Total Field Theory

FROM NEWTON TO EINSTEIN:
The Gravitational Alternative

*******************

San Francisco City College, Small Theater Auditorium.

Greenpeace Benefit

(Expanded edition)

* * * * * * * * *

October 1976

"Not long ago I was kindly admonished that the subject of this evenings' discussion - which is Einstein's 4-Dimensional Space-Time Continuum - is far too technically specialized and complicated for the majority of most otherwise knowledgeable persons: that, if I ever attempted to lecture it to an open audience, any such attempt would inevitably fail and moreover, quite possibly bore people to sleep. Such talk does not discourage me however; permit me to tell you why.

There's bound to be a few people here tonight, who need to catch up on some sleep. Of the few well intended critics who have made these heavy lidded predictions, none have read my book or attended my lectures. It's their jobs they sleep on. Such relaxed and yawning, recreationally preoccupied forecasts faithfully represent the fashionable response to any proposal that the 4-D space-time continuum can be identified or substantially communicated: without mathematics. Like gravity, the 4th Dimension is formally assigned to non-mathematical incomprehensibility. Hence, any suggestion that the fourth dimension is non-mathematically approachable is immediately evaluated by the knowing as the mark of a rank scientific novice - someone who does not know enough mathematics to understand that the 4th dimension is comprehensively accessible, only to those who do (know enough mathematics). These foregone determinations stem from the fact that there is not even the slightest history of any unsuccessful attempts to non-mathematically identify the 4th Dimension, let alone any successful one. No such accomplishments are anticipated.

The 4th Dimension is correctly equated with time and motion, while formally and consistently relegated to be non-mathematically incomprehensible and even unimaginable. An abstraction on the face of a speculative wrist watch - in those 3-dimensionally timeless words (George Gamow, GRAVITY)...

The reason why none of my somnambulant critics - most of them confidentially vanquished physicists and/or Big Bang advocates- (explosive beginners and entropic enders) have troubled themselves with reading or attending my lectures. Hopefully, this accounts for all of the more serious and important matters; so that we may address ourselves, if you will, to all of this allegory insensibility, idle chatter, inane scrawl and/or ranting bombast about gravity being the 4th Dimension.

Gravity is the 4^th dimension.

"That is an unprecedented statement. The only thing gravity and the 4th Dimension are presently recognized to have in common as far as academic physics is concerned, is what is not known about them. Specifically: neither gravity nor the 4th Dimension has ever been non mathematically identified. It is acknowledged that they exist, it is mathematically and elaborately described what they do, but it is not and it has never been comprehended what they are.

On the other hand, it is my intention to generate and popularize only one particularly prominent and inevitable question around the unprecedented statement that Gravity Is the 4th Dimension, and that question is:

Didn't we know that before? And, if not: why not?

If the statement, 'Gravity is the 4th Dimension' is incorrect, why has it never been disqualified? No one is being asked, neither of course is anyone obliged to accept or believe that gravity is the 4th Dimension. When any one at any time finds this statement seriously credible it is not because I said so, or due to the introduction of a lot of new or ponderous ideas.

The statement is found credible when it is revealed and recognized as the inevitable and quite overwhelming import of a wealth of simple, fundamental and familiar facts. Well known but hitherto unrelated facts, which, when related, reveal quite unexpected but equally unavoidable, imminent and overdue; still remarkably unrecognized (and as we shall see, stubbornly and apocryphally denied) conclusions.

Terra Incognita, revisited and Re-Cognized

(Here be unslayable Old World dragons):

As a place to start, I will cite three facts; the first of which is an excerpt concerning gravity, which is extracted verbatim from the 2nd and 3rd pages of Isaac Newton's three page (non-mathematical) Preface to The PRINCIPIA MATHEMATICA.

Then, we will review Albert Einstein's' definition of gravity from his GENERAL PRINCIPLE OF RELATIVITY.

