A Theory of Everything (That Matters): A Brief Guide to Einstein, Relativity, and His Surprising Thoughts on God by Alister McGrath- Part 6, Chapter 4- The Theory of General Relativity: Final Formulation and Confirmation
We are reviewing Alister McGrath’s new book, “A Theory of Everything (That Matters): A Brief Guide to Einstein, Relativity, and His Surprising Thoughts on God”. Chapter 4 is “The Theory of General Relativity: Final Formulation and Confirmation”. Even though we have come to admire the “wonder year” of 1905, at the time no offers of academic employment were offered. In July the University of Zurich accepted Einstein’s doctoral thesis, “A New Determination of Molecular Dimensions” but did not offer him a position. In April 1906 he was promoted to technical expert, second class, at the Bern patent office, which salary increase he was grateful for, but still not what he really wanted. Finally in October 1909, the University of Zurich appointed him an adjunct professor in theoretical physics. Two years later, he was appointed as full professor at the Karl-Ferdinand University of Prague, before returning to Switzerland in 1912 to take up a chair at the Eidgenössiche Technische Hochschule in Zurich. In 1914, Einstein was appointed director of the Kaiser Wilhelm Institute for Physics and professor in the University of Berlin. But despite the academic achievements, Einstein and Mileva Marić separated and in 1919 divorced, shortly after which Einstein married Elsa Loewenthal.
With the outbreak of the First World War in August 1914, international scientific collaboration ceased and Einstein was isolated in Germany during this period. He now had the time to try and develop a generalization of his theory of special relativity. Special relativity considered only the effects of relativity to an observer moving at constant speed. So what about bodies that were moving at changing velocities? And what about the influence of gravitational fields on space-time?
Newton had proposed gravity as a force between bodies as they moved through space, understanding space as a vast empty container. Then James Clerk Maxwell and Michael Faraday introduced the idea of electromagnetic fields and show that light is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws. Einstein came to the view that, like electricity and magnetism, gravity was conveyed through a “gravitational field” – and more radically, that this gravitational field is actually what Newton considered to be “space”. Instead of thinking of space as a container through which the planets move under the influence of gravity, we need to think of space itself as a gravitational field, which is distorted locally on account of the mass of stars.
On the basis of this approach, Einstein predicted the phenomenon of the gravitational dilation of time. The closer a body is to a large mass, with its substantial gravitational pull, the slower time runs for it. This phenomenon is now well known and important for the functioning of Global Positioning Systems (GPS), which rely on signals from satellites orbiting above the Earth to establish the observer’s position. However, as we have already stated, the atomic clocks in those satellites run 32 microseconds faster than clocks here on the surface of the Earth (I think I had that reversed in the last post – my error – see this summary here) In other words, time passes at a different rate on the surface of the Earth due to the greater effect of the Earth’s gravity.
Newton had understood matter to attract other matter across empty space – I daresay most of us still have this conception. Einstein developed the quite different idea that matter distorts space-time. Newton himself never applied his theory of universal gravitation to the behavior of light. Scientists who held that light could be thought of as a beam of particles predicted that gravity would affect its passage through space. Two predictions are of special interest. The first is John Mitchell’s 1783 prediction of “dark stars” that could not be seen because light could not break free from their gravity (a remarkable prescient intuition of black holes!). The second is the 1804 prediction of Johann Georg von Soldner that a beam of light would be deflected by the gravitational field of a star; he even calculated the extent of deflection. But Einstein did not regard light as a beam of particles affected by gravity on account of their mass, rather based on the principle of the equivalence of mass and energy, light on account of its enormous velocity had an “effective mass”. Newton thought light had mass; Einstein showed that it behaved as if it had mass. In effect, Einstein’s theory of general relativity confirmed both these predictions but place them on a different theoretical foundation. Einstein published his paper, “The Foundation of the General Theory of Relativity” in March 2016 to the German scientific journal Annalen der Physik.
McGrath says the analogy he finds most helpful in visualizing this effect is that of space-time as a trampoline with a heavy object placed on it. The trampoline fabric sags toward the heavy object and any ball rolled across the trampoline will move towards the heavy object. Why? Because it is drawn to the object, or because it naturally follows the deformation in the shape of the fabric resulting from the weight of the object? The second explanation is correct. General relativity asks us to think of the sun and planets warping space-time. The planets orbiting the sun are not really being pulled by the sun; they are actually following the curved space-time deformation caused by the sun, like the ball rolling towards the heavy object on the trampoline. All the pictures I’ve been showing are 2-dimensional representations, Einstein was theorizing that the deformation takes place in all 3 dimensions of space and the dimension of time as well! Hence the term space-time: the concepts of time and three-dimensional space regarded as fused in a four-dimensional continuum.
One of the most significant aspects of Einstein’s “The Foundation of the General Theory of Relativity” was its specific predictions of what would be observed if the theory was correct. The three main predictions Einstein made were:
- A shifting of the perihelion of the planet Mercury. Although this effect should be observed for all the planets, it would be most pronounce for Mercury because it was so close to the sun.
- The phenomenon of gravitational lensing, in which the warping of space-time due to the gravitational influence of the sun caused light to bend.
- The phenomenon of cosmological redshift. This prediction followed from Einstein’s equivalence principle noted in 1907.
