3.21 Gravity part 2: star formation and Einstein’s alternative concept

This blog follows on from 3.20 Gravity part 1: gravitational force and the solar system.

Star formation

The Sun itself and all the other stars were themselves formed by gravity. The molecules of which they are made, mainly of the gases hydrogen and helium, though not massive individually, were attracted to one another gravitationally, in the absence of any other force. As the mass built up, and the particles grew ever closer the gravitational pull between them increased. As a consequence, pressure within the gases grew and grew, leading to ever higher temperatures. A point is eventually reached at which the temperature and pressure at the core of a developing star is so extreme that the very atoms (strictly, the nuclei at their centre) begin fusing together. These nuclear fusion reactions release enormous quantities of energy, as the power of the heat, light and other forms of solar radiation testifies.

In recent times, the surroundings in which stars are formed have been brilliantly captured by photographs taken by the Hubble telescope orbiting the Earth.

The telescope lies outside the atmosphere, making its images exceptionally sharp. They reveal clearly great regions of gas and dust in the distant regions in which new stars are born.

The so-called “pillars of creation” in figure 1 consist of cosmic dust and gas, dotted with stars. Colours have been added to show the various types of atoms present (blue for oxygen, red for sulphur and green for nitrogen and hydrogen). The entire structure is 4 to 5 light years across – some 40+ million, million kms.

Figure 1: The piIlars of creation, from the Hubble telescope. Picture credit: NASA

Einstein’s concept of gravity

In one memorable discussion about gravity, Sally said she had read that there were now different theories about the cause of gravity – “was Newton wrong?” she asked. It’s true: the explanation given above about gravitational force drawing bodies to one another is based on Newton’s original concept. In the famous falling-apple story, he is credited with having seen that the apple is attracted towards the centre of the Earth by a force due to the huge mass of the Earth. In conversation with an acquaintance he is recorded as having said when watching an apple fall from a tree:

“why should it not go sideways, or upwards? but constantly to the earths centre? assuredly, the reason is, that the earth draws it. there must be a drawing power in matter. & the sum of the drawing power in the matter of the earth must be in the earths centre, not in any side of the earth. therefore dos this apple fall perpendicularly, or toward the centre”.

 Even more imaginatively, he grasped that the Moon was also attracted in a similar way, and that is what kept pulling it inwardly in an orbit around the Earth rather than flying off into the infinite beyond. This theory has proved so accurate that, even today, space missions are planned according to his formulation.   

What Sally had picked up however is that, two centuries later, Einstein had the imagination to see gravitational influence in a completely different way. His resulting theory, though it aligned perfectly with Newton’s for most practical purposes, dispensed entirely with the notion of force. Instead, the very gridlines of space (or more accurately spacetime – a four dimensional amalgam of 3-D space plus time) were distorted by the presence of mass. Where there was matter, space itself was altered. For huge masses, like a planet or star, the distortion or ‘warping’ of space around it was correspondingly large. This warping changes our intuitive sense of space as being mapped out rigidly by three imaginary straight lines – height, depth and width – the very grid itself can flex. Out in the great beyond, away from all stars, our intuitive idea holds true – the dimensions of space can be imagined as straight lines. Wherever a large mass exists, however, these lines are curved.

It’s more or less impossible to imagine this situation visually. Hard enough to even think of space itself has having a curvature, but to add in the dimension of time….. Scientists resort to mathematics to cope with the impossibility. To get some feel for what curved spacetime might mean analogies are often used, based on depicting the warping of a two-dimensional surface.

In figure 2, space is represented as a two dimensional grid which is perfectly flat away from Earth, but increasingly curved closer to the mass of the Earth. An orbiting satellite is depicted, following the lines of space, rather like a ball bearing circling around the curved surface of a spinning roulette wheel. No force is involved, just the pursuit of an orbit by conforming to the curved lines of space  – as naturally as an object continuing in a straight line out in space.

Figure 2: simplified impression of curved space

The limitation of this image is that the lines of space are in fact three-dimensional (four if we include time) and can’t be represented on a flat page. So the downward falling lines are actually all cascading inwards towards the centre of the Earth. That’s why objects fall, why a thrown ball falls – it’s following the grid lines of space towards the centre of the Earth.

An extreme example of this curvature in the fabric of spacetime occurs when a large mass is exceptionally concentrated – in extremely dense matter in other words. This possibility was originally worked out when Einstein communicated his new theory (now called the general theory of relativity)[i] to a colleague, Kurt Schwarzschild, who, at the time (1915), was serving in the trenches on the Russian front. Even in these extreme circumstances he was able to work out that for a star packed into a very small radius, the curvature of space would be so extreme that no particle, and not even light itself, would be able to escape. Like an extreme version of throwing  a ball upwards only to fall again, nothing at all would be able to escape, however powerfully it was projected upwards. Even a searchlight beam would be bent back.

