What immortal hand or eye,
Could frame thy fearful symmetry?
William Blake, ‘The Tiger’
Nothing will come of nothing
William Shakespeare, King Lear
Where do the laws that govern our Universe come from? It is one of the most basic questions that can be asked about the Universe. The answer, however, may be ridiculously trivial, according to an American physicist. ‘The laws of physics are simply the laws of nothing,’ says Victor Stenger of the University of Hawaii. ‘Put another way, they are precisely the laws that would reign in a featureless void, utterly empty of matter, energy or anything else.’
If Stenger, a retired experimental particle physicist, is right, it may shed light on arguably the ultimate cosmic question: How did something come from nothing? ‘If the laws of physics are the same laws as the laws of an empty void, the transition from nothing to something may not have been as difficult as people have assumed,’ says Stenger. ‘Our Universe may be no more than re-arranged, re-structured nothingness.’ This is highly provocative. To understand how Stenger has arrived at such a view, it is first necessary to understand an idea which has proved a powerful guiding light to physicists groping for understanding of the Universe. That idea is ‘symmetry’.
Symmetry is about the properties of an object that do not change if something is done to it. Take, for instance, a starfish. If it is rotated a fifth of a complete turn, it looks the same. Mathematicians say that a starfish is symmetric with respect to rotations about its centre – or, more precisely, with respect to rotations of a fifth of a complete turn about its centre. ‘On the face of it, symmetry appears to have nothing whatsoever to do with physics,’ says Stenger. ‘However, it turns out to be crucial.’
The surprising connection between physics and symmetry was discovered by a female German mathematician in 1918. In a remarkable paper, which Einstein among others greatly admired, Emmy Noether showed that some of the fundamental laws of physics are nothing more than the consequences of simple symmetries of space and time.
Take, for instance, the fact that the laws of physics are the same today as they were yesterday. If this were not the case and, say, the law of gravity were different yesterday, you might find that your weight has overnight gone from 70 kilograms to 150 kilograms. Because the laws of physics do not change with time, you can be sure that if you do a particular experiment on a Tuesday or on Wednesday, or any other day of the week, you will get the same result. Mathematicians say that the laws of physics are symmetric with respect to ‘translations in time’.
It is not obvious at all that a law of physics follows from this. However, Noether’s surprising discovery was that it does. Furthermore, it is one of the cornerstones of physics – the law of conservation of energy, which states that energy can never be created or destroyed, merely changed from one form into another.
And the law of conservation of energy turns out to be not the only fundamental law of physics intimately connected to symmetry. Take the fact that the laws of physics are the same in one location as in another – for instance, in New York and in London. Mathematicians say that the laws of physics are symmetric with respect to ‘translations in space’. Noether discovered that this symmetry leads to another great cornerstone of physics – the law of conservation of momentum. This states that a quantity called ‘momentum’ can never be created or destroyed. The momentum of a body – the product of its mass and its velocity – is in fact a measure of how difficult it is to stop the body moving. A slow-moving elephant has a lot of momentum and a fast-moving pigeon not nearly so much.
Another connection between the laws of physics and symmetry stems from the fact that the laws of physics are the same in any orientation. In other words, it does not matter, when you carry out an experiment, whether you align your apparatus north–south, east–west or along any other direction. Mathematicians say the laws of physics are symmetric with respect to ‘rotations in space’. Noether discovered that this symmetry leads to the law of conservation of angular momentum. This states that a quantity known as ‘angular momentum’ – a measure of how difficult it is to stop a rotating body – cannot be created or destroyed.
The $64,000 question is, of course, why should there be any connection between symmetry and the laws of physics? Why does the fact that the laws of physics are the same yesterday and today lead to the law of conservation of energy? Why does the fact that the laws of physics are the same in London and in New York lead to the conservation of momentum? And why does the fact that they are the same in any orientation lead to the conservation of angular momentum?