Yet one prediction is strikingly absent from this list – the expansion of the universe. Einstein’s first cosmological solution of his field equation indicated the universe was expanding. Einstein modified his equation, adding another term – the so-called “cosmological function or constant” – in order to yield a static universe. By 1929 the research of Edwin Hubble suggested that the observational evidence was best explained by an expanding universe. Einstein’s approach suggests that the universe expands not on account of the movement of galaxies but because space-time is expanding.
Why did Einstein not trust his original equations? Why did he introduce a “fudge factor” designed to fit the soon-to-be abandoned model of a static universe? McGrath says he has not found a convincing answer, although many suggestions have been made. As an admirer of Dutch Jewish philosopher Spinoza, maybe he genuinely believed that the universe was necessarily eternal.
We dealt with the advance of the perihelion of Mercury in Part 3. The third prediction had to wait for significant technological advances before it could be measured. The second prediction was verified in the total solar eclipse of May 29, 1919 by Sir Arthur Eddington and Sir Frank Watson Dyson, although not all physicists agreed with their conclusions at the time. This resulted in the famous Times of London headline, “Revolution in Science, New Theory of the Universe. Newtonian Ideas Overthrown”. Einstein himself gave an interview with the New York Times in April 1921 in which he emphasized that his theories were to be seen as an evolution that consolidated Newton’s heritage rather than a revolution that discarded it. Einstein thus did not regard his theories as revolutionary but as a systematic development of earlier approaches. But it was too late for popular media in Britain and the US, where he was lionized as the revolutionary thinker who had overthrown scientific orthodoxy.
Oddly enough, while the US and Britain heralded him, the German scientific establishment indulged in a campaign to discredit him as a plagiarizer and a lightweight. The ugly phrase “Jewish physics” began to be used in contrast with “German physics” that only intensified as Nazi sympathizers gained strength. It is a measure of the controversy of the times that Einstein’s 1922 Nobel Prize was issued for his work on the photoelectric effect back in 1905, rather than his relativity theories. Einstein was rightly alarmed at the rise of Nazism. McGrath says it spurred him into developing his own political, social, and religious beliefs. On December 12, 1932, Einstein and his wife left Berlin for the United States. Hitler was installed as chancellor a month later, and it was made clear that he would not be welcomed if he returned.
As remarkable as Einstein’s body of works was, he himself saw it as incomplete. Einstein’s writings of the 1910s show how driven he was for his quest for die Einheitlichkeit – “the uniformity” i.e. the fundamental unity of all phenomena. Although the general theory of relativity is still the best generalized theory of gravitation and space-time structure, it cannot account for the quantum effects that govern the sub-atomic world. Although most physicists adopt a pragmatic work-around to this problem, using general relativity to describe large-scale phenomena of astronomy and cosmology and using quantum mechanics to account for the behavior of atoms and elementary particles, Einstein himself was never satisfied.
General relativity has geometric precision and is deterministic; the world of quantum physics is shaped by uncertainties and is probabilistic. This feature caused Einstein to have serious misgivings about its viability and that led to his famous (and often misunderstood) remark to the effect that God “does not play dice”. This quote is found in a private letter from Einstein to the Hungarian physicist Cornelius Lanczos, who was then based at Princeton, dated March 12, 1942. Einstein wrote: “It seems hard to sneak a look at God’s cards. But that he plays dice and uses ‘telepathic’ methods (as the present quantum theory requires of him) is something that I cannot believe for a single moment.” This is unfortunately often simplified to “God does not play dice”. For a more complete discussion, McGrath recommends Ghirandi, Sneaking a Look at God’s Cards, pages 149-164.
In the conference in Brussels in 1927, Einstein famously clashed with Niels Bohr over quantum mechanics, launching a feud that would last until Einstein’s death in 1955. Bohr championed the strange new insights emerging from quantum mechanics. He believed that any single particle—be it an electron, proton, or photon—never occupies a definite position unless someone measures it. Until you observe a particle, Bohr argued, it makes no sense to ask where it is: It has no concrete position and exists only as a blur of probability.
Einstein scoffed at this. He believed, emphatically, in a universe that exists completely independent of human observation. All the strange properties of quantum theory are proof that the theory is flawed, he said. A better, more fundamental theory would eliminate such absurdities. In 1935 Einstein was convinced that he had refuted quantum mechanics. And from then until his death 20 years later, he devoted nearly all his efforts to the search for a unified field theory. Einstein spent the rest of his life trying to formulate “The Theory of Everything”. Einstein himself, came to believe he failed at that quest, and his critics contend he wasted his life. But McGrath believes that Einstein, was, once again, ahead of his time, he says he may have started from the wrong place, but he rightly grasped the possibility of holding together the complexities of the universe within a single grand theory. McGrath says:
Einstein’s pursuit of a unified view of the world remains important beyond the world of physics. One of the central themes of this volume is the need to reflect on Einstein’s belief that it was possible to hold together – if not to weave together into a coherent unity – his views on science, ethics, politics, and religion. The search for a unified view of reality is not limited to physicists or cosmologists. We each, in our own way, try to weave together the threads of our beliefs and commitments in the hope of creating a coherent picture of reality… We shall turn to consider these questions in the second part of this book.