The Big Bang

In the early universe—when the universe was small enough to be governed by both general relativity and quantum theory—there were effectively 4 dimensions of space and none of time.

That means that when we speak of the “beginning” of the universe, we are skirting the subtle issue that as we look backward toward the very early universe, time as we know it does not exist!

We must accept that our usual ideas of space and time do not apply to the very early universe. That is beyond our experience, but not beyond our imagination, or our mathematics. If in the early universe all four dimensions behave like space, what happens to the beginning of time?

The realization that time can behave like another direction of space means one can get rid of the problem of time having a beginning, in a similar way in which we got rid of the edge of the world.

Suppose the beginning of the universe was like the South Pole of the earth, with degrees of latitude playing the role of time. As one moves north, the circles of constant latitude, representing the size of the universe, would expand. The universe would start as a point at the South Pole, but the South Pole is much like any other point.

To ask what happened before the beginning of the universe would become a meaningless question, because there is nothing south of the South Pole.

In this picture space-time has no boundary—the same laws of nature hold at the South Pole as in other places. In an analogous manner, when one combines the general theory of relativity with quantum theory, the question of what happened before the beginning of the universe is rendered meaningless.

This idea that histories should be closed surfaces without boundary is called the noboundary condition.

Over the centures many, including Aristotle, believed that the universe must have always existed in order to avoid the issue of how it was set up.

Others believed the universe had a beginning, and used it as an argument for the existence of God. The realization that time behaves like space presents a new alternative. It removes the age-old objection to the universe having a beginning, but also means that the beginning of the universe was governed by the laws of science and doesn’t need to be set in motion by some god.

If the origin of the universe was a quantum event, it should be accurately described by the Feynman sum over histories. To apply quantum theory to the entire universe—where the observers are part of the system being observed—is tricky, however. In Chapter 4 we saw how particles of matter fired at a screen with two slits in it could exhibit interference patterns just as water waves do.

Feynman showed that this arises because a particle does not have a unique history. That is, as it moves from its starting point A to some endpoint B, it doesn’t take one definite path, but rather simultaneously takes every possible path connecting the 2 points.

From this point of view, interference is no surprise because, for instance, the particle can travel through both slits at the same time and interfere with itself.

Applied to the motion of a particle, Feynman’s method tells us that to calculate the probability of any particular endpoint we need to consider all the possible histories that the particle might follow from its starting point to that endpoint. One can also use Feynman’s methods to calculate the quantum probabilities for observations of the universe. If they are applied to the universe as a whole, there is no point A, so we add up all the histories that satisfy the no-boundary condition and end at the universe we observe today.

In this view, the universe appeared spontaneously, starting off in every possible way. Most of these correspond to other universes. While some of those universes are similar to ours, most are very different. They aren’t just different in details, such as whether Elvis really did die young or whether turnips are a dessert food, but rather they differ even in their apparent laws of nature.

In fact, many universes exist with many different sets of physical laws. Some people make a great mystery of this idea, sometimes called the multiverse concept, but these are just different expressions of the Feynman sum over histories.

To picture this, let’s alter Eddington’s balloon analogy and instead think of the expanding universe as the surface of a bubble. Our picture of the spontaneous quantum creation of the universe is then a bit like the formation of bubbles of steam in boiling water. Many tiny bubbles appear, and then disappear again. These represent mini-universes that expand but collapse again while still of microscopic size.

They represent possible alternative universes, but they are not of much interest since they do not last long enough to develop galaxies and stars, let alone intelligent life. A few of the little bubbles, however, will grow large enough so that they will be safe from recollapse. They will continue to expand at an ever-increasing rate and will form the bubbles of steam we are able to see.

These correspond to universes that start off expanding at an ever-increasing rate—in other words, universes in a state of inflation.

As we said, the expansion caused by inflation would not be completely uniform. In the sum over histories, there is only one completely uniform and regular history, and it will have the greatest probability, but many other histories that are very slightly irregular will have probabilities that are almost as high.

That is why inflation predicts that the early universe is likely to be slightly nonuniform, corresponding to the small variations in the temperature that were observed in the CMBR.

The irregularities in the early universe are lucky for us. Why? Homogeneity is good if you don’t want cream separating out from your milk, but a uniform universe is a boring universe.

The irregularities in the early universe are important because if some regions had a slightly higher density than others, the gravitational attraction of the extra density would slow the expansion of that region compared with its surroundings. As the force of gravity slowly draws matter together, it can eventually cause it to collapse to form galaxies and stars, which can lead to planets and, on at least one occasion, people.

So look carefully at the map of the microwave sky. It is the blueprint for all the structure in the universe. We are the product of quantum fluctuations in the very early universe.

If one were religious, one could say that God really does play dice.

This idea leads to a view of the universe that is profoundly different from the traditional concept, requiring us to adjust the way that we think about the history of the universe.

In order to make predictions in cosmology, we need to calculate the probabilities of different states of the entire universe at the present time. In physics one normally assumes some initial state for a system and evolves it forward in time employing the relevant mathematical equations.

Given the state of a system at one time, one tries to calculate the probability that the system will be in some different state at a later time. The usual assumption in cosmology is that the universe has a single definite history. One can use the laws of physics to calculate how this history develops with time.

We call this the “bottom-up” approach to cosmology. But since we must take into account the quantum nature of the universe as expressed by the Feynman sum over histories, the probability amplitude that the universe is now in a particular state is arrived at by adding up the contributions from all the histories that satisfy the no-boundary condition and end in the state in question.

In cosmology, in other words, one shouldn’t follow the history of the universe from the bottom up because that assumes there’s a single history, with a well-defined starting point and evolution.

Instead, one should trace the histories from the top down, backward from the present time. Some histories will be more probable than others, and the sum will normally be dominated by a single history that starts with the creation of the universe and culminates in the state under consideration.

But there will be different histories for different possible states of the universe at the present time. This leads to a radically different view of cosmology, and the relation between cause and effect. The histories that contribute to the Feynman sum don’t have an independent existence, but depend on what is being measured. We create history by our observation, rather than history creating us.

The idea that the universe does not have a unique observer-independent history might seem to conflict with certain facts we know. There might be one history in which the moon is made of Roquefort cheese.

But we have observed that the moon is not made of cheese, which is bad news for mice. Hence histories in which the moon is made of cheese do not contribute to the present state of our universe, though they might contribute to others. That might sound like science fiction, but it isn’t.

An important implication of the top-down approach is that the apparent laws of nature depend on the history of the universe. Many scientists believe there exists a single theory that explains those laws as well as nature’s physical constants, such as the mass of the electron or the dimensionality of space-time.

But top-down cosmology dictates that the apparent laws of nature are different for different histories.