04/15/08

The History of Finding Gravity

Galileo     Kepler     Newton     Einstein

When I was a child I would leap from the couch knowing that my Superman cape would carry me over the city and countryside. Such is childhood, gravity is conquered by a cape. But falling to the floor never failed. Why all this falling? As we get older we cease asking the basic questions about how things work in our Universe, and take falling as the norm. Were the ancient Greeks correct? Is down the natural state, the norm of being, and thus all things tend to fall to whatever can support them.

Gravity has a wonderful history of ideas, measurements and discoveries, stretching over 300 years from Galileo, Kepler and Newton to Einstein. And although these great thinkers found all the clues to reveal the true source of gravity, they failed to break the gravity code. They missed the most basic ingredient of the Universe, space-energy, and therefore they did not discover that gravity is the variation of space-energy. Today, ideas of gravity still focus on either Isaac Newton's action-at-a-distance theory or Albert Einstein's theory of curved space. Newton's law of gravity works very well but it is confusing and fails to show how the Universe is a connected whole. Einstein's curved space is a great step in this direction but it is overly complicated for our purposes since Einstein included extreme curvature as in black holes or when considering the entire universe.

Let's take a little tour of the history of gravity to find out what clues Galileo and others found, and then put it all together to discover a new law of gravity. The results are amazing, because this new law of gravity reveals a beautiful symmetry of space-energy, exposes a marvelous connectedness throughout the entire Universe, and shows that its fate does not depend on dark matter.

Galileo Galilei was the first true scientist of recorded history. As a young man in his twenties he thought about falling. When a cart broke free of its hitch and rolled down the hill, Galileo wondered if this roll was a slow motion version of falling. He dropped objects from his balcony but the fall was so fast that he could not figure out the how of it. He knew why things fell. After all, the classical Greeks taught that all bodies tended to move to their natural state, down. But, was there some kind of special order to the falling? He had to know. In his study he constructed a ramp to simulate the hill, and watched as his model carts rolled down the ramp. Checking against his pulse, he discovered that each roll seemed the same. He set up his pendulum to tick off even intervals of time as he marked the progress of the cart along the ramp with each tick. The distance between marks got farther apart during the descent. Galileo knew that the speed was increasing with distance and therefore time. But then everybody knew that carts speeded up when going down a hill. Galileo's great discovery was that the rate that the speed increased was very precise, and in fact this rate of increased speed (acceleration) was the same no matter where the cart was on the ramp. He had discovered that acceleration of falling was constant.

Galileo made another great discovery as the 16^th century came to a close. When the carts left the ramp and rolled across the table, they rolled some distance before stopping. As he made the table smoother and built better wheels, the carts rolled farther indicating that motion continues until something impedes it. The Greeks taught that only a "mover" causes motion and that the natural state is stillness. Galileo saw the opposite: moving bodies move of their own accord until slowed or stopped by some external influence. He discovered inertia.

About the same time as Galileo was measuring falling, Johannes Kepler was poring over a mountain of data on the motion of planets compiled by Tycho Brahe, a tireless astronomer with a passion for precision. Brahe was dead and Kepler, his former assistant, was asked to figure out what the planets were doing by using Brahe's measurements. Kings and such wanted to track the planets to avoid making bad decisions as the planets moved from constellation to constellation. One did not go to war unless the planets were favorable. Kepler, still a prisoner of erroneous Greek premise, believed that God arranged the orbits of the planets according to some mathematical perfection, such as the geometry of certain polygons. There was a harmony in the heavens not unlike musical harmony where the planets moved in perfect circles following God's perfect rules of geometry. He was determined to discover what rules God was using.

What Kepler did is a good lesson for all of us. He took Brahe's precise data and followed it to its logical conclusion, not his preconceived notions. He was an honest man. He discovered that the orbits were not circles, but were flattened circles. Being a mathematician, Kepler discovered that a planet's orbit was the shape of an ellipse. And he found that each orbit had a somewhat different amount of elliptical eccentricity. Perfection was crumbling under the weight of evidence. Kepler, trying to recover some element of harmony, studied his results looking to see if the size of the orbits followed some kind of pattern. He began to see a relationship between the time it takes for a planet to go once around in its orbit, its period of revolution, and the distance it was from the sun. The greater the distance, the longer was its period. He examined the relative values of periods and distances, and as far as we know, fell upon the fact that the cube of the distance was proportional to the square of the period. The ratio of distance cubed to period squared was the same for all the planets. He found it; there was a harmony after all. But what did it mean? Why would God use cubes and squares to place the planets? What kind of harmony was this? Kepler continued his search for meaning but the world had to wait 57 years for Newton to explain this orbital harmony.

