E.P.J. van den Heuvel is professor emeritus in Astrophysics at the University of Amsterdam. He was born in 1940 in Soest, The Netherlands, and received his Ph.D. at the University of Utrecht in 1968. He worked at the University of California, Santa Cruz (1968 to 1969), and at the Universities of Utrecht (1969 to 1974) and Brussels (1970 to 1980). In 1974 he was appointed Professor of Astrophysics in Amsterdam; until 2005 he was also Director of the Astronomical Institute there. In 1995 he was awarded the Spinoza Prize, the highest science prize of the Netherlands, and in 2002, the EU Descartes Prize, the highest science prize of the European Commission. He is member of the Royal Netherlands Academy of Arts and Sciences, and honorary fellow of the Indian Academy of Sciences, of the Royal Astronomical Society, and of the Inter University Center for Astronomy and Astrophysics (IUCAA), Pune, India. In addition, he has been knighted in the Order of the Netherlands Lion. Professor van den Heuvel’s fields of expertise include stellar evolution, the physics of neutron stars and black holes, X-ray astronomy and radio pulsars.
In the past, Natural Science was called Natural Philosophy. Isaac Newton called his main work “The Mathematical Principles of Natural Philosophy” and in my student days the faculties of Science in my country were still called “Philosophical Faculties”. Indeed, the development of science is deeply intertwined with the development of philosophical thinking, and one may wonder whether there is really a difference between the two.
A key example concerns the critical thoughts which Austrian philosopher-physicist Ernst Mach put forward about the concepts of space and inertia, which greatly influenced Albert Einstein’s ideas about these topics, and indirectly led to his General Theory of Relativity, one of the greatest achievements of scientific and philosophical thinking ever.
Mach considered Newton’s idea of an absolute space, which exists independent of any observable object, to be unacceptable. In Newton’s idea this absolute and unmovable empty space fills the entire Universe and is basically the background relative to which all motions and accelerations of objects take place. Newton had discovered that in order to get an object to move from standing still to reaching a certain velocity, it has to be accelerated, and that for getting this acceleration a force should be exerted on the object. And he discovered that the required force F is equal to the mass M of the object multiplied with the acceleration a. This is Newton’s famous equation F = M.a. The mass (amount of matter) in this equation he called the inertial mass of the object, as it signifies the resistance of the object against being set in motion ( being accelerated). For example, to impart the same acceleration to a car with a mass of 1000 kilogram as to one of 500 kilogram, one should exert twice as large a force on the former, as compared to the latter.
Another very important law which Newton discovered was the law of gravity: a body with a mass M attracts another body, with mass m, at distance r with a force which is equal to the product of the masses, divided by the square of the distance:
Here G is a number, which can be measured experimentally, which is called the gravitational constant. One sees from this equation, by dividing by m, that the acceleration of gravity produced by the body with mass M is g = - GM.m/r2 . This mass of the body which causes the gravitational acceleration, is called its gravitational mass. With this mass it exerts an attractive force on its surroundings. This is just like a magnet which attracts a piece of iron or an electric charge which attracts an opposite electric charge. This gravitational mass is a therefore a kind of attractive “gravitational charge”, which produces the gravitational attraction of the body, but appears to have nothing to do with the inertial mass. But surprisingly, Newton found that the inertial mass is equal to this gravitational mass. This fact greatly puzzled Newton and many generations of physicists after him: why are gravitational mass and inertial mass the same, while they seem to have nothing to do with one another?
Then, in 1873, Mach put forward the philosophical objection to Newton’s absolute space, that this space can never be directly observed, and therefore is an unacceptable physical concept. His opinion, as a positivist philosopher, was that physical concepts must, one way or another always have a connection with observable reality.
Mach asserted that inertial forces, such as those we experience in a merry-go-round, must in some way be related to gravitational forces, and he put forward the idea that they could be due to the combined gravitational attraction of all the masses in the Universe, that is: the attraction of the stars. Amazingly, Einstein’s General Theory of Relativity, which is a new theory of gravitation, which connects gravitation with the properties of space and time, has proved Mach right. We now know that indeed inertial forces are due to the combined gravitational workings of the entire Universe, the attractions of the most distant galaxies making the largest contribution. It is amazing to realize that every time our train or plane accelerates or brakes, or every time we sit in a merry-go-round, we feel the entire Universe pulling at us! Who would still say that the Universe has nothing to do with us?
We see here that a philosophical thought was the fundament for a new way of looking at Nature. In fact, in his rejection of absolute space, Mach had been preceded by the 18th century Irish philosopher-bishop Berkeley, who in 1721 with great foresight had said in his book “De Motu” (On Motion) that there was no need for Newton’s absolute space, because the stars could fulfil its function. Just like Mach he objected to absolute space because it is unobservable, and he noticed that when one rotates relative to the fixed stars (and thus sees the starry sky rotate), one experiences centrifugal forces: when one sees the stars stand still, one does not feel centrifugal forces. So, clearly the starry sky takes the function of Newton’s absolute space: inertial forces emerge when one is accelerated relative to the stars. This was one and a half century before Mach and almost two centuries before Einstein!
