How to Destroy the Universe (17 page)

Another method to generate energy from the Sun is known as solar thermal energy. This can be used in the home too, to heat water. It works by passing water through a network of pipes—rather like central heating radiators that work in reverse, collecting the heat that falls on them.

Similar designs have been used on a larger scale in warm parts of the world to make electricity. These work rather like Archimedes's heat ray, using arrangements of mirrors to concentrate the Sun's radiant energy to boil water. The steam produced is then used to drive turbines. Some designs have even proposed the use of molten salts rather than water to store the heat energy collected at hundreds of degrees C. One such solar concentrator system in the Nevada Desert is generating electricity at the rate of 64 megawatts (MW) using 760 long, trough-shaped reflectors that focus the Sun's rays onto absorber tubes through which liquid is pumped, heating the liquid to nearly 400°C (750°F). The hot liquid is then passed through a heat exchanger, transferring the heat energy to water, making steam that can spin a turbine. Other solar thermal power plants are located in California's Mojave Desert, Kuraymat in Egypt and Hassi R'Mel in Algeria. It was estimated in 2009 that worldwide solar thermal energy generation totals around 600 MW.

One of the major applications of solar energy has been in space-flight. Carrying batteries or other kinds of power generation equipment adds a lot of weight to a spacecraft, greatly increasing the fuel load and overall cost of the mission, so being able to tap into the free power from the Sun on the fly can bring huge savings.
The US section alone of the orbiting International Space Station derives power from a total of eight solar array wings, each measuring 35 × 12 m (115 × 40 ft) and incorporating 33,000 photovoltaic solar cells. Together they are capable of generating over 130 kW of electrical power.

Futurologists believe that solar panels in space could one day provide plentiful energy for Earth. Earth's atmosphere blocks about a third of the sunlight reaching the planet, meaning that the solar energy available to a spacecraft in orbit is about 50 percent more than can be harvested at ground level. And whereas a solar energy plant on Earth must spend 12 hours of every day in darkness, during which time it generates no power, a spacecraft can be positioned so that it's never in the shade.

In 2009, the Japanese Space Agency announced plans to build a 1 billion watt solar power station in Earth orbit. The electricity would be beamed down to the ground using lasers or microwaves, and giant satellite dishes would collect it. The scientists behind the idea believe it could produce electricity at a cost of about 9 cents per kilowatt-hour (the amount of electricity it takes to run a 1 kilowatt appliance for an hour). At the time, the price of electricity in Japan from existing sources was around six times this figure.

Space-based solar power could become even grander in the future. British physicist Freeman Dyson has suggested that an advanced civilization might surround its entire home star with a giant light-gathering device to harness every ounce of energy the star gives out. Such devices have become known as Dyson spheres. They can either be rigid structures or a flotilla of billions of smaller solar power stations forming a vast cloud that envelopes the star.

Russian astronomer Nikolai Kardashev went even further, suggesting that super-advanced races might be able to gather up all the energy released by every star in their home galaxy. This would be a truly mind-boggling amount of energy—with every second's worth being enough to power the present-day civilization on Earth for nearly 3 billion years. There can be no doubt that the power given off by the Sun and other stars is a gold mine of free energy. This just makes it even more baffling why solar energy still only accounts for a few hundredths of a percent of all the electricity that we consume.

• Curved space

• Kaluza–Klein theory

• String theory

• Compactification

• M-theory

• Escape to hyperspace

Philosophers and mystics have long mused over the possibility that there could be more dimensions to our Universe than the three of space and one of time that we can see. But it took a while for scientists to cotton on and take the idea seriously. Now extra dimensions are a feature of many theories in particle physics and, it's hoped, could soon reveal themselves in experiments.

One of the first scientists to consider the possibility of extra dimensions was the German mathematician Bernhard Riemann. In the 1850s, he developed a mathematical formalism to describe curved spaces in any number of dimensions. This was a fantastically
powerful tool. Up to that point, scientists had to rely on intuition and geometry, but these approaches only work in one, two or three dimensions. Few humans have the brain power to visualize what a cube looks like in eight dimensions, let alone the skill in geometry to be able to draw one. Riemann's analysis got round that by providing a systematic mathematical framework to study spaces, in principle, in any number of dimensions. It worked by using a matrix of numbers known as a “tensor” to describe the curvature of space at any point. Generally for an
N
-dimensional space the tensor would have
N
²
components arranged in an
N × N
matrix. So in our three spatial dimensions, it's a 3 × 3 matrix with a total of 9 components.

In the second decade of the 20th century, when Albert Einstein came to develop his general theory of relativity—a theory of gravity based on curvature of space and time—Riemann's equations were invaluable, effectively giving Einstein a ready-made toolkit with which to build his theory. One of the central tenets of relativity was that time is unified with the three dimensions of space to form a continuous four-dimensional fabric that Einstein called “space–time,” described by a 16-component 4 × 4 tensor.

In the 1920s, two mathematicians, German Theodor
Kaluza and Swede Oscar Klein, took this to the next step. They tried to unify gravity with the force of electromagnetism, the best theory of which had been developed in the 19th century by Scottish physicist James Clerk Maxwell (see
How to cause a blackout
). The electromagnetic field can be specified by one number for every dimension of space plus one for time. Quantities such as this are called vectors. Your position in space is another example—in 3D it takes three numbers (usually labeled
x, y
and
z
) to specify where you are. Kaluza and Klein tried to unify electromagnetism with gravity by adding an extra row and an extra column to the 4 × 4 space–time tensor of Einstein's general relativity and into these blank spaces adding the four components of the vector describing the electromagnetic field. The result was a 5 × 5 tensor—describing gravity and electromagnetism as curvature of a 5D space–time.

