Don't You Ever Read Anything But Serious Books? Volume 3

By Richard Lung

I perhaps felt that I wasn’t getting anywhere. But I intended to consult my notes on these theoretical and semi-technical explanations, in future, to acquire a good understanding.
I never did consult any of my notes. They just accumulated in thick bound diaries, on a shelf; the very sight of them, an embarrassment to me.
I thought perhaps I might have put all that unused note-paper to some better use, tho I could not keep a diary, to even keep myself, as Mae West recommended.
My first volume covered mainly the decade of the nineteen seventies, and early eighties, charting some of the greats; largely established writers from earlier decades.
The second volume covered largely then up-to-date interpretive psychology, no doubt put in the shade now by neuro-science. But it was psychology with a human face. This was mainly the decade of the eighties and early nineties.
This Volume 3 featured popular physics of the nineties and noughties. PCW Davies was the back-bone of this effort, tho I had practically done with my limited understanding of his popularisations by the end of the eighties. He would continue to publish prolifically.
Most of the advanced work was beyond me. And I attempted more than I could understand. Myself, the editor of these researched books is not an authority on them but a learner, sometimes a very imperfect learner. This is the fault or limitation of the editor, not of the authors of these many books, more or less studied, in his third volume of a life-times serious reading.

• Language: English
• Publisher: Richard Lung
• Release date: May 4, 2024
• ISBN: 9798224510221

Richard Lung

My later years acknowledge the decisive benefit of the internet and the web in allowing me the possibility of publication, therefore giving the incentive to learn subjects to write about them.I have been the author of the Democracy Science website since 1999. This combined scientific research with democratic reform.While, from my youth, I acknowledge the intellectual debt that I owed a social science degree, while coming to radically disagree, even as a student, with its out-look and aims.Whereas from middle age, I acknowledge how much I owed to the friendship of Dorothy Cowlin, largely the subject of my e-book, Dates and Dorothy. This is the second in a series of five books of my collected verse. Her letters to me, and my comments came out, in: Echoes of a Friend.....Authors have played a big part in my life.Years ago, two women independently asked me: Richard, don't you ever read anything but serious books?But Dorothy was an author who influenced me personally, as well as from the written page. And that makes all the difference.I have only become a book author myself, on retiring age, starting at stopping time!

Book preview

Don't You Ever Read Anything But Serious Books? Volume 3.

Copyright © 2024: Richard Lung

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Table of Contents

Don't You Ever Read Anything But Serious Books? Volume 3.

Preface to volume 3.

Einstein Theory of Relativity. JWN Sullivan.

Was Einstein Right? (Putting general relativity to the test). Clifford M Will 1988.

A Brief History of Time. Stephen Hawking 1988.

Black Holes and Baby Universes and other essays. Stephen Hawking 1993.

PCW Davies

Space and Time in the Modern Universe. (Paul) PCW Davies 1977.

The Edge of Infinity. Paul Davies 1981.

Other Worlds. Space, superspace and the quantum universe. Paul Davies 1980.

Quantum Mechanics. Paul Davies 1984.

The Search For Gravity Waves. Paul Davies 1980.

Superforce. The search for a grand unified theory of nature. Paul Davies 1984.

The Forces of Nature. PCW Davies 1986.

The Runaway Universe. Paul Davies 1978.

The Cosmic Blueprint. Paul Davies 1987.

God and the New Physics. Paul Davies 1986.

Surveys and Symmetries

The New Physics. Edited by Paul Davies 1989.

Superstrings. A theory of everything? Edited by PCW Davies & J Brown 1988.

Fundamentals of Physical Science. Krauskopf and Beiser 1969.

New Worlds In Physics. John G Taylor 1974.

Essentials of Modern Physics. Acosta, Cowan and Graham 1973.

The Nature of Physical Law. Michael Munowitz 2005.

Symmetries and Reflections. Eugene Wigner.

Perfect Symmetry. Heinz R Pagels 1985.

Waves and Particles

Atomic Physics. JC Wilmott 1975.

