Arindam Banerjee
2023-02-03 14:26:52 UTC
Note: I will be writing a series of articles about the cause of gravity in my facebook timeline, to satisfy my loyal school friends who seem interested. This is the first of such articles. I will also be posting them to sci.physics.
The cause of gravity – 1
Brief:
The formula for universal gravitation is well known to be, as the force F acting between two masses m and M, parted by a distance r from their centres of mass, as F=GmM/r^2, where G is the gravitational constant found by experiment. Recently the author has updated this formula to F=BnN/r^2 where B is a constant, and n and N are the number of protons or electrons in the masses m and M. It is obvious that as n and N are proportional to m and M, this is essentially the same formula with the difference that instead of masses, the new formula involves charges. Thus the gravitational force is expressed electrostatically, as a manifestation of electrostatic force. In other words, there is no difference between electrostatic force and gravitational force.
As such, there should be, among reasonable people, no quarrel with the new electrostatic representation of gravity, as on the surface it is a re-statement of the earlier statement. The curious may well be satisfied that an electrostatic representation of gravity may somehow explain what is so far unexplained and not understood about the manifestations of Nature: such as capillary action in plants and narrow tubes where fluid rises up defying gravity and the law of conservation of energy; and how charged winds streaming from the Sun can be formed despite the Sun’s huge gravity.
But, as presented – so far - without supporting logic as to its derivation, the new formula seems to be a trivial form of the existing formula, imparting no new knowledge. It may also seem preposterous as uncharged masses, by definition, do not emit any measurable electric field. Finally, the electrostatic forces are estimated to be as per physics literature to be some 10^39 times stronger than the gravitational force. For all these reasons, the gravitational force has been held to be something entirely independent, yet similar to the electrostatic force.
It is my purpose, in the following articles, to show that despite the above sound objections arising from the existing scientific viewpoints, indeed the gravitational force is a manifestation of electrostatic force.
Instead of the just the physics community, I will make my appeal primarily to the intelligent lay public, who are innocent of whatever passes for modern physics. For that purpose, prior to making my new points, I will try to impart a crash course in the fundamentals of electrostatics, as simply as possible. Furthermore, I will as my target audience have my old school friends, whose loyalty and faith in my abilities I most deeply cherish. My sole request to them – and all my other friends in Facebook and beyond in the online world - is to tell me, as bluntly as possible, exactly what they do not understand about what I will be writing, in further instalments on my Facebook timeline. (I will post my writings in the Usenet newsgroup sci.physics as well).
Cheers,
Arindam Banerjee, 21/4/2020
The cause of gravity – 2
Historical background:
Sir Isaac Newton, in his great work known as the “Principia”, primarily stressed upon two factors; the role of geometry in modelling reality, and the use of mathematics to make correct and accurate predictions in idealised environments, like say a body in free space surrounded by nothing. Let us have this in mind when we discuss how he managed to discover gravity, from the general level of the scientific thinking in his time
.
The scientific thinking of his time was Aristotleian. For many hundreds of years, it was believed that the Sun went around the Earth – exactly as we can all see for ourselves. The stars were the openings to Heaven, sending down heavenly light. They moved in crystal spheres that too revolved around the fixed Earth. The Christian Church devoutly followed the Aristotleian model, for it was perfectly, obviously, correct with the stars being proof of Heaven and the need to be religious and dutiful to get there, via the Church of course. Let us not forget, no one had a clue about gravity, or even force as a scientific measurement construct, for that matter.
So the ancients did their science in their own way, basically through empirical methods as they lacked the theory and the resulting mathematical modeling. To the extent they were practical, following geometry, they got good results. As an example, let us see how the Greeks calculated the distance to the Moon. They used parallax. This means that when one points to an object at one point, there is a certain angle with respect to a common plane. From another point on the same plane, there is a different angle. To experiment (P.S. try this), point at anything a bit distant with a finger or scale with just one eye. Then shut it and open the other eye. The object will have “moved” but it is just the parallax effect. You will have to shift the finger or the scale to the original object to find the angle of parallax. From the distance between your eyes, and the angle, the distance to the object can be found.
