Category Archives: Science

Eddington 1927: Practical Applications

September 1, 2018 – 3:10 PM
albert einstein
This undated file photo shows famed physicist Albert Einstein.

Reference: The Book of Physics

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Summary


This section talks about some practical applications of the relativity theory. It provides two examples:

(1) The back-pressure due to radiation should retard the motion of stars to rest but this has not been observed. The relativity theory explains it by showing that “coming to rest” has no meaning because there is no absolute velocity.

(2) Experiment shows that the mass of high-speed electrons is considerably greater than the mass of an electron at rest. The theory of relativity predicts this increase and provides the formula for the dependence of mass on velocity. 

Different values for speed and mass are obtained in different frames of reference. The theory of relativity comes from the classical theory being deficient in some respects.

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Comments


An absolute velocity scale seems to exist as an inverse of inertia scale. This makes stars pretty much fixed in space with no net back pressure due to radiation. In the case of high-speed electrons, the added kinetic energy is confused with electron’s mass. The actual mass of electron decreases with increasing velocity. Confusion arises with use of relative velocities in place of absolute velocities.

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Original Text

In these lectures I am concerned more with the ideas of the new theories than with their practical importance for the advancement of science. But the drawback of dwelling solely on the underlying conceptions is that it is likely to give the impression that the new physics is very much “up in the air”. That is by no means true, and the relativity theory is used in a businesslike way in the practical problems to which it applies. I can only consider here quite elementary problems which scarcely do justice to the power of the new theory in advanced scientific research. Two examples must suffice.

(1) It has often been suggested that the stars will be retarded by the back-pressure of their own radiation. The idea is that since the star is moving forward the emitted radiation is rather heaped up in front of it and thinned out behind. Since radiation exerts pressure the pressure will be stronger on the front surface than on the rear, Therefore there is a force retarding the star tending to bring it gradually to rest. The effect might be of great importance in the study of stellar motions; it would mean that on the average old stars must have lower speeds than young stars—a conclusion which, as it happens, is contrary to observation.

But according to the theory of relativity “coming to rest” has no meaning. A decrease of velocity relative to one frame is an increase relative to another frame. There is no absolute velocity and no absolute rest for the star to come to. The suggestion may therefore be at once dismissed as fallacious.

(2) The β particles shot out by radioactive substances are electrons travelling at speeds not much below the speed of light. Experiment shows that the mass of one of these high-speed electrons is considerably greater than the mass of an electron at rest. The theory of relativity predicts this increase and provides the formula for the dependence of mass on velocity. The increase arises solely from the fact that mass is a relative quantity depending by definition on the relative quantities length and time.

Let us look at a β particle from its own point of view. It is an ordinary electron in no wise different from any other. But it is travelling with unusually high speed? “No”, says the electron, “That is your point of view. I contemplate with amazement your extraordinary speed of 100,000 miles a second with which you are shooting past me. I wonder what it feels like to move so quickly. However, it is no business of mine.” So the β particle, smugly thinking itself at rest, pays no attention to our goings on, and arranges itself with the usual mass, radius and charge. It has just the standard mass of an electron, 9×10-28 grams. But mass and radius are relative quantities, and in this case the frame to which they are referred is evidently the frame appropriate to an electron engaged in self-contemplation, viz. the frame in which it is at rest. But when we talk about mass we refer it to the frame in which we are at rest. By the geometry of the four-dimensional world, we can calculate the formulae for the change of reckoning of mass in two different frames, which is consequential on the change of reckoning of length and time; we find in fact that the mass is increased in the same ratio as the length is diminished (FitzGerald factor). The increase of mass that we observe arises from the change of reckoning between the electron’s own frame and our frame.

All electrons are alike from their own point of view. The apparent differences arise in fitting them into our own frame of reference which is irrelevant to their structure. Our reckoning of their mass is higher than their own reckoning, and increases with the difference between our respective frames, i.e. with the relative velocity between us.

We do not bring forward these results to demonstrate or confirm the truth of the theory, but to show the use of the theory. They can both be deduced from the classical electromagnetic theory of Maxwell coupled (in the second problem) with certain plausible assumptions as to the conditions holding at the surface of an electron. But to realise the advantage of the new theory we must consider not what could have been but what was deduced from the classical theory. The historical fact is that the conclusions of the classical theory as to the first problem were wrong; an important compensating factor escaped notice. Its conclusions as to the second problem were (after some false starts) entirely correct numerically. But since the result was deduced from the electromagnetic equations of the electron it was thought that it depended on the fact that an electron is an electrical structure; and the agreement with observation was believed to confirm the hypothesis that an electron is pure electricity and nothing else. Our treatment above makes no reference to any electrical properties of the electron, the phenomenon having been found to arise solely from the relativity of mass. Hence, although there may be other good reasons for believing that an electron consists solely of negative electricity, the increase of mass with velocity is no evidence one way or the other.