Story of the W and Z. Peter Watkins 1986.

Elementary Particles. IS Hughes 1985.

Quarks. The stuff of matter. Harald Fritzsch 1984.

To acknowledge the Wonder. The story of fundamental physics. Euan Squires 1985.

The Mystery of the Quantum World. Euan Squires 1986.

The Ideas of Particle Physics. (An introduction for scientists). JE Dodd 1984.

The Double-slit experiment. Editor.

Probabilities

Wholeness and the Implicate Order. David Bohm. 1980.

Does God Play Dice? Ian Stewart. 1989.

The New Scientist Guide to Chaos. Edited by Nina Hall. 1992.

The Quantum Universe. Tony Hay and Patrick Walters. 1987.

The Arrow of Time. Peter Coveney and Roger Highfield. 1990.

Cosmic dimensions

Blinded by the Light. The secret life of the sun. John Gribbin. 1991.

In Search of the Edge of Time. John Gribbin 1992.

Journeys To The Ends Of The Universe. C R Kitchin. 1990.

The Fabric of the Cosmos. Brian Greene. 2004.

The Hidden Reality. Brian Greene. 2011.

Warped Passages. Unravelling the universes hidden dimensions. Lisa Randall 2005.

The Geometric Mean and Absolute Space-time. Editor.

Fumbled repeat cover foto.

Pocket essays (Editor)

Nuclear family.

The one strange incident in my life.

A History of Sin: The Career Politicians Persecution of Transferable Voting.

Electoral reformers and conformers.

Legal absolutism.

Test of elimination counts versus proportional counts.

Freedom versus determinism.

Binomial Single Transferable Vote Program links

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Don't You Ever Read Anything But Serious Books? Volume 3.

Preface to volume 3.

I had become dissatisfied with my reading habits, and decided I must specialise, to gain a better understanding of the scientific standards set by physics, thru the many popular accounts.

I see that I have largely abandoned popular accounts of psychology and parapsychology for those of natural science. I perhaps felt that I wasn’t getting anywhere. But I intended to consult my notes on these theoretical and semi-technical explanations, in future, to acquire a good understanding.

I never did consult any of my notes. They just accumulated in thick bound diaries, on a shelf; the very sight of them, an embarrassment to me.

I thought perhaps I might have put all that unused note-paper to some better use, tho I could not keep a diary, to even keep myself, as Mae West recommended.

My first volume covered mainly the decade of the nineteen seventies, and early eighties, charting some of the greats; largely established writers from earlier decades.

The second volume covered largely then up-to-date interpretive psychology, no doubt put in the shade now by neuro-science. But it was psychology with a human face. This was mainly the decade of the eighties and early nineties.

This Volume 3 featured popular physics of the nineties and noughties. PCW Davies was the back-bone of this effort, tho I had practically done with my limited understanding of his popularisations by the end of the eighties. He would continue to publish prolifically.

Most of the advanced work was beyond me. And I attempted more than I could understand. Myself, the editor of these researched books is not an authority on them but a learner, sometimes a very imperfect learner. This is the fault or limitation of the editor, not of the authors of these many books, more or less studied, in his third volume of a life-times serious reading.

My current profile page is: https://www.smashwords.com/profile/view/democracyscience

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Einstein Theory of Relativity. JWN Sullivan.

Table of Contents

Einstein famously pronounced God does not play dice.

Neils Bohr retorted: Stop telling God what to do.

Hawking asserted God does play dice.

Albert Einstein

THE famous Einstein theory was published in two parts. The first part, the so called 'Special' theory, was published in 1905 when Einstein was only twenty-six years of age. The 'General' theory which, besides greatly extending the special theory, gave also a solution of the problem of gravitation, was published ten years later. It is this theory that attracted the attention of the whole world, as well as the strictly scientific portion of it, by the dramatic verification, at the total solar eclipse of May 29. 1919, of one of the most startling predictions of the theory. The book under consideration--a translation of which by Robert W. Lawson is published by Methuen at 5s. net--is Einstein's own exposition, for the general public, of both theories. It may be said at once that judgmg from this book, Einstein had a rather exalted opinion of the intelligence of the general public. His exposition is superb, but it demands very close attention. He says what he has to say so compactly that the reader is in danger of missing the full significance of his statements.