Thirdly, we will review the mathematical-geometric definition of dimensions, to determine if and how the definition for physical dimensions relates to Einstein's' renowned 4th Dimension. We will summarily consider if and how the 4th Dimension relates to what Newton and Einstein have independently and formally offered, in the PRINCIPIA MATHEMATICA and the GENERAL PRINCIPLE OF RELATIVITY respectively, as their two centuries divided considerations of the identity of gravity. Respectfully submitted here, that if you will simply permit presentation of the above subjects, the non-mathematical identity of gravity, and the non-mathematical identity of the 4th Dimension, will be revealed and proven to fulfill the engagement, comprehension and agreement of the majority of intellectual facilities present here this evening. I submit furthermore that this proof will self-explicitly and irrevocably include the statements:

GRAVITY IS THE 4TH DIMENSION. ELECTRICITY IS THE 5th DIMENSION. MAGNETISM IS THE 6th DIMENSION; proceeding from there, to find the floundering Big Bang Theory an assemblage of pilfered principles alleged to be abandoned and of no further use to the advancement of science.

Finally, I respectfully submit that the unfolding all of the above proposals will be accomplished in the next approximately seventy minutes (discourse time actual) or less (This dissertation is amplified from the original presentation).

The forthcoming excerpt from Newton's Preface to The PRINCIPIA MATHEMATICA is precluded here with the clarification that, even today, gravity is colloquially thought-of and popularly accepted definitively as a pulling force of attraction; originating at the centers of individual material objects (particles - charges; systems of same); the force of which increases proportionately with increasing mass values. This definition has always been a categorical presumption applied to the unknown identity of gravity, for the sake of convenience and for apparent lack of any other alternative definition.

Newton himself understandably had difficulty accepting the existence of an 'invisible force' which he describes as 'occult', having the power to move apples and planets. Above all, he (very specifically) found - proved - the large force of the orbiting moon directly linked to the same mysterious force applying to the apple's inspiration for falling, above and upon the earth's surface - the aquatic, atmospheric and terrestrial tides; the planets orbiting the sun.

It was formerly thought that gravitational forces acting on earth were much different than forces acting elsewhere in the larger realm of solar system and universe. Newton, established for the first time, that it - the universal realms of the large and small - is all connected by a singular, commonly acting, unidentified invisible force. That is the gist of Newton's discovery - the proven extrapolation of the same force that causes relatively miniscule apples to fall, also causing the orbiting of the relatively enormous planets.

(“The ‘thump’ of a great apple, in the stillness of a crisp October morn - motivated only by the mere necessity of perfect ripeness.”

- Hawthorne.)

Newton, finally acknowledged the conditional existence of gravity; only because his own newly invented calculus confirmed that, indeed the same force that motivationally generates falling apples, does likewise generate and sustain the orbits of planets. Yet, as we are about to be reminded, Newton took great care to point out that he did not know or purport to know the identity of gravity, and that his mathematical address to gravity is not concerned with or dependent upon its causal identity, or, its direction...

Newton’s thoughts on ‘the occult (pre ‘Field Physics' recognized) force (Maxwell’s Electromagnetic Field, omni-directionally projecting <in the pattern of a spider-web> at light speed out of all material entities)’:

Special effects by Austin P. Torney

“It is inconceivable, that inanimate brute matter should, without the mediation of something else, which is not material, operate upon, and affect other matter without mutual contact. “And this is one reason why I desired that you would not ascribe inanimate gravity to me. That gravity should be innate, inherent, and essential to matter , so that one body may act upon another, at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty for thinking, can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers.”

- Isaac Newton, On Gravity.

As we shall see, the popular term 'Newtonian concept of attraction (a pulling force)', as applied to gravity, was never unconditionally endorsed by Newton. The concept of gravity as 'a pulling force of attraction' remains a speculative though understandably popular term, coined by Newton's beneficiaries. All of this is to say that the conceptualization of gravity as any sort of pulling force of attraction was not Newton's resolute conceptual or by any means exclusive definition of gravity. Allow the derivation of this last statement to be further qualified:

I wish to cite at this time what is to say the least, a most interesting alternative concept concerning the identity of (what Newton was always careful to call 'universal') gravity. An otherwise completely ignored statement which might even be correctly categorized as 'obscure', or 'inconsequential'. Were it not for the fact that this statement is made by Sir Isaac Newton. And, were it not for the fact that this statement is included in the very (3 page, non-mathematical) Preface to The PRINCIPIA MATHEMATICA.