Isaac Newton went back to his mother's farm in 1666, to wait out the run of the plague in Cambridge or so the story goes. I rather think Newton as a young Cambridge student was beginning to see a connection between falling and planetary motion and wanted private time to work it out.

Picture Newton on his mother’s farm sitting by an apple tree. He sees a neighbor’s horse in the next pasture and, knowing how much horses love apples, he tosses one over the stone fence. It flies up and then falls down. Newton thinks about it. He throws another apple. He asks himself, when does the apple start to fall? I give it an impetus; it goes to some height, and then falls to earth. If Galileo is right, it should keep on going in the line my hand directed it until something resists its motion. But no, it is leaving that line of directed flight as soon as it leaves my hand. By God, it must be falling all the time it is in the air, even when it is going up. Falling is occurring during the whole motion! It must be that, or else it would stay on a straight path. The path is a curved path all the way. But why is it falling all the time? It is as if something unseen is pulling it down. Something is interfering with its natural motion.

 Notice how Newton at age 24 had turned the accepted idea that falling is due to something inherent in the object to the new idea that falling is caused by something else, something unseen. This is an amazing breakthrough in human thinking. Newton uses a simple observation and applies to it Galileo’s discovery that objects retain a uniform, straight-line, constant-speed motion, unless acted on by an explicit influence, a push or a pull. A force. And this force must have something to do with Earth, because all things hurled upward come down. Since Galileo proved all such objects accelerate the same, Newton concluded that some force of Earth causes this specific acceleration. The acceleration is proportional to the strength of the force. Newton may have gotten this far before 1666 and needed time away from the distractions of college life to work out his theory of attraction.

He made another discovery, almost by accident. When Newton pushed on a parked wagon, no motion occurred until the push force reached a value peculiar to the given problem ¾ say 88 pounds of force for the given situation. Up to a push-force of 88 pounds, one can say the wagon was pushing back with equal force. When motion began, one might say Newton had begun pushing harder than the wagon was pushing back. But Newton noticed that less pushing force was required, once the wagon got moving. He concluded that no matter what the motion, standing still, constant speed, or acceleration,  the wagon always pushed back with equal force. The force of reaction always equaled the force of action. Every action had its equal reaction.

Pondering the ideas of mutual attraction, acceleration, and the equality of reaction, Newton discovered the underlying principles of planetary motion. How he did this is not really known. But he most certainly knew that whatever the law of attraction was, it must be consistent with the results of Galileo and Kepler. It is believed he considered the moon to be like the apple. The moon is moving through space around Earth, and if Earth suddenly lost its influence over the moon, it would fly off in a straight path to some unknown corner of the galaxy. A similar result is obtained when a rock tied to a string is spun around and released. The rock goes off in the direction it was traveling, at the moment of release. But Earth holds fast, and our moon follows a nearly circular path around Earth. Likewise, Earth, in its path around the sun falls to the sun just enough to maintain its steady orbit.

When he returned to Cambridge, Newton declared his theories of force and  planetary motion and was able to derive mathematically Kepler’s relationship between distance and orbital period. His declarations were something like the following.

 Acceleration of a body of matter is proportional to the acting force. When a force accelerates matter, the degree of acceleration depends inversely on the amount of matter influenced by the force.

 Newton was thinking in terms of what we call mechanics, which is the study of force applied to rigid bodies. We experience force as a push or pull. A rigid body is a chunk of matter that does not change in size or shape when it is pushed or pulled. There are no exactly rigid bodies, but things like tables, bricks, and forks are rigid enough to demonstrate the effect of force.

Newton's big problem was quantifying matter in such a way as to achieve a law of acceleration that would be universal, something common to all bodies of matter. He settled on using the property of weight to identify the relative value of matter from body to body. But he wanted an absolute measure of the innate character of what reacted to force. The obscure nature of his writings on this subject indicates he was not successful with any definition of matter.

We call the property of matter that reacts to force mass. Denser substances of the same volume have more mass. An iron ball has more mass than a wooden ball of the same size.