Hipparchus of Nicaea (190-120 BC) used the parallax method to get the distance to the Moon with reasonable accuracy. The ancients may not have known about force and gravity the way we do, but they did know about parallax, geometry - and Hipparachus himself is also credited with inventing trigonometry! Incidentally, the parallax method is still used to this day to find the distance of stars and galaxies from our planet.
Thus Isaac Newton was heir to the great Greek scientific traditions. He had been further influenced by Copernicus and Galileo. About these two, now: let us also get in touch with dates, we are doing some history after all!
Copernicus (1473-1543) is credited with discovering (in the West that is) the heliocentric system, that is, the Sun is fixed and the planets revolve around it. He did it without a telescope, just his naked eye with some pointing tools. And that was enough. What he found was that the angular positions of heavenly bodies (stars, planets) changed the most every six months, constantly. The same old parallax system is at work, this time instead of the space between two eyes from our earlier example, twice the distance of the Earth from the Sun! Copernicus concluded that the dominant and hallowed geometric system (Sun and planets and stars going around the Earth each in its own crystal sphere) was wrong. The explanation, to account for this anomaly, was that the Earth was revolving around the Sun. It was a perilous explanation, for it went against the doctrines of the Church. Galileo (1564-1642) was persecuted in 1633 for supporting Copernicus, by the famous Church Inquisition where he was forced to recant, and say that Copernicus was wrong and Aristotle was right. He was more fortunate than Giordano Bruno, the talented Dominican friar who was burned at the stake on 17 Feb 1600 for upholding the Copernican heliocentric view, and further stating that the universe was infinite and that other solar systems also existed.
Back to Isaac Newton (1642 – 1737). It should be obvious from the mood of his time (as presented above) that the geocentric model was absolutely dominant – all the churches expounded it, the universities taught it, all rich and important people believed it utterly. Exactly as they believe in special and general relativity, quantum theory, big bang, expanding universe, black holes, quarks, bosons, string theories, neutrinos, photons, fusion, e=mcc, spacetime, nothing can go faster than light, etc. etc. etc. these days, following Einstein, Feynman and Hawking. Newton was evidently too smart to fall for the geocentric model – but how could that make him popular with the powers that were in his time? Newton had a miserable time as a student, and did his best work when he was on his own, away from the mediocre professors professing the Aristotleian geocentric model. But, he did not have anything really substantial to smash the geocentric model. The angular differences in the positions of the heavenly bodies could be dismissed with airy hand-waving, along with some spurious explanation like wobble in the crystal spheres, as a devil’s prank to confuse the faithful.
It is said that in 1666 (that is, when Newton was 24 and Galileo had been forced to recant his views only 33 years ago) that the famous apple fell on Newton’s head, or on the ground before him. Why did it fall to the ground? A simple question, but no one had asked it before. Why was it moving faster and faster (accelerating) as it fell? Newton thought that there had to be an attractive force between the mass of the Earth and the apple, which caused it to fall. It was moving faster and faster because till it fell, the force was working constantly upon it, causing acceleration. Newton then theorised that all bodies with mass are attracted to each other. The apple falls to the Earth, but the Earth is also influenced – the Earth also moves towards the apple, but as the Earth is too big, and there are many other falls all over, the Earth’s movement is not discernible.
Newton theorized that the attractive force was proportional to the multiplicative product of the two masses attracting each other, and inversely proportional to the square of the distance separating them. This directly leads to the present formula, F=GmM/r^2. However let us not forget that the gravitational constant G was not known until Cavendish measured it in 1797-98, some 131 years after Newton had his famous insight, which had so far eluded everyone else.
If masses did attract one another, just as the Earth attracts the falling apple, then why does not the Earth fall into the Sun, like the apple falling to the ground? Either gravity operated only on Earth (thus the Earth and the Sun did not attract each other) or the sun being very small (like say Apollo’s chariot) revolved around the Earth; or - and this was supported by astronomical findings supporting Copernican model of the rotating Earth revolving around the Sun - the Earth actually moved around the Sun.
