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Newton's Laws



Both Newton and Einstein claimed that gravitational acceleration is independent of the mass or the energy being accelerated. Another idea that Newton and Einstein professed, was the equivalency of inertial mass and gravitational mass. Newton assumed these two mass units were equal without giving a reason for thinking why they should be equal. This disturbed Einstein, he wanted to know the reason why they are equal. Newton also said in the Principia, "We have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power... I have not been able to discover the cause of those properties of gravity from the phenomena, and I frame no hypotheses; for what ever is not deduced from phenomena is to be called an hypothesis; and hypothesis, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy." Mook 148

Einstein did not provide an answer to this question raised by Newton concerning the "cause" of gravity, but he did create a much more accurate model of gravity than did Newton; and, perhaps more significant, Einstein's model is far richer in its consequences. Nevertheless, one is still left with a question that asks: "How is it possible...?" Just as with Newton's model, which leads to action at a distance without a real cause, Einstein's model leaves one with a geometric curvature of space without a cause. Einstein worked till his dyeing day seeking that cause, as well as a theory that would unify the forces of nature, but to no avail. Einstein was not satisfied with Newton's simple acceptance of the principle of equivalence; he devised an idea that was to explain this principle. He claimed the following: -

"In any small region of space, the effects produced by gravitation are the same as those by an acceleration." 141

The following is a modern version of his idea. He devised a laboratory room in a spaceship, remote from any other mass influence, equipped with a rocket motor at the bottom, and the rocket is turned off. Now he turns on the rocket motor; one feels himself pressed down to the floor of the laboratory due to the constant acceleration. A ball thrown up in the room comes down with the same speed as the spaceship, for instance, 32 ft. per sec., per sec.

He now moves the rocket ship to the earth and simply hovers above the ground. Again, a ball thrown up in the room comes down, 32 ft per second, per second. Einstein thus proves, in any small region of space, the effect produced by acceleration is the same as the effect produced by gravity. It was a profound realization in the life of physics at that time; it proved that the inertial charge of mass was equal to the gravitational charge of mass. Nevertheless, no way did it explain what was inertial mass or a cause for the gravity charge. It just maintained that they are equal to one another, thus, providing an unaccountable insight.

Einstein's principle of equivalence began with the qualification: "in any small region of space." This is required for if a rocket ship laboratory room was as wide as the planet above which it hovered, and a ball was released at both ends of the room at some height above the floor, then, due to the force of gravity they would tend to come together as they descended. This is because they would be heading toward the center of the planet, and certainly to the bottom of the room; nevertheless, in an accelerated room the same size away from the planet, they would fall straight down to the floor of the room at both ends. See Fig 1, Fig 2

Another principle that Einstein postulated in "The Foundation of the General Theory of Relativity" is a principle also found in the original special theory of relativity. "The laws of physics must be the same for all observers moving in inertial (non-accelerated) reference frames." 139

According to this principle there are no privileged inertial reference frames in the universe. In the special theory this principal holds true, but Einstein wanted to extend this principle to a general theory for all motions: -

"The laws of physics must be of such a nature that they apply to systems of reference in any kind of motion." 139

In the special theory Einstein did not include accelerated reference frames, because with an actual experiment, one can feel this acceleration of its own accord, and without reference to any outside source. In other words, accelerated systems appear to be special or privileged, their acceleration seemed to be absolute, which is something that Einstein did not like about Newton's theory of absolute space, absolute time, and absolute motion. Einstein sought to extend the notion of equality of perspective, established for non- accelerating reference frames in special relativity, by stating that any and all frames of reference are equally valid for expressing the laws of physics. Einstein realized he had a problem that had to be solved first before he could extend his special theory to a general theory. Einstein solved this problem with what he called ---"the happiest thought of my life;" a thought he developed into the principle of equivalence. Einstein said of his happy though: "I was sitting in a chair in the patent office at Bern when all of a sudden a thought occurred to me: 'If a person falls freely he will not feel his own weight,' I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation." 141

For instance, standing on a scale inside an airplane, setting on the apron of the runway ready to take off, a person gets on a scale and finds he weighs 150 lbs. The plane takes off and flies 50,000 feet into the sky. The pilot puts the plane into a nose dive, 32 ft. per second, per second; standing on the scale again, he does not register any weigh at all. Why is he weightless? The pilot pulls out of the dive; the person puts on a parachute and jumps out. He has that same feeling of weightlessness he had in the plane when it was in a dive at 32 ft per second, per second. Newton says, he better start worrying, the earth is reaching out grabbing a hold of him, dragging him back to earth, so, he had better actuate his chute. Newton calculates the force by multiplying the universal gravitational constant times the mass of the earth and the person's mass, and divides the product by the square of the distance between the person and the earth. He claims the attractive force of gravity has a hold of the individual, and it will bring him down to earth. Newton claims that the person is reaching out grabbing a hold of the earth and pulling the earth toward him; this in accordance with Newton's third law, but the person, of course, has little or no effect on the earth. F = G M m / r^2, this is Newton's equation for the law of gravity.

