex structure of the world, which seriously affects the existing views concerning man's place in Nature.
After the first attempt by the Ionian philosophers to develop science on rational lines had failed, when the Platonic philosophy attributed divine character to the planets and thus transformed Astronomy, so to speak, into a branch of Humanities, it took nearly 2000 years before science recovered and could start once more its advance towards a rational interpretation of all phenomena in Nature. This advance has been stupendous during the last century. The immense success in learning how to use the energies which can be released from matter for an improvement of man's way of living - not to speak of the corresponding success in abusing this knowledge for destructive purposes - has, however, completely eclipsed the fact that science reached at the same time heights which have radically enhanced its educational importance. This is particularly true with regard to Astronomy, because our knowledge of man's position in the Universe has been deeply changed.
The central position of the Earth had to be abandoned when Copernicus's picture of the world, already foreseen by Aristarchus nearly 2000 years earlier, could no longer be suppressed. But even then man had not realised to what extent his own position in the Universe would be affected by the immense widening of his outlook. The new knowledge - which has been forthcoming during the last half century is of the utmost importance from the point of view taken here; it has opened the way to a very much deeper understanding of man's place in Nature. Problems have come within reach of natural science of such a universal character, problems concerning the past history of the Universe, the origin of the constitution of matter, the foundation of geometry, in short, problems of such a basic character that their importance in shaping the human mind and thus their educational value, cannot be overlooked. Therefore, as far as Astronomy plays an important part in revealing the universal character of the laws of nature, in building up a consistent picture of the whole Universe, its educational value is, in a certain way, unparalleled. University education, without offering to the students of a country the access to this knowledge, must be considered today to be incomplete.
In this lecture I would like to substantiate this view by three different but fundamentally important cases, which reveal the extent to which Astronomy is widening human knowledge, not by facts, which may perhaps only interest the star-gazer, but by knowledge which must affect every man's attitude towards human life. The first case concerns a problem of physics, namely, the problem of gravitation, the universal character of which has been established by Astronomy. It thus extended our knowledge far beyond the restricted realm of the Earth. The second case concerns the origin of the chemical elements, and illustrates how Astronomy promises to unveil from events that may have happened thousands of millions of years ago, the present state of the world. Finally, I shall show how astronomical research offers answers to questions which were thought to be the domain of pure mathematics; I mean the question of the origin of the laws of geometry, which hold good in the physical space.
(1) It is a fact of great significance that the conception of a gravitational force and the formulation of the first law measuring this force has been achieved by astronomy. All of Newton's results with reference to gravitation are based on astronomical observations.
One should have imagined that a phenomenon as striking as the fact that all bodies on Earth fall unless they are supported, and that they fall with the same acceleration, should have been satisfactorily understood and incorporated in the laws of physics, without being forced to have recourse to the observation of celestial bodies. But the historical facts prove that it has not been so. Only when Newton conceived that the motion of the Moon can be interpreted as a continuous falling of the Moon towards the Earth, the universal nature of gravitation was revealed.
Today, after the accuracy in experimental laboratory research has been so vastly improved, one may ask:- Would it be possible today to lay the foundations of gravitation, which we now realise to be the most fundamental manifestation of matter, merely by using terrestrial experiments in the laboratories, without any reference to astronomical observations? The answer would be definitely No! : For although all motion in the universe is governed by gravitation, the gravitational force is extremely small and only becomes dominant for masses of astronomical dimensions. The extreme minuteness of this force, when investigated with the help of masses of the size which we are used to handle in laboratories on the Earth, render an experiments on gravitation very difficult. For instance, two massive balls, each weighing one kilo, placed at a distance of four inches, exert upon each other an attraction amounting only to the weight of 7 ten-millionths of a gram; this force corresponds to the weight of a tiny ball of iron 2 thousandths of an inch in diameter.