It was obvious that the Sun was far bigger than the Earth, from the phenomena of eclipses and the knowledge of the Moon’s dimensions. It is still not known 100% that gravitation works for heavenly system, the way it does for the apple-Earth system, thus the universal theory of gravitation remains a theory, although one of the most powerful theories known, like the atomic theory. It is still a theory, for it cannot explain why ionised masses escape from the Sun’s extraordinary gravitational pull.
The Earth then has to move tangentially, always, for ever, to escape falling into the Sun. It certainly would do so if a giant hand stopped its motion! What Newton with his geometry and maths explained, clearly, was that the Earth is in fact always “falling into” the Sun, but because of its tangential velocity, “falling out” by more or less the same amount. (The” more or less” accounts for the elliptic orbit, that is, not purely circular, as Kepler (1571-1639) had worked out before Newton.)
The earlier point is worth pondering about, for a few minutes. It explains the motion of all satellites. The tangential motion allows the satellites to not fall back to the Earth, and keep constantly revolving unless the tangential speed is reduced by drag of some kind, including rocketry.
Another point about gravity – the gravitational force simply depends upon the existence of mass. It never changes for that mass. It is constant, always there. This mass always attracts, thus its force never changes, it is exerted all around in all angles. Always, always…. Such is the fundamental design of the Universe. Can we probe a bit deeper into its cause, now? I think some more groundwork is necessary.
22/04/2020
The cause of gravity – 3
The conception of force
Force is the central issue in physics – or at least, it should be the central issue in physics. It is from force that all things move, or stay put. Force moved over distance is work, and work has the same units as energy. Energy, then, is expended when a force moves over a distance. There is a vast difference between force and energy – as I see it, force is for the physicists to better understand the workings of the Universe; and energy is for the businessmen to make money. So it is, that as far as possible, to understand the fundamentals of Nature, I avoid the use of the energy concept.
The difference between force and energy is tricky. It is easy to confuse one for the other, and most people untrained in physics may do so. Force must have direction – it is thus called a vector. Because forces have direction, two separate forces operating in the same direction add up to one double-force. In opposite directions, they cancel out to zero. But energy has no direction. It is thus called a scalar quantity. Energy is usually defined as the capacity of a body to do work. It is further postulated that energy is always conserved. Its form however changes: when we drop a ball to the ground, the potential energy of the ball at the start changes to the maximum kinetic energy just near the point of impact. After this, though, the thinking is not that clear. After impact, the kinetic energy is converted to heat energy. Instead of saying that this energy is lost, we say, as per classical physics, that the entropy, a mathematical concept about the state of disorder in the universe, has increased. I have never been happy with this explanation – it seems to me pretty self-evident that energy is continuously getting created by the Sun and Earth, being used for various purposes, before being radiated out for destruction into deep space. Thus, energy is pretty slippery. It is always getting used up. We need money to use energy, if we cannot make use of the natural sources like the Sun and wind and water and geothermal.
Is force equally slippery?
As far as I can see, Leonardo da Vinci (1452-1519), in his Notes, made the first-ever proper description of force with the following statements:
“Force I define as a spiritual power, incorporeal and invisible, which with brief life is produced in those bodies which as the result of accidental violence are brought out of their natural state and condition. I have said spiritual because in this force there is an active, incorporeal life; and I call it invisible because the body in which it is created does not increase in weight or in size; and of brief duration because it desires perpetually to subdue its cause, and when this is subdued it kills itself.”
Such a definition of force is slippery indeed! From da Vinci’s definition, secularized, force is the “result of accidental violence” brought out “natural state and condition”. Thus it is random and violent. It is “brief in duration”, meaning it is transient, certainly nothing permanent. A perpetual desire to “subdue its cause” means that it is revolutionary. When successful in that “it kills itself” so is suicidal. This appears as quite a statement of the violent political mood of his times, based upon sneaky opportunisms, as elaborated upon by his contemporary Machiavelli (1469-1527)!
