12 Issues for the Future
243
report on it. The model provides an answer to the question: what happens
before the Big Bang? But leads to another question, what happens before t =
0, and the commencement of “eternal inflation”?
12.4 Interfaces between Theories
It is at the interface between theories where some of the most challenging
areas of physics lie. We have seen, for instance, how, as the number of
molecules interacting with each other in a gas increases, physicists were
forced to resort to a statistical approach to the problem. It is not that they
believed that the laws of mechanics did not hold, but only that they could
not be solved for a system containing so many molecules. This led to the
development of thermodynamics, which in itself has been applied to areas
way outside of physics, such as the description of crowd behaviour at rock
concerts.
The success of Quantum Mechanics and Relativity in the 20th Century,
coupled with the continuing dominance of Newtonian Mechanics for the
solution of the physics problems of everyday life (building bridges, cars,
rocket ships, etc.) has led us to several important new interfaces. These are
discussed below.
Newton meets Einstein
The interface between classical mechanics and relativity presents comparatively few problems. The Theory of Special Relativity could be applied in
Newton’s domain, where the velocities of objects are small compared with
the velocity of light, as it is accurate there. However, it is too difficult to use
in most cases, so we prefer to stick with Newton’s formulation. This example
is the ideal case of a smooth transition between two different theories operating in overlapping regions, where the classical theory can be regarded as a
high-accuracy approximation of the other.
Similarly, the field equations of Einstein’s theory of General Relativity
reduce to Newton’s theory of gravity when the space-time curvature is relatively small (i.e. the gravitational fields are “weak”) and the speed of the
objects is much less than that of light. Except for the fact that Einstein’s field
equations are horrendously difficult to solve, we would therefore be able to
discard Newton’s theory completely. Certainly some of the concepts in the
theories of relativity (e.g. mass-energy equivalence, and the dependence of
simultaneity, time dilation and the contraction of length on the motion of
243
report on it. The model provides an answer to the question: what happens
before the Big Bang? But leads to another question, what happens before t =
0, and the commencement of “eternal inflation”?
12.4 Interfaces between Theories
It is at the interface between theories where some of the most challenging
areas of physics lie. We have seen, for instance, how, as the number of
molecules interacting with each other in a gas increases, physicists were
forced to resort to a statistical approach to the problem. It is not that they
believed that the laws of mechanics did not hold, but only that they could
not be solved for a system containing so many molecules. This led to the
development of thermodynamics, which in itself has been applied to areas
way outside of physics, such as the description of crowd behaviour at rock
concerts.
The success of Quantum Mechanics and Relativity in the 20th Century,
coupled with the continuing dominance of Newtonian Mechanics for the
solution of the physics problems of everyday life (building bridges, cars,
rocket ships, etc.) has led us to several important new interfaces. These are
discussed below.
Newton meets Einstein
The interface between classical mechanics and relativity presents comparatively few problems. The Theory of Special Relativity could be applied in
Newton’s domain, where the velocities of objects are small compared with
the velocity of light, as it is accurate there. However, it is too difficult to use
in most cases, so we prefer to stick with Newton’s formulation. This example
is the ideal case of a smooth transition between two different theories operating in overlapping regions, where the classical theory can be regarded as a
high-accuracy approximation of the other.
Similarly, the field equations of Einstein’s theory of General Relativity
reduce to Newton’s theory of gravity when the space-time curvature is relatively small (i.e. the gravitational fields are “weak”) and the speed of the
objects is much less than that of light. Except for the fact that Einstein’s field
equations are horrendously difficult to solve, we would therefore be able to
discard Newton’s theory completely. Certainly some of the concepts in the
theories of relativity (e.g. mass-energy equivalence, and the dependence of
simultaneity, time dilation and the contraction of length on the motion of