He begins with a question which is fundamental for his whole theory, and that is the status of the axioms of geometry. His own words are:

We cannot ask whether it is true that only one straight line goes through two points. We can only say that Euclidean geometry deals with things called 'straight lines,' to each of which is ascribed the property of being uniquely determined by two points situated on it. The concept 'true' does not tally with the assertions of pure geometry, because by the word 'true' we are eventually in the habit of designating always the correspondence with a 'real' object; geometry, however, is not concerned with the relation of the ideas involved in it to objects of experience, but only with the logical connexion of these ideas among themselves.

This estimate of the status of Euclidean geometry is justified by the fact that any number of non-Euclidean geometries exist. For two thousand years Euclid's axioms were regarded as necessities of thought. But early in the nineteenth century it was discovered that certain of Euclid's axioms could be denied and others substituted for them, and yet that perfectly self-consistent systems of geometry could be constructed. It follows that Euclid's axioms are not necessary truths. They are 'conventions'. We may adopt them or not, as we please. Consequently, in applying geometry to the real world, we are at liberty to apply that system of geometry we find most convenient. All systems of geometry are equally logical and no one is more 'true' than another, just as it is no more true that there are three feet in a yard than it is that there are one hundred centimetres in a metre. Which system we employ is a matter of convenience. In his general theory of relativity Einstein finds it convenient to use a non-Euclidean geometry.

AFTER some preliminary remarks dealing with our methods of measuring the positions of bodies Einstein enunciates his 'special' theory of relativity which is to the effect that two observers in uniform translatory motion with respect to one another find the same laws for natural phenomena. By uniform translatory motion is meant motion at a constant speed in a straight line, i.e. without rotation or acceleration of any kind. Now Newton had said, long ago, that two such observers will find the same laws for mechanics. But will they find the same laws for optics and for electricity? Einstein says that they will, but this statement, when we come to think about it, is a very puzzling one. Consider, for instance, the fact that light. travels at 186,000 miles per second for a given observer. Could it have the same velocity for a second observer moving relatively to the first? It seems obvious that it could not. An aeroplane does not pass a moving train at the same pace that it passes one at rest. Nevertheless, Einstein asserts that light will have the same velocity for two observers, whatever their relative motion. He says:

As a result of an analysis of the physical conceptions of time and space, it became evident that in reality there is not the least incompatibility between the principle of relativity and the law of propagation of light, and that by systematically holding fast to both these laws a logically rigid theory could be arrived at.

He then proceeds to show that the notion of simultaneity is a relative one. Events which are simultaneous for one observer are not slmultaneous for an observer moving relatively to the first. Two such observers will not agree in their estimates of the time-lapse between two events. Neither will their distance measurements agree. What are the relations between the space and time measurements of such observers, supposing them to get the same velocity for light? This is a purely mathematical problem, and Einstein gives the solution, which we need not quote. But we must realize clearly what he has done here, for this is the basis of the whole theory. He has shown that observers in uniform relative motion will obtain the same laws of nature for phenomena provided they use different space and time measurements, and he has shown just what these differences would be. Now it is a fact of experiment that such observers do obtain the same laws of nature. Not only the famous Michelson-Morley experiment on light, described by Einstein, but many other experiments bear out this statement. It follows that observers in relative motion naturally adopt space and time measurements which differ in the way described by Einstein. In other words, each observer has his own spacetime framework. There is no absolute space and time, the same for all observers.