It will not be difficult to see how much da Vinci’s conception of force - which in his day had to be purely mechanical - influencing later scientists like Galileo, led to the formulation of the well-known Newtonian laws of motion. The phrase “natural state and condition” is known as inertia, formulated in the first law of motion. “Result of accidental violence” refers to acceleration, and is formulated in the second law of motion. The statement “when this is subdued it kills itself”, refers to the third law of motion which states that to every action there is an equal and opposite reaction.
From the above discussion we find that the conception of mechanical force is not just slippery; it is random, violent, transient and suicidal. Nothing constant about force! And yet, with such conception of force, formed from the greatest minds in the West, all the wonderful works in engineering have been done, from locomotives to jet engine airplanes; from muskets to missiles; small cars to huge ships! As force is slippery, so energy too is slippery. Energy mutates from one form to another. Just like force, its magnitude depends upon the frame of reference with respect to any observer. Thus two jet airplanes flying side by side may gently nudge each other, with minimal force or expenditure of energy involved. But if they collide, meaning the reference frames are opposite now, the forces involved and the energy spent in the disaster is enormous.
The above conception of force, so widely accepted because it was correct, makes Isaac Newton’s discovery of gravity all the more remarkable. For gravity is not slippery, nor random, nor violent, transient and suicidal. It is the very opposite. It is constant, spreading out in all directions, relatively very gentle, and permanent. Being all that, it is gravity which holds us all together on this planet; and it is gravity that makes the entire universe a permanent moving system composed of unlimited quantities of matter. Gravity, thus, is an entirely different kind of force. As we shall see, it is a much muted form of electrostatic force. Till now, despite their basic similarity, gravity and electrostatic forces are held to be independent: one is not the manifestation of the other.
A few more points: the random nature of mechanical force had led Leonardo da Vinci to conclude that a device that would perennially give out energy (a perpetual motion machine) was impossible. Even when gravity was discovered as a constant force, this was found to be true. This inability to construct a perpetual motion machine was a factor in the definition of the law of conservation of energy, that energy could neither be created nor destroyed. Certainly this law is much appreciated by the fossil fuel industries!
Researching Leonardo da Vinci’s comment on the nature of force, this time with a more modern mindset, we note the words “I have said spiritual because in this force there is an active, incorporeal life”. Now concentrate on the words “in this force” and “life”. Da Vinci is not talking of force as an expression of the inanimate – for him all forces relate to life and spring from some unknown higher purpose, thus blurring the line between physics and metaphysics.
“Life force” thus is essentially internal. It comes from within, but is related to without. Going by da Vinci’s perception, it is inherently random and self-destructing. But what if it can be made to act otherwise, with the purpose of steady movement in one direction? What if instead of being pushed around by external forces, bodies can push themselves with internal “life force”? We all know that this is a dream monetized by science fiction. Can this fiction become fact? Can we overcome the effects of gravity with internal force?
For over twenty years, I have wrestled with the above issues. My work has been presented online. In 2000 I published in my “adda” website my book “To the Stars!”. It attracted minimal interest, till in 2003 an article by myself was published in the Science Section of Outlook Magazine, in India. I got fiercely hostile reactions to my article, which surprised me before I got disgusted with the low quality of scientific temper, from low personal attacks. For example, one Garg, a junior scientist in the employ of the Govt. of India, offered gratuitous abuse.
The link for that article is at https://www.outlookindia.com/magazine/story/newt-is-old-hat/220728
I now believe, that the editors thought that I was attacking Newton with my new ideas, and that was the reason for its publication!