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Eddington 1927: The Velocity of Light

August 31, 2018 – 7:48 PM
abstract-speed-of-light

Reference: The Book of Physics

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Summary

In general velocity is relative, but Einstein postulates the velocity of light to be absolute in vacuum. Absolute means that the velocity of light is the same relative to every particle of matter in the universe. According to Einstein, as an observer moves, his own space contracts and time dilates, such that he measure the speed of light to be the same. 

The velocity of light of 299,796 km/s coincides with the grain of the world. “It is the speed at which the mass of matter becomes infinite, lengths contract to zero, and clocks stand still.” There are other “velocities” that correspond to the various wormholes which may casually cross the grain.  However, neither matter, nor energy, nor anything capable of being used as a signal can travel faster than 299,796 kilometres per second, provided that the velocity is referred to one of the frames of space and time considered here. The speed, exceeding 299,796 kilometres a second, is, so to speak, achieved by prearrangement, and has no application in signaling.

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Comments


In truth the velocity of light only appears to be same relative to every particle of matter in the universe because it is extremely large compared to the range of velocities possible for matter. The space (wavelength) of the moving object expands and its time duration (frequency) lessens commensurate with its absolute motion, but that is negligible for matter. On a cosmic scale our visual perception of cosmic events is delayed because of finite speed of light.

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Original Text

A feature of the relativity theory which seems to have aroused special interest among philosophers is the absoluteness of the velocity of light. In general velocity is relative. If I speak of a velocity of 40 kilometres a second, I must add “relative to the earth”, “relative to Arcturus”, or whatever reference body I have in mind. No one will understand anything from my statement unless this is added or implied. But it is a curious fact that if I speak of a velocity of 299,796 kilometres a second it is unnecessary to add the explanatory phrase. Relative to what? Relative to any and every star or particle of matter in the universe.

It is no use trying to overtake a flash of light; however fast you go it is always travelling away from you at 186,000 miles a second. Now from one point of view this is a rather unworthy deception that Nature has practiced upon us. Let us take our favourite observer who travels at 161,000 miles a second and send him in pursuit of the flash of light. It is going 25,000 miles a second faster than he is; but that is not what he will report. Owing to the contraction of his standard scale his miles are only half-miles; owing to the slowing down of his clocks his seconds are double-seconds. His measurements would therefore make the speed 100,000 miles a second (really half-miles per double-second). He makes a further mistake in synchronizing the clocks with which he records the velocity. (You will remember that he uses a different Now line from ours.). This brings the speed up to 186,000 miles a second. From his own point of view the traveler is lagging hopelessly behind the light; he does not realise what a close race he is making of it, because his measuring appliances have been upset. You will note that the evasiveness of the light-flash is not in the least analogous to the evasiveness of the rainbow.

But although this explanation may help to reconcile us to what at first seems a blank impossibility, it is not really the most penetrating. You will remember that a Seen-Now line, or track of a flash of light, represents the grain of the world-structure. Thus the peculiarity of a velocity of 299,796 kilometres a second is that it coincides with the grain of the world. The four-dimensional worms representing material bodies must necessarily run across the grain into the future cone, and we have to introduce some kind of reference frame to describe their course. But the flash of light is exactly along the grain, and there is no need of any artificial system of partitions to describe this fact.

The number 299,796 (kilometres per second) is, so to speak, a code-number for the grain of the wood. Other code-numbers correspond to the various wormholes which may casually cross the grain. We have different codes corresponding to different frames of space and time; the code-number of the grain of the wood is the only one which is the same in all codes. This is no accident; but I do not know that any deep inference is to be drawn from it, other than that our measure-codes have been planned rationally so as to turn on the essential and not on the casual features of world-structure.

The speed of 299,796 kilometres per second which occupies a unique position in every measure-system is commonly referred to as the speed of light. But it is much more than that; it is the speed at which the mass of matter becomes infinite, lengths contract to zero, clocks stand still. Therefore it crops up in all kinds of problems whether light is concerned or not.

