Materialism versus idealism: Einstein's relativity PART TWO

Materialism versus idealism: Einstein's relativity PART TWO 

BY MARTIN ZARROP, from Bulletin Vol. 7 No. 18

LET US suppose that you awake one morning and find yourself inside a closed box. In order to gain information about the motion of the box, you perform a simple experiment. 

Take two coins (of different denominations) from your pocket, hold them apart at arm’s length and release them. 

If the coins remain motionless, what conclusions can be drawn? 

The most obvious one - probably brought to mind by seeing TV pictures of the Apollo astronauts - is that the box has been transported to some region of outer space, far distant from any massive object. 

In other words, we may conclude that gravity is absent and that the coins, therefore, continue to "float." 

However, we may alternatively draw the conclusion that the box and its contents are falling freely in a gravitational field. As all objects fall with the same acceleration, the simple experiment that our observer has performed would yield the same result. 

Therefore the principle of equivalence does not allow the observer to differentiate immediately between "free fall" under gravity and no gravity at all. 

We have to add the word "immediately" for the following reason. 

If the box was falling in the earth’s gravitational field, then the coins would move towards each other as the earth’s centre approached. 

This is because the "vertical" lines traced out by falling bodies converge at the centre. 

Such an effect would not appear for our "outer-space" observer (except a negligible one due to small gravitational attraction of the coins for each other). 

Therefore the free-falling observer only "eliminates" the gravitational field "locally" - but the field itself maintains a real existence, gravity is a real force. 

We can draw a parallel with our "everyday" view of the earth itself. We can assume for most purposes that the surface in our immediate vicinity is flat, wherever we may be. However, we know that, overall, the earth is (approximately) spherical. 

In other words, we can only "eliminate" gravity locally, just as we can only "eliminate" the curvature of the earth locally. Neither the "roundness" of a sphere nor gravity are illusory. 

Let us now return to our "general" observer, enjoying his ride on the big dipper. 

If he is completey enclosed and unable to watch the scenery go by or feel the wind, he may interpret his sensations in terms of a changing force of gravity. 

At the top of a loop he feels lighter, at the bottom he feels heavier. 

As he travels round a bend, gravity appears to change direction. Close your eyes next time you are on a big dipper and try it! 

Here we have the box experiment in reverse - instead of "eliminating" gravity, we appear to "create" it. 

We have therefore reached the position at which we can say that an observer executing the most complex acrobatics can be considered equivalent to a stationery observer being influenced by some complex gravitational force. 

To take a simple case: it has been proposed by space scientists to construct space stations in the form of rotating wheels. 

The rotation creates a "force" and all bodies, including the astronauts, are held to the rim of the wheel as if it were motionless and a real gravitational field existed. For the astronauts, "down" is "away from the hub." 

The equivalence principle has therefore eliminated the need for special observers. In fact, every observer can be considered "special" if we are allowed to "manipulate" gravity. 

Einstein’s general theory of relativity expresses this mathematically - if there are no special observers, then the form of the laws of nature must be the same for every observer.

In this way, the equivalence principle is built into natural law from the start and therefore so is gravity. 

For Einstein this was the strength of his theory: 

"The possibility of explaining the numerical equality of inertia and gravitation by the unity of their nature gives to the general theory of relativity, according to my conviction, such a superiority over the conceptions of classical [i.e. Newtonian] mechanics, that all the difficulties encountered in development must be considered as small in comparison." (‘Meaning of Relativity’, p. 57.) 

Difficulties there certainly were. Einstein’s equations are complex and their solution involves lengthy mathematical calculations in the few cases where they can be solved.

However, two things were essential. 

Firstly that, where the gravitational field is weak, we must be able to get back (as an approximation) to Newton’s theory of gravitation and, secondly, that the new theory should predict new qualities of matter, detectable in practice. 

Einstein himself verified that his theory "contained" that of Newton and also "transcended" it. It reveals a real unity of inertia and motivity. 

Whereas Newton has to express quite separately the force of gravity and the motion of matter acted on by gravity, they appear as inseparable in Einstein’s theory. 

His experimental predictions are far more difficult to check. Quantitative differences with Newton are infinitesimally small and require highly refined techniques to detect.

Probably the most famous prediction concerned the planet Mercury, the nearest to the sun. Astronomers could not account completely for Mercury’s orbit even when the disturbances caused by the gravitational fields of all the known planets were included. 

The discrepancy was extremely small but detectable. The orbit of Mercury was slowly rotating round the sun, taking about three million years for each revolution. 

Perhaps some unknown planet, situated between Mercury and the sun was the cause? Calculations were made and the necessary properties of such a body were estimated, but the astronomers. could detect nothing. Vulcan, the new planet, didn’t exist. 