Since the weight of all bodies on the Earth diminishes inversely to the square of the distance from the Earth's centre, one could test the law also by comparing the weight of the same body at various heights over the Earth's surface. Two masses of absolutely equal weight on the Earth's surface, say each of 5 kilos, or about half a stone, would differ by only about 30 milligrams, if the one were put on a scale 70 feet higher than the scale supporting the second mass. This illustrates that the gravitation is, by nature, a cosmic force, which becomes paramount only when masses act upon one another, having masses like the stars and planets. It was thus the natural course that gravitation should be discovered and formulated as an exact law, with reference to the mutual action of celestial bodies.
Now celestial bodies cannot be placed and weighed on scales; their masses, therefore, in Astronomy have to be measured according to other principles, for which Kepler laid the foundation. He asserts in the third of his laws describing the motion of the planets that for all members of the solar system the ratio of the squares of their periods of revolution around the Sun over the cubes of their mean distances from the Sun has the same constant value. Newton's law of gravitation revealed the nature of this constant; it is mainly the mass of the Sun. Strictly speaking, Kepler's third law is not quite correct. In truth, the sum of the Sun's and the planet's mass enter in each case. But, since the solar mass is, at the least, a thousand times greater than the mass of the largest planet, Jupiter, Kepler's law works as a good first approximation. Applying Kepler's law the mass of the Sun can be determined, when we know the mean distance of the planet from the Sun and the period of its revolution around the Sun. The latter is always determinable with great accuracy; the art of measuring accurate distances of celestial bodies has been developed by astronomers to the highest imaginable perfection. In this way the mass of the Sun and also that of the other members of the Solar system became known. The resulting values are by no means rough estimates, but accurate determinations; for the astronomical observations of the celestial bodies are unsurpassed by their accuracy. It may be of interest to realise once, how extremely accurate astronomical observations allow us to follow the motion of a celestial body, so that the slightest irregularities do not escape discovery.
Let us assume that by some unknown reason, other than the Earth's attraction, the Moon's distance from the Earth had increased by one-hundred-thousandth of its expected value, i.e. by not more than 2.5 miles, say, during a hundred months, that means in the course of about 8 years. The resulting change in the apparent size of the Moon, reduced by 1/100,000, would be practically unobservable. However, applying Kepler's third law, one would find that during that time-interval the Moon would have lagged behind in its orbit by half of the apparent diameter of its disc. This is such a large difference between expected and actual position of the Moon in the sky relative to the surrounding stars, that even one thousandth of this value would not have escaped the watchful eyes of the Astronomers.
The law of gravitation has thus given to Astronomers an extremely accurate means of measuring masses, and what is in addition of basic importance, these methods may be applied to all celestial bodies, as far as Astronomers can extend their observations; naturally, provided that the same law of gravitation governs the motion of celestial bodies all over the Universe. Thus it was given to Astronomy to prove, for the first time, the universal character of one of the laws of Nature.
When observers studied the stars in more detail, many systems of bodies were discovered, hundreds or thousands of light-years away from the Earth, systems consisting of two or more stars revolving around each other. A detailed study revealed that their motion can only be satisfactorily understood if the same law of gravitation applies to their motion as that governing the motion of the members of the solar system. Thus the universal character of gravitation has been safely established. The educational value of such knowledge, proving that man can discover and safely establish laws which rule in the Universe, far beyond the realm of the Earth, can hardly be overestimated. But not only that has been achieved. In the motion of the planets small deviations from the predicted motion according to Newton's law were discovered, as soon as theory and observations had become accurate enough. These deviations became the starting point for a further development of the theory of gravitation; from this knowledge, as I shall try to show later, we hope to reach a deeper understanding of the foundations of geometry in physical space.
The planet nearest to the Sun is Mercury, revolving in 88 days around the Sun. Accurate observations extending at present over more than a century, disclose that the orbit, which if the Sun's gravitation were alone acting, should be a closed ellipse - remaining as a whole fixed relative to the stellar system, each revolution being completed in a time strictly prescribed by Kepler's third law - that this orbit appears actually to be closed about one-half of a second of time later than predicted by Kepler's law.