Newton figured that a force is acting upon the falling individual; because the first law states: every body continues in a state of rest, or of uniform motion in a straight line, unless compelled to change that state by a force impressed upon it. In a person's free fall situation; Newton claims the force of the earth's gravity is reaching out, pulling him down to the earth. Einstein knew he had his work cut out for him. He had to eliminate that action at a distance; a notion which even Newton did not like to admit, yet had to accept for the want of a better reason. Newton did not like the idea, and said so to friends. Einstein thought about the notion of the free fall affect. He figured this same affect would happen to an object floating around in a box if the box suddenly accelerated up at 32 ft per second, per second. The object then would appear to fall to the bottom of the box to any one in the box at the rate of 32 ft per second, per second. Hence, its gravitational mass is equal to its inertial mass; consequently, the effect of acceleration produces the effect of gravitation. Now all he had to do was to accelerate a falling person to the earth without the earth acting upon the person with the action at a distance which, at that time, did not make any sense to Einstein.

In order for Einstein to accomplish this idea, he developed the "Spacetime Continuum" and the idea of a geodesic in spacetime as referring to the connections between events in spacetime. For one thing, he needed to eliminate the sun's force of attraction, which was thought to cause the earth to fall toward the sun due to this gravitational tug. In order to do this he devised the idea of a four dimensional continuum, three in space and one in time. If he rid the sun of acting at a distance, then, this would solve his problem.

First consider how Newton's force of gravity works; it has to do with Newton's laws of motion, noted above, which are spelled out as follows: stated in the Principia: 32

Law 1: Every body continues in its state of rest, or of uniform motion in a right (straight) line, unless it is compelled to change that state by forces impressed upon it.

Law 2: The change of motion is proportional to the motive force impressed; and is made in the direction of the right (straight) line in which that force is impressed.

Law 3: To every action there is always an opposed and equal reaction: or, mutual actions of two bodies upon each other are always equal, and directed to contrary parts. (opposite direction)

First, Newton thought that the earth was trying to move in a straight line according to his first law. Second, he assumed that since the earth was not going in a straight line, as required by the first law, then a force was acting upon it, changing its direction toward the sun. Third, he assumed the sun was exercising a force of attraction upon the earth, due to the sun's massive size; and, according to his second law, he could calculate both the direction and the magnitude of the applied force. Newton's third law permitted him to know and understand what he thought was a "fictional" force, commonly called "centrifugal force". The attraction of the sun's gravitational force provoked an equal and opposite reaction by the earth; as a result, the forces balanced each other causing the earth to orbit the sun.

This was the line of reasoning with which Einstein had to contend. The solution he used to solve his problem he called the General Theory of Relativity. It involves the use of a non-Euclidean geometry; and, a set of mathematical rules invented by earlier mathematicians named Gauss and Riemann. It has to do with a non-Euclidean continuum and tensor calculus. Einstein developed equations for dealing with this metric form of spacetime. The theory deals with a set of covariant equations that will determine the components Gik of the metric tensor, which involves differential tensor calculus. Einstein, 154

The calculations are deep and involved in mathematical know how which Einstein first had to learn himself. It has to do with non-Euclidean geometry which will not be formally developed. Accordingly, one can get a somewhat better picture of what was going through his mind if one reviews what he thought about space; what goes on in space, and what he thought is happening to the space around the sun due to the sun's mass.

Einstein said in his book "Relativity:" --- "It is indeed an exacting requirement to have to ascribe physical reality to space in general, and especially to empty space. Time and again since remotest times philosophers have resisted such a presumption. Descartes argued somewhat on these lines: space is identical with extension, but extension is connected with bodies; thus, there is no space without bodies; hence, no empty space." 136

Einstein refuted Descartes argument then turned around and said, ..."We shall see later, however, that the general theory of relativity confirms Descartes' concept in a roundabout way." 136

Einstein, having done away with the "Ether Theory", had to admit that space had its own reality in order for his General Relativity Theory to work; space is capable of "Elasticity". One of Einstein's proofs was that light, coming from a star close to the sun, bends toward the sun, thus, displacing the star in the heavens as seen from the earth. See Fig 3

Einstein claimed the sun caused the space to bend toward it; the star's light is actually moving in a straight line. In addition, the earth, as well as all the planets as required by Newton's first law, will move in a straight line. Because the sun is bending the space around it; consequently, they follow the bend of the space around the sun. Einstein's tensor calculus shows how this bend is accomplished, bit by bit, in the form of differential equations. Einstein gave no reason or cause why the sun should bend the space around it.

