A Brief History of Time - Stephen Hawking | Page 6

of
observations on the basis of a model that contains only a few arbitrary \
elements, and it must make definite
predictions about the results of future observations. For example, Arist\
otle believed Empedocles’s theory that
everything was made out of four elements, earth, air, fire, and water. T\
his was simple enough, but did not make
any definite predictions. On the other hand, Newton’s theory of gravi\
ty was based on an even simpler model, in
which bodies attracted each other with a force that was proportional to \
a quantity called their mass and
inversely proportional to the square of the distance between them. Yet i\
t predicts the motions of the sun, the
moon, and the planets to a high degree of accuracy.
Any physical theory is always provisional, in the sense that it is only \
a hypothesis: you can never prove it. No
matter how many times the results of experiments agree with some theory,\
you can never be sure that the next
time the result will not contradict the theory. On the other hand, you c\
an disprove a theory by finding even a
single observation that disagrees with the predictions of the theory. As\
philosopher of science Karl Popper has
emphasized, a good theory is characterized by the fact that it makes a n\
umber of predictions that could in
principle be disproved or falsified by observation. Each time new experi\
ments are observed to agree with the
predictions the theory survives, and our confidence in it is increased; \
but if ever a new observation is found to
disagree, we have to abandon or modify the theory.
At least that is what is supposed to happen, but you can always question\
the competence of the person who
carried out the observation.
In practice, what often happens is that a new theory is devised that is \
really an extension of the previous theory.
For example, very accurate observations of the planet Mercury revealed a\
small difference between its motion
and the predictions of Newton’s theory of gravity. Einstein’s gene\
ral theory of relativity predicted a slightly
different motion from Newton’s theory. The fact that Einstein’s pr\
edictions matched what was seen, while
Newton’s did not, was one of the crucial confirmations of the new the\
ory. However, we still use Newton’s theory
for all practical purposes because the difference between its prediction\
s and those of general relativity is very
small in the situations that we normally deal with. (Newton’s theory\
also has the great advantage that it is much
simpler to work with than Einstein’s!)
The eventual goal of science is to provide a single theory that describe\
s the whole universe. However, the
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approach most scientists actually follow is to separate the problem into\
two parts. First, there are the laws that
tell us how the universe changes with time. (If we know what the univer\
se is like at any one time, these physical
laws tell us how it will look at any later time.) Second, there is the \
question of the initial state of the universe.
Some people feel that science should be concerned with only the first pa\
rt; they regard the question of the
initial situation as a matter for metaphysics or religion. They would sa\
y that God, being omnipotent, could have
started the universe off any way he wanted. That may be so, but in that \
case he also could have made it
develop in a completely arbitrary way. Yet it appears that he chose to m\
ake it evolve in a very regular way
according to certain laws. It therefore seems equally reasonable to supp\
ose that there are also laws governing
the initial state.
It turns out to be very difficult to devise a theory to describe the uni\
verse all in one go. Instead, we break the
problem up into bits and invent a number of partial theories. Each of th\
ese partial theories describes and
predicts a certain limited class of observations, neglecting the effects\
of other quantities, or representing them
by simple sets of numbers. It may be that this approach is completely wr\
ong. If everything in the universe
depends on everything else in a fundamental way, it might be impossible \
to get close to a full solution by
investigating parts of the problem in isolation. Nevertheless, it is cer\
tainly the way that we have made progress
in the past. The classic example again is the Newtonian theory of gravit\
y, which tells us that the gravitational
force between two bodies depends only on one number associated with each\
body, its mass, but is otherwise
independent of what the bodies are made of. Thus one does not need to ha\
ve a theory of the structure and
constitution of the sun and the