Special effects by Austin P. Torney

From the beginning of the 1st to the end of the 2nd page of Newton's three page Preface to The PRINCIPIA MATHEMATICA, Newton is discussing the motions of falling objects and orbiting planets; by way of his applied mathematical descriptions of the effects of the force of gravity. At this time, Newton offers the following statement about what causes the gravitationally induced motions of planets & apples, quote:

Last sentence of first paragraph, verbatim, translated to English from the Latin…

“For I am induced by many reasons to suspect that they may all depend on certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other and cohere in regular figures or are mutually repelled and recede from each other, which forces, being unknown, philosophers have hitherto attempted the search of Nature in vain.”

That quote and its extraction will henceforth be referred to here, as THE GRAVITATIONAL ALTERNATIVE. Not my gravitational alternative; Newton's Gravitational Alternative to be exact. I repeat the quote (of particles and systems-of-particles: of matter), 'are either mutually impelled towards each other and cohere in regular figures (orbits; juxtapositions), or, are mutually repelled and recede from each other.'

It implies directly and categorically, that gravity may in fact be the opposite of the universally considered impelling or 'pulling force of attraction'; that is to say, Isaac Newton and his formal definitions, directly and resolutely suggest that gravity may in fact be a repelling or pushing force.

It is difficult to over dramatize the very existence of this statement, its author, and especially its contextual implications. It categorically allows that everything Newton mathematically confirms and describes in The PRINCIPIA MATHEMATICA - from orbiting planets, falling apples, aquatic, terrestrial, and atmospheric tides - all the large and small phenomena of gravity - is caused by one of two kinds of forces: the conventionally considered impelling or pulling force of attraction, or, its exact opposite, a repelling/ pushing force. That is fact #1.

Fact #1 evokes at least one question: Allowing possible advantage in Newton's Gravitational Alternative that gravity may in fact be a repelling (pushing) force rather than an impelling (pulling) force, how might any such advantage be experienced and applied? That question and its derivation might still be deemed obscure and inconsequential, if its direct unequivocal answer did not exist, most profoundly, at the heart-foundation of the latest and most advanced generalized theory of gravity in the history of Physical Science. That being Albert Einstein's GENERAL THEORY OF RELATIVITY.

In the first quarter of this century, Albert Einstein, in observing the already well known inversely proportional equivalence of gravitational and inertial mass values (which will be explained, shortly), described this equivalence as: 'an astonishing coincidence', and then applied the cause of his astonishment to the monumental task of formulating an unprecedented theoretical generalization concerning the identity of gravity. That, being none other than the General Principle Of Relativity; which principle is quite literally the foundation upon which rests Einstein's entire General Theory of Relativity. The most advanced statement about gravity, to date.

The General Principle is also misnomered as the 'Equivalence Hypothesis', or, more appropriately, 'The Principle Of Equivalence', which states: 'There is no way to distinguish the effects produced by the inertial force of acceleration (a pushing/repelling force) from the effects produced by gravitational force (assumed to be a 'pulling/impelling force: identity unknown').

For those already familiar with the General Principle of Relativity that is clear enough. But, to the uninitiated it may sound a bit complicated. Fortunately, there is a simple and excellent demonstration which clarifies the import of this statement. The explanation originally used by Einstein to point out the meaning and implications of the GENERAL THEORY OF RELATIVITY, is since then often utilized by relativist writers and physicists for the same reason. The explanation spoken of here is popularly termed 'the elevator analogy'.

Special effects by Austin P. Torney

Illustrations A & B

An elevator car is depicted as falling down the shaft of a very high building after having parted its restraining cables. A group of human passengers perform experiments. They hold out objects and release their grip on them - the objects (cannonballs, bb-shots, pound of butter, wristwatch, etc.) remain suspended in midair; they do not accelerate downward. Because, all of the released objects are falling within and along-with the elevator and its passengers at 32 ft. per-second-per-second (16 ft per second, squared); in accordance with Newton's laws of gravitation (on or of, earth).

