A Brief History of Time: Chapters 9–12

This energy is dissipated as heat, and increases the amount of disorder in the universe.

Our subjective sense of the direction of time, the psychological arrow of time, is therefore determined within our brain by the thermodynamic arrow of time.

Like the uncertainty principle, Godel’s incompleteness theorem may be a fundamental limitation on our ability to understand and predict the universe, but so far at least it hasn’t seemed to be an obstacle in our search for a complete unified theory.

The Godel solution and the cosmic string space-time start out so distorted that travel into the past was always possible.

There are many versions of this paradox but they are essentially equivalent: one would get contradictions if one were free to change the past.

One I shall call the consistent histories approach. It says that even if space-time is warped so that it would be possible to travel into the past, what happens in space-time must be a consistent solution of the laws of physics.

The other possible way to resolve the paradoxes of time travel might be called the alternative histories hypothesis. The idea here is that when time travelers go back to the past, they enter alternative histories which differ from recorded history.

One would avoid these problems if what I call the chronology protection conjecture holds. This says that the laws of physics conspire to prevent macroscopic bodies from carrying information into the past.

The reason to believe that chronology protection operates is that when space-time is warped enough to make travel into the past possible, virtual particles moving on closed loops in space-time can become real particles traveling forward in time at or below the speed of light.

Ultimately, however, one would hope to find a complete, consistent, unified theory that would include all these partial theories as approximations, and that did not need to be adjusted to fit the facts by picking the values of certain arbitrary numbers in the theory. The quest for such a theory is known as “the unification of physics.”

The main difficulty in finding a theory that unifies gravity with the other forces is that general relativity is a “classical” theory; that is, it does not incorporate the uncertainty principle of quantum mechanics.

Rather similar, seemingly absurd infinities occur in the other partial theories, but in all these cases the infinities can be canceled out by a process called renormalization. This involves canceling the infinities by introducing other infinities.

String theories, however, have a bigger problem: they seem to be consistent only if space-time has either ten or twenty-six dimensions, instead of the usual four!

However, I believe there may not be any single formulation of the fundamental theory any more than, as Godel showed, one could formulate arithmetic in terms of a single set of axioms.

There really is a complete unified theory (or a collection of overlapping formulations), which we will someday discover if we are smart enough.