Non-mathematically, the connection between physics and symmetry is not easy to see – which is of course why nobody noticed it before Noether in 1918. ‘Nevertheless, it is possible to get a hint of why there is a connection,’ says Stenger. ‘Imagine a car travelling along a road, which is featureless apart from telegraph poles spaced at regular intervals. Imagine also that the car’s speed is constant and a movie is taken of the car.’
According to Stenger, it will be impossible to determine simply from watching the movie where exactly the car is along the road. After all, every telegraph pole will look exactly like every other telegraph pole. This shows that the inability to distinguish one location of the car from another – translational symmetry – is in some way connected with the fact that the speed, or momentum, of the car is not changing. If, however, the car’s momentum does change – if it brakes to a sudden halt – the telegraph poles are no longer indistinguishable. One is singled out as special – the one nearest to where the car stops – breaking the translational symmetry. ‘The example of the car hopefully hints that there is a deep connection between symmetry and the laws of physics,’ says Stenger.
The laws that Noether was able to show were mere consequences of symmetries are all symmetries of either space on its own or of time on its own. But is there a symmetry of space and time together? The answer is an emphatic yes. The symmetry leads to one of the greatest ideas in the history of science – Einstein’s ‘special’ theory of relativity.
The laws of physics turn out not only to be the same in different orientations of space but also in different orientations of space and time together. This takes a bit of explaining. After all, how is it possible to rotate something in time? Well, it is only possible to do so if time is a dimension much like a dimension of space. This, it turns out, is exactly what Einstein discovered in 1905.
According to Einstein, the space and time dimensions are so similar that intervals of time can in fact change into intervals of space and vice versa. The reason is that we have been hoodwinked into believing that space and time are actually fundamental things. In fact, they are merely artefacts of our particular viewpoint. One person’s interval of space is not the same as another person’s interval of space. And the same goes for time.
Imagine a stick suspended from the ceiling of a square shed so that it can swing about horizontally just like a giant compass needle. And say we can view the stick only through a window in one wall of the shed and a window in the adjacent wall. Furthermore, it is gloomy in the room so we cannot actually tell that it is a suspended stick, just an ‘object’ with a certain extent when we view it through one window and a certain extent when we view it through the other window. We might decide to call these its ‘length’ and ‘width’.
Now, say the shed is on a turntable and is rotating about the object (this is a very odd shed!) – as we look through the windows, we will see the width gradually turn into the length and vice versa. Gradually, the truth will dawn on us. We were stupid to describe the object in terms of its ‘width’ and ‘length’. These are not fundamental things at all but merely artefacts of our viewpoint.
So it is with space and time. In reality, there is a thing called space-time – a seamless blending together of space and time. Just as the way we divide the extent of the stick into width and length depends on our viewpoint, the manner in which we split space-time into space and time depends on our viewpoint. The only difference is that, in the case of space-time, what determines our particular view of it is not anything as crude as a window we are looking through but how fast we are moving.
In fact, as pointed out earlier, you have to be travelling close to the speed of light to appreciably change your viewpoint of space and time. The speed of light, however, is roughly a million times faster than a passenger jet. Consequently, we never see space turn into time and time into space. We have been hoodwinked into believing space and time are fundamental because we live our lives in the cosmic slow lane. That is why it took the genius of Einstein to see the truth. Space and time are but projections of the seamless entity of space-time. They are like shadows on a wall. Space-time is the fundamental thing.
In practice, intervals of space are measured with a ruler and intervals of time with a clock. Rulers and clocks therefore look different depending on your viewpoint – how fast you are moving past them. More precisely, as pointed out before, moving rulers shrink and moving clocks slow down. It makes not the slightest difference whether you think it is the clocks and rulers that are moving or you. As Einstein realised, the only motion that is in any way meaningful is ‘relative’ motion.
The precise way space ‘contracts’ and time ‘dilates’ for a moving observer is given by a mathematical formula called the ‘Lorentz transformation’. Einstein postulated that all observers moving at uniform speed have equally valid viewpoints. Consequently, the laws of physics must be the same when space and time are subject to a Lorentz transformation. In the jargon, they are symmetric under a Lorentz transformation. Here we come back to Noether. ‘The existence of a symmetry, as Noether discovered, always implies a law of physics,’ says Stenger. ‘In this case, the law turns out to be one not often considered to be a law – the law of the conservation of the speed of light.’