Given that the earth follows a straight line path that curves around the sun; what happens to the falling person when he jumps out of a plane? Is he following a straight line? The answer is in the affirmative. Thus, as he follows the earth around the sun, that straight line curves toward the earth; indeed, the space around the earth is also curved inwardly. Einstein's theory of gravity did not answer Newton's question: "How is it possible? Einstein's theory proposed that the geometrical curvature of space around mass caused bodies to follow the curved space around mass; which objects normally would follow a straight line path according to Newton's first law. If a body's velocity does not equal the escape velocity of earth, as the moon's velocity does, it simply moves inwardly toward the earth, following the curved space around the earth, as both move through space. Einstein merely states it as a fact, without giving the cause for space being non-Euclidean. His theory proposes space to be non-Euclidean around mass, although in space away from mass, his theory proposes space to be Euclidean. Experiment seems to indicate that both conditions are true. The question remains; " Why? ". Why does the earth follow a geodesic around the sun?


Not only is space non-Euclidean around mass, and perhaps Euclidean the further away from mass one gets, regardless, one must treat space as a whole body, as a single unit. It just so happens there is an experiment a person can make that, when properly interpreted, actually proves that space must be physically treated as a single unit. Nevertheless, this single unit, as will be discuss later, is "quantized" in a very special way. It is an experimental fact that the Foucault Pendulum, once set in motion, maintains its orientation relative to the universe as a whole, regardless of what direction its initial thrust is made, east-west, north-south, or any direction in between. The pendulum always maintains that same fixed direction in space, relative to infinity, despite the rotation of the earth.

The Foucault Pendulum is quite an ordinary pendulum, except it has a very long suspension cord with a very heavy bob on its end. Once set in motion, it will continue to swing for hours. On the floor is a ring indicating the east-west, north-south, and the other compass points. As the pendulum swings it gradually reorients itself. For instance, if set to swing east-west it will progressively move itself toward the north-south plane. Set up at the north pole, its oscillatory plane would make a complete turn about the vertical axis in a period of 24 hours. It's swing completely ignores the rotation of the earth; the earth turns beneath it. By orienting his pendulum, first to the sun, Foucault found that, after a month had past, it appears the oscillatory plane turned more rapidly than the sun, in fact, it was fully 15 degrees off. Again, reorienting it to the star Sirius, Foucault found that even this celestial unit moves relative to the pendulum swing. Finally, he discovered that the pendulum will not maintain its orientation to any celestial unit, in fact, the further out in space a galaxy exits, the longer it maintains its loyalty to that orientation. He finally concluded that the pendulum maintains its orientation to space as a single unit, to the universe as a whole; for the pendulum orients itself stationary relative to the, so called, fossil glow. This radiation, which is receive on earth, comes from what seems like infinite space. Some physicist think this energy originated some fifteen to twenty billion light-years ago in what they call the Big Bang. An Austrian physicist, Ernst Mach, saw this as the presence of a mysterious influence emanating from the mass of the universe as a whole. It is called "Mach's Principle." As will be noted later; it is not mass that presents the mysterious force, it is the expansion of space that maintains a presence and an influence on all mass. This force unites mass in a universal system. There is a force operating on Foucault's Pendulum. Once set in motion, it becomes a free agent, accountable only to the force of space as a whole unit; or of the universe as a whole. The Pendulum will swing in that orientation until all of its peripheral energy is used up, or unless it is otherwise deviated. This makes one realize that the universe, as a whole, is ever present at every place, and at every instant of time; it exercises a force that all mass must adhere to. See Fig 4 --- below


The role of mass in Newton's philosophy, and the laws of nature he contrived, first consisted of material points, which moved in absolute space, and absolute time, with absolute motion. Space and time being the framework where relations between these material points took place. Secondly, the role of mass concerned inertia; an inertial system suspended in space and time. Newton's physical reality was that all inertia systems are material points, regardless of their extended features or chemical processes and makeup, and moved independent of the observer, or of space and time. Space and time are only the stage within and upon which physical entities and happenings took place. If all matter disappeared, space and time would remain as a stage upon which other physical things could arise to take their place and make things happen again.