Just what is mass? From Newton’s law of acceleration, it is what resists force; it results in inertia, the tendency for a stationary body of matter to stay at rest ¾ or if in motion, it is the tendency to stay in motion and resist change of that motion. Mass and inertia are related. Does this help define mass? Perhaps, but a standard of mass is needed, such that all measurements of force have a common reference. And so by the late 19^th century, physicists finally agreed on the standard. The Standard Mass is a chunk of platinum, kept at the International Bureau of Weights and Measures near Paris. By definition it is exactly one kilogram of mass. Put this one-kilogram of mass on an American weight scale, and gravity at the Earth’s surface will pull on it to register 2.2 pounds of force. Although this concept of mass is a staple of physics, it obscures our search for gravity. The world needed Einstein to redefine mass, but that gets ahead of our story. The secret to gravity is buried in the concept of energy and the basic particles of matter. But first we must see what Newton said about the cause of falling.

Newton's most astounding declaration upon his return to Cambridge was, there is a force of attraction, a force of gravitation, between all bodies of matter,( rocks, celestial bodies, balls of cotton, atoms, literally all bodies of matter attract each other).

How Newton came to his law of gravity is not clear. In fact it is a complete muddle. But then, that is often the case when one is exploring for new ideas. It is only after the theory survives the tests of experiments and becomes immersed in a larger body of logic that simpler means of derivation are found. In 1666, Newton had as a starting point the results of Galileo and Kepler and his own concepts of force. These were:

·        All falling bodies have the same acceleration. Galileo.

·        A body displays uniform motion (constant speed or at rest) unless a force is applied. Galileo and Newton.

·        The planets move around the sun, such that the ratio of the cube of the distance to the square of the orbital period is a constant (this ratio has the same value for all planets in our solar system). Kepler.

·        Acceleration is caused by force, and is proportional to the magnitude of the force and is moderated by its mass. That is: a = F/m. Newton.

·        Every action has an equal reaction. Every force is balanced by another force. Newton. 

From this base of knowledge, Newton declared his Law of Gravity:

 For any two bodies, this force of mutual attraction is proportional to the product of their masses divided by the square of the distance, r, between the centers of each body.

 Newton's law of attraction is not an equation; it is a proportionality. The law needed to be modified such that all measurements are consistent. To do this Newton's followers inserted a term, usually given by the letter G, that they treated as a constant throughout the Universe. Little did they realize that G is a measure of the tension of space, as we shall see later. But even so, the stage is now set to see Newton solving the problem of planetary motion. How did he do it? Unfortunately, we do not know. Newton did not reveal his path of discovery. As is often the case in physical science, once a discovery has been made and experimentally verified, the history of its original development disappears. But Newton in his own way used his law of gravity and verified  Kepler's law of cubes and squares. It was a huge triumph for Newton. There was no mysterious harmony of planetary motion. The planets moved according to the dictates of gravity. But Isaac Newton himself did not celebrate. His countrymen and the world did celebrate. The mystery of motion was codified in the laws of gravity and inertia. It was the dawn of The Enlightenment.

By the late 17^th century Newton’s colleagues were writing Newton’s gravity equation as we know it today:

where M is the mass of one body (such as Earth) and m is the mass of another body (such as a truck) and R is the distance between their centers (the Earth-truck distance is just earth’s radius).

 This problem of an arbitrary definition of mass and the artifact G haunted Newton. His law of gravitation is simple and works very well, but it lacks fundamental elegance because of the arbitrariness of mass and G. Much later, Albert Einstein overcame the difficulties of mass, but his field theory still required the use of G to produce a meaningful measure of force. Mass is energy, and the Universe tells us what G is. When we finally reach elegant simplicity, we will know what gravity is. But let us first follow Newton's lead a little farther.

His lectures made him famous and earned him Knighthood, but Sir Isaac Newton waited more than 20 years to write the compendium he called Mathematical Principles of Natural Philosophy. The results are brilliant, but the geometrical methods he presents, as a derivation, are extremely tedious, and very difficult to understand. It is likely that Newton searched diligently for a better theory because in 1691 he wrote:

 "That gravity should be innate, inherent and essential to Matter, so that one Body may act upon another at a Distance thro' a Vacuum, without the mediation of anything else, by and through which their Action and Force may be conveyed one to another, is to me so great an Absurdity that I believe no (competent thinking) Man … can ever fall into it."

 For Newton, "a most subtle spirit" maintained this "action at a distance".  This subtle spirit, we now know to be space-energy. But that is getting ahead of this story of discovery. Where are we in our search for gravity? Newton analytically described the force of gravity, and celestial mechanics is founded on scientific reasoning as well as careful measurements. The precision of space calculations for planets and space probes, based on this simple theory, is astounding. But we still come back to the basic question of "what is pulling?" Saying the word “mass” is not an answer, because mass is just a construct to help us give quantity to force and acceleration.

