Farewell to Reality (25 page)

We ran into problems thrown up by the uncertainty principle when we considered the energy of the vacuum. But we get even more headaches when we apply the uncertainty principle to spacetime itself. General relativity assumes that spacetime is certain: it is ‘here' or ‘there', curves this way or that way, at this or that rate. But the uncertainty principle
hates
certainty. It insists that we abandon this naive notion of smooth continuity and deal instead with a spacetime twisted and tortured and riddled with bumps, lumps and tunnels — ‘wormholes' connecting one part of spacetime with another.

The American physicist John Wheeler called it quantum or spacetime ‘foam'. A picturesque description, perhaps, but constructing a theory on it is like trying to build on a foundation of wet sand.

There are further problems. Aside from having to confront the essentially chaotic nature of spacetime at the ‘Planck scale', we also have to acknowledge that we're now dealing with distances and volumes likely to catch us out in one of the most important assumptions of conventional quantum field theory — that of point particles.

In the quantum field theories that comprise the standard model of particle physics, the elementary particles are treated as though they have no spatial extension.
^*
All of the particle's mass, charge and any other physical property it might be carrying are assumed to be concentrated to an infinitesimally small point. This would necessarily be true of elementary particles in any quantum field theory of gravity.

Obviously, the assumption of point particles is much more likely to be valid when considering physics on scales much larger than the particles themselves. But as we start to think about physics at the dimensions of the Planck length — 1.6 hundredths of a billionth of a trillionth of a trillionth (1.6 × 10
^-35
) of a metre, we must begin to doubt its validity.

Quantum theory and general relativity are two of the most venerated theories of physics, but, like two grumpy old men, they just don't get along. Both are wonderfully productive in helping us to understand the large-scale structure of our universe and the small—scale structure of its elementary constituents. But they are volatile and seem destined to explode whenever one is shoehorned into the other.

The physics of the very small and the physics of the very large are seemingly incompatible, even though the very large (the universe) was once very, very small. A straightforward resolution of the problem is not forthcoming. Quantum gravity lies far beyond the standard model of particle physics and general relativity, and so far beyond the current authorized version of reality.

The fine—tuning problem

When we use it to try to make sense of the world around us, science forces us to abandon our singularly human perspective. We're obliged to take the blinkers off and adopt a little humility. Surely the grand spectacle of the cosmos was not designed just to appeal to our particularly human sense of beauty? Surely the universe did not evolve baryonic matter, gas, dust, stars, galaxies and clusters of galaxies just so that
we
could evolve to gaze up in awe at it?

Of course, the history of science is littered with stories of the triumph of the rational, scientific approach over human mythology, superstition and prejudice. So, we do not inhabit the centre of the solar system, with the sun and planets revolving around the earth. The sun, in fact, is a rather unspectacular star, like many in our Milky Way galaxy of between 200 and 400 billion stars. The Milky Way is just one of about 200 billion galaxies in the observable universe. It makes no sense to imagine that this is all for our benefit.

This is the Copernican Principle.

What, then, should we expect some kind of ultimate theory of everything to tell us? I guess the assumption inherent in the scientific practice of the last few centuries is that such a theory of everything will explain
why
the universe and everything in it
has
to be the way it is. It will tell us that our very existence is an entirely natural consequence of the operation of a (hopefully) simple set of fundamental physical laws.

We might imagine a set of equations into which we plug a number of perfectly logical (and inescapable) initial conditions, then press the ‘enter' key and sit back and watch as a simulation of our own universe unfolds in front of our eyes. After a respectable period, we reach a point in the simulation where the conditions are right for life.

We are not so naïve as to imagine that science will ever completely eliminate opportunities for speculation and mythologizing. There are some questions that science may never be able to answer, such as what (or who, or should that be Who?) pressed the ‘enter' key to start the universe we happen to live in. But surely the purpose of science is to reduce such opportunities for myth to the barest minimum and replace them with the cold, hard workings of physical mechanism.

Here we run into what might be considered the most difficult problem of all. The current authorized version of reality consists of a marvellous collection of physical laws, governed by a set of physical constants, applied to a set of elementary particles. Together these describe how the physical mechanism is meant to work. But they don't tell us where the mechanism comes from or why it has to be the way it is.

What's more, there appears to be no leeway. If the physical laws didn't quite have the form they do have, the physical constants were to have very slightly different values, or the spectrum of elementary particles were marginally different, then the universe we observe could not exist.
^*

This is the fine—tuning problem.

We have already encountered some examples of fine—tuning, such as the mass-energy scales (and the relative strengths) of gravity and the weak and electromagnetic forces. More fine—tuning appears to be involved in the vacuum energy density, or the density of dark energy, responsible for the large-scale structure of the universe.

In 1999, the British cosmologist Martin Rees published a book titled
Just Six Numbers,
in which he argued that our universe exists in its observed form because of the fine—tuning of six dimensionless physical constants.

As I've already said a couple of times, physicists get a little twitchy when confronted with too many coincidences. Here, however, we're confronted not so much with coincidences but rather with conspiracy on a grand scale.

Now, we should note that some physicists have dismissed fine—tuning as a non—problem. The flatness and horizon problems in early big bang cosmology appeared to demand similarly fantastic fine—tuning but were eventually ‘explained' by cosmic inflation. Isn't it the case here that we're mistaking ignorance for coincidence? In other words, the six numbers that Rees refers to are not fine—tuned at all: we're just ignorant of the physics that actually governs them.

But our continued inability to devise theories that allow us to deduce these physical constants from some logical set of ‘first principles', and so explain why they have the values that they have, leaves us in a bit of a vacuum.