The scientist’s interest in the absoluteness of this velocity is very great; the philosopher’s interest has been, I think, largely a mistaken interest. In asserting its absoluteness scientists mean that they have assigned the same number to it in every measure-system; but that is a private arrangement of their own—an unwitting compliment to its universal importance. (In the general relativity theory, chapter VI, measure-systems are employed in which the velocity of light is no longer assigned the same constant value, but it continues to correspond to the grain of absolute world-structure.) Turning from the measure-numbers to the thing described by them, the “grain” is certainly an absolute feature of the wood, but so also are the “worm-holes” (material particles). The difference is that the grain is essential and universal, the worm-holes casual. Science and philosophy have often been at cross-purposes in discussing the Absolute—a misunderstanding which is I am afraid chiefly the fault of the scientists. In science we are chiefly concerned with the absoluteness or relativity of the descriptive terms we employ; but when the term absolute is used with reference to that which is being described it has generally the loose meaning of “universal” as opposed to “casual”.

Another point on which there has sometimes been a misunderstanding is the existence of a superior limit to velocity. It is not permissible to say that no velocity can exceed 299,796 kilometres per second. For example, imagine a search-light capable of sending an accurately parallel beam as far as Neptune. If the search-light is made to revolve once a minute, Neptune’s end of the beam will move round a circle with velocity far greater than the above limit. This is an example of our habit of creating velocities by a mental association of states which are not themselves in direct causal connection. The assertion made by the relativity theory is more restricted, viz.—

Neither matter, nor energy, nor anything capable of being used as a signal can travel faster than 299,796 kilometres per second, provided that the velocity is referred to one of the frames of space and time considered in this chapter. (Some proviso of this kind is clearly necessary. We often employ for special purposes a frame of reference rotating with the earth; in this frame the stars describe circles once a day, and are therefore ascribed enormous velocities.)

The velocity of light in matter can under certain circumstances (in the phenomenon of anomalous dispersion) exceed this value. But the higher velocity is only attained after the light has been passing through the matter for some moments so as to set the molecules in sympathetic vibration. An unheralded light-flash travels more slowly. The speed, exceeding 299,796 kilometres a second, is, so to speak, achieved by prearrangement, and has no application in signaling.

We are bound to insist on this limitation of the speed of signaling. It has the effect that it is only possible to signal into the Absolute Future. The consequences of being able to transmit messages concerning events Here-Now into the neutral wedge are too bizarre to contemplate. Either the part of the neutral wedge that can be reached by the signals must be restricted in a way which violates the principle of relativity; or it will be possible to arrange for a confederate to receive the messages which we shall send him to-morrow, and to retransmit them to us so that we receive them to-day. The limit to the velocity of signals is our bulwark against that topsy-turvydom of past and future, of which Einstein’s theory is sometimes wrongfully accused.

Expressed in the conventional way this limitation of the speed of signaling to 299,796 kilometres a second seems a rather arbitrary decree of Nature. We almost feel it as a challenge to find something that goes faster. But if we state it in the absolute form that signaling is only possible along a track of temporal relation and not along a track of spatial relation the restriction seems rational. To violate it we have not merely to find something which goes just 1 kilometer per second better, but something which overleaps that distinction of time and space—which, we are all convinced, ought to be maintained in any sensible theory.

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Eddington 1927: The Four-Dimensional World

August 31, 2018 – 11:56 AM
1. BQ_space_gazing_480x320

Reference: The Book of Physics

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Summary

For some time now we have been immersed in a four-dimensional world—the three dimensions of space and the fourth dimension of time. It is not difficult to conceive of events as ordered in four dimensions. It includes the history of an object.

The appearance of a four-dimensional world in this subject is due to Minkowski. Einstein showed the relativity of the familiar quantities of physics; Minkowski showed how to recover the absolute by going back to their four-dimensional origin and searching more deeply.

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Comments

The four dimensions apply to the substance. The substance has its own dimension of matter, energy and thought.

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Original Text

I do not know whether you have been keenly alive to the fact that for some time now we have been immersed in a four-dimensional world. The fourth dimension required no introduction; as soon as we began to consider events it was there. Events obviously have a fourfold order which we can dissect into right or left, behind or in front, above or below, sooner or later—or into many alternative sets of fourfold specification. The fourth dimension is not a difficult conception. It is not difficult to conceive of events as ordered in four dimensions; it is impossible to conceive them otherwise. The trouble begins when we continue farther along this line of thought, because by long custom we have divided the world of events into three-dimensional sections or instants, and regarded the piling of the instants as something distinct from a dimension. That gives us the usual conception of a three-dimensional world floating in the stream of time. This pampering of a particular dimension is not entirely without foundation; it is our crude appreciation of the absolute separation of space-relations and time-relations by the hour-glass figures. But the crude discrimination has to be replaced by a more accurate discrimination. The supposed planes of structure represented by Now lines separated one dimension from the other three; but the cones of structure given by the hourglass figures keep the four dimensions firmly pinned together. (In Fig. 4 the scale is such that a second of time corresponds to 70,000 miles of space. If we take a more ordinary scale of experience, say a second to a yard, the Seen-Now lines become almost horizontal; and it will easily be understood why the cones which pin the four dimensions together have generally been mistaken for sections separating them.)