The General Theory of Relativity, which Einstein published in 1915, gives a revolutionary new view of gravity, as a manifestation of the geometry of space. Gravity is a very weak force and plays a crucial role only if one studies the behaviour of large amounts of matter. It is therefore important for understanding the evolution of our world on the largest scales: the structure of planets, stars, galaxies and of the entire Universe. Einstein discovered in 1916 to his great dismay that his new type of gravity will make the Universe unstable and forces it to contract. Since his conviction was that the Universe must be eternal and stable – which means that the factor time does not play a role in the structure of the Universe- he added an extra term to the mathematical equations of his gravity theory, a term which – so he thought – would make the Universe stable and static. This term, containing the so-called Cosmological Constant, indicated by Greek letter Λ, in fact implies that empty space (vacuum, in which no matter is present) contains energy which exerts a repulsive force which counteracts the gravitational attraction of the matter in the Universe, and in this way saves the Universe from contracting and keeps it in balance. However, in 1917 astronomer Willem de Sitter in the Netherlands showed that – contrary to what Einstein had thought – this Λ-term does not stabilize the universe, because the equilibrium which Einstein had thought to attain is an unstable one. Even the slightest possible disturbance, such as the random motion of a few molecules away from their equilibrium position will make the Universe unstable, such that the repulsive gravity Λ-term will cause the Universe to start expanding at an accelerated pace, which would mean that all galaxies fly away from each other. In 1929 Edwin Hubble precisely discovered this: all galaxies are flying away from each other, meaning that the Universe is expanding. It was then briefly thought that this was indeed due to the repulsive Λ-gravity term of the de Sitter Universe. But it was soon realized that also Einstein’s original equations of 1915, without the repulsive gravity term, allowed expanding mathematical solutions, which had already been found in 1923/1924 by Russian physicist-genius Alexander Friedman and, independently, in 1927 by Belgian Catholic priest Georges Lemaitre. Since that time there was no longer a need for the repulsive gravity term, which always had seemed like an artificial and not very elegant addition to the simple and elegant original form of the General Theory of Relativity of 1915. Einstein later, in the 1940s, remarked to physicist George Gamow that his introduction in 1916 of the repulsive Cosmological Constant gravity had been his “biggest blunder”. The de Sitter Λ-model of the Universe, with its accelerated expansion of the Universe, was since about 1935 almost forgotten. Amazingly, however, in 1998 this model made a miraculous come-back when it was discovered, by careful studies of the brightness of very distant exploding stars, that the expansion of the Universe is accelerating. It was soon realized that the simplest way to explain this acceleration is by means of Einstein’s Cosmological Constant Λ-term, which implies that the empty space (vacuum) of the Universe contains an unknown type of energy which drives the galaxies in the Universe apart at an accelerated pace. This mysterious energy, which appears to constitute about 73 per cent of the total energy content of the Universe, is called “Dark Energy”. Its existence has since been proved by a variety of observations, but its origin is still one of the greatest unsolved mysteries of present-day physics. The three discoverers of Dark Energy were awarded the 2011 Physics Nobel Prize.
This story shows how even the greatest scientists/philosophers can be fooled by prejudices: Einstein by thinking that time and evolution cannot play a role in the Universe. It also shows that – contrary to what most physicists and mathematicians tend to think- not always the most elegant and simplest form of a theory – in this case General Relativity – is the correct one. Always Nature - that is: observation and experiment – is the final judge, deciding which theory is the correct one.
This brings me to the other great achievement of twentieth century physics: quantum mechanics, and to how poor a machine our brain is for understanding Nature and for gaining a feeling of how Nature really works.
