Lecture 5: Spacetime

Introduction

1 We now have most of the ingredients of a theory of peace. In this and the next lecture I want to compare the theory to the modern physical theories of relativity and quantum mechanics.

2 Recall where we got to last week:

We fight because there is not enough to go around. One approach to life is that it is only possible to get more by taking it from somebody else. This is often true, but it is not necessarily true.

Our universe in infinite and creative. What I hope to show is that is possible in principle to deploy our resources to make certain that the needs of every person are met. There will then be no need to use violence to deprive one another of the necessities of life.

Mathematics is the science of symbols. I have taken the view that everything in the universe is a symbol. Symbols have a duality. They are at once a thing and a space. Mathematically the problem of peace is the same as creating enough space for every thing to exist without having to take space from another.

Local theory

3 I think the fundamental scientific breakthrough of this century was Einstein's use of the relativity principle.

4 Let me recall what I am trying to do. I grew up in a system where the world was a chattel of god. God decides what happens, and we more or less tag along, consoling ourselves with the notion that we have free will.

5 That world, in other words, is being operated by remote control.

6 The opposite of remote is local. Relativity is a local theory. It is a theory that says that life comes from below rather than from above. In other words it says we are climbing into the unknown.

7 This fits in with my theological platform. I wish to replace a remote god with a local god. I claim that god is not other than the universe, god is the universe. It is my hope that this new starting point will eventually provide us with the theoretical foundation to live in peace.

8 The fundamental unit in relativity theory, the point, is considered autonomous. If points are to remain autonomous, and yet there is to be communication between them, there must be a system of translation.

9 We experience the translation problem ourselves. There are language barriers on the earth, and you must learn a few languages if you want to travel around freely. You cannot always force people to learn your own language.

10 Structures are generated by uniting points. In other words, structures are generated by points learning to communicate. That is, structures are generated by translation. Each successive layer of the universe, therefore, requires a new level of translation. To translate something is to be able to understand its language.

11 There is a whole industry devoted to understanding the language of the universe. It is called science. One of the major outputs of science is war machines. This is a terrible mistake, because we do not understand the generation of structure properly.

12 War is an attempt to make the other ones see things our way. It is an attempt to impose our language on them. It is a violation of local theory. If we wish to communicate with them, we should learn their language, and vice versa.

13 We must learn the lesson of local theory. That we must abandon an pretensions to remote control. We must give up trying to force people into predetermined moulds and respect their autonomy.

14 Now I believe that what I have been saying in rather passionate words can be translated into science. In scientific words, my thesis is that the route to peace lies through making everything as local as possible. These lectures are a first attempt to understand what this might mean in political terms.

15 Mathematically, what I think we are talking about is space.

Dimension

16 Local theory demands translation, and translation requires consistency or order, so we need to understand the description of order in space.

17 What is order? In the long run, I think order means counting. To count is to put the numbers one after another in a named order that everyone learns as part of their very early education.

18 The basic idea of counting is the notion of adding one. Since the order is generated by counting, the order must be generated by adding one. Once you know how to add one, the mathematical world is your oyster.

19 Now enter George Cantor. Cantor transformed the simple notion of adding one into something very much richer, the theory of transfinite numbers. Cantor's theorem can be stated very succinctly: Any symbol, even an infinite one, necessarily generates a distinct new symbol which possesses a greater degree of infinity.

20 This applies to any symbol. Therefore, like adding one, it is a process that has no end. Like counting, it produces an ordered sequence of symbols, since each transfinite symbol contains all the transfinite symbols which proceed it. Since the new symbol is also distinct from all the symbols that precede it, it must be greater than them. From this point of view the transfinite symbols are just like the natural numbers.

21 The special property of transfinite symbols is that each succeeding symbol contains all possible interpretations of the symbol preceding it. The transfinite symbols can therefore be seen as the raw material for translation. Each transfinite symbol contains all possible translations of the symbol before it and all we need to do to arrive at a translation is to select one that is consistent.

22 Solving a problem seems to be a matter of translation. We have a problem when we find two symbols that do not appear to fit together. The solution to the problem is to find a new space in which they do fit, that is a translation. Sometimes it takes a long time to find the translation. Some problems have a very long history.

23 What Cantor has done is show that in intelligence terms, adding one is exactly the same as solving whatever problem you have before you at this very moment. Cantor's theory comprehends the two extremes of existence. At one end, it is just counting. At the other end, it is life.

24 The problem we are faced with is the little matter of mutual assured destruction. East and West cannot fit together. They need to learn how to communicate, which means we need a new space, a translation. This translation I call the theology of peace.

25 In computer terms, what we need to know is the fastest algorithm for sorting out the problem of mutual assured destruction. The answer comes back from relativity. Local theory.

