SPACE AND TIME

E a r t h / m a t r i X
SCIENCE TODAY SERIES

Introduction

chapter one

chapter two

chapter three

chapter four

chapter five

Hawking’s A Brief History of Time, A Commentary

Charles William Johnson

CHAPTER TWO

CHAPTER TWO: SPACE AND TIME

As we stated earlier, we are going to discuss Hawking`s treatment of concepts of space and time, and the word-concepts around these two concepts. It is necessary to talk about word-concepts which we are unable to define at this moment in history: space and time. We shall also be speaking about them without actually knowing what exactly they are or represent. Such is the frustration and the state of our current knowledge about reality. We speak about events which we are ignorant about.

From a theoretical conception viewpoint, we can understand that reality consists of spacetime/movement, and that by accounting for these aspects of reality in our analysis, we can actually relate to reality itself and know whether we have identified the spacetime/movement coordinates of a particular event. Yet, again, we do not know what spacetime actually is.

Upon examining Hawking`s comments about space and time, we shall be able to distinguish the pitfalls of a theoretical conception that does not account for spacetime as it exists, but as it is perceived, and as it is expressed in limited language. This may be best exemplified by the first proposition of Hawking in this chapter which is of significance for our analysis.

PROPOSITION: "The lack of an absolute standard of rest meant that one could not determine whether two events that took place at different times occurred in the same position in space.

From this statement Hawking goes on to argue the case that absolute position (space) does not exist He offers the example of a ping pong ball struck in a traveling train, which hits the ceiling of the train car on the same spot, but actually is not the same spot because the train is traveling down the tracks. Anyone outside of the train car would see that the ping pong ball struck the roof of the car many feet apart, even though it might appear to be the same spot on the car's ceiling.

From such an example, it is argued that the same spot, place is relative; meaning relational to its conditions of spacetime/movement. Hawking is on the verge of understanding this from the perspective of spacetime: that each spacetime/movement event is unique; occurs only once. That the relationship of the ping pong ball striking the train car's roof is each time a specific event. In other words, the concept of the same does not in fact exist ---ever--- in terms of spacetime/movement: each spacetime event is exclusive of all the rest. Every spacetime event exists only once, and thus can only be related to other spacetime/movement events.

In terms of spacetime/movement there is no such thing as "absolute" position in space, in as much as spacetime is movement (constant). The word-concepts of the "same" and "absolute" exist only in relation to specific matter-energy events.

Something similar occurred with respect to the concept of time, whereby Albert Einstein proposed the abandonment of the concept of an "absolute" time as well. "The fundamental postulate of the theory of relativity, as it was called, was that the laws of science should be the same for all freely moving observers, no matter what their speed. ...all observers should measure the same speed of light, no matter how fast they are moving. This simple idea has some remarkable consequences. Perhaps the best known are the equivalence of mass and energy, summed up in Einstein`s famous equation E = mc2 (where E is energy, m is mass and c is the speed of light), and the law that nothing may travel faster than the speed of light. Because of the equivalence of energy and mass, the energy which an object has due to its motion will add to its mass. In other words, it will make it harder to increase its speed. As an object approaches the speed of light, its mass rises ever more quickly, so it takes more and more energy to speed it up further. It can in fact never reach the speed of light, because by then its mass would have become infinite, and by the equivalence of mass and energy, it would have taken an infinite amount of energy to get it there. For this reason, any normal object is forever confined by relativity to move at speeds slower than the speed of light. Only light, or other waves that have no intrinsic mass, can move at the speed of light." (pp.20-21)

The basis of these ideas refers mainly to the "observer". In another essay we have discussed Einstein`s formula E = mc2 in greater detail. Suffice it to say here that these suppositions refer mainly with the observer and the task of "measuring" spacetime/movement events. The idea that "the energy which an object has due to its motion will add to its mass" is probably one of the greatest fallacies existing today within physics; at least, the way in which it is explained. Mass (that is, matter-energy) cannot be created out of nowhere, as we know it, and simply by the fact that some event "travels" at a certain speed does not mean that its mass is incremented, especially when we are unable to even measure mass in movement.