By 1700, gravity had reached its second plateau of discovery, and got stuck for another 200 years. Physicists were busy studying all aspects of mechanics, heat, electricity, magnetism, and optics. Great strides were made, but in most cases, some form of action-at-a-distance was required to extend scientific discovery. To solve this riddle, physicists invented another word, “field,” and the “theory of fields” had become the solution to "what is pulling?" It really doesn’t provide a good solution to our fundamental understanding of gravity, but it does point in the right direction.

The idea of fields comes from the magnet. Just about every student has seen the demonstration of magnetic fields, where iron filings are sprinkled on a sheet of paper that covers a bar or horseshoe magnet. Tapping the paper lightly causes the bits of iron to bounce free of the friction of the paper and line up as tiny bar magnets under the influence of the "magnetic field." If done correctly, lines of iron filings connect one end of the magnet with the other. These lines are called “lines of force” that "reveal" the presence of the magnetic field. The lines go from one end of the magnet to the other end, forming a closed loop. Aluminum filings don’t work. Wood sawdust doesn’t reveal magnetic fields. But aluminum filings, sawdust, and everything else do get pulled toward the center of Earth. Every substance reveals the presence of the gravity field. Its lines of force are fairly straight, and each line of force originates at the center of mass of each body, then extends into space.

The theory of fields is a powerful tool and remains the cornerstone of teaching advanced physics. Unfortunately, it has become the litmus test for concepts in physics and blocks new roads to discovery. Even Einstein got mired in its seductive grasp, but not before showing that mass refers to the more basic idea of energy. Einstein showed us how to convert from mass to energy using the squared speed of light as the scaling factor, giving us his most famous equation, E=mc². When we use this concept, we refer to E as the mass-energy as derived from the mass term, m.                                                

Exactly what is energy? When I hold a barbell in my hand, I need a tight grip because of Earth's pull on the barbell. As I lift the barbell, my muscles do work, giving the barbell an energy equal to its weight times the height of the lift. My muscles provide this energy increase for the barbell, and because my muscles are not efficient, some energy is expended in my muscles, heating them up. I drive my car up a hill and increase the energy of the car because of the height of the hill. My car is not perfectly efficient, and the car's engine and drive train heat up. In both cases a mass, barbell or car, was given an increase in gravity energy by inefficient means. I drop the barbell, and it hits the floor. What happened to its gravity energy? The car rolls down the hill and is stopped with the brakes. What happened to its gravity energy? In both cases you need a thermometer to find out. The barbell and floor heat up a bit. The car's brakes get hot. The gravity energy went to heat. At some earlier time this energy was in the form of fuel, food, or gasoline. Earlier yet, it was solar heat-energy converted to plants and fossil fuel. What is heat?

By the middle of the 19^th century, it was well established by careful measurements that energy is always traceable. It just moves from one form to another. It does not vanish. The energy it took from human muscle, horse muscle, or combustion engine has been converted to heat in the bearings and wheels, and most important to us, into the energy of its position. It is higher than it was, and has a stored (potential) energy relative to positions down the hill. When it is released, it will fall as Galileo’s carts did, pick up speed (accelerate), and gain motion-energy during the decent.

Energy, in its various forms, mechanical, chemical and heat, was fairly well understood by the 1870s. The science of thermodynamics explained the principles of conversion from one form to another. When all the atoms making up the cart have the common motion of going down the hill, we describe this motion-energy as kinetic energy. The energy transferred to the brake shoe by friction is disbursed throughout the atoms of the brake, causing them to vibrate faster, and vibrate in random directions. Temperature is a measure of random molecular vibration and is the relative measure of heat energy for any substance.

When we say that heat energy is in the form of vibrating atoms we are using classical mechanics as applied to atomic theory as if there were little springs connecting the atoms. This is all figurative speech. Even when we appeal to wave mechanics and talk about states of energy belonging to any ensemble of atoms we are still being figurative. The energy of atomic vibration is given the more formal name of phonon. All bodies above absolute zero temperature (-273.3C) emit and absorb photons. A body at higher temperature than its surroundings will emit more photons than it absorbs and in that way transfer its excess energy to surrounding bodies. Photons are energy. We can say that bodies store their received photon energy in the form of phonons. It is as if phonons are trapped photons.