It also leaves the door wide open.

Clueless

There are further problems that I could have chosen to include in this chapter, but I really think we have enough to be going on with. On reading about these problems it is, perhaps, easy to conclude that we hardly know anything at all. We might quickly forget that the current authorized version of reality actually explains an awful lot of what we can see and do in our physical world.

I tend to look at it this way. Several centuries of enormously successful physical science have given us a version of reality unsurpassed in the entire history of intellectual endeavour. With a very few exceptions, it explains every observation we have ever made and every experiment we have ever devised.

But the few exceptions happen to be very big ones. And there's enough puzzle and mystery and more than enough of a sense of work—in—progress for us to be confident that this is not yet the final answer.

I think that's extremely exciting.

Now we come to the crunch. We know the current version of reality can't be right. There are some general but rather vague hints as to the directions we might take in search of solutions, but there is no flashing illuminated sign saying ‘this way to the answer to all the
puzzles'. And there is no single observation, no one experimental result, that helps to point the way. We are virtually clueless.

Seeking to resolve these problems necessarily leads us beyond the current version of reality, to grand unified theories, theories of everything and other, higher speculations. Without data to guide us, we have no choice but to be idea—led.

Perhaps it is inevitable that we cross a threshold.

^*
But it's worth remembering that under certain circumstances it is possible to form superpositions of macroscopic dimensions, such as (for example) superpositions of a couple of billion electrons travelling
in opposite directions
around a superconducting ring with a diameter over a hundred millionths of the metre. Okay, these aren't cat-sized dimensions, but precisely where are we supposed to draw the line?

^*
In principle, these fundamental physical constants simply ‘map' the physics to our human, terrestrial (and arbitrary) standards of observation and measurement.

^**
Count them. There are three generations each consisting of two leptons and two flavours of quark which come in three different colours (making 24 in total), the anti—particles of all these (making 48), twelve force particles — a photon, W
^±
and Z
⁰
and eight gluons (making 60) — and a Higgs boson (61).

^*
The nutritional information on a box of cornflakes indicates an energy content of 1,604 kJ (thousand joules) per 100 grams. This is chemical energy, released when the cornflakes are combusted or digested.

^*
A googol is 10
¹⁰⁰
. I had to look it up.

^*
Hang on, I hear you cry. What about the uncertainty principle? Doesn't the assumption of point—like properties for an elementary particle mean a consequent assumption of certainty in its location in space? Actually, no, it doesn't. An elementary particle like an electron may be thought of as being ‘smeared' out in space because the amplitude of its wavefunction is not fixed on a single point; it is extended. But it is not the particle itself that is smeared out. What is smeared out is the probability — calculated from the modulus—square of the wavefunction — of ‘finding' the point—like electron within this space.

^*
And, of course, we would not exist to puzzle over what had gone wrong.

Part II

The Grand Delusion

7

Thy Fearful Symmetry

Beyond the Standard Model: Supersymmetry and Grand Unification

Concepts are simply empty when they stop being firmly linked to experiences. They resemble social climbers who are ashamed of their origins.

Albert Einstein
¹

I guess I should now come clean. Time to own up.

When I introduced the standard model of particle physics in Chapter 3, I talked about symmetry only in the context of symmetry-breaking and the role of the Higgs field. Readers with more than a passing acquaintance with the standard model will know that this is far from the whole story.

Arguably one of the greatest discoveries in physics was made early in the twentieth century. This discovery provides us with a deep connection between critically important laws of conservation — of mass-energy, linear and angular momentum, and many other things besides — and basic symmetries in nature. And this was a discovery made not by a leading physicist, but a
mathematician.

In 1915, German mathematician Emmy Noether deduced that the origin of the structure of physical laws describing the conservation of quantities such as energy and momentum can be traced to the behaviour of these laws in relation to certain continuous symmetry transformations.

We tend to think of symmetry in terms of transformations such as mirror reflections. In this case, a symmetry transformation is the act of reflecting an object as though in a mirror, in which left reflects right. We push this further along. We let top reflect bottom, front reflect back. We claim that an object is symmetrical if it looks the same on either side of some centre or axis of symmetry. If the object is unchanged (
the technical term is ‘invariant') following such an act, we say it is symmetrical.

These are examples of
discrete
symmetry transformations. They involve an instantaneous ‘flipping' from one perspective to another, such as left-to-right. But the kinds of symmetry transformations identified with conservation laws in Noether's theorem are very different. They involve gradual changes, such as continuous rotation in a circle. Rotate a perfect circle through a small angle measured from its centre and the circle obviously appears unchanged. We conclude that the circle is symmetric to continuous rotational transformations. We find we can't do the same with a square. A square is not symmetric in this same sense. It is, instead, symmetric to discrete rotations through right angles.

Noether discovered that the dynamics of physical systems (the disposition of energy and momentum during a physical change) are governed by certain continuous symmetries. These symmetries are reflected in the equations — and hence the laws — describing the dynamics. The operation of these various symmetries means that the dynamical quantities that they govern are also conserved quantities. Thus, each law of conservation (of energy and momentum) is connected with a continuous symmetry transformation.

Changes in the energy of a physical system are invariant to continuous changes or ‘translations' in
time.
In other words, the mathematical relationships which describe the energy of a physical system now will be exactly the same a short time later. This means that these relationships do not change with time, which is just as well. Laws that broke down from one moment to the next could hardly be considered as such. We expect such laws to be, if not eternal, then at least the same yesterday, today and tomorrow.