This small deviation in position, not more than a tenth-of-a-second of arc per revolution, slowly builds up, in the course of hundreds of revolutions of Mercury, to a deviation between Newton's theory and observations which is quite considerable and is now safely established. All attempts to account for this deviation within the frame of Newton's law of gravitation failed. The way was thus open for a refined theory, able to explain the planetary motions more accurately and to account also for such a small deviation. This has been done by Einstein's general theory of relativity. It predicts accurately this additional small movement of Mercury which the observations had revealed. For the other planets, more distant from the Sun, this additional effect becomes insignificant. No other observations than astronomical observations could ever have revealed such a minute shortcoming of Newton's theory. It can therefore be safely asserted that the complete knowledge which we have about gravitation as the universal force, which governs the motion of all celestial bodies in the Universe, rests on the observations provided by research in Astronomy.
(2) A very different situation opens up, if we enquire whether Astronomy is able to contribute essential knowledge concerning the nature of the matter which fills the Universe. Not so very long ago the setting of such a problem would not have been considered as reasonable. For, only a century ago, it was more or less a dogma, that astronomical research would never be able to penetrate into such secrets as the chemical and physical constitution of the stars, which were known to be separated from us by tremendous distances through empty space. But at that time the true character of light and other radiation was still unknown; it was not realised that radiation discloses the most intimate properties of the radiating matter. Since the beginning of this century the theory of radiation has been in the forefront of physical research. It has taught us that a detailed spectral analysis of the light emitted by any light source, like a star, transmits to us the most intimate knowledge not only about the chemical elements that give rise to the radiation, but also about the physical conditions, as to pressure and temperature, etc., under which the atoms are radiating. This opened to Astronomy the possibility of extending physical and chemical research to the farthest ends of the Universe, from where the powerful modem telescopes receive the light of distant stars and star systems which may have travelled millions of years before reaching the telescope. Thus it is not surprising that Astrophysics, the branch of Astronomy which specialises in the physical and chemical study of celestial bodies, discovered chemical elements long before these elements were known to the chemists on the Earth. The existence of helium, for instance, the gas which plays such an important part today in many branches of science, was predicted from the analysis of solar light long before Ramsay managed to show that the Earth's atmosphere contains this gas in small amounts and hence also long before it could be obtained in sufficiently large supplies from the oil wells in Texas and Oklahoma.
Similarly the existence of the metal Scandium was astronomically assured, before Eberhard in Potsdam showed that this metal exists in many minerals on the Earth, although always in low concentration.
But the most fundamental contribution which Astronomy promises to give to our chemical knowledge has only lately been revealed. It concerns the problem of the origin of the chemical elements in the Universe. During the last years the complete pattern according to which the chemical elements on the Earth are built up from three main elementary particles - protons or hydrogen nuclei, neutrons and electrons-has been discovered. Every atom has its place in this pattern, and where a gap appeared, that means, where it should have been possible to build up an atom out of a given number of protons, neutrons and electrons - although perhaps so far no such atom has been discovered - it could be proved that such an atom would have only a very short lifetime, i.e. be unstable and so would be difficult to discover. Careful investigations then usually found traces of such predicted elements.
These facts make the universal character of the chemical elements practically imperative. For, other chemical elements than the known ones could only be conceived, if other elementary particles of quite a different character existed in the Universe from which different atoms could be built up; and if they only existed outside of the Earth. No indication of such a state of affairs exists. On the contrary, all observations indicate a common chemical constitution for the various celestial bodies. We have today justifiable hopes that we shall reach an understanding of the problem how were the chemical elements formed, and when were the stars built up? We have already very definite knowledge that the radiation of the stars, in particular that of the Sun, depends on the building up of heavier chemical elements from hydrogen. It is a safely established fact that hydrogen is the brick, from which all stellar matter is made. The energy source, which provides the radiation of a star, is the burning up of hydrogen into helium, the next heavier element. This formation of helium out of hydrogen releases an immense amount of energy; sufficient, if a star starts with an adequate amount of hydrogen, to guarantee its radiation for a time considerably longer than the age of the Earth, which is at least a few thousand-million years old. The combustion of hydrogen is ignited at temperatures of about five to ten million degrees. But temperatures of such a height must exist inside every star, whose mass is of the order of the solar mass. For, the stellar matter near to the centre of the Sun must be able to support the weight of the overlying matter, and can only do this, unless the structure of the atoms be crushed, if the temperature rises to a sufficient height towards the centre. Although we shall never actually be able to observe the physical conditions under which stellar matter exists deep inside a star, we can make very definite statements concerning its density and temperature. Inside the Sun the temperature of its matter must rise to values of at least 10 to 20 million degrees.