IF an observer B, carrying a clock and also carrying a yard measure pointing in the direction of his motion moves past an observer A then, from A's point of view, B's yard measure is short of a yard and his clock is going slow. And the discrepancy is greater the greater B's velocity relative to A. If B passed A with the velocity of light then we reach the highly astonishing result that from A's point of view B's yard measure would be of zero length and his clock would not be going at alI! This means that the velocity of light is a limiting velocity. No object in the universe can possibly move at a speed greater than the speed of light. Einstein proceeds to work out some of the consequences of this theory:

The most important result of a general character to which the special theory of relativity has led is concerned with the conception of mass. Before the advent of relativity, physics recognized two conservation laws of fundamental importance, namely, the law of the conservation of energy and the law of the conservation of mass; these two fundamental laws appeared to be quite independent of each other. By means of the theory of relativity they have been united into one law.

Mass and energy have become, in fact, inter-changeable terms. A body radiating energy thereby loses mass; a body receiving energy thereby gains mass. As a body moves faster, its energy, and therefore its mass; increases. At the velocity of light its mass would be infinite. We may mention that these deductions from Einstein's theory have been verified by experiment. Thus the swiftest electrons we can produce artificially have speeds within a few per cent. of that of light, and their mass is found to increase to just the extent calculated by Einstein. The reader should remember, in reading this book, that he is not dealing with speculations 'in the air.' Countless experiments have confirmed Einstein's conclusions.

Einstein concludes this part of his exposition with an account of Minkowski's 'four-dimensional space.' The central idea of this must be understood before the general theory can be tackled. It is thus described by Einstein:

Space is a three-dimensional continuum. By this we mean that it is possible to describe the position of a point (at rest) by means of three numbers (co-ordinates) x, y, z, and that there is an indefinite number of points in the neighbourhood of this one, the position of which can be described by co-ordinates such as X1, Y1, Z1, which may be as near as we choose to the respective values of the co-ordinates x, y, z, of the first point. In virtue of the latter property we speak of a 'continuum,' and owing to the fact that there are three co-ordinates we speak of it as being 'three-dimensional.'

Similarly, the world of the physical phenomena which was briefly called 'world' by Minkowski is naturally four-dimensional in the space-time sense. For it is composed of individual events, each of which is described by four numbers, namely, three space co-ordinates x, y, z, and a time co-ordinate, the time-value t. The 'world' is in this sense also a continuum; for to every event there are as many 'neighbouring' events (realized or at least thinkable) as we care to choose, the co-ordinates X1, Y1, Z1, T1, of which differ by an indefinitely small amount from those of the event x y z t originally considered. That we have not been accustomed to regard the world in this sense as a four-dimensional continuum is due to the fact that in physics, before the advent of the theory of relativity, time played a different and more independent role, as compared with the space co-ordinates. It is for this reason that we have been in the habit of treating time as an independent continuum. As a matter of fact, according to classical mechanics, time is absolute, i.e. it is independent of the position and the condition of motion of the system of co-ordinates. . . The four-dimensional mode of consideration of the 'world' is natural on the theory of relativity, since according to this theory time is robbed of its independence.

We say that space has three dimensions because we require three measurements to specify the position of a point in space. For instance, to specify the position in a room of the tip of an electric light bulb we would have to give its distances from two walls and its distance from the floor or the ceiling. Whatever method we adopted we should have to give at least three measurements, That is why we call space three-dimensional. And space is continuous because we can have points in space as close together as we like. The three distances of a point from our frame of reference (such a frame, for instance, as the two walls and the ceiling) are called the 'co-ordinates' of the point.

But if we are specifying an event we want to say when as well as where it happened. We must give, therefore, the moment of time of its occurrence. This is called its time co-ordinate. In calculations the space co-ordinates are usually denoted by x, y, z; and the time coordinate by t.

