Human Universe. Andrew Cohen
we wouldn’t have E=mc2, we wouldn’t really understand nuclear or particle physics, how the Sun shines or how radioactivity works. We wouldn’t understand the universe.
Something important bothered Einstein after he published his theory in 1905, however. Newton’s great achievement – the all-conquering Universal Law of Gravitation – did not fit within the framework of special relativity, and therefore one or the other required modification. Einstein’s response to this problem was typically Einsteinian: he thought about it very carefully, and, in November 1907, whilst sitting in his chair in the patent office in Bern, he found the right thread to pull. Looking back at the moment in an article written in 1920, Einstein described his idea with beautiful, and indeed child-like, simplicity.
‘Then there occurred to me the “glücklichste Gedanke meines Lebens”, the happiest thought of my life, in the following form. The gravitational field has only a relative existence in a way similar to the electric field generated by magnetoelectric induction. Because for an observer falling freely from the roof of a house there exists – at least in his immediate surroundings – no gravitational field [his italics]. Indeed, if the observer drops some bodies then these remain relative to him in a state of rest or of uniform motion, independent of their particular chemical or physical nature (in this consideration the air resistance is, of course, ignored). The observer therefore has a right to interpret his state as “at rest”.’
I am well aware that you might object quite strongly to this statement, because it appears to violate common sense. Surely an object falling under the action of the gravitational force is accelerating towards the ground, and therefore cannot be said to be ‘at rest’? Good, because if you think that then you are about to learn a valuable lesson. Common sense is completely worthless and irrelevant when trying to understand reality. This is probably why people who like to boast about their common sense tend to rail against the fact that they share a common ancestor with a monkey. How, then, to convince you that Einstein was, and indeed still is, correct?
Most of the time, books are better at conveying complex ideas than television. There are many reasons for this, some of which I’ll discuss in a future autobiography when my time on TV is long over. But when done well, television pictures can convey ideas with an elegance and economy unavailable in print. Human Universe contains, I hope, some of these moments, but there is one sequence in particular that I think fits into this category.
NASA’s Plum Brook Station in Ohio is home to the world’s largest vacuum chamber. It is 30 metres in diameter and 37 metres high, and was designed in the 1960s to test nuclear rockets in simulated space-like conditions. No nuclear rocket has ever been fired inside – the programme was cancelled before the facility was completed – but many spacecraft, from the Skylab nosecone to the airbags on Mars landers, have been tested inside this cathedral of aluminium. To my absolute delight, NASA agreed to conduct an experiment using their vacuum chamber to demonstrate precisely what motivated Einstein to his remarkable conclusion. The experiment involves pumping all the air out of the chamber and dropping a bunch of feathers and a bowling ball from a crane. Both Galileo and Newton knew the result, which is not in question. The feathers and the bowling ball both hit the ground at the same time. Newton’s explanation for this striking result is as follows. The gravitational force acting on a feather is proportional to its mass. We’ve already seen this written down in Newton’s Law of Gravitation. That gravitational force causes the feather to accelerate, according to Newton’s other equation, F=ma. This equation says that the more massive something is, the more force has to be applied to make it accelerate. Magically, the mass that appears in F=ma is precisely the same as the mass that appears in the Law of Gravitation, and so they precisely cancel each other out. In other words, the more massive something is, the stronger the gravitational force between it and the Earth, but the more massive it is, the larger this force has to be to get it moving. Everything cancels out, and so everything ends up falling at the same rate. The problem with this explanation is that nobody has ever thought of a good reason why these two masses should be the same. In physics, this is known as the equivalence principle, because ‘gravitational mass’ and ‘inertial mass’ are precisely equivalent to each other.
Einstein’s explanation for the fact that both the feathers and the bowling ball fall at the same rate in the Plum Brook vacuum chamber is radically different. Recall Einstein’s happiest thought. ‘Because for an observer falling freely from the roof of a house there exists … no gravitational field’. There is no force acting on the feathers or the ball in freefall, and therefore they don’t accelerate! They stay precisely where they are: at rest, relative to each other. Or, if you prefer, they stand still because we are always able to define ourselves as being at rest if there are no forces acting on us. But, you are surely asking, how come they eventually hit the ground if they are not moving because no forces are acting on them? The answer, according to Einstein, is that the ground is accelerating up to meet them, and hits them like a cricket bat! But, but, but, you must be thinking, I’m sitting on the ground now and I’m not accelerating. Oh yes you are, and you know it because you can feel a force acting on you. It’s the force exerted by the chair on which you may be sitting, or the ground on which you are standing. This is obvious – if you stand up long enough then your feet will hurt because there is a force acting on them. And if there is a force acting on them, then they are accelerating. There is no sleight of hand here. The very beautiful thing about Einstein’s happiest thought is that, once you know it, it’s utterly obvious. Standing on the ground is hard work because it exerts a force on you. The effect is precisely the same as sitting in an accelerating car and being pushed back into your seat. You can feel the acceleration viscerally, and if you switch off your common sense for a moment, then you can feel the acceleration now. The only way you can get rid of the acceleration, momentarily, is to jump off a roof.
This is wonderful reasoning, but of course it does raise the thorny question of why, if there is no such thing as gravity, the Earth orbits the Sun. Maybe Aristotle was right after all. The answer is not easy, and it took Einstein almost a decade to work out the details. The result, published in 1916, is the General Theory of Relativity, which is often cited as the most beautiful scientific theory of them all. General Relativity is notoriously mathematically and conceptually difficult when you get into the details of making predictions that can be compared with observations. Indeed, most physics students in the UK will not meet General Relativity until their final year, or until they become postgraduates. But having said that, the basic idea is very simple. Einstein replaced the force of gravity with geometry – in particular, the curvature of space and time.
Imagine that you are standing on the surface of the Earth at the equator with a friend. You both start walking due north, parallel to each other. As you get closer to the North Pole, you will find that you move closer together, and if you carry on all the way to the Pole you will bump into each other. If you don’t know any better, then you may conclude that there is some kind of force pulling you both together. But in reality there is no such force. Instead, the surface of the Earth is curved into a sphere, and on a sphere, lines that are parallel at the equator meet at the Pole – they are called lines of longitude. This is how geometry can lead to the appearance of a force.
Einstein’s theory of gravity contains equations that allow us to calculate how space and time are curved by the presence of matter and energy and how objects move across the curved spacetime – just like you and your friend moving across the surface of the Earth. Spacetime is often described as the fabric of the universe, which isn’t a bad term. Massive objects such as stars and planets tell the fabric how to curve, and the fabric tells objects how to move. In particular, all objects follow ‘straight line’ paths across the curved spacetime that are known in the jargon as geodesics. This is the General Relativistic equivalent of Newton’s first law of motion – every body continues in a state of rest or uniform motion in a straight line unless acted upon by a force. Einstein’s description of the Earth’s orbit around the Sun is therefore quite simple. The orbit is a straight line in spacetime curved by the presence of the Sun, and the Earth follows this straight line because there are no forces acting on it to make it do otherwise. This is the opposite of the Newtonian description, which says that the Earth would fly through space in what we would intuitively call a ‘straight line’ if it were not for the force of gravity acting between