Stephen J. Hawking Essay, Research Paper

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.

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