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Reference: The Book of Physics

Note: The original text is provided below.
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Summary

Since the speed of matter is negligible compared to the speed of light, the “seen-now” lines will get agreement from anywhere in the universe. The “seen-now” lines will actually make a cone when all spatial dimensions are taken into account. Eddington limits it to Here-Now but that is not necessary.

Eddington also extends the “seen-now” lines into future, and postulates a “neutral wedge”. But none of this is necessary because anything above the “seen-now” lines is based on calculations, whether it is about instantaneous now or actual future. 

Eddington states, “As the speed of matter approaches the speed of light its mass increases to infinity, and therefore it is impossible to make matter travel faster than light.” This statements erroneously considers the external force required to increase the velocity of a particle as its “additional mass.”

In fact, a matter particle, as an isolated system, will decrease in its mass and inertia to increase in velocity. If external force is involved, then more force will be required to push a particle that offers less inertia. For example, a photon has no mass or inertia; therefore, it becomes impossible to accelerate it even with an infinite amount of push. Matter is very limited in its velocity before it looses its identity as matter and converts into a quanta of energy.

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Comments

As the sense of intuition is better understood, the limitations due to the finite speed of light may be lifted.

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Original Text

Let us now try to attain this absolute view. We rub out all the Now lines. We rub out Yourself and Myself, since we are no longer essential to the world. But the Seen-Now lines are left. They are absolute, since all observers from Here-Now agree about them. The flat picture is a section; you must imagine it rotated (twice rotated in fact, since there are two more dimensions outside the picture). The Seen-Now locus is thus really a cone; or by taking account of the prolongation of the lines into the future a double cone or hour-glass figure (Fig. 4). These hour-glasses (drawn through each point of the world considered in turn as a Here-Now) embody what we know of the absolute structure of the world so far as space and time are concerned. They show how the “grain” of the world runs.

Father Time has been pictured as an old man with a scythe and an hour-glass. We no longer permit him to mow instants through the world with his scythe; but we leave him his hour-glass.

Since the hour-glass is absolute its two cones provide respectively an Absolute Future and an Absolute Past for the event Here-Now. They are separated by a wedge-shaped neutral zone which (absolutely) is neither past nor future. The common impression that relativity turns past and future altogether topsy-turvy is quite false. But, unlike the relative past and future, the absolute past and future are not separated by an infinitely narrow present. It suggests itself that the neutral wedge might be called the Absolute Present; but I do not think that is a good nomenclature. It is much better described as Absolute Elsewhere. We have abolished the Now lines, and in the absolute world the present (Now) is restricted to Here-Now.

Perhaps I may illustrate the peculiar conditions arising from the wedge-shaped neutral zone by a rather hypothetical example. Suppose that you are in love with a lady on Neptune and that she returns the sentiment. It will be some consolation for the melancholy separation if you can say to yourself at some—possibly prearranged —moment, “She is thinking of me now”. Unfortunately a difficulty has arisen because we have had to abolish Now. There is no absolute Now, but only the various relative Nows differing according to the reckoning of different observers and covering the whole neutral wedge which at the distance of Neptune is about eight hours thick. She will have to think of you continuously for eight hours on end in order to circumvent the ambiguity of “Now”.

At the greatest possible separation on the earth the thickness of the neutral wedge is no more than a tenth of a second; so that terrestrial synchronism is not seriously interfered with. This suggests a qualification of our previous conclusion that the absolute present is confined to HereNow. It is true as regards instantaneous events (point-events). But in practice the events we notice are of more than infinitesimal duration. If the duration is sufficient to cover the width of the neutral zone, then the event taken as a whole may fairly be considered to be Now absolutely. From this point of view the “nowness” of an event is like a shadow cast by it into space, and the longer the event the farther will the umbra of the shadow extend.

As the speed of matter approaches the speed of light its mass increases to infinity, and therefore it is impossible to make matter travel faster than light. This conclusion is deduced from the classical laws of physics, and the increase of mass has been verified by experiment up to very high velocities. In the absolute world this means that a particle of matter can only proceed from Here-Now into the absolute future—which, you will agree, is a reasonable and proper restriction. It cannot travel into the neutral zone; the limiting cone is the track of light or of anything moving with the speed of light. We ourselves are attached to material bodies, and therefore we can only go on into the absolute future.