The observers in the elevator are unaware of their predicament. They understand and explain the suspension of objects and themselves in mid-air, by presuming they are outside the gravitational influence of the earth, and logically conclude that they are 'free-floating' in deep outer space where there is no significantly measurable force of gravity at all (a *macrocosmic weak force - the opposite of *microcosmic strong nuclear binding force; * generally misperceived as being unrelated; two different kinds of forces. The record proves they are qualitatively the same force, quantitatively occurring in two different - large and small/ tenuously thin and densely compacted - places/coordinate systems)... Refer to Illustration A

It is an apparently sensible conclusion - that they are in a coordinate system which is free-floating in deep space. In leaping from the floor, they float smoothly toward the ceiling with a velocity directly proportional to the vigor of their individual leaps. If/when they push a suspended/floating object in any direction, that object continues to move in a straight line with uniform velocity, until it strikes the wall of the elevator car. Galileo's and Newton's Laws Of Inertia prevail exclusive of gravity, and are obeyed.

Newton's Laws of Gravity are pointless to consider in the elevator at this time; because there are no significantly measurable gravitational effects in it, to influence its passengers and their experiments. The environment of the interior elevator is therefore purely and exclusively an inertial system, destitute of gravity and gravitational effects.

THERE IS NO WAY FOR THE OBSERVERS INSIDE THE ELEVATOR TO DETERMINE WHETHER THEY ARE FALLING IN A GRAVITATIONAL FIELD (as they actually are), OR SIMPLY 'FREE-FLOATING' IN THE VOID OF DEEP SPACE, FREE OF ANY GRAVITATIONAL INFLUENCE WHATSOEVER.

Then Einstein alters the situation of the elevator and its passengers. (Refer to Illustration B) This time the experimenting passengers are still in the elevator, but they actually are in the void of deep space, far away from any appreciable gravitational influence. A cable is attached to the roof of the elevator car and an arbitrary force winches-in the cable at 32 feet per-second squared (the descent rate of free falling objects on earth). The elevator is therefore accelerating 'upward' through space (any direction in which the elevator car happens to be pulled by the cable, is 'upward' relative to the passengers within it). Again, the observers within the elevator have no idea where they are, and again they evaluate their situation by performing experiments. Their feet now rest firmly on the floor; they now have their 'normal' (as experienced on earth) body weight to support. Confirmed by scaled weight measurement (The observers are actually measuring and obtaining inert mass values; not realizing they are not measuring gravitational mass values): their coordinate system having found the two values identical under the accelerating circumstances; indistinguishable from each other.

Inertial & Gravitational Mass Values; which are not supposed to have anything to do with each other, are likewise indistinguishable at this *juncture; which Einstein called *’astonishing’ - the *coincidental confluence of two different methods of measuring and defining mass value; arriving at exactly the same - unrelated coordinates. *A pound of butter offers exactly a pound of resistance to acceleration: when the acceleration exactly - and 'coincidentally' - equals the descent rate of objects in free-fall @ 32' per second squared, on earth.

When the passenger’s in Einstein’s elevator jump, they do not float to the ceiling because the floor is constantly accelerating upward beneath them at the descent-rate for free-falling objects on earth. When the observers and various objects are weighed on a standard scale within the elevator at this time, they all have their 'normal' earth-weight (heavy mass value ); due to their resistance - generated by physical matter - negative inertia: the tendency of all bodies at rest to remain at rest and offer resistance to outside forces acting upon them, including non-uniform motion. That is to say: inert mass value , opposing the acceleration (non-uniform motion) of the elevator floor.

If the elevator were accelerating at less than 32 ft. per-second, the objects and observers would weigh correspondingly less than their normal earth weight. If the elevator were accelerating at more than 32 ft. per-second, the objects and observers would weigh correspondingly more than their normal earth weight. When the observers in the test elevator release objects from their grip, the objects appear to descend vertically - 'fall'/accelerate-'downward' @ 32 ft. per-second (per second). When objects are tossed or pushed in a horizontal direction, those objects do not move in a straight line in accordance with the laws of inertia; instead the paths of the tossed objects - due to the acceleration of the elevator car - describe a parabolic curve; descending vertically at 32 feet per second squared, relative to the floor; in accordance with the laws of gravitation.

The observers remain unaware that their room is accelerating (ascending ever-faster) through deep space. They understandably conclude from direct experience and experimentation, that they are situated in quite ordinary circumstances in a windowless room on earth, influenced by conventional gravity.