This says that the speed of light appears exactly the same for everyone in uniform motion – that is, travelling at constant speed – no matter what their speed. In fact, the Lorentz transformation is simply a recipe which tells everyone what must happen to their intervals of space and intervals of time so that they all measure precisely the same speed for a beam of light.*
Because of the conservation of the speed of light, whether a light beam is coming towards you or going away from you, it will always appear to be travelling at the same speed. Contrast this with a motorbike that is travelling at 100 kilometres per hour on a road where you are travelling in a car also at 100 kilometres per hour. If the motorbike is travelling your way, it will appear to be standing still; if it is coming towards you, it will appear to be travelling at 200 kilometres per hour. Light, in marked contrast to the motorbike, appears to everyone, no matter what their motion, to travel at the same speed. It really is the rock on which the Universe is built, with space and time but shifting sand.
No doubt this all seems very complicated. We are talking, after all, about Einstein’s special theory of relativity. However, everything Einstein discovered is connected to a very simple symmetry of space-time. Specifically, a Lorentz transformation, which slows time and shrinks space for a moving observer, turns out to be nothing more than a rotation in space-time.
Recall that time is actually a dimension much like the three dimensions of space – north–south, east–west and up–down. A total of four dimensions is impossible to imagine. However, if two space dimensions are conveniently ignored, space-time can be imagined as a two-dimensional map with, say, time going up the page and space going across the page.
In a real map, the location of, say, a castle, might be specified as 5 kilometres north of a certain town and 0 kilometres east. Now, say you rotate the north–south and east–west directions so that north is now off at some angle to the vertical. The location of the castle might now be 3 kilometres from the town in the new north direction and 4 kilometres in the new east direction. In the new ‘coordinate system’, some of the old east–west coordinate has changed into new north–south coordinate, and vice versa.
Well, in a space-time map, something similar happens. If the space and time directions are rotated, some of what was time becomes space and vice versa. And this is entirely equivalent to a Lorentz transformation. So, saying that the laws of physics – and, specifically, the speed of light – are unchanged under a Lorentz transformation is equivalent to saying the laws are the same no matter what the orientation of the directions of space and time.*
There is actually nothing deep or significant about this. If, rather than describing the location of a castle on a map one way, we described its location another way, it would be surprising if it changed anything essential about the castle. ‘All Einstein did was extend this straightforward reasoning to space-time,’ says Stenger. ‘He simply said that, no matter how we view an object in space-time, its essential features should remain the same.’
In fact, this goes to the heart of what all the symmetries of space-time are about. They are about making sure that the fundamental laws of physics are the same for everyone, no matter what their viewpoint.
The fact that the laws of physics are symmetric under translations of space means that, if we did an experiment in London and referred all our measurements to New York – which in practice would mean adding about 5,000 kilometres to any measurements made in the direction joining London to New York and would not be a sensible thing to do – we would get the same result. Similarly, the fact that the laws of physics are symmetric under translations in time means that, if we did an experiment and referred all our time measurements to the time the dinosaurs vanished 65 million years ago, it would not affect the outcome. Also, the fact that the laws of physics are symmetric under rotations in space-time means that if we made all of our measurements using a coordinate system rotated in space-time – entirely equivalent to a coordinate system travelling through space at constant velocity – that would make no difference either.
There are clearly situations, however, when the laws of physics do depend on your viewpoint. Say you are in a plane which is changing its speed, or ‘accelerating’. Drop a ball in the aisle and it will not fall vertically to the ground as it does in a plane flying at constant speed. The greater the acceleration, as indicated by how hard you are pushed back in your seat, the farther from the vertical the ball will fall. Obviously, the laws of physics do not appear the same from the viewpoint of two people undergoing different accelerations.