Events in the absolute future are not absolutely Elsewhere. It would be possible for an observer to travel from Here-Now to the event in question in time to experience it, since the required velocity is less than that of light; relative to the frame of such an observer the event would be Here. No observer can reach an event in the neutral zone, since the required speed is too great. The event is not Here for any observer (from Here-Now); therefore, it is absolutely Elsewhere.

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Reference: The Book of Physics

Note: The original text is provided below.
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Summary

Eddington starts this section by pointing out how time is perceived for everyday use is so very different from the time we sense subjectively. The fact is that the time for everyday use is based on the behavior of matter; but the time that we sense subjectively is based on the behavior of our thoughts. We may say that changes in matter provide the perception of “matter-time” for everyday use; and changes in thought provide the perception of “thought-time” that we have consciousness of.

The matter-time has been woven into the structure of the classical physical scheme. But it is not the same as the thought-time that we are conscious of. The difference becomes obvious when we are waiting in the doctor’s office; the time appears to pass very slowly.

Eddington talks about how Einstein’s theory links the nature of time to the nature of space. This means matter-time has the same relationship with matter-space, as thought-time has with thought-space. Eddington identifies thought-time as “interval,” but it is actually “thought-interval” and not “matter-interval.” When we represent the enduring world as a three-dimensional space leaping from instant to instant through time, we are relating matter-space to matter-interval, and not to thought-interval.

Eddington then considers the situation, “If two people meet twice they must have lived the same time between the two meetings, even if one of them has travelled to a distant part of the universe and back in the interim.” In this case, the thought-interval will be very different for the two people, but their matter-interval will be the same.

Eddington then states, “If the speed of travel is very great we may find that, whilst the stay-at-home individual has aged 70 years, the traveler has aged 1 year.” This is obviously false because body would respond to the matter-interval, which is the same for both individuals. This confusion is due to incomplete math of the special theory of relativity, which does not take into account the relationship between speed and rigidity of substance.

Matter will not stay matter at terrific speeds. It will reduce to electromagnetic radiation. The math of Special relativity is applicable only  within the range of speeds that matter can have; and that too in an approximate manner.

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Comments

I could not summarize the misinterpretations in this chapter without commenting on it within the summary itself. It is interesting to see an established scientist misinterpreting the incomplete mathematics of a theory.

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Original Text

I have sometimes thought it would be very entertaining to hear a discussion between the Astronomer Royal and, let us say, Prof. Bergson on the nature of time. Prof. Bergson’s authority on the subject is well known; and I may remind you that the Astronomer Royal is entrusted with the duty of finding out time for our everyday use, so presumably he has some idea of what he has to find. I must date the discussion some twenty years back, before the spread of Einstein’s ideas brought about a rapprochement. There would then probably have been a keen disagreement, and I rather think that the philosopher would have had the best of the verbal argument. After showing that the Astronomer Royal’s idea of time was quite nonsensical, Prof. Bergson would probably end the discussion by looking at his watch and rushing off to catch a train which was starting by the Astronomer Royal’s time. 

Whatever may be time de jure, the Astronomer Royal’s time is time de facto. His time permeates every corner of physics. It stands in no need of logical defence; it is in the much stronger position of a vested interest. It has been woven into the structure of the classical physical scheme. “Time” in physics means Astronomer Royal’s time. You may be aware that it is revealed to us in Einstein’s theory that time and space are mixed up in a rather strange way. This is a great stumbling-block to the beginner. He is inclined to say, “That is impossible. I feel it in my bones that time and space must be of entirely different nature. They cannot possibly be mixed up.” The Astronomer Royal complacently retorts, “It is not impossible. I have mixed them up.” Well, that settles it. If the Astronomer Royal has mixed them, then his mixture will be the groundwork of present-day physics. 

We have to distinguish two questions which are not necessarily identical. First, what is the true nature of time? Second, what is the nature of that quantity which has under the name of time become a fundamental part of the structure of classical physics? By long history of experiment and theory the results of physical investigation have been woven into a scheme which has on the whole proved wonderfully successful. Time—the Astronomer Royal’s time—has its importance from the fact that it is a constituent of that scheme, the binding material or mortar of it. That importance is not lessened if it should prove to be only imperfectly representative of the time familiar to our consciousness. We therefore give priority to the second question. 