Arindam Banerjee
25 April 2020
The cause of gravity – 4
Measuring fundamental constants (G) and the meaning of research
(start rant)
Today the entire field of physics is thoroughly institutionalised, with standardised thinking dedicated to perpetuating the established orthodoxies, like any religion. These high priests – in the field of what is called “modern physics” involving the theories of relativity, publish their weird notions, with amazing smoke screens of mathematical gibberish to confuse the most intelligent lay persons, in select journals and conferences, to maintain their high prestige. Their efforts are very expensively funded by the Governments and various rich parties, blindly supporting the high priests ensconced in universities and Govt. laboratories. Amateurs or hobbyists have no place in this closed system. The best they can do is to publish their work online; in social media, email, etc. unless they spend thousands of dollars for publication in some vague journal which will be automatically derided by the establishment because of its low ratings. In this system success is measured in terms of the money squeezed out from the higher powers for some “output”. Like gravity waves, quarks, red shift, big bang, string theory, black holes, bosons, neutrinos… you name it, there will always be more coming!
So much is this notion prevalent, that only the expenditure of millions or billions of dollars involving vast projects such as making black holes, or fusion energy, is considered solely necessary to finding something new and wonderful – which, however hardly ever happens. Anything revolutionary in physics, involving low budgets and lone endeavour is automatically discarded as cranky or plain wrong if it goes against the grain of the orthodoxies.
(end rant)
The greatest advances in physics did not require huge investments in money and manpower. What was needed was insight, dedication, patience, skill, tenacity… of the talented amateur, working with minimal help. Sir Isaac Newton is the best known example, as the discoverer of the force of gravity. But his discovery in 1666 was far from complete. He could only indicate that the gravitational force between two masses was proportional to the product of the two masses, and inversely proportional to the square of the distance between their centres of gravity. Newton did not know what the proportionality constant was. We now know it as the gravitational constant G.
It was only in 1798 (that is 135 years after Newton’s discovery) that the Gravitational Constant was found from measurement, by Henry Cavendish. The experiment was painstakingly done by Cavendish, but the apparatus itself was simple. A recent attempt to recreate a model of the original apparatus is shown in the Youtube video film
Cavendish’s experiment was conducted in a large sealed room, to prevent air currents. Two lead balls, spaced widely apart were joined by a thin light rod. A fine string suspended these two balls from their centre of mass, from the ceiling. Two heavy lead balls were placed near the suspended balls, such that they could each attract the suspended ball in the same direction so as to produce the maximum twisting effect (torque) upon the string. How much the string would twist, could be found out by the angular displacement of a very light long strip connected to the twisting string. The movement of the edge of this strip could be tracked from its initial position to find the angular displacement.
So much (from above) I have got from the literature, and the rest is my own construction, relating to the necessary calibration and measurement. The gravitational force is very small. And yet, it can be measured correctly with proper application. The main issue is calibration, for any measurement.
What we have to know is how much the thread twists for a certain torque (twisting action). Let us say that the length of the suspended rod with its attached balls is ten meters. Torque is equal to the force F multiplied by the distance r to the point of twist. Or T=F*r. With equal force from the other end it is T=F*r + F*r = 2Fr or F.d. The torque motion will be resisted by the material in the string – it cannot twist indefinitely - after a certain angle (depending upon the quality) the string will no longer twist as a result of the torque. Thus T= k.theta, where theta is the angle of twist and k is a constant depending upon the quality of the string. F.d=k.theta then; now we need to find k.
The issue of calibration now comes in. Let us see how it can be done. From about 10 cm from the centre of the suspending string, tie a fine thread to the rod on both sides. Slide it over a pulley to a suspended mass of say 1 gram, on both sides. A continuous torque now acts on the suspended string. It will twist by a certain angle, then stop twisting. Measure that angle. Now make more experiments with increasing or decreasing weights, and changing the distances involved, to get many values of theta, and from F, d and theta, so many values of k which should all be more or less the same for a given torque applied with various values of F and d. Numerous experiments average out the experimental error, statistically, to get k.
