Intro. Ch. 1 Ch. 2 Ch. 3 Ch. 4 Ch. 5 Ch. 6 Ch. 7 Ch. 8 Ch. 9 Ch.10 Ch.11 Ch.12 App.1 App.2 App.3 Biblio. Index |
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## Chapter 2: Time2.01 We hope to show in this chapter that the natural impressions we all possess of the true nature of Time are illusory and confusing. It is one thing to expose these false impressions by careful argument, and several books have been published in recent years suggesting that many thinkers, both physicists and philosophers, are now facing up to the problems posed by such prejudices. But it is much more difficult to purge them from our thinking, for they can creep back insidiously and upset our reasoning in subtle ways.
2.03 We are unable to visualise four dimensions, but for purposes of illustration we can often dispense with one of the space dimensions, and the z co-ordinate can be omitted. We may then represent events on a perspective drawing with the x and y axes in the horizontal plane and the t axis drawn vertically upwards. The life-history of a small body or a particle of matter is represented by a line which we call its "world-line", showing its continued existence throughout a period of time, and its movement is represented by the slope of this line, the angle it makes with the t-axis.The state of the world at the particular time we call “now” or the “present” is represented by everything on a horizontal plane drawn for a particular value of t. And we can imagine the progress of time being represented by this plane moving slowly upwards at constant speed. The strange fact that our mathematical descriptions of the world contain nothing corresponding either to the “now” plane, or to its upward movement, need not imply that our impressions are wrong; perhaps the mathematical descriptions are just incomplete.
2.05 Indeed it did not require Einstein to show that the notion of a “flowing” time is a nonsense. If the time is continually flowing or changing, as our natural intuition suggests, with respect to what does it change? One thing can change only with respect to another. Usually when we talk about change we mean change with respect to time itself. The rate at which a vehicle changes its position is its speed, measured perhaps in miles per hour. The rate at which an investment earns interest is measured as a percentage per annum. Mathematicians represent the rate of change of any quantity x by the symbol dx/dt. But time cannot be said to change with respect to itself; dt/dt is meaningless.
The world lines of particles of matter and radiation then become lines radiating from the pole, always extending in a generally outward direction, but deviating slightly from the lines of longitude to show their intrinsic motion, and meeting each other where our picture needs to represent their collisions. The homogeneity of the early universe, which was so finely tuned to give us the sort of world we now find, is represented on our picture by “boundary conditions” which these world lines must satisfy close to our “North Pole”. A familiar and useful analogy is provided by the electric field around a small charged body; the distribution of charge on its surface provides the boundary conditions which determine the electric field close to the surface, and this in turn determines uniquely the direction and strength of field throughout the whole space influenced by the charged body. In the same way, the whole future of the universe is constrained by the boundary conditions at the big bang. That future is not uniquely determined because of various types of uncertainty which we shall discuss later, but the general macroscopic picture is dominated by the very low entropy represented by the homogeneity of the world-line distribution near the pole, and the Second Law is our description of the increasing entropy at greater distances (i.e. later times), and particularly by the clumping together of world-lines under the influence of gravity.
2.22 The tendency to imagine things moving on a space-time diagram is more persuasive than may be imagined, and has led some capable thinkers into error. One sometimes reads about the possibility of things moving “backwards in time”, and an author may illustrate the idea with a space-time diagram like that shown here. We are asked to believe that the line from A to B represents a particle moving forwards in time between two points, whereas if the movement on the diagram were from B to A, it would represent a particle moving in reversed time.But what is the difference between the behaviour of these two particles? The first is at x_{1} at time t_{1} and at x_{2} at time t_{2}; the second is at x_{2} at time t_{2} and at x_{1} at time t_{1}. So they are both at A at the same moment and both are at B at the same moment. They travel together from the point A to the point B, and may indeed be the same particle. This is clearly not how the authors expect us to think about it, for they had tried to distinguish a particle "moving" from A to B from one "moving" from B to A. We must always remember that the space-time diagram is static; it will serve its purpose of banishing our temporal illusions only if we firmly disallow any view of it which involves movement.
2.24 A similar space-time diagram can be used to illustrate the distance- and time-transformations of Special Relativity, and this can drive home the point that the future and the past cannot differ in certainty in the way our intuition suggests. Suppose that I am standing on the platform at York while you pass on the London to Edinburgh express, and suppose that a large meteorite crashes onto a typical star 800 light years away. The diagram shows how our two “now” planes would be related, and shows it to be quite possible that the event occurred half an hour ago relative to your “now”, but will not occur for another half hour for me. Does the event lie in the immutable past or in the uncertain future? It is clear that no such distinction can exist.
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