But I may add that Einstein’s theory, having cleared up the second question, having found that physical time is incongruously mixed with space, is able to pass on to the first question. There is a quantity, unrecognized in pre-relativity physics, which more directly represents the time known to consciousness. This is called proper-time or interval. It is definitely separate from and unlike proper-space. Your protest in the name of commonsense against a mixing of time and space is a feeling which I desire to encourage. Time and space ought to be separated. The current representation of the enduring world as a three-dimensional space leaping from instant to instant through time is an unsuccessful attempt to separate them. Come back with me into the virginal four-dimensional world and we will carve it anew on a plan which keeps them entirely distinct.  We can then resurrect the almost forgotten time of consciousness and find that it has a gratifying importance in the absolute scheme of Nature. 

But first let us try to understand why physical time has come to deviate from time as immediately perceived. We have jumped to certain conclusions about time and have come to regard them almost as axiomatic, although they are not really justified by anything in our immediate perception of time. Here is one of them. 

If two people meet twice they must have lived the same time between the two meetings, even if one of them has travelled to a distant part of the universe and back in the interim. 

An absurdly impossible experiment, you will say. Quite so; it is outside all experience. Therefore, may I suggest that you are not appealing to your experience of time when you object to a theory which denies the above statement? And yet if the question is pressed most people would answer impatiently that of course the statement is true. They have formed a notion of time rolling on outside us in a way which makes this seem inevitable. They do not ask themselves whether this conclusion is warranted by anything in their actual experience of time. 

Although we cannot try the experiment of sending a man to another part of the universe, we have enough scientific knowledge to compute the rates of atomic and other physical processes in a body at rest and a body travelling rapidly. We can say definitely that the bodily processes in the traveler occur more slowly than the corresponding processes in the man at rest (i.e. more slowly according to the Astronomer Royal’s time). This is not particularly mysterious; it is well known both from theory and experiment that the mass or inertia of matter increases when the velocity increases. The retardation is a natural consequence of the greater inertia. Thus so far as bodily processes are concerned the fast-moving traveler lives more slowly. His cycle of digestion and fatigue; the rate of muscular response to stimulus; the development of his body from youth to age; the material processes in his brain which must more or less keep step with the passage of thoughts and emotions; the watch which ticks in his waistcoat pocket; all these must be slowed down in the same ratio. If the speed of travel is very great we may find that, whilst the stay-at-home individual has aged 70 years, the traveler has aged 1 year. He has only found appetite for 365 breakfasts, lunches, etc.; his intellect, clogged by a slow-moving brain, has only traversed the amount of thought appropriate to one year of terrestrial life. His watch, which gives a more accurate and scientific reckoning, confirms this. Judging by the time which consciousness attempts to measure after its own rough fashion—and, I repeat, this is the only reckoning of time which we have a right to expect to be distinct from space—the two men have not lived the same time between the two meetings. 

Reference to time as estimated by consciousness is complicated by the fact that the reckoning is very erratic. “I’ll tell you who Time ambles withal, who Time trots withal, who Time gallops withal, and who he stands still withal.” I have not been referring to these subjective variations. I do not very willingly drag in so unsatisfactory a time-keeper; only I have to deal with the critic who tells me what “he feels in his bones” about time, and I would point out to him that the basis of that feeling is time lived, which we have just seen may be 70 years for one individual and 1 year for another between their two meetings. We can reckon “time lived” quite scientifically, e.g.  by a watch travelling with the individual concerned and sharing his changes of inertia with

velocity. But there are obvious drawbacks to the general adoption of “time lived”. It might be useful for each individual to have a private time exactly proportioned to his time lived; but it would be extremely inconvenient for making appointments. Therefore the Astronomer Royal has adopted a universal time-reckoning which does not follow at all strictly the time lived.