26 The point, in this case, is the human individual. In human terms, local theory means we must all take ourselves as inviolable and learn how to communicate with everyone else. That, I believe, is the lesson of local theory and the idea I am trying to translate into english in these lectures.

Space

27 I have spoken already about the duality of symbols. For every definite locality there is a space, so local theory leads us naturally to the study of space, something which mathematics is good at.

28 What is space? Intuitively it is that mysterious non-stuff that spaceships and satellites travel around in. It is the nothing between everything else.

29 Mathematically, space is an aggregate of dimensions. Perhaps you remember from geometry that a line is a one dimensional space, a plane is two dimensional, and so on.

30 There are two ideas in the mathematical definition of dimension. The first is independence. The dimensions of space are independent because you can move along one without moving along the others. You can go east without travelling north, and vice versa.

31 The second property of a dimension is that it is in some way infinite. A line is a one dimensional object that stretches to infinity on both directions.

32 This definition of dimension will remind you of our definition of symbol. A symbol is an independent thing which can point to an infinity of other things. From now on we will assume that symbol and dimension mean the same thing.

33 We can supplement these general ideas about space with some actual information about the space we live in. The person to listen to is Albert Einstein. I will try to give you a faithful translation of some of his thoughts.

Relativity

34 Einstein wished to fit together the behaviour of different systems that are in relative motion. An example of the problem would be two motor cars passing on a highway.

35 We assume that the laws of physics are the same everywhere. That is an expression of local theory. Yet it is a fact that when you pass another car the clocks in the other car will seem to be going slower than your clock and things with a certain fixed length, like cigarettes, will appear shorter.

36 These effects are very small at human speeds. When you get near the sped of light, however the differences that relativity must explain can become huge.

37 The apparent difference is due to the relative motion of the two cars. The problem is to find the law that explains the apparent difference. Once we know this law, we can translate the phenomena we observe in the other car into their equivalent in our car.

38 The translation between uniformly moving frames of reference is Einstein's special theory of relativity.

39 The special theory looks simple, but it is quite subtle and produces some unexpected results. One is the equivalence of mass and energy.

40 The relationship between mass and energy is expressed by the famous equation E = mc ², energy is equal to mass times the velocity of light squared. This equivalence of mass and energy helped physicists develop the theory that brought us nuclear energy and nuclear weapons.

General relativity

41 The special theory of relativity allows us to translate the laws of physics between bodies that are moving uniformly in a straight line. The general theory of relativity, as its name implies, does away with any restriction in the sort of motion involved. The general theory allows us to translate the laws of physics between any two points in the universe, no matter how they are moving.

42 The general theory explains gravitation, that symbol which keeps us standing on the earth, keeps the moon and the planets in their orbits, and explains the large scale structure of the universe. Einstein began his study of gravitation with what he called 'the happiest thought of my life':

'I was sitting in a chair in the patent office at Bern when all of a sudden the thought occurred to me: "If a person falls freely, he will not feel his own weight". I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation.'

43 I am working on a hunch, throughout these lectures that the theory of peace will turn out to look rather like the theory of gravitation.

44 The point of connection is weightlessness. I believe there is a point of view from which peace and weightlessness will appear to be the same thing. My goal is to find that point of view.

45 Let me try to give you some feeling for the connection I seek.

46 We all experience life. My knowledge of other people suggests that we share many experiences. This common pool of experience is what we call human nature. Art and literature and music provide me with some insight into the experience and nature of people in places, cultures and times I have not seen.

47 If this theory is to have any bearing at all on the question of human peace, it must fit the whole range of human experience. For me, it must fit my experience. If it is to gain wide acceptance it must fit your experience as well.

48 Renee Descartes was a seventeenth century philosopher and mathematician who was pursuing certain knowledge. After much reflection he came to one irrefutable fact, which he expressed with the most famous phrase in all philosophy: Cogito ergo sum. I think therefore I am.

49 I know I exist. I take this to be the basic experience of life. I am often aware that there is a definite and separate object, corresponding to the symbol jeff nicholls, which is me.

50 I have special access and special presence to myself. But this presence is not continuous. I am often asleep or so engrossed in something that I am not aware of myself. When I am aware of myself, I also seem to be aware of time. When I am not aware of myself, time does not exist for me, or, as we say, time flies.

51 My evidence for this is the pile of toast that has been burnt and the number of times the washing machine has overflowed while I have been trying to write these lectures.

52 My working definition of peace so far is peace is not just the absence of war, but the whole structure of what exists. This definition is helpful, but it does not describe the personal experience of peace.

53 What is the personal experience of peace? I suggest that there is no such thing. In the limit there is no experience of peace and, vice versa, peace is the absence of experience.

54 I suggest that peace is the state of being completely involved in something. Although you may be able to recall what happened in intimate detail, you will know that you were not experiencing yourself and you were not conscious of the passage of time while you were involved.