Such temperatures are sufficient to ignite the atomic processes from which Helium atoms will be formed out of four protons. This process is accompanied by a loss of mass amounting to nearly 0.8% of the mass of the four hydrogen atoms involved in each building-up process. This mass defect, released in the form of energy, yields the huge amount of radiation breaking out of the surface of a star like the Sun. There are two atomic processes which lead to the formation of Helium; but there is not yet full agreement which of them is the most efficient and therefore the most essential. They differ, however, in one very important instance. The one depends purely on the presence of hydrogen at suitable temperatures and density; the other depends, in addition, on the presence of atoms of heavier elements, in particular of carbon and nitrogen. This latter process will consequently only be ignited in stellar matter which consists already of a mixture of light and heavier elements. It presupposes, therefore, the creation of heavy atoms in the Universe. The other process does not depend explicitly on the existence of any other atoms than protons. This raises the question, when and how were the heavy atoms created? The evolution of stars and the creation of the chemical elements in the Universe thus become two intimately interlocked problems. The astronomical problem of the evolution of stars has moved into the forefront of many basic investigations of atomic physics.
The puzzling riddle is the fact that we cannot yet understand how and where the elements heavier than Helium were created; for, the stellar matter inside radiating stars does not reach temperatures and densities, even in the central region of a star, sufficiently high to make the creation of elements heavier than Helium possible. Our knowledge of the world in its present state can therefore not explain the existence of heavy atoms. Either the present state of the Universe was preceded by another, during which stellar matter reached much higher temperatures, of the order of thousands of million degrees; or during the huge creative processes which we observe when a new star flashes up, the building up of heavy atoms happens, so to speak, before our eyes.
The general expansion of the Universe, which was discovered when the modern large telescopes brought distant star systems, even more distant than a hundred million light years away from us, within reach, gives some indications in favour of the first alternative. If we are entitled to follow the development of the Universe thousands of million years backwards into the past, when all its matter was condensed in a very much smaller volume, and if we are entitled to apply to this early stage of the Universe the same laws of nature that govern our present world, then we may indeed expect that conditions more favourable for the creation of heavy elements may have prevailed for a short phase. But actually it is not necessary to venture so far back into the past and to make such daring extrapolations. In the world, as it exists now, astronomers frequently observe the appearance of so-called new stars, Novae. The name is slightly misleading; for, this flushing up of a bright star, sometimes within a few hours, represents a catastrophal process going on in a formerly faint star. The amount of energy released may be a million times as large as the normal radiation of a star. How these atomic explosions are ignited we do not yet know, but the frequency of their occurrence and the apparently systematic relation to stars of special spectral type, indicates that the appearance of a Nova is by no means a rare occurrence. During such an outburst conditions favourable for the creation of heavy atoms may be produced for a short time; these atoms will be scattered through inter-stellar space, and in the course of time lead to the present admixture of heavy elements to the matter filling inter-stellar spaces, from which stars are formed.
It is beyond the scope of this lecture to enter into more details concerning this intricate problem. I only wish to show and emphasise that astronomy is no longer a removed branch of science, interesting only for the star-gazer. Astronomy has, in many respects, conquered the key position for the most fundamental problems of physics and, as we have just seen, also of chemistry.