Nevertheless, the desire to write down the laws of physics in a way that does not depend on viewpoint is a powerful one. How, after all, could physicists hold up their heads if their ‘universal’ laws were different in different situations – for instance, for people undergoing different accelerations?
For a decade after his discovery of the special theory of relativity, Einstein struggled to find a way to write down the laws of motion in a way that is the same for everyone, no matter what their acceleration. In 1915, at the height of the First World War, he succeeded. He could do it on one condition. The condition was that a force with a very particular behaviour be added to region of space which is undergoing acceleration. The force is gravity!
Gravity, according to Einstein, is therefore not a real force at all. It is a force we invent merely so that the laws of physics still make sense to people accelerating at different rates. In fact, gravity is like other ‘fictitious’ forces such as ‘centrifugal force’. If you are in car rounding a sharp bend, you will find yourself flung outwards. So that the laws of physics – for instance, the laws that describe how a ball dropped in the car falls to the floor – still make sense, it is necessary to invent an outward force called ‘centrifugal force’. No such force exists, however, as is obvious to anyone observing you from outside the car. They can see that you are not flung outwards towards the car door. Rather, it is the car door that comes towards you because the car is following a curved path and you are continuing to move in a straight line under your ‘inertia’.
The Earth orbiting the Sun is like you in the car going round the bend. It is not being constrained to circle the Sun by the ‘force’ of gravity. It is simply flying through space in a ‘straight’ line because of its inertia. Of course, it does not look like the Earth is moving in a straight line. But that is just because we are using the wrong definition of a straight line!
It was Einstein’s genius to realise that space-time is actually warped by the presence of a mass like the Sun. As mentioned before, we cannot see this warpage because, as lowly three-dimensional creatures, we cannot directly experience something four-dimensional. But, just as a cannon ball on a trampoline creates a valley in the fabric of the trampoline, the Sun creates a valley in the fabric of space-time around it. And, on a warped surface, a straight line – that is, the shortest distance between two points – is a curve. This is why the Earth, which is doing nothing more than travelling under its own inertia along the shortest path possible through warped space-time, is circling the Sun.
The theory in which Einstein was able to write down the laws of physics in a so-called covariant form that was the same for everyone is called the general theory of relativity. The ‘general’ denotes that it applies to people no matter what their state of motion, not just to ‘special’ people who happen to be in uniform motion with respect to each other.
Noether made her discovery of the significance of symmetry to physics in the field of ‘dynamics’, which deals with the way in which bodies move through space. From symmetries of space and time separately, she was able to deduce great conservation laws such as the conservation of energy. It later became apparent to physicists that Einstein’s special theory of relativity was also a consequence of a symmetry of space-time, but a symmetry of space and time combined. And symmetry proved its worth also in the general theory of relativity. To restore symmetry and make sure everyone, no matter what their motion, experienced the same laws of physics, it was necessary to invent a force – the force of gravity.
But Noether’s discovery that symmetry underpins the world turns out to be an enormously fruitful idea with far-reaching implications for physics. The reason is that symmetries of space and time are not the only symmetries that spawn laws of physics. There are other, far more abstract, symmetries. ‘And it is nature’s most abstract symmetries that have the most profound consequences – especially in the field of quantum theory,’ says Stenger.
While general relativity describes the behaviour of big things like stars and the whole Universe, quantum theory generally describes the behaviour of small things like atoms and their constituents. The theory’s founding idea can be stated in a sentence: in the microscopic world of atoms and their constituents, particles behave like waves and waves like particles. The behaviour of an atom or an electron is therefore described by a wave – actually, an abstract, mathematical wave but a wave with concrete consequences nonetheless. How this quantum wave spreads through space is in turn described by the ‘Schrödinger equation’.*
As mentioned before, the quantum wave is not in fact observable directly. The only thing with real, ‘physical’ significance is the square of the wave height at any point in space. This turns out to be the ‘probability’ of finding the particle at that point. It can be anything between 0 per cent and 100 per cent.