Einstein’s theory, applied to the movement of a planet round the sun, predicted the rotation as a new quality of planetary motion. 

The "discrepancy" was a necessary part of Mercury’s motion. Quantitatively, the agreement between observation and theoretical prediction was almost 100 per cent! 

Only two other predictions have been checkable experimentally, with satisfactory results for Einstein. 

The regions where Einstein’s theory will be decisively tested and its limits discovered will probably be where the most powerful gravitational fields occur - the interior of stars -  unless we are able to create such fields in the laboratory. 

For a theory so little tested in the laboratory, its persistence over 55 years stands as a tribute to its firm theoretical foundations. 

ON AN astronomical scale, gravity is the dominant force. 

Although it is extremely weak in comparison with those forces which come into play within the atom (and is therefore neglected in fundamental particle theory), it far "outdistances" the atomic forces. 

While the latter are effective over distances of about a millionth of a centimetre, the gravitational pull of a planet such as the Earth can be considered to extend millions of miles into space and, in fact, never vanishes completely. 

It decides whether or not a body can "hold" an atmosphere (the moon can’t), just as surely as it governs the motion of the planets round the sun at distances of thousands of mil- lions of miles. 

Astronomical observation also supports the conclusion that gravitational attraction is responsible for the rotation of certain neighbouring stars around each other and that, therefore, gravity is not something peculiar to our small corner of the universe.

The gravitational field is an all-pervading form of’ "matter in motion," which suggests that any theory of gravitation, including both Einstein’s and Newton’s, should lead us to certain conclusions about the structure of the physical universe as a whole. 

However, we must insist that Einstein’s general-relativity is not a final, all-embracing theory that can tell us "everything" about the universe, all the "fine detail." 

"Holes"

In fact, being a theory of gravitation, even solid matter, as well as the electromagnetic field, can be taken inte account only as "external" factors, introduced artificially. Solid matter, insofar as it appears naturally, does so as ‘holes’ in the gravitational field, the content of the ‘holes’ being open to conjecture, as far as relativity is concerned. 

Astronomical observation, particularly with the use of the radio-telescope, has given us a fairly detailed picture of the observable universe. 

On this scale, the distances involved are so immense that it is necessary to deal in lightyears rather than miles. 

As light travels about six million million miles in a year, we can begin to grasp the "smallness" of our own solar system. 

The moon is a mere one and-a-third light-seconds away while a trifling distance of eight light-minutes separates us from the sun. 

At the speed of light you can be out of the solar system in 5 1/2 hours! 

The nearest star (not visible from the northern hemisphere) is Proxima Centauri and at a distance of 4.2 light-years (l.y.) it is about a million times further away from us than the nearest planet. 

However, looking up into the sky, it is apparent that the stars do not form a uniform pattern. 

On a clear moonless night, the Milky Way - a great belt of mainly faint stars - is seen to stretch trom horizon to horizon. 

In fact, it forms part of a complete circle dividing the sky into two equal halves.

It has been concluded that our sun is part of a system of 200 billion stars - the galaxy - shaped like a disk or a watch. 

The disk is about 20,000 Ly. across and 1,000 ly. thick. 

When we gaze at the Milky Way, we are seeing the galaxy "edge-on." 

It has been calculated that our sun is very close to the central plane of the galaxy and about halfway from its centre to the rim. 

What lies outside the galaxy? If by this we mean concentrations of solid matter, then we will have to travel 1 1/2 million l.y. until we reach ... another galaxy. 

In fact, galaxies (extragalactic nebulae) appear at fairly regular intervals in space at approximately this distance between neighbours.

Astronomers have observed millions of such star-systems with optical and radio tele- scopes that can "see" hundreds of millions of light-years into space. 

It is useful to use a scale model in order to grasp the relative magnitudes of the tremendous distances involved.

- The earth, travelling 1,200 times faster than an express train, makes a journey of 600 million miles around the sun every year.

Let us represent this journey by a pin-head one-sixteenth of an inch in diameter. 

This fixes the scale of our model and shrinks the sun to a speck of dust less than a three-thousandth of an inch in diameter!

The nearest star in the sky must be placed 225 yards away and to contain even the hundred stars nearest to our sun, we must build our model a distance of a mile in every direction. 

Encompass

To encompass our galaxy we need to cover an area considerably larger than the continent of Asia and then travel about 30,000 miles to reach the next galactic system. 

Even on this scale, therefore, we would still have to go some millions of miles to reach the edge of the observable universe. 

The. total ‘number of stars in our model would be comparable to the number of specks of dust in London. 

However, to scale, we need to put the specks about a quarter of a mile apart. 

This gives some idea of how empty space is of solid matter - about equivalent to six specks of dust in Waterloo Station, evenly spaced out! 