Furthermore, "in other words, the theory of relativity put an end to the idea of absolute time! It appeared that each observer must have his own measure of time, as recorded by a clock carried with him, and that identical clocks carried by different observers would not necessarily agree." (p.21) These premises upon which Hawking is basing his own study of time are generally accepted throughout the study of physics. However, we should point out that in spite of an attempt made by Einstein to make space and time relational, and also non-absolute, we must draw attention to the fact that he was always speaking basically about the problem of measuring space and time.

It is not that each observer has his own measure of time, which is totally irrelevant to the spacetime/movement event that we are examining, but rather that spacetime/movement events mean a distinction in spacetime itself..

We are quite capable of comprehending different spaces. This is a rather easy mental visualization that we can easily carry out regarding any event (object). To consider space A as distinct from space B requires very little mental abstraction. However, to consider that time A and time B are distinct, relational events is not easily obtained mentally. We are, in spite of all the writing about time being itself relational to space, quite strapped by the idea of an absolute time.

This conceptualization is strengthened by the fact that even Einstein, after drawing the relationship between space and time, continued to speak of 3 dimensions of space and 1 dimension of time. This is now called the 3-1 split.

However, it is understandable, in terms of spacetime/movement (and not in terms of word-concepts) that if space and time are relational, there must be an equal, relational number of dimensions in both facets of reality. This is mere positivistic logic. We are not in fact even considering what spacetime means in terms of itself here, but merely arguing on the basis of the idea of relational aspects of reality.

Such a consideration would show us that by considering that the space occupied by this table is distinct from the space occupied by this chair, also means that the time occupied by this table is distinct from the time occupied by this chair. In other words, in as much as each space-event is distinct (exclusive) from all other space-events, so it is that all time-events are distinct from all other time-events. No two spacetime events can occupy the same spacetime coordinates.

There is a different time in this table as from that chair, as well as a different space in both.

Conceptually and mentally it is extremely difficult for us to conceive time as being distinct and relational to itself. We have difficulty in understanding or apprehending that time can be related to time; although it is easier for us to understand that space can be related to space.

However, this is precisely the theoretical conception that is lacking in our everyday understanding and comprehension of spacetime/movement. All space is exclusive (relational to) all other space. All time is exclusive (relational to) all other time. All movement is exclusive (relational to) all other movement.

What is spacetime/movement: I do not know.

Yet, I can talk about it and think conceptually in relation to it, and relate to it as I am part of it.

PROPOSITION: "(An event, in this sense, is something that takes place at a single point in space, at a specified point in time.)" (p.22)

The word-concept "point" is a mental abstraction that we make regarding a specific spacetime/movement event; it does not exist as such. No matter how small a point we draw, it is always divisible in terms of spacetime; in other words it is arbitrary. In fact, in drawing three supposed lines through the "same" point in order to identify a point-event, in fact, we are creating an arbitrary idea. A dimension of spacetime/movement cannot be reduced to the idea of three lines intersecting the same point. Such a physical visualization of spacetime/movement is probably the most simplistic one available, after the idea of a single point-event!

PROPOSITION: "The theory of relativity does, however, force us to change fundamentally our ideas of space and time. We must accept that time is not completely separate from and independent of space, but is combined with it to form an object called space-time". (p.23)

In this accepted postulate by Hawking, we can see the difficulty in speaking about spacetime. As it was once commented by none other than V.I. Lenin, that in the effort to unite reality one must first separate it; the same occurs here. As we make an attempt to unify reality, to join together space and time, at least in our explanations, we are basically maintaining them as separate entities. It becomes difficult to conceptualize spacetime as spacetime; period.

Spacetime is spacetime. It is not a question that space combines with time to form spacetime. This mechanical explanation does not help the visual conceptualization, but merely represents a roundabout manner of identifying what spacetime is.