The beauty of energy is its precise conservation. It never vanishes. Energy never appears from nowhere. It can always be traced. The equation of energy always balances, whether it is on the atomic scale, the human scale, or the cosmic scale. Conservation of energy is a powerful tool. It is the key concept for understanding gravity. The energy of gravitation is another form of energy. All isolated systems of particles and bodies have a tendency to eventually reach a state of uniform energy. Energy transfers will occur until the energy is uniformly distributed. Unless its wheels are blocked, the cart will roll down the hill. If a hole opens to the center of Earth, the cart will fall into the hole, and eventually wind up at Earth’s center. To understand gravity, we must explore the energy of gravity.

We inquire into the structure of matter to understand where the mass-energy lies, because gravity depends on the way in which mass-energy is distributed. We are after the fundamental particles of matter and their distributions of energy because energy distribution is gravity. We will examine the three constituents of ordinary matter: photons, protons, and electrons.

Our most familiar form of energy is light. It is energy that is never at rest and has no mass that you can put on a scale. Photons interact strongly with matter, exhibiting reflection, absorption, refraction, scattering, and other effects. In a sense, photons get trapped by matter, raising its energy content. Put the pot on to boil, and the heat source (electric stove coil or burning gas) radiates a lot of photons to the pot. The photon energy gets absorbed, and the temperature goes up.

Photons are energy. When they are absorbed in the energy wave structure of atoms, the matter has increased energy. Energy is mass. The photon-absorbing body of matter will behave as if it has increased mass. What can we say about the electrons, protons, and neutrons themselves? Are they energy too? When a neutron is knocked out of a nucleus in some high-energy event, as in a particle accelerator, the freed neutron decays into a proton and an electron. The only stable fundamental particles comprising all known matter are the electron and the proton. Photons, electrons, and protons have strong interactions, suggesting that their energy-wave properties are harmonic resonators. It is as if the atom is a collection of tiny strings of oscillating energy, all in some kind of harmonic resonance. Their energy structures link in many specific phase relationships. Fortunately it is not necessary to work out all this complexity to solve the problem of gravity. It is the basic energy structure of a proton and electron that gives us gravity, but in a surprising way.

A particle, modern relativists say, does not gain mass with speed; it gains energy. The distinction between mass and energy has become a blur. Mass is a term of convenience. When talking about subatomic particles such as electrons, protons, and photons, the concept of mass as having geometrical structure leads only to confusion. This sad state of affairs is a result of treating reality as consisting only of particles. When physics ignores the role space plays in particle mechanics, mass and energy are difficult to define, and the relationship between the gravity force and other forces can not be obtained.

Proton and electron are photon-like energy in disguise. All of matter is a complex configuration of energy. Fortunately, we do not need to figure out the complexity of matter to understand the basics of gravity. Albert Einstein based his theory of gravitation (General Relativity) on matter being able to change the geometry of space. We can ignore the details of his space-tensor theory, and still extract the final clue we need to find the secret of gravitation.

The equivalence of inertial and gravitational mass led Einstein to develop his General Theory of Relativity in 1916 while doing research in Berlin. Space, he said, has a property that transforms inertia to force. Matter, because of its mass-energy, bends space giving it curvature. We are not aware of space curvature, since we live where space is weakly curved and our local space seems to be a three dimensional space described by Euclidean geometry. We do not experience the curvature except by gravity acting as a force field.

The result of his very complex multi-dimensional theory is that local curvature of space is proportional to the local mass-energy. He wrote this in a differential form, where a change in curvature is given in terms of a change in energy. If we extend Einstein's theory by taking his differentials with respect to radial distance from any body we find that his radial curvature is a force given as a radial change in energy. But what energy is this?

Einstein's energy decreases moving away from a central body of matter. What energy is decreasing? Now we have come, finally, to the central crisis of gravity. Gravity is a property of energy, but of what energy? Twentieth century physics avoids this question and deals only in particles and their fields of force. Mass has its force field and we call it gravity; charge has its force field and we call it electromagnetism; protons and neutrons are influenced by a very short range force field we call the nuclear force. Space is populated by fields and each field acts on its own kind of particle. What a mess! Then to top it off, standard physics searches for ways to unify these fields, as if they are all really the same basic thing in different disguises. Confusing as all this field structure is, it works pretty well. Field physics becomes field engineering and useful products such as electric motors, television, and cell phones are made. All this concrete usefulness convinces us there is actually some basic underlying phenomenon that explains the workings of the Universe. The key to understanding the structure of our Universe is to study nature from the point of view of its energy variations. It will be a lot easier if we think of particles as energy condensations, and fields as energy variations.