THERE IS NO WAY FOR THE OBSERVERS TO DETERMINE FROM WITHIN THE ELEVATOR (coordinate system) WHETHER THEY ARE AT REST IN THE EARTH'S GRAVITATIONAL FIELD; WHERE ALL OBJECTS ARE 'PULLED' DOWNWARD @ 32 ft. per-second BY GRAVITY, or: WHETHER THEY ARE ACCELERATING IN AN INERTIAL SYSTEM (which they are in this case, @ 32 ft. per-second squared): WHERE THERE IS NO GRAVITY WHATSOEVER.

From his imaginative and now renowned 'elevator analogy', Einstein formulated a conclusion of unprecedented theoretical importance; that being: The General Principle of Relativity: THERE IS NO WAY TO DISTINGUISH THE MOTION PRODUCED BY INERTIAL FORCES (acceleration/ centrifugal and centripetal force), FROM MOTION PRODUCED BY GRAVITATIONAL FORCE. This is the General Principle of Relativity. Fact #2.

It borders on being a statement of the obvious, but we are about to see that sometimes it isn't so obvious at all. That people in general everywhere, actively refuse to recognize it, altogether - the greatest problem - and the most importantly unrecognized solution - in science, since 1916.

It is particularly noteworthy, because the Classical and Contemporary popular concept of UNIVERSAL GRAVITATION remains, that is to say, continues to be, a 'pulling force of attraction'. Yet, here we find Contemporary Theoretical Physics - specifically Einstein's General Theory of Relativity - equating gravity with acceleration as - and which is - a 'pushing or repelling force'.

That is to say, in 1686, Newton categorically and formally allowed that gravity 'may be' in fact, a repelling force. Then, in 1916, we have Einstein's General Principle of Relativity equating gravity with acceleration, which is, once again, a repelling force. What I call: Newton's Gravitational Alternative - and Einstein's General Theory; on the same table. Historically 220 years apart. Lightning struck in the same place - ominously joined, since the resiliently unrecognized and stubbornly unattended opportunity afforded, in The (Einstein's) General Theory, of 1916.

Isaac's apple in Albert's elevator

F=GMM
____________

r squared

Again, this elicits a question: If we are to seriously consider gravity as a repelling force, how might it be meaningfully construed as such? That is to say, how do we apply Newton's Gravitational Alternative, combined with Einstein's General Principle, to correspond with the anthropomorphic Gravitational Experience?

We will return to this question and its answer by way of a brief comparative investigation of what relationship if any exists between Einstein's concept of gravity, derived from the General Theory of Relativity, and Einstein's concept of the 4th Dimension, which is also, as we shall see, more than coincidentally derived from the General Theory of Relativity.

A brief review the definition of dimensions as applied to the three recognized dimensions of space, follows. Let it be qualified firstly that, in colloquial language, the term 'dimensions' may be correctly applied to any number of descriptions, such as 'dimensions' of music or thought or color for example. But, in physics there is only one definition for dimensions, which we will reconsider, immediately after the following statement concerning contemporary academic physics and its representative posturing toward the subject of the (Einstein's) allegedly 'acknowledged' *4th Dimension (*of 'time and motion'). Mathematicians and physicists are of the consensus agreement that, when the definition of the 4th Dimension is applied to Reality-At-Large as Einstein proved it is in fact, then one automatically departs the realm of conscious experience and comprehensibility. This is the reason for example, that in one renowned case the reputedly omniscient, ever-present yet conceptually elusive 4th Dimension was professionally referenced as, 'a mathematical abstraction on anyone's wrist-watch'.

This is also the reason the 4th Dimension is a favorite conscript among science fiction writers and metaphysicists. There is unflappable security in speculations and improvisations of a subject, about which there is no recognized non-mathematical comprehension; no recognized absolutes or authorities (when the allegory expert falsely emerges everywhere, waxing of discovery, while claiming his subject is functionally unfindable). A haven for befuddled academic refugees: a jingoistic proving ground that endorses (and/or ambivalently disqualifies) everything and/or anything; according to the needs of the sometimes desperately ignorant, pretentious, scientifically name-saked 'authorities' and historical revisionists. Innocent ignorance is exonerated in this consideration.