In practice, what all this schizophrenic wave-particleness means is that a particle like an atom can do all the things that a wave can do. It is a well-known property of waves, for instance, that, if two waves can exist – say, a big wave spreading on a pond and a small ripple – then a combination of the two can also exist – a big wave with a small ripple superimposed on it. This has dramatic implications in the world of atoms. If there is a quantum wave with a high probability of an atom being in one place and another quantum wave with a high probability of the atom being in another place, there can – as noted earlier – be a superposition of the two waves, which corresponds to the atom being in two places at once (see Chapter 4, ‘Keeping It Real’).
And this is just one of the countless peculiarities of the quantum world.
Back to symmetry. Think of the quantum wave again. It turns out that there is an important subtlety when it comes to the wave height. It is described not by an ordinary number but by a ‘complex number’. Such a number has a ‘real’ part – just an ordinary number – and an ‘imaginary’ part. It is not crucial here to know what an imaginary number is.* The key thing is simply that a complex number has two components. This means it can be visualised on a two-dimensional map.
Think of the north–south direction as the real direction and the east–west direction as the imaginary direction. Any complex number can be represented by a dot somewhere on the map. Picture a line drawn to the dot from the map’s centre, or ‘origin’ – the spot where the north–south and east–west directions meet. It has an extent in the real direction and an extent in the imaginary direction. The line is therefore an equivalent way of representing the complex number. Think of it as an arrow pointing out from the origin.
Now, recall that at any point in space the height of the quantum wave squared is the probability of finding the particle at that particular point. Well, the square of the wave height is just the square of the length of the arrow. So, as long as the arrow stays the same length, the probability will be unchanged. Here we are getting to the point. The length of the arrow stays the same if it is rotated about the origin, no matter what direction it ends up pointing. For technical reasons which are not worth going into, physicists call such a rotation a ‘phase shift’.
What all this means is that, if the arrow representing the height of the quantum wave of a particle at each point in space is rotated by the same amount, it makes no practical difference to the particle. Physicists say the quantum wave is symmetric with respect to ‘rotations in complex space’ or, equivalently, symmetric to a ‘global’ phase change. In fact, just to confuse matters with even more jargon, they have a special phrase for this symmetry. They call it a global ‘gauge’ symmetry.
A symmetry, as Noether discovered, implies a law of physics. So what law does this symmetry lead to? The answer turns out to be the law of conservation of electric charge.
Electric charge comes in two types – positive or negative. Electrons, for instance, carry a negative charge and protons a positive charge. Particles with the same charge repel each other while particles with opposite charges attract each other. It has long been known that electric charge, like energy and momentum, can never be created or destroyed. But why? Noether insight provides the answer. Ultimately, it is down to an abstract symmetry – the fact that the quantum wave is symmetric with respect to global rotations in complex space.
Now you see the power of Noether’s idea. Even the most ridiculously abstract symmetries – not even of anything concrete like space and time – spawn laws of physics. But the abstract symmetries of the quantum wave do not end here. There is another, very surprising, symmetry which has profound implications for physics.
Say the arrow representing the height of the quantum wave of a particle is rotated by a different amount at each point in space. The probability of finding the particle at each point in space will remain the same. Nevertheless, the laws of physics – specifically, the Schrödinger equation that governs the motion of a quantum particle – will not be the same. The reason is that the Schrödinger equation permits the quantum wave to mingle, or ‘interfere’, with itself. This just means that, at places where crests of one component of the quantum wave coincide with crests of another, the wave is boosted and, at places where crests coincide with troughs, it is snuffed out.
Crucially, it is the direction of the arrow at any point that tells us whether there is a peak or a trough in the quantum wave (or any possibility between). So, if the arrows are rotated by different amounts at different points in space, it will affect how the quantum wave interferes with itself. Consequently, the quantum wave will not be symmetric under ‘local’ rotations in complex space, or equivalently to local phase changes.