Now Minkowski showed that the space and time co-ordinates of an event are not independent of one another. Two flashes of light may be separated by ten yards for one observer and occur at an interval of ten seconds. But for a second observer, moving relatively to the first, they may be more than ten yards apart and occur at an interval of more than ten seconds. A certain combination of distance and time will be the same for both observers, but the distances and times taken separately will not be the same, That particular combination of distance and time that all observers will find to be the same is called the 'interval.' Minkowski showed that the interval could be regarded as a 'distance in a four-dimensional space.' This four-dimensional space we split up into a three-dimensional space and a one-dimensional time--and each observer splits it differently. The actual four-dimensional quantity involved--the 'interval' is the same for all of them, but they spIlt it up dlfferently into so much of space and so much of time. This result is very interesting, but there is one particular aspect of it which is ot the greatest importance for the relativity theory. This aspect is described by Einstein as follows:

But the discovery of Minkowski, which was of importance for the formal development of the theory of relativity does not lie here. It is to be found rather in the fact of his recognition that the four-dimensional space-time continuum of the theory of relativity, in its most essential formal properties, shows a pronounced relationship to the three-dimensional continuum of Euclidean geometrical space.

That is to say the geometry of this four-dimensional space of Minkowski's is a Euclidean geometry. The whole 'special' theory of relativity can be explained as the geometry of a four-dimensional 'Eudidean' space. This fact gave Einstein a very important clue for developing his theory. For Einstein was dissatisfied with his special theory. We have pointed out that that theory says that the laws of nature are the same for observers in uniform translatory motion with respect to one another, and only for such observers. Einstein comments:

But no person whose mode of thought is logical can rest satisfied with this condition of things. He asks: 'How does it come that certain reference bodies (or their states of motion) are given priority over other reference-bodies (or their states of motion)? What is the reason for this preference?'

Einstein wants to know why the laws of nature should not be the same for all observers, whatever their state of motion. We have found that uniform motion makes no difference. What difference does non-uniform motion make? His solution of this question is Einstein's most dazzling achievement. We begin with his famous account of the man in the box.

As reference body let us imagine a spacious chest resembling a room with an observer inside who is equipped with apparatus. Gravitation naturalIy does not exist for this observer. (Einstein imagines the man in the chest to be right away in empty space.) He must fasten himself with strings to the floor, otherwise the slightest impact against the floor will cause him to rise slowly towards the ceiling of the room.

To the middle of the lid of the chest is fixed externalIy a hook with rope attached, and now a 'being' (what kind of a being is immaterial to us) begins pulling at this with a constant force. The chest, together with the observer, begin to move 'upwards' with a uniformlv accelerated motion. In course of time their velocIty will reach unheard-of values--provided that we are viewing all this from another reference-body which is not being pulled with a rope.

But how does the man in the chest regard the process? The acceleration of the chest will be transmitted to him by the reaction of the floor of the chest. He must therefore take up this pressure by means of his legs if he does not wish to be laid out full length on the floor. He is then standing in the chest in exactly the same way as anyone stands in a room of a house on our earth. If he release a body which he previously had in his hand, the acceleration of the chest will no longer be transmitted to this body, and for this reason the body will approach the floor of the chest with an accelerated relative motion. The observer will further convince himself that the acceleration of the body towards the floor of the chest is always of the same magnitude, whatever kind of body he may happen to use for the experiment.

THE point Einstein is leading up to is clear from the above passage in italics. For it is characteristic of the gravitational force, and of the gravitational force alone, that it is entirely independent of the physical or chemical constitution of the bodies on which it operates. The man in the chest will naturally conclude that he and his chest are in a gravitational field. Einstein goes on:

Of course he will be puzzled for a moment as to why the chest does not faII in this gravitational field. Just then, however, he discovers the hook in the middle of the lid of the chest and the rope which is attached to it, and he consequently comes to the conclusion that the chest is suspended at rest in the gravitational field.

From this illustration we can grasp Einstein's conception of the essential difference between uniform and non-uniform motion. An observer in non-uniform motion may be regarded as existing in a gravitational field. The laws of phenomena for observers in non-uniform motion, therefore, are the laws of phenomena in gravitational fields. But we must be careful in reading this example not to suppose that Einstein means to say that a gravitational field is always merely apparent. There is a gravitational field for the man in the chest although there is no gravitational field from the point of view of an observer outside the chest. But there is no possible observer for whom the gravitational field of the earth does not exist.

