Stephen J. Hawking by Rachel Finck

Stephen Hawking was born in January of 1942 in Oxford, England. He grew

up near London and was educated at Oxford, from which he received his BA in 1962,

and Cambridge, where he received his doctorate in theoretical physics. Stephen

Hawking is a brilliant and highly productive researcher, and, since 1979, he has

held the Lucasian professorship in mathematics at Cambridge, the very chair once

held by Isaac Newton. Although still relatively young, Hawking is already being

compared to such great intellects as Newton and Albert Einstein. Yet it should

be noted that since the early 1960s he has been the victim of a progressive and

incurable motorneurone disease, ALS, that now confines him to a wheelchair.

This affliction prevents Hawking from reading, writing, or calculating in a

direct and simple way. The bulk of his work, involving studying, publishing,

lecturing, and worldwide travel, is carried on with the help of colleagues,

friends, and his wife. Of his illness, Hawking has said that it has enhanced

his career by giving him the freedom to think about physics and the Universe.

Stephen Hawking has written many essays involving the unified theory,

which is a theory summarizing the entire of the physical world; a theory that

would stand as a complete, consistent theory of the physical interactions that

would describe all possible observations. Our attempts at modeling physical

reality normally consists of two parts: a) A set of local laws that are obeyed

by the various physical quantities, formulated in terms of differential

equations, and b) Sets of boundary conditions that tell us the state of some

regions of the universe at a certain time and what effects propagate into it

subsequently from the rest of the universe. Presently, physicist are still

trying to unify two separate theories to describe everything in the universe.

The two theories are the general theory of relativity and quantum mechanics.

Albert Einstein formulated the general theory of relativity almost

single-handedly in 1915. First, in 1905, he developed the special theory of

relativity, which deals with the concept of people measuring different time

intervals, while moving at different speeds, yet measuring the same speed for

the speed of light, regardless of velocity. In 1915, he developed the general

theory of relativity. This theory dealt with the concept of gravity as a

distortion of space-time, and not just a force within it.

Einstein’s original equations predicted that the universe was either

expanding or contracting. Einstein’s equations showed that mass and energy are

always positive, which is why gravity always attracts bodies toward each other.

Space-time is curved back onto itself like the surface of the earth. It was

then theorized that what if matter could curve a region in on itself so much

that it could cut itself off from the rest of the universe. The region would

become what is known as a black hole. Nothing could escape it, although objects

could fall in. To get out, the objects would have to move faster than the speed

of light, and this was not allowed by the general theory of relativity. In 1965,

Hawking along with Roger Penrose proved a number of theorems that showed the

fact that space-time was curved in on itself so that there would be

singularities where space-time had a beginning or an end.

“The fact that Einstein’s general theory of relativity turned out to

predict singularities led to a crisis in physics. (Hawking)” The equations of

general relativity cannot be defined as a singularity. This means that general

relativity cannot predict how the universe should begin at the big bang. Thus,

it is not a complete theory. It must be paired with quantum mechanics.

In 1905, the photoelectric effect was written about by Einstein, which

he theorized could be explain if light came not in continuously variable amounts,

but in packets of a certain size. A few years earlier, the idea of energy in

quanta had been introduced by Max Planck.

The full implications of the photoelectric effect were not realized

until 1925, when Werner Heisenberg pointed out that it made it impossible to

measure the position of a particle exactly. To see where a particle is, you

have to shine a light on it. As Einstein showed, you had to use at least one

quanta of light. This whole packet of light would disturb the particle and

cause it to move at some speed in some direction different than its state before

the light was shined. In this way, it was theorized that the more accurately

you want to measure the position of the particle, the greater the energy packet

you would have to use and thus the more you would disturb the particle. This

dilemma is called the Heisenberg uncertainty principle.

Einstein’s general theory of relativity is a classic theory because it

does not take into account the uncertainty principle. One therefore has to find

a new theory that combines general relativity and the uncertainty principle. In

most situations, the difference between the general relativity theory and the

new theory is very small. However, the singularity theorems that Hawking proved

show that space-time will become highly curved on very small scales. The

effects of the uncertainty principle will then become very important.

The problems that Einstein had with quantum mechanics is that he used

the commonsense notion that a particle has a definite history. And that a

particle has a definite location. But, it must be taken into account that a

particle has an infinite set of histories. A famous thought experiment called

Shroedinger’s cat helps to illustrate this concept. Let’s say that a cat is

placed in a sealed box and a gun is pointed at it. The gun will only go off if

a radioactive nucleus decays. There is exactly a 50% chance of this happening.

Later on, before the box is opened, there are two possibilities of what happened

to the cat: the gun did not go off, and the cat is alive, or the gun did go off,

and the cat is dead. Before the box is opened, the cat is both alive and dead

at the same time. The cat has two separate histories.

Another way to think of this was put forth by a physicist Richard

Feynman. He contributed that a system didn’t just have a single history in

space-time, but it had every possible history. “Consider, for example, a

particle at point A at a certain time. Normally, one would assume that the

particle would move in a straight line away from A. However, according to the

sum over histories, it can move on any path that starts at A. (Hawking)” It’s

like what happens when you place a drop of ink on blotting paper, and it

diffuses along every path away from its point of origin.

In 1973, Stephen Hawking began investigating what effect the uncertainty

principle would have on a particle in the curved space-time near a black hole.

He found that the black hole would not be completely black. The uncertainty

principle would allow particles to leak out of the black hole at a steady rate.

Although, the discovery came as a complete surprise, “It ought to have been

obvious. The Feynman sum over histories says that particles can take any path

through space-time. Thus it is possible for a particle to travel faster than

light. (Hawking)”

In 1983, Stephen Hawking proposed that the sum of histories for the

universe should not be taken over histories in real time. Rather, it should be

taken over histories in imaginary time that were closed in on themselves, like

the surface of the earth. Because these histories didn’t have any singularities

or any beginning or end, what happened to them would be determined entirely by

the laws of physics. This means, what happened in imaginary time could be

calculated. “And if you know the history of the universe in imaginary time, you

can calculate how it behaves in real time. In this way, you could hope to get a

complete unified theory, one that would predict everything in the universe.

(Hawking)”

Imaginary time is a concept that Hawking has made a particular advance

in as a physicist. It seems obvious that the universe has a unique history, yet

since the discovery of quantum mechanics, we have to consider the universe as

having every possible history. To grasp the concept of imaginary time, think of

real time as horizontal line. Early times are on the left, and late times are

on the right. Then think of lines going 90 from the horizontal line of real

time. These lines, which are at right angles to real time, represent imaginary

time. The importance of imaginary time lies in the fact that the universe is

curved in on itself, leading to singularities. At the singularities, the

equations of physics cannot be defines, thus one cannot predict what will happen.

But the imaginary time direction is at right angles to real time. This means

that it behaves in a similar way to the three directions that correspond to

moving in space. Then, the curvature of space can lead to the three directions

and the imaginary time direction meeting up around the back. These would form a

closed surface, like the surface of the earth. Stephen Hawking as a physicist

has many much progress in the use of imaginary time in the way the field of

physics thinks.