It is so low "on the average" that if we take a sphere whose radius stretches from here to the nearest star and fill it with matter at the average density, the total mass of its contents would equal that of only 100 gallons of water, approximately.

This picture is, of course, simplified. 

The "gaps" between the stars and the galaxies contain regions of gas as well as gravitational fields, electromagnetic fields and other radiation. 

One of the problems, for example, which has not yet been resolved is where "cosmic rays" come from - showers of high-energy particles which originate in outer space and find their way to Earth. 

It has also been discovered that the Earth is continually bombarded with intense beams of fundamental particles called neutinos, which are so penetrating and interact so weakly with solid matter that they pass right through the earth without being stopped. 

It requires several lightyears of solid lead to stop a neutrino beam! 

This then is the overall picture of the universe as revealed by experiment; "matter in motion" taking many different forms. 

This raises a number of problems. 

Valid

Why should we assume that Einstein’s theory is valid over such vast distances?

Firstly, because of the long-range nature of the gravitational force and, secondly, because of Mach’s Principle. 

If we are convinced that the inertial properties of a body in the solar system are not determined by "absolute space," but by a necessary interaction with other matter, then we are forced to consider the system of galaxies "as a whole." 

Why? Suppose that inertia was determined only by the distribution of matter in our own galaxy. 

Because the galaxy is disk-shaped and not spherical, we would expect to find different "resistances" to moving a body in the plane of the galaxy from moving it out of this plane. 

No such effect has been detected and we must therefore go further afield - to the system of galaxies, fairly evenly distributed throughout space. 

There is one important property of this system that we haven’t mentioned. 

The universe appears to be expanding, in the sense that the galaxies are moving away from each other. 

Our nearest "neighbours" are receding at about 150 miles per second and the velocity increases with distance. 

If we take a galaxy which is five times further away, it recedes five times as fast and so on. 

Static 

The main difficulty with the attempts at developing a model of the universe during the 19th century was the assumption that the universe was static. 

In particular, this led to the astounding conclusion that if the stars were evenly spread out over the whole of space then, instead of seeing a dark sky at night, we should observe the entire sky burning with the intensity of a star’s surface! 

This ‘paradox’ (due to Olbers, 1826) is resolved once the expansion is taken into account and this was verified experimentally in the 1920s by Hubble and his co-workers.

However, Newtonian theories of the universe (cosmologies) are merely of academic interest, in the sense it is assumed today that Einstein’s work has superseded them.

However, once we try and build an Einsteinian model of the universe we seem to get rather strange results. 

For instance, Einstein’s original static model turned out to be both infinite yet bounded. 

If an observer travelled far enough he could return to his starting point! 

Straight lines somehow become loops - all the assumptions that we hold as ‘obvious’ about geometry are challenged. 

THE WORD ‘geometry’ - at least for those who can recall their school-days - usually conjures up the memory of sitting for long hours, poring over incomprehensible tangles of lines and attempting to prove various theorems which appeared to have little to do with anything. 

The theorems themselves follow from a small number of assumptions (axioms) which were laid down by the Greek mathematician Euclid and form a logically consistent system. 

For the modern geometer (or any pure mathematician) the question of whether these assumptions, or the conclusions that can be drawn from them, have any connection with the real world is unimportant. 

However, Euclid’s work in geometry (literally, "earth measurement") attempted to establish certain "truths" about the structure of the universe. 

For our purpose, the main conclusions of Euclidean geometry are that a straight line is the shortest distance between two points and that two parallel lines never meet. 

Until the advent of Einstein’s general theory of relativity, these truths about the real world were never challenged, even though Lobachevsky in 1826 showed that it was possible to construct other ‘geometries’ by omitting certain of Euclid’s axioms. 

Certainly, Newton took it as real that we live in a "three-dimensional Euclidean space" and, as with his theories of mechanics and gravitation, this assumption holds good providing we remain within certain limits, which we have already discussed. 

We reject absolute space apart from matter and consider space as the quantitative aspect of matter’s extension. 

Fields 

Between material bodies, there exist physical fields (gravitational, electromagnetic, nuclear, etc.) and when we talk about the structure of "space," we are in fact discussing the structure of these fields. 

In other words, we replace Newton’s statement that "absolute space is three-dimensional Euclidean space" by "within certain limits, 3-D Euclidean geometry is an accurate approximation to the real, physical fields."

Cosmic space - the space of Einstein’s general theory - is the quantitative aspect of the gravitational field’s extension. 

It is in this way that geometry and gravitation become linked. 

Space and geometry are no longer part of a fixed background against which matter moves, acted on, by disembodied forces. There is a continuous interaction between material bodies and the gravitational field and Einstein had to develop a geometry which reflected the field’s structure. 

