Stephen Hawking: The Grand Design

In the Game of Life, as in our world, self-reproducing patterns are complex objects. One estimate, based on the earlier work of mathematician John von Neumann, places the minimum size of a self-replicating pattern in the Game of Life at ten trillion squares-roughly the number of molecules in a single human cell.

One can define living beings as complex systems of limited size that are stable and that reproduce themselves. The objects described above satisfy the reproduction condition but are probably not stable: A small disturbance from outside would probably wreck the delicate mechanism. However, it is easy to imagine that slightly more complicated laws would allow complex systems with all the attributes of life. Imagine a entity of that type, an object in a Conway-type world. Such an object would respond to environmental stimuli, and hence appear to make decisions. Would such life be aware of itself? Would it be self-conscious? This is a question on which opinion is sharply divided. Some people claim that self-awareness is something unique to humans. It gives them free will, the ability to choose between different courses of action.

How can one tell if a being has free will? If one encounters an alien, how can one tell if it is just a robot or it has a mind of its own? The behavior of a robot would be completely determined, unlike that of a being with free will. Thus one could in principle detect a robot as a being whose actions can be predicted. As we said in Chapter 2, this may be impossibly difficult if the being is large and complex. We cannot even solve exactly the equations for three or more particles interacting with each other. Since an alien the size of a human would contain about a thousand trillion trillion particles even if the alien were a robot, it would be impossible to solve the equations and predict what it would do. We would therefore have to say that any complex being has free will-not as a fundamental feature, but as an effective theory, an admission of our inability to do the calculations that would enable us to predict its actions.

The example of Conway ’s Game of Life shows that even a very simple set of laws can produce complex features similar to those of intelligent life. There must be many sets of laws with this property. What picks out the fundamental laws (as opposed to the apparent laws) that govern our universe? As in Conway ’s universe, the laws of our universe determine the evolution of the system, given the state at any one time. In Conway ’s world we are the creators-we choose the initial state of the universe by specifying objects and their positions at the start of the game.

In a physical universe, the counterparts of objects such as gliders in the Game of Life are isolated bodies of matter. Any set of laws that describes a continuous world such as our own will have a concept of energy, which is a conserved quantity, meaning it doesn’t change in time. The energy of empty space will be a constant, independent of both time and position. One can subtract out this constant vacuum energy by measuring the energy of any volume of space relative to that of the same volume of empty space, so we may as well call the constant zero. One requirement any law of nature must satisfy is that it dictates that the energy of an isolated body surrounded by empty space is positive, which means that one has to do work to assemble the body. That’s because if the energy of an isolated body were negative, it could be created in a state of motion so that its negative energy was exactly balanced by the positive energy due to its motion. If that were true, there would be no reason that bodies could not appear anywhere and everywhere. Empty space would therefore be unstable. But if it costs energy to create an isolated body, such instability cannot happen, because, as we’ve said, the energy of the universe must remain constant. That is what it takes to make the universe locally stable-to make it so that things don’t just appear everywhere from nothing.

If the total energy of the universe must always remain zero, and it costs energy to create a body, how can a whole universe be created from nothing? That is why there must be a law like gravity. Because gravity is attractive, gravitational energy is negative: One has to do work to separate a gravitationally bound system, such as the earth and moon. This negative energy can balance the positive energy needed to create matter, but it’s not quite that simple. The negative gravitational energy of the earth, for example, is less than a billionth of the positive energy of the matter particles the earth is made of. A body such as a star will have more negative gravitational energy, and the smaller it is (the closer the different parts of it are to each other), the greater this negative gravitational energy will be. But before it can become greater than the positive energy of the matter, the star will collapse to a black hole, and black holes have positive energy. That’s why empty space is stable. Bodies such as stars or black holes cannot just appear out of nothing. But a whole universe can.

Because gravity shapes space and time, it allows space-time to be locally stable but globally unstable. On the scale of the entire universe, the positive energy of the matter can be balanced by the negative gravitational energy, and so there is no restriction on the creation of whole universes. Because there is a law like gravity, the universe can and will create itself from nothing in the manner described in Chapter 6. Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist. It is not necessary to invoke God to light the blue touch paper and set the universe going.

Why are the fundamental laws as we have described them? The ultimate theory must be consistent and must predict finite results for quantities that we can measure. We’ve seen that there must be a law like gravity, and we saw in Chapter 5 that for a theory of gravity to predict finite quantities, the theory must have what is called supersymmetry between the forces of nature and the matter on which they act. M-theory is the most general supersymmetric theory of gravity. For these reasons M-theory is the only candidate for a complete theory of the universe. If it is finite-and this has yet to be proved-it will be a model of a universe that creates itself. We must be part of this universe, because there is no other consistent model.

M-theory is the unified theory Einstein was hoping to find. The fact that we human beings-who are ourselves mere collections of fundamental particles of nature-have been able to come this close to an understanding of the laws governing us and our universe is a great triumph. But perhaps the true miracle is that abstract considerations of logic lead to a unique theory that predicts and describes a vast universe full of the amazing variety that we see. If the theory is confirmed by observation, it will be the successful conclusion of a search going back more than 3,000 years. We will have found the grand design.

Alternative histories • a formulation of quantum theory in which the probability of any observation is constructed from all the possible histories that could have led to that observation.

Anthropic principle • the idea that we can draw conclusions about the apparent laws of physics based on the fact that we exist.

Antimatter • each particle of matter has a corresponding anti-particle. If they meet, they annihilate each other, leaving pure energy.

Apparent laws • the laws of nature that we observe in our universe-the laws of the four forces, and the parameters such as mass and charge that characterize the elementary particles-in contrast to the more fundamental laws of M-theory that allow for different universes with different laws.