PROPOSITION: "An event is something that happens at a particular point in space and at a particular time." (p.23)

Here we have a little more of the kind of explanation. He is referring to the 3-1 split, whereby "one can specify it by four numbers or coordinates. Again, the choice of coordinates is arbitrary; one can use any three well-defined spatial coordinates and any measure of time. In relativity, there is no real distinction between the space and time coordinates, just as there is no real difference between any two space coordinates". (pp.23-24)

"It is often helpful to think of the four coordinates of an event as specifying its position in a four-dimensional space called space-time. It is impossible to imagine a four-dimensional space. I personally find it hard enough to visualize three-dimensional space!" (p.24)

In fact, we visualize it everyday in everything we do. We live in spacetime; we visualize it through all of our distinct senses.

The problem arises in that spacetime is not four-dimensional as such. In fact, we would have to question the very word-concept of "dimensions" in order to discuss this aspect of spacetime more efficiently.

PROPOSITION: "Similarly, we do not know what is happening at the moment farther away in the universe: the light that we see from distant galaxies left them millions of years ago, and in the case of the most distant object that we have seen, the light left some eight thousand million years ago. Thus, when we look at the universe, we are seeing it as it was in the past." (p.28)

Every possible spacetime/movement event that we see (in present tense) is past time.

---------------------TIMELINE------------------

Event (ended) ------------------light/observer

On-going event---light/observer

Present is always past.

Present is always future practice; practice is future.

PROPOSITION: "Einstein made the revolutionary suggestion that gravity is not a force like other forces, but is a consequence of the fact that space-time is not flat, as had been previously assumed: it is curved, or "warped", by the distribution of mass and energy in it". (p.29)

Again, the language reveals theoretical conception. It is not a question of mass-energy being distributed in space-time, but rather that mass-energy (as we have stated) are specific forms of space-time.

If we write stating that mass-energy are separate from space-time, and that they fit within space-time, as something other than space-time themselves, then we return to the absolute conceptualization of space and time (but merely now unified in one word-concept), maintaining mass and energy separate from spacetime itself.

The visualization that is required, and thus the writing of this visualization becomes possible, would propose that space-time/movement is related in the following manner to other concepts:

SPACE-TIME/MOVEMENT

MATTER-ENERGY

MASS-ENERGY

All of these distinct levels are relational; in fact represent the terms of reality on different levels of conceptualization. They are not separate entities: mass is a form of matter (energy); matter is a form of energy; energy is a form of matter; and, matter-energy or energy-matter are forms of spacetime/movement.

Hence, more specifically stated and theoretically conceived: the existence of spacetime/movement produces the specific forms of matter-energy, and within the regions of matter-energy spacetime/movement appear to be "warped".

Again, however, warped does not exist. What exists is that the effects of the relations of matter-energy (spacetime/movement) do not follow ideal straight lines as conceived under certain conditions of spacetime/movement within a relation of gravity, but seem or appear to be warped lines of events.

PROPOSITION: "Bodies like the earth are not made to move on curved orbits by a straight path in a curved space, which is called a geodesic....In general relativity, bodies always follow straight lines in four-dimensional space-time, but they nevertheless appear to us to move along curved paths in our three-dimensional space."(p.30)

All of these propositions regarding curved space-time, in fact, reflect a theoretical conception that maintains as separate entities that which is called space, time, matter or mass, and energy. The so-called celestial bodies (sun, earth) are conceived as beings that "actually curve" space-time itself. Nothing can curve space-time like that; this would mean that matter-energy had properties far beyond the very properties of existence!

Spacetime/movement means the existence of matter-energy events (such as celestial bodies), and the relation of spacetime in these terms means the existence of certain phenomena known as gravity, and the curving of light, etc.

It is totally distinct to conceive a) spacetime/movement determining the existence of planets and gravity as a relationship of spacetime itself; and totally another thing to b) conceive of matter-energy planetary events to be situated within space-time and thereby warping space-time itself.