55 We now have two definitions of peace. From one point of view, it is the whole structure of what exists. From another point of view, it is the absence of experience of self.

56 This is akin to the state of weightlessness in free fall. To be at peace is to be freely falling through reality, or as some would say, going with the flow. What we have to do is get this idea from poetry to practical politics.

57 What Einstein found, after years of struggle, was that the phenomenon we call gravitation is nothing other than a manifestation of the structure of spacetime itself. In other words, gravitation is not a structure in spacetime, it is the structure of spacetime.

58 There is evidence to suggest that the theory of gravitation describes the only possible structure of physical space.

59 The shape of spacetime is determined by the energy of objects in the space. As these objects move, so the shape of spacetime changes. The shape of spacetime, in turn, determines the course taken by objects falling freely through it.

60 Einstein's theory of gravitation is all local. It says that any object moving through space can determine its path from local information alone.

61 The general theory allows us to translate between any two points in the universe, no matter what their relative motion. This translation process generates a new space. Special relativity can operate in two dimensions, one of space and one of time. General relativity operates in four dimensions, one of time and three of space.

62 The situation is analogous to the process of translating from one language into another. Imagine you are truly bilingual in English and Chinese. You can translate any sentence that you can understand in English into an equivalent sentence in Chinese, and vice versa. The English and Chinese sentences are different representations of the same meaning.

63 Because you are bilingual, you can take any element of the aggregate of English sentences and pair it up with the set of possible partners in the aggregate of Chinese sentences. Somewhere in you mind, therefore, is an aggregate which comprises all the pairings of English and Chinese sentences.

64 We may consider the aggregates of English and Chinese sentences an infinite dimensional spaces. The aggregate of pairings of English and Chinese sentences is a new space of transfinite dimension.

65 The aggregate of pairings of points in two dimensional spacetime is four dimensional spacetime. This, I think, is how four dimensional spacetime is created from two dimensional spacetime.

66 Where does two dimensional spacetime come from? I suggest that it is the aggregate of all pairings of all times. To see how this can be let us return to the theory of transfinite numbers.

67 We begin with the natural numbers one, two, three, ... . Let us identify them with time. This is not too hard to accept.

68 Clocks tick. A clock is simply a ticker attached to a device to count the ticks. Each tick adds one to the count.

69 Further we have in physics a quantity called the quantum of action, which suggests that the world processes itself in discrete steps or ticks. Since we believe all phenomena are quantised, it would be natural to find the source of quantisation in the most primitive of all phenomena, time.

70 We also note that time provides us with a very basic means of ordering things. How do we place the runners in a race? In order of time of arrival. How do we order the days of our lives, which may appear to be very nearly identical? We number them with a complicated system called the calendar. This reminds us that we have said that counting is the basic generation of order.

71 The cardinal number of the aggregate of all natural numbers is the first transfinite number, known as aleph zero. The next transfinite number that arises out of aleph 0 is aleph 1. Aleph is the first letter of the Hebrew alphabet.

72 Aleph 1 is famous in mathematics because it is believed to be the cardinal number of the continuum, that is of space. So if we identify the natural numbers with time, Cantor's theorem tells us that space arises out of time as a matter of symbolic consistency.

73 Since each cardinal number contains its predecessors, space contains time, giving us spacetime.

74 Where does time come from? We have noted that the transfinite numbers form an ordered sequence like the natural numbers. They can therefore be paired with the natural numbers and identified with time. The transfinite numbers arise out of one another because the universe is consistent. Cantor proved this. Time, therefore, is a product of the requirement of consistency, which we hold to be the foundation of the universe.

Conclusion

75 This will do for the moment. In this lecture we have taken a brief look at the classical theory of spacetime, developed from the work of thousands of years by Albert Einstein. We have made a tentative link between the theory and our hypothesis, that the only law of nature is that the universe is consistent.

76 We have followed the development of space from one to four dimensions. There is no mathematical limit on the number of dimensions a space may have. The physics of infinite dimensional spaces is quantum mechanics, which is where we go to next.

77 We have found, in Einstein's four dimensional spacetime, a clue to the definition of peace. What we need to do now is to express this clue in a language that will carry us through to infinite dimensional spaces, which we assume include not only us, but nations, planets and galaxies as well.

78 Now these lectures do sound very serious and solemn. That is because I can't think of any other way to put these ideas across in the way that I want to. I am serious with all the seriousness of a person who does not want to be blown up.

79 On the other hand there is Goedel's theorem, that says to me that every seriousness us surrounded by an infinity of uncertainty. These lectures, therefore, must be seen also as a fantasy in search of a proof.

Originally broadcast on 2BOB Radio, Taree, NSW on 18 June 1987

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