Quantum mechanics was pioneered also by Einstein, in his 1905 paper in which he gave the solution of the puzzling observed behaviour of the photoelectric effect. He showed that this effect is the result of the quantisation of the energy of light. He put forward that light and other electromagnetic radiations consist of a stream of energy packages: the photons. We knew at that time already for about a century that light is a wave-phenomenon, and apparently these waves come in packages, a kind of particle. Later it was found that also particles of matter, for example electrons, have a wave character, and in fact also are wave packages. Quantum mechanics is a highly mathematical theory to explain this combined wave-particle behaviour of matter and radiation. It was built by Niels Bohr, Erwin Schrȍdinger, Werner Heisenberg, Paul Dirac and others in the 1920s, and has been extremely successful for explaining the behaviour of atoms, nuclei and radiations. While General Relativity describes the behaviour of nature at the largest possible scales, quantum mechanics describes its behaviour at the smallest possible scales: of atoms, nuclei, elementary particles and electromagnetic radiation, and of how matter and radiation interact with each other. Quantum mechanics is very strange: it tells us that a particle can be at the same time here and at another place; can at the same time be a particle and a wave. And also that the behaviour of an elementary particle cannot be fully predicted, but only with a certain statistical probability. This seems completely crazy, but has been confirmed by thousands of laboratory experiments. The mobile phone in our pocket and the computer on our desk would not be able to function if the silicon atoms in their microchips did not obey these crazy counter-intuitive laws of quantum mechanics. Theoretical physicists have been knocking their brains out in trying to find flaws in the idea that at microscopic scales nature is not fully predictable (deterministic). No such flaws have been found and time and again experiments have confirmed that at the micro-level nature behaves in this strange way. Without this strange behaviour neither atomic bombs nor mobile telephones nor lasers nor glass-fiber communication would be possible. A large amount of philosophical thinking has been devoted in trying to understand the deeper meanings of quantum mechanics and of nature’s behaviour at the micro-level. But so far all this effort has been in vain. As famous physics Nobel laureate Richard Feynman remarked: “Nobody really understands quantum mechanics”. Apparently we will have to accept that this is just how nature behaves, and that our brains are not fit for probing deeper into this strangeness.
Here we run into the problem that our brains, which developed only quite recently from those of our ape-like ancestors, find many things in the behaviour of nature strange and counter-intuitive. This goes back a long way: when we look out of our window it appears that the Earth is flat and is standing still. But we know now that it is a sphere which rotates around its axis with at the equator a speed of some 1800 km per hour – twice the speed of a commercial jet plane - and moves in its orbit around the Sun with a speed of close to 30 km per second. In four hours we have moved over some 430 000 km, more than the distance from here to the Moon. But we feel nothing of these enormous velocities. It appears to our senses that the Earth is flat and at rest. In 1632 Galileo Galilei was condemned by the church for his conviction that the Earth is moving. The strange fact that we do not feel motion with a fixed speed was first realized by this Italian genius, which was one of the greatest discoveries of physics ever made. Everybody nowadays knows this: when we fly in a jet plane to our holiday destination we have a speed of about 900 km per hour. But in the plane we walk around, drink our coffee, eat our meals, just as though the plane were standing still on the ground. The only thing which we notice is an acceleration: when the plane takes off, we are pressed against the back of our seats, and when the plane slows down for the landing, we shoot forward. This is why we need seatbelts: at a sudden braking, inertia propels us forward with respect to the plane, because the entire Universe is pulling at us, as explained in the beginning of this article.
It has taken the ape-like brains of humans thousands of years to realize these strange and counter-intuitive laws of nature. Clearly, our ape-like intuition is not a good guide if we wish to understand how nature really works. Our everyday intuition and thinking fools us time and again, and the effort of trying to gain an understanding of the world by pure thinking, without paying attention to careful observation of how nature around us really behaves, almost always leads us completely astray.
I give here the following famous example of a philosopher that went astray in my own field of astronomy by overestimating the powers of his pure thought.
Famous French philosopher Auguste Comte predicted in 1835 about the stars that ”…we will never be able by any means to determine their chemical composition, nor their density or temperature”. Only 25 years later, German physicists Kirchhoff and Bunsen discovered, by analysing the light of flames, that each chemical element that is brought into the flame produces its own characteristic spectrum, consisting of a distinct pattern of lines at specific wavelengths of the light, a pattern which is characteristic for each element and different from that for every other element. When one finds for example the pattern of lines of the element iron in the spectrum of the light of a star, one knows that iron is present in the star. In this way we now know that the same 92 chemical elements that we know on Earth are present in the Sun and in stars and galaxies out to the edges of the observable Universe, some 13 billion lightyears away. From this we know now that the same laws of nature that rule the structure of atoms here on earth, are valid throughout the Universe, and that the Universe thus exhibits a majestic unity. Also, thanks to the laws of governing radiations and atoms, discovered by Max Planck, Einstein and others, we can nowadays accurately measure the temperatures and densities of stars, something Auguste Comte also had deemed totally impossible forever.