Let us imagine the man looking through a window in his moving chest and observing the passage of a ray of light outside. Since the man's motion is an accelerated motion the ray of light would appear to him curved. But since, according to Einstein, there is no essential difference between accelerated motion and a gravitational field, it follows that light passing through a gravitational field should follow a curved path. Einstein prophesied, therefore, that this would be so and, as all the world knows, the prophecy was verified at the eclipse expedition of May 29, 1919.

This case exemplified a procedure which is pretty general in the theory. We imagine an artificial gravitational field and find what would happen to phenomena in that field. We then use this result to say what would happen to phenoinena in a real gravitational field. Also, by finding the laws obeyed by these artificial fields themselves we can deduce the laws obeyed by real gravitational fields. This is what Einstein has done, and it is perhaps the most celebrated part of his achievement. He has found the true laws for gravitation and shown that Newton's law is only approximate.

But to do this, he had greatly to extend Minkowski's idea, mentioned above. He found that if Minkowski's four-dimensional space was permeated by a gravitational field, then its geometry was not Euclidean. He had to apply non-Euclidean geometry. Einstein, in his desire to omit no steps from the argument, gives the reader an outline of the method by which he did this. The reader will probably find this the most obscure part of his book. There would be no point in quoting it and still less in summarising it. It is best for the reader who is not a mathematician to take this part of the argument for granted. Suffice it to say that the laws of motion in a non-Euclidean space can be worked out, and that they are found to give just the motions we observe in the case of the planets. Thus the actual motion of Mercury had never been satisfactorily explained on Newton's theory. The difference between observation and calculation was slight, but it was there, and the greatest mathematicians had exerted themselves in vain to explain it. Einstein's theory, in a perfectly natural and unforced way, clears up the whole mystery. Einstein's own words are:

Since the time of Leverrier, it has been known that the ellipse corresponding to the orbit of Mercury . . . is not stationary with respect to the fixed stars, but that it rotates exceedingly slowly in the plane of the orbit and in the sense of the orbital motion. The value obtained for this rotary movement of the orbital ellipses was 43 seconds of arc per century, an amount ensured to be correct to within a few seconds of arc. This effect ean be explained by means of classical mechanics only on the assumption of hypotheses which have little probability, and which were devised solely for this purpose.

On the basis of the general theory of relativity, it is found that the ellipse of every planet round the sun must necessarily rotate in the manner indicated above; that for all the planets, with the exception of Mercury, this rotation is too small to be detected with the delicacy of observation possible at the present time; but that in the case of Mercury it must amount to 43 seconds of arc per century, a result which is strictly in agreement with observation.

THIS result, the deflection of light mentioned above, and the shift of the lines of the sun's spectrum towards the red, are the three great experimental confirmations of Einstdn's general theory.

It may help the reader to grasp the central idea of Einstein's general theory if it be put in the following way. The natural motion of a body, left to itself, is, in Euclidean space, motion in a straight line and with a constant velocity. Now the planets do not move in straight lines with uniform velocity. Why? Newton said because there is a force of gravitation emanating from the sun and pulling them out of the straight line. Einstein says No, there is no force of gravitation at all. The planets do not move in straight lines because they are not moving in a Euclidean space, at all, but in a non-Euclidean space, where their actual motions are their natural motions. And his general conditions for this non-Euclidean space are what he calls the law of gravitation. His law of gravitation, therefore, is not the law of a force; it is a set of geometrical conditions. As a matter of fact, Einstein does not need the notion of 'force' at all.

In the last part of his book Einstein deals with his notion of a finite universe. We are accustomed to think of the universe as consisting of matter (in the form of stars) distributed pretty uniformly throughout infinite space. It can be shown that, on Newton's law of gravitation, such a universe is impossible. The gravitational force would be infinite. And there are grave objections to such a universe also on relativity theory. Einstein therefore supposes that our universe is finite. But, although finite, it is unbounded. He illustrates the idea by asking us to consider perfectly flat creatures living on the surface of a sphere. Such creatures could wander forward on this sphere for ever without meeting any boundary. Nevertheless their space, that is the area of their sphere, is of finite size. Analogously, the mathematics of a sort of three-dimensional spherical surface can be worked out. It will be of finite size but it will have no boundaries. Einstein supposes that the space we live in is of this kind.