The implication of this theoretical idea was that no-one would actually see such a hyper-dense star as no light would have escaped from it to reach our telescopes. The place where it was located would simply appear black.  The idea of such bizarre objects seemed so outlandish that the possibility of their existence was not taken seriously by scientists at the time. In 1939, however, the American physicist Robert Oppenheimer managed to predict that under certain conditions a star could collapse under the inward gravitational pull of its own mass to such an extreme degree. The name “black hole” was subsequently given to these proposed objects. Finally in 2015 the presence of actual black holes was confirmed by a novel instrument capable of detecting ripples in the gravitational field surrounding it. The extremely sensitive ‘LIGO’ apparatus was able to record a very feint signal from the merger of two black holes, each roughly 30 times the mass of the sun, which took place over a billion years ago. The merger momentarily distorted the gravitational field, causing ripples in the very fabric of space to travel outwards, getting ever weaker as they did so.

Tiny as the ripples were, the LIGO detector (figure 3), with its two perpendicular arms spread over four kilometers each, proved capable of detecting them; it is able to measure a displacement of 10-19 m: less than a billionth of a  billion of a meter. Click to see a thirty second video simulating the event

Figure 3: the LIGO detector. Image credit: LIGO Laboratory

Telescopes have developed to such an extent in recent years that an image of a black hole has finally been made. Figure 4 shows the absence of light at the centre in a 2019 photograph of a black hole, 500 million trillion kilometers away. It was captured by a set of eight telescopes around the world, coordinated into one gigantic ‘Event Horizon Telescope’. The image confirms the features of a black hole developed theoretically from Einstein’s theory of gravitation. 

Figure 4: Image of a black hole captured in 2019. Image credit: Event Horizon Telescope collaboration et al.

Why are thing as they are?

The mathematical representation of Newton’s gravitational equation is central to the way gravity is presented in school syllabuses: F = G m1m2/r2 (Force = the gravitational constant  x mass of one thing x mass of the other thing/distance between them squared). The tack taken by the discussion group at this point, was rather different, however. Helen asked: “Why is gravity such a weak force”? The technical answer is: because ‘G’ in the equation – the so-called gravitational constant – is very small. This tautological explanation was not enough to satisfy her (it’s  0.000000000667 in standard units by the way). Undaunted she looked up ‘the cause of gravity’ on her mobile phone and got the more informative answer: “scientists have no idea why gravity happens”.

The line of questioning had, in effect, come up against to the very boundaries of science as a discipline. Science has developed over centuries through meticulous observation and measurement of things that occur. New data inspires new ideas about the causes of things which are then put to the test in carefully designed experiments. Helen’s question made demands of a different order: she wasn’t looking just for a description of the effects of gravity but for something more like an understanding of its essence. “Some people would say the deep explanation of gravity lies with God and, like God, it’s unknowable” she ventured. Malcolm, a confident atheist, bridled at this point, responding that “there’s dishonesty in this kind of religious argument – wherever there’s a mystery, you just call it God”.

Whichever stance you take in relation to religion, the question of why gravity is weak strays beyond the realm of physics into that of philosophy (the word metaphysics means ‘beyond physics’). Physics and religion do not simply stand in simple opposition to one another. Galileo, who despite being tried for heresy in 1633 and placed under house arrest for his scientific insights, maintained his belief in God throughout. He saw science as revealing the beauty of God’s creation. In our own times, the respected physicist Paul Davies reflected on this in a 2007 article for the New York Times:

The laws of gravitation and electromagnetism [and others]— are expressed as tidy mathematical relationships. But where do these laws come from? [When I ask] my physicist colleagues why the laws of physics are what they are… [their] favourite reply is, “There is no reason they are what they are — they just are.” … both religion and science are founded on faith — namely, on belief in the existence of something outside the universe, like an unexplained God or an unexplained set of physical laws.

In fact, the ‘gravitation constant’ G, mentioned above is just one of several fixed numbers that characterise our universe. Another is the speed of light in a vacuum, another the electric charge on fundamental particles such as the electron and proton. These numbers are specific, precise and necessary. They are ‘just right’ for holding atoms together, and indeed the universe as a whole – what has been described as our ‘Goldilocks’ universe.

Persistent questioning in science discussion groups often leads from practical issues to ever deeper enquiries about why things are as they are. It forces us to think about what to expect from explanations. When we are taught how gravitational force depends on the masses and distances involved, deeper questions are quietly by-passed: what is meant by force and mass, for example. Explanations of this kind enable us to describe the way gravity operates and to predict how to land a probe on a distant planet. They don’t tell us why this is so, however.    

In concluding the discussion she had sparked off, Helen reflected on how the people in whom we have faith today are less the priests of earlier times and more the doctors and scientists who get us through pandemics. It’s they who interpret the ways of the world for us. “They have to be relied upon” Paul added, “especially in such times. But let us not forget they are subject to the same weaknesses as the rest of us: vanity and self-interest for example”. Richard, who’d said little up to this point, countered that “at least what they tell us is tempered by truth and objectivity, compared to many other voices”. A suitably balanced view of the real world to conclude the discussion with.

© Andrew Morris 20th May 2022