Einstein found it necessary to develop his theory mathematically through a geometry originally developed by Reimann. Because of the intimate connection between space and time (see part I) this geometry is four-dimensional, by which we mean that any point is fixed by four coordinates - three for space and one for time. 

Einstein calls such a point an "event." Minkowski showed in 1908 how 4-D geometry could be used as a framework for the special theory. 

"Nobody has ever noticed a place except at a time," he said, "or a time except at a place." 

In Minkowski’s mathematical world, the universe is stripped to the limit of its physical qualities. All that remains is a space-time skeleton, the four-dimensional bones.

Einstein takes over Minkowski’s method in his general theory. It is at this point that the mathematical vultures descend and, aided by a multitude of god-fearing physicists, attempt to confuse the issue. 

Reality 

The mathematical model becomes the reality and the real world vanishes. 

The physicist Hermann Weyl refers to "the constructive mathematical method of our modern physics, which repudiates 'qualities'." In other words, it is the mathematical symbols (expressing quantities) which are real, while the qualitative aspects of processes are illusory!

Sir James Jeans is even more explicit. He tells us: "The theory of relativity washes away the ether...The so-called electric and magnetic forces, then, are not physical realities...They are not even objective, but are subjective mental constructs" i.e. abstract symbols reflecting...nothing! They are "waves of knowledge"! 

Here we have the usual idealist confusion between the theoretical reflection of reality and reality itself. 

An architect may design a house by drawing its plan and elevation on a (two-dimen sional) sheet of paper, but this cannot replace the real, three-dimensional dwelling! 

In Einstein’s theory, the mathematical model gives us a picture of the real world as a projection into 3-D of a 4-D structure, similar to the relation between the house and the architect’s plan. In this case, it is the "plan" which is real. 

In order to get an idea of what the 4-D picture tells us, consider the surface of a sphere. Suppose that a flat, two-dimensional creature lives on it and has no conception of motion other than along the surface. 

His "world" would be far different from Newton’s and his "geometry" would bear little resemblance to Euclid’s. 

If he moved in a ‘straight line’, he would in fact trace out part of a circle. This is the shortest distance between two points (or geodesic) on a sphere. If he continued along this path, he would return to his starting point! 

Unbounded 

Secondly, parallel lines meet. If two of the flatmen start at the "equator" and move "northwards" (i.e. in parallel directions) along "straight lines," then their paths intersect at the "north pole!" 

Finally, the surface of a sphere is finite but unbounded. It has a measurable area, but our creatures can travel forever without coming to an edge. 

This gives an idea of some of the models of the universe put forward and derived from relativity theory. If we suppose that our sphere is a balloon which is being inflated and represent the galaxies as ink spots evenly spaced on its surface, then our observer (without occupying a special position in his universe) sees the galaxies as receding away from him.

This appears to be close to our own view of the universe. 

However, the limits of the 4-D models are oven to experimental investigation and it is early days yet. 

The limitations of Einstein’s theory have already been discussed. It describes the gravi- tational field alone and in its original form solid matter and electromagnetism had to be introduced artificially. 

In "The Meaning of Relativity," Einstein says: 

"The starting point of the theory was the recognition of the unity of gravitation and inertia (principle of equivalence)... The principle of equivalence, however, does not give any clue as to what may be "the more comprehensive mathematical structure on which to base the treatment of the total field comprising the entire physical reality...The first problem is: how can the field structure be generalized in a natural way?" (pp: 127-128.) 

This search for the "Unified Field Theory" preoccupied Einstein for most of his life -  how to generalize his theory so that physical fields, other than the gravitational field, would be included in a "natural" way. 

However, Einstein admits that (as yet) no physical principle like the equivalence principle is forthcoming on which to base such a generalized theory and that therefore he is looking for a "natural" mathematical extension. 

Weakness 

    This is the basic weakness of all such attempts that have been made. Mathematicians and physicists have constructed models of five (and even more) dimensions to no avail. 

What we have attempted to show throughout these articles is that space, time, mass and ‘energy are quantitative aspects of four mutually related modes of existence of matter - extension, motion, inertia and motivity. 

Insofar as Einstein based his work on this approach, he made giant steps forward. 

His attempts to generalize his theory to include all phenomena came to a dead end..

The fragmentation of science in the 20th century, together with the uneven development of scientific research, made his attempts all the more futile. 

Billions of dollars have been spent on lines of research, particularly into fundamental particles, in the drive for new forms of energy and more powerful weapons. Gravitational theory has remained for the most part of academic interest. 

"If it works use it" - this empirical thinking coupled with massive funds has yielded results up to a point, but now runs into immense difficulties. 

Einstein stands out as the last great theoretical physicist of his generation. Insofar as he proceeded from materialist conceptions - although he was never a Marxist - it is necessary to defend his work against all those who have attempted to obscure this essential core of his earlier theories.