We are accustomed to think of a man apart from his duration. When I portrayed “Myself” in Fig. 2, you were for the moment surprised that I should include my boyhood and old age. But to think of a man without his duration is just as abstract as to think of a man without his inside. Abstractions are useful, and a man without his inside (that is to say, a surface) is a well-known geometrical conception. But we ought to realise what is an abstraction and what is not. The “four-dimensional worms” introduced in this chapter seem to many people terribly abstract. Not at all; they are unfamiliar conceptions but not abstract conceptions. It is the section of the worm (the man Now) which is an abstraction. And as sections may be taken in somewhat different directions, the abstraction is made differently by different observers who accordingly attribute different FitzGerald contractions to it. The non-abstract man enduring through time is the common source from which the different abstractions are made.

The appearance of a four-dimensional world in this subject is due to Minkowski. Einstein showed the relativity of the familiar quantities of physics; Minkowski showed how to recover the absolute by going back to their four-dimensional origin and searching more deeply.

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Eddinton 1927: Absolute Distinction of Space and Time

August 31, 2018 – 9:52 AM
space-time

Reference: The Book of Physics

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Summary

The information that we can directly perceive is limited to the lower cone. We may call it the region of absolute past. Information for rest of the region has to be calculated. The actual difference between time and space seems to be that time represents the state of awareness; whereas, space represents what one is aware of.

Our knowledge of the world comes from the inference and interpretation of our physical and mental sensations. Space is more than the three mathematical dimensions. Space may refer to all the dimensions of this universe. Time has to do with awareness. There are many dimensions of consciousness too. 

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Comments

Eddington’s view of time and space is subjective and difficult to understand.

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Original Text

By dividing the world into Absolute Past and Future on the one hand and Absolute Elsewhere on the other hand, our hour-glasses have restored a fundamental differentiation between time and space. It is not a distinction between time and space as they appear in a space-time frame, but a distinction between temporal and spatial relations. Events can stand to us in a temporal relation (absolutely past or future) or a spatial relation (absolutely elsewhere), but not in both. The temporal relations radiate into the past and future cones and the spatial relations into the neutral wedge; they are kept absolutely separated by the Seen-Now lines which we have identified with the grain of absolute structure in the world. We have recovered the distinction which the Astronomer Royal confused when he associated time with the merely artificial Now lines.

I would direct your attention to an important difference in our apprehension of time-extension and space-extension. As already explained our course through the world is into the absolute future, i.e. along a sequence of time-relations. We can never have a similar experience of a sequence of space-relations because that would involve travelling with velocity greater than light. Thus we have immediate experience of the time-relation but not of the space-relation. Our knowledge of space-relations is indirect, like nearly all our knowledge of the external world—a matter of inference and interpretation of the impressions which reach us through our senseorgans. We have similar indirect knowledge of the time-relations existing between the events in the world outside us; but in addition we have direct experience of the time-relations that we ourselves are traversing— a knowledge of time not coming through external sense-organs, but taking a short cut into our consciousness. When I close my eyes and retreat into my inner mind, I feel myself enduring, I do not feel myself extensive. It is this feeling of time as affecting ourselves and not merely as existing in the relations of external events which is so peculiarly characteristic of it; space on the other hand is always appreciated as something external.

That is why time seems to us so much more mysterious than space. We know nothing about the intrinsic nature of space, and so it is quite easy to conceive it satisfactorily. We have intimate acquaintance with the nature of time and so it baffles our comprehension. It is the same paradox which makes us believe we understand the nature of an ordinary table whereas the nature of human personality is altogether mysterious. We never have that intimate contact with space and tables which would make us realise how mysterious they are; we have direct knowledge of time and of the human spirit which makes us reject as inadequate that merely symbolic conception of the world which is so often mistaken for an insight into its nature.

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Eddington 1927: Absolute Past and Future

August 30, 2018 – 9:03 PM
Fig 4

Reference: The Book of Physics

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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.

Fig 4

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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