But let us not be too hasty. What will it take to restore the symmetry? Well, clearly the quantum wave will have to be rotated by a different amount at each point so that the relative directions of all the arrows are the same as they were before. This seems a very tall order. However, remarkably, there is a way to do it. Recall the way in which Einstein restored the symmetry in his general theory of relativity. He simply added a ‘field’ of force everywhere in space – gravity. Well, in this quantum case the symmetry can also be restored by adding a field of force. That field of force is the electromagnetic field.
The electromagnetic field is responsible for all electrical and magnetic phenomena and, in fact, glues together all normal matter, including the atoms in your body. In 1873, the Scottish physicist James Clerk Maxwell summarised all the properties of electricity and magnetism in his laws of electromagnetism. It was a tour de force of nineteenth-century physics. Yet it turns out that everything Maxwell struggled to understand for more than a decade is merely the consequence of a simple symmetry principle: the laws of motion for a quantum particle must be the same under arbitrary rotations in complex space at different points in space. According to modern-day physicists, the electromagnetic field exists for one reason, and one reason only – to restore local ‘gauge’ symmetry.
The remarkable fact that laws of physics respect local gauge symmetry has proved a powerful way of finding new laws of physics. A local gauge symmetry, for instance, always requires the existence of a ‘field’ to maintain the symmetry. An example of a gauge field is the ‘strong’field of force that glues together quarks. The field is exactly what is required to restore gauge symmetry. In turn, new particles are manifestations of the fields, localised ‘knots’ in the fields, if you like – in the case of the strong field, ‘gluons’.
Symmetries may abound in nature. However, one thing is clear when we look around at the Universe. It does not look very symmetric. Far from it. One place in our Solar System is not the same as another place. For instance, the region of space currently occupied by Jupiter is not the same as the location of space 10 million kilometres from Jupiter along the line joining Jupiter to the Sun. Whereas the former place contains a giant ball of swirling gas 1,000 times bigger than the Earth, the latter contains only a few shreds of hydrogen gas.
This illustrates an important point. The underlying laws of physics may be symmetric. However, the detailed consequences of these laws need not be.
Think of a pencil perfectly balanced on its point. In this situation, the law of gravity is perfectly symmetric. There is a vertical force – down towards the centre of the Earth – but there is no sideways force whatsoever. The sideways force is therefore the same in all directions – in the jargon, it is symmetric with respect to orientation in space.
But, as we all know, a pencil balanced on its tip is not stable. It is constantly being buffeted by air molecules and the slightest imbalance in that buffeting is enough to cause the pencil to fall. It might fall in the direction of north or east or in any direction at all. It does not matter. The point is (no pun intended!) that one direction will turn out to be special – the direction in which the pencil falls.
Here, we see that, although the underlying law of gravity is symmetric with respect to orientation in space, the consequence of that law is not. Physicists talk of the symmetry ‘spontaneously breaking’.
As it is for pencils, so it is for the Universe. Physicists have a strong belief that the fundamental laws of the Universe are symmetric but that, in creating the world, the symmetry has been spontaneously broken.
In general, symmetries spontaneously break as the temperature drops. Take water. The liquid looks the same at every point and in every direction too. It is symmetric, in other words. Cool it until it freezes, however, and the molecules line themselves up regularly in a ‘crystal lattice’ in which certain directions are distinguishable from all others. What is more, cracks and fissures may spontaneously appear. Things no longer look the same at every place and the same in every direction. Ice is less symmetric than water. Cooling the water caused the symmetry to spontaneously break.
The significance of this for the Universe is profound. The Universe began almost 13.7 billion years ago in a dense, hot state – the Big Bang – and has been expanding and cooling ever since. Because the Universe was hotter in the past, we would expect it to have been more symmetric. And, in fact, our experiments prove this to have been the case.
Take two of nature’s four fundamental forces – the electromagnetic force and the weak force. These have a very different character. For instance, the electromagnetic force has an infinite range whereas the weak force has an extremely short range. This difference can be traced back to the ‘carriers’ of the two forces.