According to it the time-lapse does not depend on how the object under consideration has moved in the meanwhile. I admit that this reckoning is a little hard on our returned traveler, who will be counted by it as an octogenarian although he is to all appearances still a boy in his teens. But sacrifices must be made for the general benefit. In practice we have not to deal with human beings travelling at any great speed; but we have to deal with atoms and electrons travelling at terrific speed, so that the question of private time-reckoning versus general time-reckoning is a very practical one. 

Thus in physical time (or Astronomer Royal’s time) two people are deemed to have lived the same time between two meetings, whether or not that accords with their actual experience. The consequent deviation from the time of experience is responsible for the mixing up of time and space, which, of course, would be impossible if the time of direct experience had been rigidly adhered to. Physical time is, like space, a kind of frame in which we locate the events of the external world. We are now going to consider how in practice external events are located in a frame of space and time. We have seen that there is an infinite choice of alternative frames; so, to be quite explicit, I will tell you how I locate events in my frame. 

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Reference: The Book of Physics

Note: The original text is provided below.
Previous / Next

Summary

We need to find Nature’s own frame of space. But nature may not have such a frame. We may have to take a different approach. According to Eddington, the recognition of relativity leads us to seek a new way of unravelling the complexity of natural phenomena.

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Comments

This new way of unravelling the complexity of natural phenomena was provided by Einstein. But now there is another approach possible using the Theory of Substance, that does not require much change from classical conceptions.

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Original Text

Let us now return to the observer who was so anxious to pick out a “right” frame of space. I suppose that what he had in mind was to find Nature’s own frame—the frame on which Nature based her calculations when she poised the planets under the law of gravity, or the reckoning of symmetry which she used when she turned the electrons on her lathe. But Nature has been too subtle for him; she has not left anything to betray the frame which she used. Or perhaps the concealment is not any particular subtlety; she may have done her work without employing a frame of space. Let me tell you a parable.

There was once an archaeologist who used to compute the dates of ancient temples from their orientation. He found that they were aligned with respect to the rising of particular stars. Owing to precession the star no longer rises in the original line, but the date when it was rising in the line of the temple can be calculated, and hence the epoch of construction of the temple is discovered. But there was one tribe for which this method would not work; they had built only circular temples. To the archaeologist this seemed a manifestation of extraordinary subtlety on their part; they had hit on a device which would conceal entirely the date when their temples were constructed. One critic, however, made the ribald suggestion that perhaps this particular tribe was not enthusiastic about astronomy.

Like the critic I do not think Nature has been particularly subtle in concealing which frame she prefers. It is just that she is not enthusiastic about frames of space. They are a method of partition which we have found useful for reckoning, but they play no part in the architecture of the universe. Surely it is absurd to suppose that the universe is planned in such a way as to conceal its plan. It is like the schemes of the White Knight—

But I was thinking of a plan
To dye one’s whiskers green,
And always use so large a fan
That they could not be seen.

If this is so we shall have to sweep away the frames of space before we can see Nature’s plan in its real significance. She herself has paid no attention to them, and they can only obscure the simplicity of her scheme. I do not mean to suggest that we should entirely rewrite physics, eliminating all reference to frames of space or any quantities referred to them; science has many tasks to perform, besides that of apprehending the ultimate plan of structure of the world. But if we do wish to have insight on this latter point, then the first step is to make an escape from the irrelevant space-frames.

This will involve a great change from classical conceptions, and important developments will follow from our change of attitude. For example, it is known that both gravitation and electric force follow approximately the law of inverse-square of the distance. This law appeals strongly to us by its simplicity; not only is it mathematically simple but it corresponds very naturally with the weakening of an effect by spreading out in three dimensions. We suspect therefore that it is likely to be the exact law of gravitational and electric fields. But although it is simple for us it is far from simple for Nature. Distance refers to a space-frame; it is different according to the frame chosen. We cannot make sense of the law of inverse-square of the distance unless we have first fixed on a frame of space; but Nature has not fixed on any one frame. Even if by some self-compensation the law worked out so as to give the same observable consequences whatever space-frame we might happen to choose (which it does not) we should still be misapprehending its real mode of operation. In chapter VI we shall try to gain a new insight into the law (which for most practical applications is so nearly expressed by the inverse-square) and obtain a picture of its working which does not drag in an irrelevant frame of space. The recognition of relativity leads us to seek a new way of unravelling the complexity of natural phenomena.

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