The rest of the experiment is simple. Just get the very heavy balls of lead near to the suspended balls, at right angles and as near as possible without touching. The small balls will be attracted by this extra mass near them, and the torque will be created till the suspended string twists by an angle theta. Knowing k and theta, the torque T is known. Knowing the torque T and the distance d, the gravitational force F between the suspended ball of mass m and the heavy ball of mass M is known. Various values of F can be found with increasing or decreasing the static balls; that is fro. Now at the end position, the distance between the centres of gravity of the suspended ball of mass m and the heavy ball M is found. This is r. So now we have all that is needed to find the gravitational constant G from the formula
G = F*r*r/(m*M)
With this formula, Cavendish could work out the mass of the Earth, knowing g, the acceleration due to gravity. Every apple of mass m falls to the Earth with mass M, by the law of universal gravitation (it is assumed now that as per Newton not just lead balls in an experiment are attracted with the constant G, but all bodies in the universe) it falls with a force F which by Newton’s second law is equal to m.g
The above equation can be written as M=F*r*r/(G.m) With F=mg, it is M=r*r*g/G
For the fun of it, let us put in the values to get the mass of the Earth! r is the Earth’s radius which is 6371 Km or 6371000 m. g on the surface is 9.8 m/sec/sec. G is found to be 6.674*10^-11 in MKS units. The calculator result is that the mass of the Earth is 5.96 *10^24 Kg. How nice! Knowing the mass of the Earth we can also find the mass of the Sun, Moon and so on. In the practical sense, we can know how much force is exerted by the Earth on distant objects like satellites or space vehicles.
**** NEW ****
So far we have been dealing with the known. Research to most means looking things up, but as a professional researcher I do not call that research; I call that search. Research (re-search or search again and again and again…) means looking at an established search in a new way each time, with a slightly different angle, with the knowledge of relevant new knowledge and finally with special insight (from the Divine, in my case and with all my heroes in science: Plato, da Vinci, Newton, Maxwell, Tesla, my great-uncle Sir U N Brahmachari) for its own sake, or for some practical purpose.
Applying that notion of research to the notion of the gravitational constant G, what do we find?
**** INSIGHT ****
We find that none of the masses involved in the experiment were charged with electricity.
*****************
Which amounts to, the law of universal gravitation may or may not apply to charged masses. This explains why ions stream out of the Sun, despite the Sun’s huge gravitational force. However up till now, we had assumed that charged masses were subject to gravitational forces, so the ion streaming from the Sun is a mystery.
But what is charge? Sir Isaac Newton had no idea about charge, no clue about electricity. Cavendish may have had some idea, for his apparatus was a large torsion balance, used to measure electrostatic forces. We will go into the details of electrostatics in the next instalment. That will be the prelude to expressing the equation of universal gravitation in electrostatic terms.
Arindam Banerjee
29 April 2020
Further comments in my facebook post: 29 April 2020
understand this, that the Gravitational Constant was measured only with masses with no charge in them. Both were uncharged. This is a small but vital point. It shows that assuming that the law of universal gravitation is valid for charged masses is an assumption. It is the job of the researcher, that is, one who searches old stuff with new eyes, to point this out. And that is what I have done. And will be doing, in later instalments.
With the measurement of the slightest twist of a string, one may thus weigh the Earth, Sun, Moon and the planets! Direct the course of spaceships! Such is the power of the correct theory. Or rather, the more correct theory. Science is always provisional, that is, in for change.
Thus I wonder, how much mad those around the likes of da Vinci, Galileo, Newton, Cavendish, Franklin, Faraday thought them to be! They would not have had the faintest clue of what was going on. They would stoutly believe in established notions expounded from some pulpit or altar. Things have not changed, have they!?
The cause of gravity – 5
The fundamentals of electrostatic attraction leading to the structure of the atom
To recapitulate the thesis: “The formula for universal gravitation is well known to be, as the force F acting between two masses m and M, parted by a distance r from their centres of mass, as F=GmM/r^2, where G is the gravitational constant found by experiment. Recently the author has updated this formula to F=BnN/r^2 where B is a constant, and n and N are the number of protons or electrons in the masses m and M. It is obvious that as n and N are proportional to m and M, this is essentially the same formula with the difference that instead of masses, the new formula involves charges. Thus the gravitational force is expressed electrostatically, as a manifestation of electrostatic force. In other words, there is no difference between electrostatic force and gravitational force.”