The carrier of the electromagnetic force is the photon and the carriers of the weak force are the W-, W+ and Z0 bosons. The ‘range’ of a force turns out to be inversely related to the mass of the force carriers. It is because the photon has no mass that the range of the electromagnetic force is infinite. And it is because the three ‘vector bosons’ have large masses – around about 100 times the mass of a proton – that the weak force has a very short range.
The situation with the electromagnetic and weak forces is very messy and unsymmetric. However, the belief among physicists is that, early in the Universe, when the temperature was much higher, things were very different. The vector bosons, instead of having large masses, had no mass, just like the photon. The two forces were identical. They behaved as a single ‘electroweak force’. Spontaneous symmetry breaking turned a single massless force-carrier into four very different force-carrying particles. Sure enough, physicists confirmed this scenario in the early 1980s when they recreated the temperature of the early Universe at CERN, the European centre for particle physics near Geneva, and demonstrated the existence of the unified electroweak force.
The belief among physicists, then, is that, although the Universe is far from symmetric today, it was very different in its youth. In fact, if we could run the history of the Universe backwards like a movie in reverse, we would find that the Universe in its earliest moments was in a state of maximum possible symmetry. Every location would be like every other location, every direction like every other direction. The Universe would look the same from every conceivable point of view. It would conform to every conceivable symmetry, concrete and abstract. ‘This strikes me as highly suggestive,’ says Stenger. ‘Why? Because the state of maximum symmetry is also the state of a completely empty void.’
Stenger amplifies what he means. Take a void, empty of matter, energy and everything else. Clearly, things look the same from every location. The void has translational symmetry. Also, things look the same in every orientation. The void has rotational symmetry. Nothing ever changes so things look the same at every time. The void exhibits time translational symmetry. In fact, the void also exhibits all the abstract symmetries of modern physics because – well, they are abstract and so do not require any matter, energy or anything.
Remarkably, then, the deep, underlying symmetries of our Universe – the symmetries which are at the root of the fundamental laws of physics – are nothing more than the symmetries of the void. ‘What are we to make of this?’ says Stenger.
Well, for one thing, he says, we can answer the question: Where do the laws of physics come from? ‘The laws of physics are the laws of nothing,’ says Stenger. And, if this is not difficult enough to stomach, there is more. If the ultimate laws of the Universe are the same as the laws of nothingness, then maybe it becomes easier to answer the arguably ultimate cosmic question: How did something come from nothing?
According to Stenger, such a transition would require no change in the laws of physics. There is no need to imagine there being no laws of physics and then the laws of physics coming into being – along with everything else – in the Big Bang. There was total continuity. The same laws of physics existed when there was nothing as they do today when there is something.
But, even though the transition from nothing to something required no change in the laws of physics, it still does not explain why the transition occurred. Why did the void not just sit there, doing nothing. Why did it change?
Stenger has an analogy. Think of water again, which has no structure, and ice, which does have structure. At the lower temperature, it is the state with structure – the state with something – that is the more stable. In this case, when the temperature drops, nothing changes into something. Stenger therefore hazards a controversial guess at why nothing turned into the something of the Universe. ‘Because something is more stable than nothing!’ he says.
Stenger admits he is echoing the Nobel Prize-winning physicist Frank Wilczek of the Massachusetts Institute of Technology. In 1980, writing in the magazine Scientific American, Wilczek pointed out that modern theories which describe how the fundamental building blocks of matter interact with each other suggest that the Universe can exist in different ‘phases’ analogous to the liquid and solid phases of water. In the different phases, the properties of matter are different – for instance, a particular particle might have no mass in one phase and a mass in another. And the laws of physics might be more symmetric in one phase than in another, just as the phase in which H2O is a liquid is more symmetric than the phase in which it is ice.
Here, Wilczek makes a crucial observation. ‘In these theories the most symmetrical phase of the universe turns out to be unstable,’ says Wilczek.
