Hawking, Stephen - Does God Play Dice

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Does God Play Dice?

This lecture is about whether we can predict the future, or whether it is arbitrary and random.

In ancient times, the world must have seemed pretty arbitrary. Disasters such as floods or

diseases must have seemed to happen without warning, or apparent reason. Primitive people

attributed such natural phenomena, to a pantheon of gods and goddesses, who behaved in a

capricious and whimsical way. There was no way to predict what they would do, and the only

hope was to win favour by gifts or actions. Many people still partially subscribe to this belief,

and try to make a pact with fortune. They offer to do certain things, if only they can get an A-

grade for a course, or pass their driving test.

Gradually however, people must have noticed certain regularities in the behaviour of nature.

These regularities were most obvious, in the motion of the heavenly bodies across the sky. So

astronomy was the first science to be developed. It was put on a firm mathematical basis by

Newton, more than 300 years ago, and we still use his theory of gravity to predict the motion

of almost all celestial bodies. Following the example of astronomy, it was found that other

natural phenomena also obeyed definite scientific laws. This led to the idea of scientific

determinism, which seems first to have been publicly expressed by the French scientist,

Laplace. I thought I would like to quote you Laplace's actual words, so I asked a friend to track

them down. They are in French of course, not that I expect that would be any problem with this

audience. But the trouble is, Laplace was rather like Prewst, in that he wrote sentences of

inordinate length and complexity. So I have decided to para-

phrase the quotation. In effect

what he said was, that if at one time, we knew the positions and speeds of all the particles in

the universe, then we could calculate their behaviour at any other time, in the past or future.

There is a probably apocryphal story, that when Laplace was asked by Napoleon, how God

fitted into this system, he replied, 'Sire, I have not needed that hypothesis.' I don't think that

Laplace was claiming that God didn't exist. It is just that He doesn't intervene, to break the

laws of Science. That must be the position of every scientist. A scientific law, is not a scientific

law, if it only holds when some supernatural being, decides to let things run, and not intervene.

The idea that the state of the universe at one time determines the state at all other times, has

been a central tenet of science, ever since Laplace's time. It implies that we can predict the

future, in principle at least.

In practice, however, our ability to predict the future is severely

limited by the complexity of the equations, and the fact that they

often have a property called chaos. As those who have seen

Jurassic Park will know, this means a tiny disturbance in one

place, can cause a major change in another. A butterfly flapping

its wings can cause rain in Central Park, New York. The trouble is,

it is not repeatable. The next time the butterfly flaps its wings, a

host of other things will be different, which will also influence the

weather. That is why weather forecasts are so unreliable.

Despite these practical difficulties, scientific determinism,

remained the official dogma throughout the 19th century.

However, in the 20th century, there have been two developments

that show that Laplace's vision, of a complete prediction of the future, can not be realised. The

first of these developments was what is called, quantum mechanics. This was first put forward

in 1900, by the German physicist, Max Planck, as an ad hoc hypothesis, to solve an

outstanding paradox. According to the classical 19th century ideas, dating back to Laplace, a

hot body, like a piece of red hot metal, should give off radiation.

It would lose energy in radio

waves, infra red, visible light, ultra violet, x-rays, and gamma

rays, all at the same rate. Not only would this mean that we would

all die of skin cancer, but also everything in the universe would be

at the same temperature, which clearly it isn't. However, Planck

showed one could avoid this disaster, if one gave up the idea that

the amount of radiation could have just any value, and said

instead that radiation came only in packets or quanta of a certain

size. It is a bit like saying that you can't buy sugar loose in the

supermarket, but only in kilogram bags. The energy in the

packets or quanta, is higher for ultra violet and x-

rays, than for infra red or visible light. This

means that unless a body is very hot, like the Sun, it will not have enough energy, to give off

even a single quantum of ultra violet or x-

rays. That is why we don't get sunburn from a cup of

coffee.

