Illustrated Theory of Everything: The Origin and Fate of the Universe (6 page)

As the universe expanded, the matter particles got farther apart. One would beleft with an expanding universe that contained hardly any particles. It wouldstill be in the supercooled state, in which the symmetry between the forces isnot broken. Any irregularities in the universe would simply have beensmoothed out by the expansion, as the wrinkles in a balloon are smoothedaway when you blow it up. Thus, the present smooth and uniform state of theuniverse could have evolved from many different nonuniform initial states.The rate of expansion would also tend toward just the critical rate needed toavoid recollapse.

Moreover, the idea of inflation could also explain why there is so much matterin the universe. There are something like 1,080 particles in the region of theuniverse that we can observe. Where did they all come from? The answer isthat, in quantum theory, particles can be created out of energy in the form ofparticle/antiparticle pairs. But that just raises the question of where the energycame from. The answer is that the total energy of the universe is exactly zero.The matter in the universe is made out of positive energy. However, the mat-ter is all attracting itself by gravity. Two pieces of matter that are close to eachother have less energy than the same two pieces a long way apart. This isbecause you have to expend energy to separate them. You have to pull againstthe gravitational force attracting them together. Thus, in a sense, the gravita-tional field has negative energy. In the case of the whole universe, one canshow that this negative gravitational energy exactly cancels the positive ener-gy of the matter. So the total energy of the universe is zero.

Now, twice zero is also zero. Thus, the universe can double the amount of pos-itive matter energy and also double the negative gravitational energy withoutviolation of the conservation of energy. This does not happen in the normalexpansion of the universe in which the matter energy density goes down as theuniverse gets bigger. It does happen, however, in the inflationary expansion,because the energy density of the supercooled state remains constant while theuniverse expands. When the universe doubles in size, the positive matter ener-gy and the negative gravitational energy both double, so the total energyvery large amount. Thus, the total amount of energy available to make parti-cles becomes very large. As Guth has remarked, “It is said that there is no suchthing as a free lunch. But the universe is the ultimate free lunch.”

THE END OF INFLATION

The universe is not expanding in an inflationary way today. Thus, there hadto be some mechanism that would eliminate the very large effective cosmolog-ical constant. This would change the rate of expansion from an acceleratedone to one that is slowed down by gravity, as we have today. As the universeexpanded and cooled, one might expect that eventually the symmetry betweenthe forces would be broken, just as supercooled water always freezes in the end.The extra energy of the unbroken symmetry state would then be released andwould reheat the universe. The universe would then go on to expand and cool,just like the hot big bang model. However, there would now be an explanationof why the universe was expanding at exactly the critical rate and why differ-ent regions had the same temperature.

In Guth’s original proposal, the transition to broken symmetry was supposed tooccur suddenly, rather like the appearance of ice crystals in very cold water.The idea was that “bubbles” of the new phase of broken symmetry would haveformed in the old phase, like bubbles of steam surrounded by boiling water.The bubbles were supposed to expand and meet up with each other until thewhole universe was in the new phase. The trouble was, as I and several otherpeople pointed out, the universe was expanding so fast that the bubbles wouldbe moving away from each other too rapidly to join up. The universe would beleft in a very nonuniform state, with some regions having symmetry betweenthe different forces. Such a model of the universe would not correspond towhat we see.

In October 1981 I went to Moscow for a conference on quantum gravity. Afterthe conference, I gave a seminar on the inflationary model and its problems atthe Sternberg Astronomical Institute. In the audience was a young Russian,Andrei Linde. He said that the difficulty with the bubbles not joining up couldbe avoided if the bubbles were very big. In this case, our region of the universecould be contained inside a single bubble. In order for this to work, the changefrom symmetry to broken symmetry must have taken place very slowly insidethe bubble, but this is quite possible according to grand unified theories.Linde’s idea of a slow breaking of symmetry was very good, but I pointed outthat his bubbles would have been bigger than the size of the universe at thetime. I showed that instead the symmetry would have broken everywhere atthe same time, rather than just inside bubbles. This would lead to a uniformuniverse, like we observe. The slow symmetry breaking model was a goodattempt to explain why the universe is the way it is. However, I and severalother people showed that it predicted much greater variations in themicrowave background radiation than are observed. Also, later work castdoubt on whether there would have been the right kind of phase transition inthe early universe. A better model, called the chaotic inflationary model, wasintroduced by Linde in 1983. This doesn’t depend on phase transitions, and itcan give us the right size of variations of the microwave background. The infla-tionary model showed that the present state of the universe could have arisenfrom quite a large number of different initial configurations. It cannot be thecase, however, that every initial configuration would have led to a universelike the one we observe. So even the inflationary model does not tell us whythe initial configuration was such as to produce what we observe. Must we turnto the anthropic principle for an explanation? Was it all just a lucky chance?That would seem a counsel of despair, a negation of all our hopes of under-standing the underlying order of the universe.

QUANTUM GRAVITY

In order to predict how the universe should have started off, one needs laws thathold at the beginning of time. If the classical theory of general relativity wascorrect, the singularity theorem showed that the beginning of time would havebeen a point of infinite density and curvature. All the known laws of sciencewould break down at such a point. One might suppose that there were new lawsthat held at singularities, but it would be very difficult even to formulate lawsat such badly behaved points and we would have no guide from observations asto what those laws might be. However, what the singularity theorems reallyindicate is that the gravitational field becomes so strong that quantum gravita-tional effects become important: Classical theory is no longer a good descrip-tion of the universe. So one has to use a quantum theory of gravity to discussthe very early stages of the universe. As we shall see, it is possible in the quan-tum theory for the ordinary laws of science to hold everywhere, including at thebeginning of time. It is not necessary to postulate new laws for singularities,because there need not be any singularities in the quantum theory.