Wilczek speculates that the Universe began in the most symmetrical state possible and that, in that state, no matter existed. A second state of the Universe was possible with less symmetry and less energy. The fact that it had less energy is crucial. In nature, things tend to seek out the lowest-energy state. For instance, a ball rolls down a slope until it reaches the lowest point, where it has the lowest ‘potential energy’. Consequently a patch of the less symmetrical phase eventually appeared and grew rapidly.
Phase changes are invariably accompanied by a release of energy. For instance, when the gas phase of water – steam – turns into the liquid phase – water, a large amount of heat is unleashed, as anyone will attest who has been scalded by the steam from a boiling kettle. According to Wilczek, the energy released when the Universe went from the symmetric state with no matter to a less symmetric state manifested itself in the creation of a storm of super-hot fundamental particles. ‘This event might be identified with the Big Bang,’ he says.
According to Wilczek, the fact that the Universe has no net electrical charge – that is, every particle with a negative charge is balanced by a corresponding equal but opposite positive charge – would then be guaranteed, because the Universe lacking matter had been electrically neutral. ‘The answer to the ancient question “Why is there something rather than nothing?” says Wilczek, ‘would then be that “nothing” is unstable.’
Or, to put it in Stenger’s words: ‘Something is more stable than nothing.’
So, have Wilczek and Stenger really found a plausible answer to the ultimate cosmic question: Why is there something rather than nothing? Philosopher Stephen Law of Heythrop College at the University of London is not so sure. According to Law, the Achilles’ heel of the idea that something is more stable than nothing is that it is backed up by observations of water/ice and so on – in other words, observations of the nature of its actual laws. ‘The question then is: why is the Universe governed by these laws, rather than other laws – laws in which nothing turns out to be more stable than something?’ he says. ‘We are still left with an unexplained something – these laws plus the principle that nothing is less stable than something.’
Stenger believes this is to misunderstand what the laws of physics in fact are. ‘The whole expression “the Universe is governed by laws” is wrong,’ he says. ‘The “laws” are entirely human inventions that follow from “nothing”. The Universe looks just like it should if it has no laws at all.’
The laws of physics, he points out, do not follow from any unique or surprising properties of the Universe. ‘Rather they arise from the very simple notion that, whatever mathematical “laws” you write down to describe measurements, your equations cannot depend on the origin or direction of the coordinate systems you define in the space of those measurements or in any abstract “space” used to describe those laws,’ says Stenger. ‘In other words, they cannot depend on your point of view.’
According to Stenger, except for the complexities that result from spontaneously broken symmetries, the laws of physics may be the way they are because – well – they cannot be any other way. Ultimately, there is nothing to explain. The Universe is simply structured, re-arranged nothing. We, and everything around us, are simply patterns in the void.
* Historically, physicists came to this the other way round. Einstein postulated that the laws of motion must appear the same to all observers moving at constant speed relative to each other. This was something Galileo had noticed – a ball dropped to the deck of a moving ship fell in exactly the same way as a ball dropped on stationary dry land, so the laws of motion are the same whatever your velocity. Einstein, in addition, postulated that the laws of electricity and magnetism – electromagnetism – must also appear the same to all observers. Because it had been discovered by James Clerk Maxwell that light was actually an ‘electromagnetic’ wave, this meant that the speed of light must appear the same to everyone irrespective of their speed. These considerations led Einstein to the Lorentz transformation.
* There is a slight twist here. Time and space dimensions are subtly different from each other, as we might have expected from our everyday experience – we can move in any direction in space but are more restricted in time. So, in all this talk about rotations of the space and time directions, the time dimension is actually ‘imaginary’, which has a very specific mathematical meaning.
* Physicists call the quantum wave the ‘wave function’.
* An imaginary number is some multiple of the square root of a negative number such as -1. Such a square root does not exist, hence the term ‘imaginary’! Nevertheless, the square of an imaginary number does exist. And, because it exists, it is possible to manipulate imaginary numbers and still finish up with their squares – numbers that do exist. Physicists have found it extraordinarily fruitful to represent many quantities in nature by complex numbers – a combination of real and imaginary numbers.