Human Universe. Andrew Cohen

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СКАЧАТЬ 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 it and the Sun. Straight lines in curved spacetime look curved to us for precisely the same reason that lines of longitude on the surface of the Earth look curved to us; the space upon which the straight lines are defined is curved.

      This is all well and good, but there may be a question that has been nagging away in your mind since I told you that the ground accelerated up and hit the feathers and the bowling ball at Plum Brook like a cricket bat. How could it possibly be that every piece of the Earth’s surface is accelerating away from its centre, and yet the Earth stays intact as a sphere with a fixed radius? The answer is that if a little piece of the Earth’s surface at Plum Brook were left to its own devices, it would do precisely the same thing as the feather and the bowling ball; it would follow a straight line through spacetime. These straight lines point radially inwards towards the centre of the Earth. This is the ‘state of rest’, if you like – the natural trajectory that would be followed by anything. The geodesics point radially inwards because of the way that the mass of the Earth curves spacetime. So a collapsing Earth would be the natural state of things without any forces acting – one in which, ultimately, all the matter would collapse into a little black hole. The thing that prevents this from happening is the rigidity of the matter that makes up the Earth, which ultimately has its origin in the force of electromagnetism and a quantum mechanical effect called the Pauli Exclusion Principle. In order to stay as a big, spherical, Earth-sized ball, a force must act on each little piece of ground and this must cause each piece of ground to accelerate. Every piece of big spherical things like planets must continually accelerate radially outwards to stay as they are, according to General Relativity.

      From what I’ve said so far, it might seem that General Relativity is simply a pleasing way of explaining why the Earth orbits the Sun and why objects all fall at the same rate in a gravitational field. General Relativity is far more than that, however. Very importantly, it makes precise predictions about the behaviour of certain astronomical objects that are radically different from Newton’s. One of the most spectacular examples is a binary star system known rather less than poetically as PSR J0348+0432. The two stars in this system are exotic astrophysical objects. One is a white dwarf, the core of a dead star held up against the force of gravity by a sea of electrons. Electrons behave according to the Pauli Exclusion Principle, which, roughly speaking, states that electrons resist being squashed together. This purely quantum mechanical effect can halt the collapse of a star at the end of its life, leaving a super-dense blob of matter. White dwarfs are typically between 0.6 and 1.4 times the mass of our Sun, but with a volume comparable to that of the Earth. The upper limit of the mass of a white dwarf is known as the Chandrasekhar limit, and was first calculated by the Indian astrophysicist Subrahmanyan Chandrasekhar in 1930. The calculation is a tour de force of modern physics, and relates the maximum mass of these exotic objects to four fundamental constants of nature – Newton’s gravitational constant, Planck’s constant, the speed of light and the mass of the proton. After almost a century of astronomical observations, no white dwarf has ever been discovered that exceeds the Chandrasekhar limit. Almost all the stars in the Milky Way, including our Sun, will end their lives as white dwarfs. Only the most massive stars will produce a remnant that exceeds the Chandrasekhar limit, and the vast majority of these will produce an even more exotic object known as a neutron star. In the PSR J0348+0432 system, quite wonderfully, the white dwarf has a neutron star companion, and this is what makes the system so special.

      If the remains of a star exceed the Chandrasekhar limit, the electrons are squashed so tightly onto the protons in the star that they can react together via the weak nuclear force to produce neutrons (with the emission of a particle called a neutrino). Through this mechanism, the whole star is converted into a giant atomic nucleus. Neutrons, just like electrons, obey the Pauli Exclusion Principle and resist being squashed together, leading to a stable dead star. Neutron stars can have masses several times that of our Sun, but quite astonishingly are only around 10 kilometres in diameter. СКАЧАТЬ