Although still relatively young, Hawking is already beingcompared to such great intellects as Newton and Albert Einstein. Yet it shouldbe noted that since the early 1960s he has been the victim of a progressive andincurable motorneurone disease, ALS, that now confines him to a wheelchair. This affliction prevents Hawking from reading, writing, or calculating in adirect 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 enhancedhis 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 thatwould stand as a complete, consistent theory of the physical interactions thatwould describe all possible observations. Our attempts at modeling physicalreality normally consists of two parts: a) A set of local laws that are obeyedby the various physical quantities, formulated in terms of differentialequations, and b) Sets of boundary conditions that tell us the state of someregions of the universe at a certain time and what effects propagate into itsubsequently from the rest of the universe. Presently, physicist are stilltrying 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 almostsingle-handedly in 1915.
First, in 1905, he developed the special theory ofrelativity, which deals with the concept of people measuring different timeintervals, while moving at different speeds, yet measuring the same speed forthe speed of light, regardless of velocity. In 1915, he developed the generaltheory of relativity. This theory dealt with the concept of gravity as adistortion of space-time, and not just a force within it. Einstein’s original equations predicted that the universe was eitherexpanding or contracting.
Einstein’s equations showed that mass and energy arealways 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 wasthen theorized that what if matter could curve a region in on itself so muchthat it could cut itself off from the rest of the universe. The region wouldbecome what is known as a black hole. Nothing could escape it, although objectscould fall in.
To get out, the objects would have to move faster than the speedof 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 thefact that space-time was curved in on itself so that there would besingularities where space-time had a beginning or an end. “The fact that Einstein’s general theory of relativity turned out topredict singularities led to a crisis in physics. (Hawking)” The equations ofgeneral relativity cannot be defined as a singularity. This means that generalrelativity 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, whichhe 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 inquanta had been introduced by Max Planck. The full implications of the photoelectric effect were not realizeduntil 1925, when Werner Heisenberg pointed out that it made it impossible tomeasure the position of a particle exactly.
To see where a particle is, youhave to shine a light on it. As Einstein showed, you had to use at least onequanta of light. This whole packet of light would disturb the particle andcause it to move at some speed in some direction different than its state beforethe light was shined. In this way, it was theorized that the more accuratelyyou want to measure the position of the particle, the greater the energy packetyou would have to use and thus the more you would disturb the particle.
Thisdilemma is called the Heisenberg uncertainty principle. Einstein’s general theory of relativity is a classic theory because itdoes not take into account the uncertainty principle. One therefore has to finda new theory that combines general relativity and the uncertainty principle. Inmost situations, the difference between the general relativity theory and thenew theory is very small. However, the singularity theorems that Hawking provedshow that space-time will become highly curved on very small scales.
Theeffects of the uncertainty principle will then become very important. The problems that Einstein had with quantum mechanics is that he usedthe commonsense notion that a particle has a definite history. And that aparticle has a definite location. But, it must be taken into account that aparticle has an infinite set of histories. A famous thought experiment calledShroedinger’s cat helps to illustrate this concept.
Let’s say that a cat isplaced in a sealed box and a gun is pointed at it. The gun will only go off ifa 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 happenedto 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 deadat the same time.
The cat has two separate histories. Another way to think of this was put forth by a physicist RichardFeynman. He contributed that a system didn’t just have a single history inspace-time, but it had every possible history. “Consider, for example, aparticle at point A at a certain time. Normally, one would assume that theparticle would move in a straight line away from A.
However, according to thesum over histories, it can move on any path that starts at A. (Hawking)” It’slike what happens when you place a drop of ink on blotting paper, and itdiffuses along every path away from its point of origin. In 1973, Stephen Hawking began investigating what effect the uncertaintyprinciple 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 uncertaintyprinciple 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 beenobvious.
The Feynman sum over histories says that particles can take any paththrough space-time. Thus it is possible for a particle to travel faster thanlight. (Hawking)”In 1983, Stephen Hawking proposed that the sum of histories for theuniverse should not be taken over histories in real time. Rather, it should betaken over histories in imaginary time that were closed in on themselves, likethe surface of the earth.
Because these histories didn’t have any singularitiesor any beginning or end, what happened to them would be determined entirely bythe laws of physics. This means, what happened in imaginary time could becalculated. “And if you know the history of the universe in imaginary time, youcan calculate how it behaves in real time. In this way, you could hope to get acomplete unified theory, one that would predict everything in the universe. (Hawking)”Imaginary time is a concept that Hawking has made a particular advancein as a physicist.
It seems obvious that the universe has a unique history, yetsince the discovery of quantum mechanics, we have to consider the universe ashaving every possible history. To grasp the concept of imaginary time, think ofreal time as horizontal line. Early times are on the left, and late times areon the right. Then think of lines going 90 from the horizontal line of realtime. These lines, which are at right angles to real time, represent imaginarytime.
The importance of imaginary time lies in the fact that the universe iscurved in on itself, leading to singularities. At the singularities, theequations 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 meansthat it behaves in a similar way to the three directions that correspond tomoving in space.
Then, the curvature of space can lead to the three directionsand the imaginary time direction meeting up around the back. These would form aclosed surface, like the surface of the earth. Stephen Hawking as a physicisthas many much progress in the use of imaginary time in the way the field ofphysics thinks.