No discourse on the 4th Dimension, whether physics or science fiction, would be complete without directly suggesting that it is 'unimaginable', or, 'incomprehensible', or 'something else', or 'someplace else' ('far out').

Yet, it is agreed that the 4th Dimension is 'time & motion'; somehow integrally combined with the 3 recognized Dimensions of Space; existing always and everywhere. Therefore we need very little imagination or faith in Einstein, to know that we are perpetually witnessing and experiencing the 4th Dimension, in simply being conscious of the reality we are part of; by which we are constantly surrounded. We can correctly go one step further. We can be confident that the 4th Dimension has been, and continues to be overlooked. That is, we can know that some very fundamental constituent or phenomenon of reality - with which we are all familiar, but which has yet to be recognized, is the 4th Dimension - the 4-Dimensional space-time continuum to be exact.

Today's physical scientists tell us that 'the 4th Dimension is time and motion'. They say this because they know Einstein proved it mathematically. But it is not a non-mathematically satisfactory answer, because it does not contribute to any further comprehension of what the 4th Dimension is, relative to the colloquial 3-Dimensional Experience. Time and Motion are measurable and comprehensible in Three Dimensions. Why not in 4? What is it about proven and measured 4-dimensional reality that has not been recognized? Why has it not been recognized?

NOTE:
All of the below authorities proclaim that the 4th Dimension is non-mathematically 'incomprehensible', even 'unimaginable'.

Readers are cautioned against concluding that these authorities are right, and encouraged to read the accompanying discourse, and draw their own non-mathematically facilitated conclusions.

"In 1916, Albert Einstein published his General Relativity, a mathematical theory of gravitation which replaced Newtonian concepts with abstractions so difficult that it took a decade even for most mathematicians to grasp them. The essence of Einstein's theory was that the presence of matter distorts space and makes it curve. The concept of space curvature stemmed from many dimensional, non-straight-line geometry created abstractly through equations. Just as a surface can curve in ordinary 3-Dimensional space, so in non-Euclidean geometry a 3-Dimensional space can itself curve in 4-dimensional space. No one can visualize such a curved space because humanity is not 4-Dimensional..."
- LIFE Science Library, THE UNIVERSE, p. 179

"When events occur in 3-Dimensional Space it is not possible to draw an actual graph of 4-Dimensional space-time, but mathematicians have ways of handling such graphs without actually drawing them."
- Martin Gardner, RELATIVITY FOR THE MILLION, p. 98

"The 4-Dimensional world of relativistic physics is the world where force and matter are unified; where matter can appear as discontinuous particles or as a continuous field. In these cases, however, we can no longer visualize the unity very well. Physicists can 'experience' the 4-Dimensional space-time world throughout the abstract mathematical formalism of their theories, but their visual imaginations - like everybody else's - is limited to the 3-Dimensional world of the senses. Our language and thought patterns have evolved in this 3-Dimensional world and therefore we find it extremely hard to deal with the 4-Dimensional reality of Relativistic Physics."
- Fritjov Capra, THE TAO OF PHYSICS, P 150

"This concept is very difficult to visualize. It is a consequence of the 4-Dimensional space-time character of the sub-atomic world and neither our intuition nor our language can deal with this image very well."
- Capra, THE TAO OF PHYSICS, p. 80

"In the General Theory of Relativity, the framework of the Special Theory is extended to include gravity. The effect of gravity, according to General Relativity, is to make space-time curved. This, again, is extremely hard to imagine. We can easily imagine a 3-Dimensionally curved surface, such as the surface of an egg. The meaning of the word 'curvature' for 2-Dimensional curved surfaces is thus quite clear; but when it comes to 3-Dimensional space - let alone 4-Dimensional space-time - our imagination abandons us. Since we cannot look at 3-Dimensional space 'from outside', we cannot imagine how it could be 'bent' in some direction."
- Ibid, p. 173

"The reader is cautioned against concluding that time is an additional physical dimension in the sense that it can be seen and felt like a material object. No one in our universe can see in 4 Dimensions or more because of the way our universe is constructed."
- James A. Coleman, RELATIVITY FOR THE LAYMAN, p. 69