Table of Contents
In this chapter we consider the beginning of time, the point in the big bang known as the Planck epoch. During this time the universe was sufficiently dense and energetic that all the fundamental forces, including gravity, were merged into one grand force. Quantum mechanics is generally associated only with the world of the very small, but during the Planck epoch the entire observable universe was tiny. Under such conditions, quantum mechanics and gravity must merge into quantum gravity. Unfortunately, at this time physicists do not have a theory of quantum gravity. So we speculate on what such a theory might be like, and what it might tell us.
The basis for quantum mechanics is the recognition that everything has a wavelike nature, even those things we normally consider particles. By the same token, those things that we usually consider waves (e.g., light) also have a particle nature. The evolution of quantum systems is governed by the Schroedinger equation. However, the Schroedinger equation gives only the evolution of the probabilities associated with a system. Interpreting what this means is somewhat difficult, given our usual expectations regarding the nature of reality. According to the Copenhagen interpretation of quantum mechanics, a system exists in a superposition of states so long as it remains unobserved. An "observation," which it must be understood refers to any interaction that requires a variable to take a value and need not imply a conscious agent, collapses the wavefunction. The collapse of the wave function means that the system abruptly ceases to obey Schroedinger's equation; what was previously probabilities becomes a known quantity. The story of ``Schroedinger's cat'' illustrates. A cat is locked in a box containing a vial of poison, which will be broken by a quantum process such as the decay of a radioactive atom. This event has some probability, which may be calculated, of occurring during any particular time interval. While the cat is in the box, unobserved, we cannot know whether the event has taken place or not and thus whether the cat is alive or dead. A strict application of the Copenhagen interpretation demands that the cat be neither alive nor dead, or perhaps both alive and dead, in some superposition of states according to the probability that the atom has decayed; in this view, the cat becomes alive or dead only when the experimenter opens the box to investigate. Schroedinger's cat illustrates difficulties with "standard" quantum mechanics as applied to complex systems such as living beings. Schroedinger himself meant this thought experiment to show that quantum mechanics, a young science at the time, did not apply to such systems. Yet when we seek to apply quantum mechanics to cosmology, we know that it must apply to the universe as a whole, and thus there is no such thing as "classical" behavior; everything is ultimately quantum.
When we ponder the Planck era, we are led to questions about the nature of space and time themselves. What is it that provides the ``arrow of time,'' the perception that we move into the uncertain future and leave behind the unchangeable past. The laws of physics are time symmetric, meaning that they work the same whether time runs forward or backward. (A substitution of -t for t everywhere gives the same equations). The one exception is the second law of thermodynamics which states that entropy must increase with time. This means that a complicated system will tend to evolve toward its most probable state, which is a state of equilibrium (and maximum disorder). If the sense of the arrow of time comes from the second law this means that the big bang had to start in a state of low entropy (high order), and the arrow of time results from the universal evolution from this initial state to the final disordered state, be it big crunch or the heat death of the ever expanding universe. We are led to ask whether the theory of quantum gravity explains why the initial big bang was in a low entropy state. Is quantum gravity a theory that is not time symmetric? Does the second law of thermodynamics, an empirical relationship first discovered by engineers in the nineteenth century, tell us something about the most profound secrets of the universe?
Although we have no established theory of quantum gravity, some promising starts have been made. One of the most studied is string theory, in which reality at the Planck scale of distance and time is described by the quantum oscillations of strings and loops. String theories require that many more spatial dimensions exist than our familiar three. At least ten spatial dimensions exist in these theories, but only three are of cosmic scale; the rest are compactified into "coils" the size of the Planck distance. Thus the very early universe may have undergone a "proto-inflation" in which three spatial dimensions grew into those that make up the observable universe. String theories are not yet well understood and many details remain to be worked out, but so far they can at least unify gravitation and the other fundamental forces in a natural way. They are not the only candidates, however; another theory envisions that the exotic level of the Planck scale consists of a foam of quantized space and time. Perhaps someday we shall have a better understanding of the mysteries of the Planck scales. Such a discovery would be at least as momentous as general relativity itself.
|Points to Ponder|
|Potential Pitfalls||You should appreciate that some of the material in this chapter is more speculative than what has previously been presented. However, quantum mechanics per se is not speculative. It is very well supported by experimental evidence. It is the interpretation of quantum mechanics that is subject to some debate.|
|Questions & Answers||
Questions and Answers related to Chapter 16.
Here is an internet page on Measurement in Quantum Mechanics
For addtional information on advanced physics theory try this page on Superstring Theory.