We have dealt with the development of gravitational force at some length, in the earlier instalments. To validate the thesis that there is no difference between electrostatic force and gravitational force, let us see how the electrostatic force was developed to the point where it could be seen as being deeply involved in the basic elements of matter, that is, atoms.
From the second volume of the revered Halliday and Resnick, we learn that Thales of Miletus, in 600 BC, knew that a rubbed piece of amber will attract bits of straw. This results from electrostatic forces. Prior to this, it was known that certain naturally occurring “stones” (magnetite) will attract iron. This is magnetism. These two sciences developed quite separately until 1820, when Hans Christian Oersted (1777-1851) observed that an electric current in a wire can affect a magnetic compass needle. This discovery led to the entire new science of electromagnetism.
For our purpose, to show that there is no difference between electrostatic force and gravitational force, the sciences of magnetism and electromagnetism are not relevant. We will concentrate upon electrostatics, first by presenting the historical background.
If we suspend a glass rod, and rub it with silk, remove the silk stuck to it, then bring near it a second glass rod also rubbed with silk, we will find that the rods repel each other. The American Benjamin Franklin (1706-1790) was the first to distinguish between positive and negative charges. The former related to the kind of charge on the rod; the latter to the kind of charge on the silk. In its normal or neutral state, all matter (that is, what is measured as mass) contains equal amounts of positive and negative charges. When material bodies like glass and silk, or rubber and fur, are rubbed together, a small amount of charge is transferred from one to the other, upsetting the electric neutrality of each.
From the point of view of electrostatics, matter is of two types – conductors and insulators. A conductor – usually a metal – is what will not develop a charge when rubbed, unless it is attached to an insulator like glass or rubber, and the conductor is not touched by the hands in the rubbing process. Metals, the human body, the Earth are conductors of electricity as the charges can move in such conductive matter. Charges cannot move in insulators like glass, hard rubber, plastic, mica.
The Hall effect shows that only negative charges are free to move in conductors, but in electrolytes both positive and negative charges can move. It is now known that the actual charge carriers in metals are free electrons, but this was not known to the early experimenters, who had no clue even about atoms let alone electrons. What they knew was that if an insulated conductor was contacted with a charged insulator, then the charge would be transferred to the insulated conductor and spread all over the surface evenly. They knew that the charge would be passed on, and halved if an equal sized uncharged conductor would be touched by a charged conductor (both being insulated!). It is with such a background that the torsion balance was devised to measure the quality and quantity of the electrostatic forces by Charles Augustin de Coulomb (1736-1806). (We have already seen how Cavendish used a much enlarged torsion balance to find the gravitational constant G in 1797-98.) Thanks to Internet, we can easily get details from such sites as:
http://ffden-2.phys.uaf.edu/104_2012_web_projects/cicely_shankle/Page%202%20-%20Coulomb%27s%20Experiment.html
which explain and extol the ground-breaking work he did in 1785. Coulomb’s first experimental results show that the force between charges is inversely proportional to the square of the distance between them, that is F ∞ 1/r^2. These forces act as per Newton’s third law, that is, act on the line joining them but pointing in opposite directions. Further he showed that the force was proportional to the quantities of charge q1 and q2 on the charged spheres such that overall the formula for force, known now as Coulomb’s law, is F∞ q1*q2/r^2. With a proportionality constant k, this becomes
F=k*q1*q2/r^2, and is the fundamental formula for electrostatics.
It is immediately clear that this formula is structurally similar to F=G*m1*m2/r^2, the law of universal gravitation, which by 1785 was more than 100 years old. However it was also noted that the force of gravitation was much weaker, and always attractive. In other words, the attraction between two masses, with charge, would vary with design – but in the case for gravity, the attraction would always be the same. This realisation placed gravity as an entirely separate force, and to this day this remains the standard scientific standpoint.