We can get a rough idea of the size of this universe. A ray of light would go all round this spherical universe in about one thousand million years. Light sent out a thousand million years ago would come back to the place it started from and, if it had not become too scattered by passing through gravitational fields en route, would unite again in a focus at that point. It may be, therefore, that some of the stars we see are really ghosts--the images of stars that were there a thousand million years ago, but which have since moved on to other parts of the universe, or which have even become extinct or perished in a collision.

But this part of Einstein's theory, although it solves certain difficulties, must not be taken as on the same level of evidence as the rest of his theory. The rest of the theory may fairly be regarded as proved. The theory of the finite universe is still only a speculation. Even as it stands, however, the theory has been justly described by a great mathematician as 'the greatest synthetic achievement of the human mind.'

J W N Sullivan

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Was Einstein Right? (Putting general relativity to the test). Clifford M Will 1988.

Table of Contents

No doubt a much more up-to-date assessment could be readily found on the Internet. This editor just happens to have these old notes. Besides that, I vaguely recall a Centenary celebration of the general theory, on television. I believe it was the very year that gravity waves were at last detected. These being a prediction of the general theory, and perhaps its greatest triumph.

I believe the scarcity of experimental verifications has been well and truly reversed, since this book by Clifford Will was written. Einstein himself said he would feel sorry for the Lord, if such a beautiful theory were proved wrong.

According to the general relativity centenary TV program, Einstein was giving lectures on his new theory, and correcting himself as he went along. What is more, he had attracted the interest of David Hilbert, to work on the theory. One of the greatest mathematicians in the world, who set his colleagues a project of unsolved questions, was breathing down his neck! In the opinion of the program makers, against the odds, Einstein completed his calculations.

Space-time is curved, as the gravitational red shift experiment is really testing for, rather than general relativity as a theory in particular.

1889 and 1908, Eotvos experiments showed that mass (or inertial mass) and weight (or gravitational mass) of different materials is the same (to a few parts in a billion). That is, different bodies suffer the same acceleration in a gravitational field.

The nineteen sixties and seventies saw updated versions by Dicke; Braginsky: bodies of different composition fall towards the sun with the same acceleration.

Discredited rival theories to general relativity still agreed on the principle of equivalence; not on the field equations, to determine how much curvature there is; the equivalence principle telling how matter responds to it: freely falling bodies move along geodesics.

A clock rate can be blue-shifted or red-shifted (speeded up or slowed down with shorter or longer wave-lengths of light). A clock emits or receives light. A clock is a device that performs some physical activity repetitively at a well-defined constant; e.g. the mechanical sweep of a second-hand, a strobe light (whose flashes as well as being, say, blue-shifted would appear to the observer at the bottom of a tower, to arrive more quickly, so he would argue the clock at the top of the tower was ticking faster than his ground clock: the clock rate blue-shifted).

Atomic clocks are based on the waves of an electro-magnetic signal: the emission of light with a constant stable well-defined frequency. Gravitational red shift affects all clocks equally whether mechanical, biological or atomic.

To get gravitational red shift, the clocks, emiter and receiver (absorber e.g. of gamma rays) must be separated in height. Therefore they must be connected by a signal but this makes it impossible to determine whether the shift is due to the clocks or the signal. The effective gravitational red shift without intervening signal can be infered using atomic clocks and jet aircraft, as in 1976, by Robert Vessot and Martin Levine with NASA. In 1960, the Pound and Rebka experiment was the first successful measurement.

The time-dimension in a space-time diagram is virtually straight with time as a unit of length, multiplied by C the speed of light (one second of time being approximately