Planck regarded the idea of quanta, as just a mathematical trick, and not as having any

physical reality, whatever that might mean. However, physicists began to find other behaviour,

that could be explained only in terms of quantities having discrete, or quantised values, rather

than continuously variable ones. For example, it was found that elementary particles behaved

rather like little tops, spinning about an axis. But the amount of spin couldn't have just any

value. It had to be some multiple of a basic unit. Because this unit is very small, one does not

notice that a normal top really slows down in a rapid sequence of discrete steps, rather than as

a continuous process. But for tops as small as atoms, the discrete nature of spin is very

important.

It was some time before people realised the implications of this quantum behaviour for

determinism. It was not until 1926, that Werner Heisenberg, another German physicist, pointed

out that you couldn't measure both the position, and the speed, of a particle exactly. To see

where a particle is, one has to shine light on it. But by Planck's work, one can't use an

arbitrarily small amount of light.

One has to use at least one quantum. This will disturb the

particle, and change its speed in a way that can't be

predicted. To measure the position of the particle

accurately, you will have to use light of short wave length,

like ultra violet, x-rays, or gamma rays. But again, by

Planck's work, quanta of these forms of light have higher

energies than those of visible light. So they will disturb the

speed of the particle more. It is a no win situation: the

more accurately you try to measure the position of the

particle, the less accurately you can know the speed, and vice versa. This is summed up in the

Uncertainty Principle that Heisenberg formulated; the uncertainty in the position of a particle,

times the uncertainty in its speed, is always greater than a quantity called Planck's constant,

divided by the mass of the particle.

Laplace's vision, of scientific determinism, involved knowing the positions and speeds of the

particles in the universe, at one instant of time. So it was seriously undermined by

Heisenberg's Uncertainty principle. How could one predict the future, when one could not

measure accurately both the positions, and the speeds, of particles at the present time? No

matter how powerful a computer you have, if you put lousy data in, you will get lousy

predictions out.

Einstein was very unhappy about this apparent randomness in

nature. His views were summed up in his famous phrase, 'God

does not play dice'. He seemed to have felt that the

uncertainty was only provisional: but that there was an

underlying reality, in which particles would have well defined

positions and speeds, and would evolve according to

deterministic laws, in the spirit of Laplace. This reality might be

known to God, but the quantum nature of light would prevent

us seeing it, except through a glass darkly.

Einstein's view was what would now be called, a hidden

variable theory. Hidden variable theories might seem to be the most obvious way to

incorporate the Uncertainty Principle into physics. They form the basis of the mental picture of

the universe, held by many scientists, and almost all philosophers of science. But these hidden

variable theories are wrong. The British physicist, John Bell, who died recently, devised an

experimental test that would distinguish hidden variable theories. When the experiment was

carried out carefully, the results were inconsistent with hidden variables. Thus it seems that

even God is bound by the Uncertainty Principle, and can not know both the position, and the

speed, of a particle. So God does play dice with the universe. All the evidence points to him

being an inveterate gambler, who throws the dice on every possible occasion.

Other scientists were much more ready than Einstein to modify

the classical 19th century view of determinism. A new theory,

called quantum mechanics, was put forward by Heisenberg, the

Austrian, Erwin Schroedinger, and the British physicist, Paul Dirac.

Dirac was my predecessor but one, as the Lucasian Professor in

Cambridge. Although quantum mechanics has been around for

nearly 70 years, it is still not generally understood or appreciated,

even by those that use it to do calculations. Yet it should concern

us all, because it is a completely different picture of the physical

universe, and of reality itself. In quantum mechanics, particles don't have well defined

positions and speeds.

Instead, they are represented by what is called a wave function. This is

a number at each point of space. The size of the wave function gives the

probability that the particle will be found in that position. The rate, at

which the wave function varies from point to point, gives the speed of the

particle. One can have a wave function that is very strongly peaked in a

small region. This will mean that the uncertainty in the position is small.

But the wave function will vary very rapidly near the peak, up on one

side, and down on the other. Thus the uncertainty in the speed will be

large. Similarly, one can have wave functions where the uncertainty in the speed is small, but

the uncertainty in the position is large.

The wave function contains all that one can know of the particle, both its position, and its

speed. If you know the wave function at one time, then its values at other times are

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Hawking, Stephen - Does God Play Dice

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