But, as astute readers may have noticed, something was missing. Sixteen components of Einstein's gravitational tensor plus two times the four components in Maxwell's electromagnetic vector only gave 24 components, whereas a 5 × 5 tensor should have 25. Kaluza and Klein concluded that for their 5D theory to work they needed to introduce an extra field specified by a single number—a so-called “scalar” quantity. Another example of a scalar is mass. One number—giving the amount in, say, kilograms—is enough to specify how
much an object weighs. They interpreted this number as a new field of particles pervading space. Today, these particles are a feature of most theories of fundamental physics that invoke higher dimensions. However, back in the 1920s there was no evidence that such additional particle fields existed, and so the theory was abandoned. Shortly after Kaluza and Klein put forward their theory, a science-fiction writer came up with a name for extra dimensions of space. In his 1934 short story
The Mightiest Machine
, author John Wood Campbell described them using the word “hyperspace.” And the name has stuck.

By the 1960s and '70s, the discovery of weird new particles of nature had become a common occurrence. Particle physicists spoke of quarks, gluons, mesons and other subatomic exotica from the particle world. And so Kaluza–Klein theory made something of a comeback. Only it wasn't quite the same theory Kaluza and Klein had originally envisaged. Quantum theory was now well established, and so any fundamental physics theory would need to deal with quantum particles and wave-functions, and the old theory took account of neither.

The new version of Kaluza–Klein theory would not deal with particles either, preferring to think in terms of pieces of string. The motivation for this was simple:
particle physics didn't work. True, it had provided good descriptions of all the forces of nature, and even successfully unified electromagnetism and the weak force. But that was where the success seemed to end. Attempts to unify the other forces in nature—especially gravity—resulted in divergences, instances where calculations relating to physical quantities give ridiculous infinite answers. Some physicists believed the reason for this stemmed from modeling particles such as quarks and electrons as points of zero size—when in reality they must have some physical extent, or they wouldn't exist. So a few theorists began replacing zero-dimensional point particles in their theories with tiny one-dimensional “strings” of energy.

As the idea was developed it became clear that a string would behave rather like the string on a guitar, in that waves could exist on it. Waves of different frequencies would produce different notes—and each note would correspond to a particular species of subatomic particle. The calculations also revealed that the strings would be almost infinitesimally tiny—the difference in size between a fundamental string and a proton being equal to the size difference between a proton and the whole Solar System. This naturally meant that testing the theory would be difficult. Physicists were quite capable of building detectors to study protons and electrons but seeing down to the level of strings would be another matter entirely.

This difficulty in testing string theory has brought criticism from many quarters. Proponents say that there are subtle, indirect tests of the theory that can be carried out using the Large Hadron Collider particle accelerator at CERN on the Franco–Swiss border. Like Kaluza–Klein theory before it, string theory predicts the existence of an extra scalar quantity in the equations, corresponding to a new particle of matter. In string theory, this particle is named the “dilaton”—though it is, as yet, undetected. Also in keeping with the Kaluza–Klein model, string theory requires space—time to have extra dimensions, lots of extra dimensions. The most common versions of string theory operate in a total of 10 space–time dimensions—adding six extra spatial dimensions to the usual three of space plus one of time.

If there are all these extra dimensions of space then why don't we see them? The string theorists have an answer to this one too. They say that the dimensions are hidden from view by a process known as compactification, which effectively amounts to rolling them up very tightly. Imagine a sheet of paper. This has two dimensions. Now roll it up as tightly as you can and view it from a distance. The tighter you roll it and the further away you view it from, the more it will look just like a one-dimensional line: one of its dimensions has
been compactified. Assuming string theory is correct, you might ask why it is that our Universe has six little spatial dimensions and three big ones. Couldn't we have five big ones and four little ones, or any other combination?

There's a very good reason why our Universe can't have fewer than three large dimensions: because it has life in it. Life requires a flow of energy—living creatures need to eat. And this energy, or food, must come in and pass through some kind of digestive tract, where it is processed and the waste products finally excreted. But in two dimensions such a tract would divide a creature into two. Without the third dimension there can be no extra structure to hold it together. Using the existence of life to make inferences about fundamental physics may seem like a weak argument. But it's actually
a surprisingly powerful method of scientific reasoning, called the anthropic principle (see
How to create life
).

The anthropic principle also means it's unlikely the number of large space dimensions could be more than three and still allow us to exist. Physicists have shown that in this case, the orbits of planets around the Solar System and even the motions of electrons around atomic nuclei could become unstable—planets would crash into their parent stars or fly off into space, and matter itself would fall apart. Worse still, pizza wouldn't be very palatable in a large number of dimensions. An ordinary two-dimensional, disc-shaped pizza has a quantity of nice topping proportional to the disk's area -π
r
²
, where
r
is the radius of the disk. On the other hand, the same pizza has an amount of rather bland crust that's proportional to the disc's outer circumference -2π
r
. That means the ratio of crust to topping in two dimensions is 2π
r
/ π
r
²
, which is just 2/
r
. The general form of this formula for an
N
-dimensional pizza is a little more tricky to calculate, but turns out to be just
N
/
r
. So when
N
is large, your pizza is mostly crust. Yuk.