The warping of space-time by matter-energy (or by mass-energy) does not exist as stated. What exists is that spacetime/movement means the existence of matter-energy and the effects thereof.

The relationship of matter-energy (spacetime/movement) in specific manifestations such as planets/celestial bodies produces certain effects such as gravity. These effects do not affect spacetime/movement as such.

PROPOSITION: "Light rays too must follow geodesics in space-time. Again, the fact that space is curved means that light no longer appears to travel in straight lines in space. So general relativity predicts that light should be bent by gravitational fields". (p.31)

The event of light travels in relation to the matter-energy events . The concept of "straight" lines in space is a theoretical invention of man. For the light follows the relationship of the spacetime/movement events to which it is related at its moment of existence.

It is not a question that the "light appears to bend", but it actually does follow the path around the path of influence of the matter-energy event near its path. (See Figure 2.9 of Hawking)

PROPOSITION: "Another prediction of general relativity is that time should appear to run slower near a massive body like the earth. This is because there is a relation between the energy of light and its frequency (that is, the number of waves of light per second): the greater the energy, the higher the frequency. As light travels upward in the earth`s gravitational field, it loses energy, and so its frequency goes down. (This means that the length of time between one wave crest and the next goes up.) " (p.32)

This proposition now confirmed in the use of clocks at different altitudes above the earth surface does not have to do with appearances. Rather, we can understand from what we stated earlier, that time is distinct at every time-event point.

It is not a question that time is distinct only at certain levels of altitude, but that time is distinct in all spacetime/movement events. The time in my left little finger is distinct from the time in my right little finger. However, this is immeasurable to us, and we can only conceive of it theoretically. And, even then it is difficult to make such a theoretical conception or visualization.

Again, it is not a question of appearances, but of actual time differentiation. All time events are exclusive of all the other time events.

Because of the relationships of spacetime/movement involved, it is possible to consider that my right little finger can age more quickly/slowly than my left little finger, depending upon the spacetime relations concerned.

Time, then, as a measure of specific events, is determined by space/movement, or spacetime/movement itself. Hence, time, like space, is everywhere distinct and exclusive of all other time (space).

PROPOSITION: "Newton`s laws of motion put an end to the idea of absolute position in space. The theory of relativity gets rid of absolute time. ... In the theory of relativity there is no unique absolute time, but instead each individual has his own personal measure of time that depends on where he is and how he is moving." (p.33)

What we know as time and its specific manifestations depends upon spacetime/movement: distinct space, distinct time, distinct movement mean distinct time manifestations; no doubt.

In other words, space (or matter-energy) is not placed within time as such. Things do not exist within time. Things that exist, events are spacetime themselves. Each individual is spacetime/movement; not that he/she has his/her own personal measure of time.

In the general theory of relativity, "space and time are now dynamic quantities: when a body moves, or a force acts, it affects the curvature of space and time ---and in turn the structure of space-time affects the way in which bodies move and forces act. Space and time not only affect but also are affected by everything that happens in the universe." (p.33)

In other words, spacetime/movement produce the bodies, the so-called forces, and are therefore affected by their own existence.

PROPOSITION: "Roger Penrose and I showed that Einstein`s general theory of relativity implied that the universe must have a beginning and, possibly, an end."(p.34).

This is another way of saying that present must have past and future. That is, specifically, the universe (present time) must have a beginning (past time) and an end (future time).

Upon making the interpretation of the word-concepts handled by Hawking into the facets of spacetime/movement, we see that what Einstein implied is not necessarily anything complex or absurd. Hawking will attempt to show that there is no beginning nor end, which mean specific idealized events of past and future.

Introduction chapter one chapter two chapter three chapter four chapter five

Earth/matrix
Science Today

Science in Ancient Artwork Series and Science Today ISSN-1526-3312
©1995 - 2009 Copyrighted by Charles William Johnson. All rights reserved. Reproduction prohibited.
The text and all images of this website are copyright protected.