The first understanding that arose to overthrow Newton's philosophy was the "field concept, " it took the place of material points, i.e., the inertial system of points. The simplest form of the field concept was heat. The law of heat conduction being represented by differential equations, which embraced all special cases of heat; a function of coordinates and of time. The relationship was only a preview of the concept of fields to be presented later. No doubt many physicists had a hand in the ideas, although Michael Faraday was the one credited with this new concept. Faraday ushered in the real field concept of mass in his experiment with electricity and magnetism. James Clerk Maxwell, with his mathematical skills, developed Faraday's ideas into a system of equations that are the hall mark of electrodynamics; even until today. See Fig 5

From their experiments, Michelson-Morley assumed that the earth and all the planets did not disturb the ether field, they considered the field parts were at rest with one another. They did not find the ether wind they thought must exists as the earth traveled through space.

Lorentz treated ether particles as the embodiment of space absolutely at rest. When Lorentz once assumed this attitude about the ether, he was able to devise a set of transformation equations vastly different from the Galileo transformation equations; thus, he solved the Michelson-Morley experiment paradox.

Einstein found there seemed to be a defect with the ether theory. It was not compatible with his special theory of relativity. Lorentz supposed the ether not moving. Einstein eliminated it entirely in order for his four dimensional spacetime continuum to take hold and make sense. There was no absolute time; and there was no absolute space and there was no ether. Einstein's idea had to do with the notion of simultaneous events.


It was thought that a number of events, occurring in space at the same time, were seen by all relative observers at the same time; simultaneously. On close analysis, Einstein discovered what was considered to be two events happening simultaneously for one person, may not appear to be simultaneous for another person. Einstein used two separate lightning bolts hitting a railroad tract. Exactly at the midpoint between the flashing bolts a person standing beside the bank of the tract. At the time the lightning bolts strike the railroad tract a passenger train passes by. The stage is set; Einstein's special relativity theory says the person on the railroad bank sees both of these flashes from the lightning bolts, simultaneously, and measures the speed of light to be 186,000 miles per second. The person in the passenger train, moving down the track, sees the lightning bolt that struck the track in front of him first, then, he sees the flash from the lightning bolt which struck the tract to the rear of the train second, that is, a little time later on. The idea that then comes to light is that the relativity theory says that in both instances, the person on the moving train measures the speed of light at 186,000 miles per second, in both instances, regardless of how fast he is moving. Each time the traveler measures the speed of light, the first flash first and the second flash second, the speed of light is at the same rate of speed, 186,000 miles per second, regardless of his own speed. Everyone thought a person should subtract the speed of the train from the speed of the light ray to get the proper speed of light. Einstein's theory says, no way, the speed of light travels independent of its source or the observer; it registers the same speed, 186,000 miles per second for all inertial frames of reference moving non-accelerated. He used a set of transformation equations exactly like the Lorentz equations to show what occurs under different circumstances. These equations tell one that the train and rulers shrink in the direction of travel and that clocks on the train slow down depending upon the rate of speed. Instruments adjust in a physical way so that measurements of light move at the same rate of speed as the person on the bank. In this way the laws of nature all act the same way for all people moving relative to one another regardless of their relative speeds. Einstein replace Newton's absolute space and time with his "Spacetime Continuum". See fig 7


Considering Quantum Mechanics; this energy quantum theory began with Max Planck and his discovery that energy travels in tiny bundles. He claimed energy equals the frequency times a small quantity called the erg/second, represented by the letter h, now referred to as Planck's constant. Heinz R. Pagels in his book, "The Cosmic Code - Quantum Physics as the Language of Nature", reveals how physicist view energy and mass today. He tells how the modern field theory had its birth in the attempt to unite quantum mechanics with relativity into a single theory, this was back in the 1930's. Physicists were trying to delineate the interactions between photons and electrons using mathematics that described experimentally, the relativistic quantum field theory. Pagels explains that according to the quantum field theory, the intensity of the electromagnetic field, at a point in space, gives one the odds for finding a photon. He goes on to say anyone can get a feeling for the theory if one imagines an infinite 3-D mattress of ordinary steel springs floating in space. All these tiny springs are attach to one another forming a grid lattice pervading all of the three-dimensional space as a 3-D mattress. This entire lattice of springs represents a quantum field. He supposes it to be an electron field. If a single spring in the lattice is plucked, it will vibrate. This vibrating spring corresponds to the quantum, an electron associated with the field. If another distant spring is plucked it would represent another electron in the field. E = h f He imagines a second mattress of heavier springs, super-imposed on the first as representing a quark field. A vibration in that field corresponds to the quark particle, thus, each different mattress of springs, pervading all of space, corresponds to a different particle, according to what spring mattress was plucked. He then supposes them to be linked together with springs that represent the gluons. This space of connected spring mattresses, and also lattices, now represents an interacting quantum field theory. He then proposes that all should view the springs as being invisible.

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