We don’t yet have a complete and consistent theory that combines quantummechanics and gravity. However, we are thoroughly certain of some featuresthat such a unified theory should have. One is that it should incorporateFeynman’s proposal to formulate quantum theory in terms of a sum over histo-ries. In this approach, a particle going from A to B does not have just a singlehistory as it would in a classical theory. Instead, it is supposed to follow everypossible path in space-time. With each of these histories, there are associateda couple of numbers, one representing the size of a wave and the other repre-senting its position in the cycle-its phase.The probability that the particle, say, passes through some particular point isfound by adding up the waves associated with every possible history thatpasses through that point. When one actually tries to perform these sums,however, one runs into severe technical problems. The only way around theseis the following peculiar prescription: One must add up the waves for particlehistories that are not in the real time that you and I experience but take placein imaginary time.

Imaginary time may sound like science fiction, but it is in fact a well-definedmathematical concept. To avoid the technical difficulties with Feynman’s sumover histories, one must use imaginary time. This has an interesting effect onspace-time: The distinction between time and space disappears completely. Aspace-time in which events have imaginary values of the time coordinate issaid to be Euclidean because the metric is positive definite.In Euclidean space-time there is no difference between the time direction anddirections in space. On the other hand, in real space-time, in which events arelabeled by real values of the time coordinate, it is easy to tell the difference. Thetime direction lies within the light cone, and space directions lie outside. Onecan regard the use of imaginary time as merely a mathematical device-ortrick-to calculate answers about real space-time. However, there may be moreto it than that. It may be that Euclidean space-time is the fundamental conceptand what we think of as real space-time is just a figment of our imagination.When we apply Feynman’s sum over histories to the universe, the analogue ofthe history of a particle is now a complete curved space-time which representsthe history of the whole universe. For the technical reasons mentioned above,these curved space-times must be taken to be Euclidean. That is, time isimaginary and is indistinguishable from directions in space. To calculate theprobability of finding a real space-time with some certain property, one addsup the waves associated with all the histories in imaginary time that have thatproperty. One can then work out what the probable history of the universewould be in real time.

THE NO BOUNDARY CONDITION

In the classical theory of gravity, which is based on real space-time, there areonly two possible ways the universe can behave. Either it has existed for an infi-nite time, or else it had a beginning at a singularity at some finite time in thepast. In fact, the singularity theorems show it must be the second possibility. Inthe quantum theory of gravity, on the other hand, a third possibility arises.Because one is using Euclidean space-times, in which the time direction is onthe same footing as directions in space, it is possible for space-time to be finitein extent and yet to have no singularities that formed a boundary or edge.Space-time would be like the surface of the Earth, only with two more dimen-sions. The surface of the Earth is finite in extent but it doesn’t have a boundaryor edge. If you sail off into the sunset, you don’t fall off the edge or run into asingularity. I know, because I have been around the world.

If Euclidean space-times direct back to infinite imaginary time or else startedat a singularity, we would have the same problem as in the classical theory ofspecifying the initial state of the universe. God may know how the universebegan, but we cannot give any particular reason for thinking it began one wayrather than another. On the other hand, the quantum theory of gravity hasopened up a new possibility. In this, there would be no boundary tospace-time. Thus, there would be no need to specify the behavior at theboundary. There would be no singularities at which the laws of science brokedown and no edge of space-time at which one would have to appeal to God orsome new law to set the boundary conditions for space-time. One could say:”The boundary condition of the universe is that it has no boundary.” The uni-verse would be completely self-contained and not affected by anything outsideitself. It would be neither created nor destroyed. It would just be.

It was at the conference in the Vatican that I first put forward the suggestionthat maybe time and space together formed a surface that was finite in size butdid not have any boundary or edge. My paper was rather mathematical, how-ever, so its implications for the role of God in the creation of the universe werenot noticed at the time-just as well for me. At the time of the Vatican confer-ence, I did not know how to use a no boundary idea to make predictions aboutthe universe. However, I spent the following summer at the University ofCalifornia, Santa Barbara. There, a friend and colleague of mine, Jim Hartle,worked out with me what conditions the universe must satisfy if space-timehad no boundary.

I should emphasize that this idea that time and space should be finite withoutboundary is just a proposal. It cannot be deduced from some other principle.Like any other scientific theory, it may initially be put forward for aesthetic ormetaphysical reasons, but the real test is whether it makes predictions thatagree with observation. This, however, is difficult to determine in the case ofquantum gravity, for two reasons. First, we are not yet sure exactly which the-ory successfully combines general relativity and quantum mechanics, thoughwe know quite a lot about the form such a theory must have. Second, anymodel that described the whole universe in detail would be much too compli-cated mathematically for us to be able to calculate exact predictions. Onetherefore has to make approximations-and even then, the problem ofextracting predictions remains a difficult one.

One finds, under the no boundary proposal, that the chance of the universebeing found to be following most of the possible histories is negligible. Butthere is a particular family of histories that are much more probable than theothers. These histories may be pictured as being like the surface of the Earth,with a distance from the North Pole representing imaginary time; the size of acircle of latitude would represent the spatial size of the universe. The universestarts at the North Pole as a single point. As one moves south, the circle of lat-itude get bigger, corresponding to the universe expanding with imaginary time.The universe would reach a maximum size at the equator and would contractagain to a single point at the South Pole. Even though the universe wouldhave zero size at the North and South poles, these points would not be singu-larities any more than the North and South poles on the Earth are singular.The laws of science will hold at the beginning of the universe, just as they doat the North and South poles on the Earth.