As a student every astronomer hears this story and becomes careful about believing claims of philosophers about science. Nevertheless, all of us scientists work according to an implicit tacit philosophy about how to do research, about what is good science and about what are good and reliable theoretical concepts, and about what is bogus science. Scientists learn these implicit philosophical concepts through their training, by carrying out research under the guidance of experienced scientists: “learning by doing”. Natural sciences are the study of nature and, as was first realized by Greek thinkers some 2500 years ago, the study of nature means: careful observation of natural phenomena, and carrying out careful experiments. And this has remained the basis of the natural sciences ever since. It has always struck me how strongly progress of my own field of astronomy is driven by often totally unexpected new observational discoveries, of objects or phenomena, ranging from neutron stars to black holes, exoplanets, gamma-ray bursts , Dark Matter, which constitutes some 23 per cent of all mass-energy in the Universe and Dark Energy which constitutes some 73 per cent of all mass energy. The last-mentioned discoveries – for which there still is no theoretical explanation - have degraded our “normal” matter of atoms, of which men, planets,, stars and galaxies consist, to represent only a tiny four per cent of the mass-energy content of the Universe. This is the ultimate Copernican Principle: first the Earth was found to not be the centre of the solar system, then the sun was found not to be in the centre of our Galaxy, and our Galaxy to not be in the centre of our Universe, but only one of hundreds of billions of galaxies in an expanding Universe. And now even the matter of which we consist appears not to be the main constituent of the Universe! How insignificant can we be!
One may wonder why a famous philosopher such as Comte made the blunder described earlier in this article. I think that this has to do with a quite general phenomenon that I see all around me among theorists, also in physics and astronomy, which is: overconfidence in the power of our brains to fathom by pure thinking how the real world works and is built, combined with a gross underestimate of how complex and unpredictable the real world is. I would call this: “the arrogance of the theorist”, who overestimates his or her own brainpower. Comte thought that it would never be possible to find out what stuff stars and planets are made of and what their temperatures and densities are, just because he could not imagine the existence of atoms, and of the quantum jumps which electrons in atoms make, which produce the spectral lines of the light emitted by the atoms of the different elements. He highly overestimated the power of his own imagination.
In science, observation and experiment are the “reality check” and every time a theorist wanders away too far from experiment and observation, he/she faces the danger of wandering into the domain of speculation and wishful thinking. The only way to pull the theorist back into the world of reality is to ask: what phenomena does your new theory predict that I can test by experiment or observation? It characterizes the great theorists like Newton, Einstein, Planck, Bohr and many others that their theories are (1) meant to explain phenomena observed in nature (in the case of Newton, Kepler’s laws of planetary motions, in Einstein’s case the observations of Michelson and Morley about the constancy of the velocity of light, the observations of the photo-electric effect and the observation that free falling objects are “weightless”), and (2) that these theories make predictions about so far unknown phenomena, which can be tested by experiment or observations. For example, Einstein’s General Theory of Relativity predicted the deflection of light rays from stars by the gravitation of the Sun, confirmed in 1919 in solar eclipse observations, and the redshift of starlight due to gravity, also confirmed, and the excess motion of the perihelion of the planet Mercury, also confirmed with high precision.
A key question is: how do scientists make discoveries and conceive new theories about the world? As philosopher Karl Popper has noticed, the answer is: by trial and error. In some sciences, courses are given in “the methodology of science”. In the views of Popper and myself, there is only one methodology of science: trial and error. This is, undoubtedly, also the way in which Newton and Einstein worked: you try something and think fully through all of the consequences of your new idea or theory, and perhaps build an instrument to test this theory. Soon enough you find out whether the consequences of your new idea fit reality (experiment, observation) or not. In the latter case you reject your idea or theory and try something else, until you find some theory that does not lead to contradictions or to conflicts with observations or experiments. That might then be a good theory to explore further. This trial and error method is the method that any sensible creature on Earth uses: a chimpanzee in trying to reach a piece of food, a rat in a maze, and a human being. Clearly, this is not the method which Comte used: he highly overestimated the power of his own brains in trying to be able to make absolute and true statements about reality.
One of the most miraculous aspects of the Universe is that it appears possible for us humans to decipher the laws according to which nature works: that the Universe is understandable. As mentioned above, this is thanks to the fact that the Universe exhibits a marvellous unity, with everywhere the same 92 chemical elements, showing that the same laws of quantum mechanics, nuclear physics that rule the structure of matter here on earth, are valid throughout the entire Universe. Physicists have discovered that these laws can be reduced to three basic forces that rule all that happens in the Universe: the electroweak force (which rules electromagnetism and the weak nuclear force that causes radioactivity), the strong nuclear force (which binds protons and neutrons together in atomic nuclei), and gravity. The holy grail for which physicists nowadays are searching is a theory that would demonstrate that these three forces are three different aspects of one universal force. There are bold theorists nowadays that claim that the so-called string theory should be able to achieve this over-arching unity. But so far string theory has been unable to make even one prediction that is testable by experiment or observation.
Whether the search for this “final theory” of everything, which would explain all of nature, will ever be successful, therefore remains to be seen. Such a theory should at the same time also be able to explain the great unsolved mysteries of the nature of Dark Matter and Dark Energy, described above. If achieved, this would be the greatest triumph of natural philosophy ever.