Before I prove my thesis in the next instalment, let us study the development of atomic structure from an electrostatic point of view. John Dalton proposed his atomic theory in 1803, a fair while after Coulomb’s experiments. Not being chemical in nature, the atomic theory was irrelevant to the development of electrostatics and its possible relationship with the force of gravity. However, its impact led to the realisation that charge, like atoms, could also be indivisible and finite and thus a group (when static) or flow (when moving) of “corpuscular” particles as found by J J Thomson in 1897. The term we use today for Thomson’s corpuscle is electron. It had been coined by G. J. Stoney in 1891, to denote the unit of charge relating to passing electric current through chemicals. Thomson’s colleague Joseph Larmor also used that term, in his theory that the electron was an aetheric component – not a part of an atom (for that would mean violation of the atomic theory which held that atoms could not be further divided). (Aether is the fundamental component of the universe, supporting all radiation from all sources as the medium for electromagnetic waves, being an infinitely fine, infinitely elastic solid through which all matter flows without resistance. – my definition, following 19th century natural philsophers.)
The site https://history.aip.org/history/exhibits/electron/jjelectr.htm gives details about J J Thomson’s experiments with cathode rays in cathode ray tubes. In brief, a cathode ray tube is just a glass tube with electrodes at both ends. When a high voltage difference is applied to the electrodes, and the gas in the tube taken out (like any light bulb) there is a glow in the tube, following from a flow of current which meant that charge was flowing through the near-vacuum, causing picturesque effects. The general consensus was that these “cathode rays” were like light rays propagating through aether. However, the cathode rays could be deflected by magnetic fields, unlike light rays. The rays also passed through very thin foil – unlike light. Scientists Perrin, Wiechert and Lenard found out respectively in 1896-1897 that the cathode rays carried a negative charge; the ratio of their mass to charge was over a thousand times smaller than the hydrogen ion; if the rays were particles they were extremely small as they had a good range despite material obstructions.
Thomson made his breakthrough when he made a near perfect vacuum for the cathode ray tube. Previous experiments had failed to bend the cathode rays in an electric field, which raised the suspicion that they were not charged particles after all. He surmised that the remaining gas is the tube was being made conductive by the cathode rays; so acting as a sheath to the cathode rays. Charged particles do not bend to an electric field when they are enclosed in a conductive sheath. After evacuating the gases from the tube, Thomson found that indeed the electric field was bending the cathode rays (incidentally this is the science behind the old television sets). This was the final proof – negatively charged “corpuscles”, very small in size, constituted the cathode rays. Thomson stated that as his first hypothesis; the second was that these corpuscles are constituents of the atom; the third was that the corpuscles are the only constituents of the atom.
The second and third hypotheses met with scepticism. While the second hypothesis has been accepted (with difficulty by the scientists of his time, for it violated the atomic theory – it was easier to visualise massless fluid charges associated with indivisible atoms) the third has not been accepted. How could atoms be built up from these “corpuscles”? Where was the positive charge? Thomson co-proposed an atomic model, known as the “plum pudding” or “raisin cake model”: thousands of tiny, negatively charged corpuscles swarm inside a cloud of massless positive charge. In insulators, these corpuscles were more or less stuck unless rubbed off. In conductors, they moved. Under electric voltage (in evacuated tubes) they moved in free space. The massless positive charge (the pudding or cake) never moved, of course. When the corpuscles were squeezed out, by physical pressure or electric potential, the atoms showed their positive charge; which remained so until the absorption of the missing corpuscles to regain charge neutrality. In this way, the natural phenomena relating to electrostatics were adequately explained. For this atomic model, J J Thomson got the powerful support of another Thomson, Lord Kelvin, the venerable scientist after whom the Kelvin temperature scale is named. It was Lord Kelvin who had proposed the “plum pudding” atomic structure in 1902. J J Thomson worked on substantiating this model from 1903 to 1907.
The Japanese physicist Hantaro Nagaoka proposed an alternative model in 1904 – here the atom resembled the solar system or the planet Saturn, with rings of electrons surrounding a concentrated positive charge. (Ency. Brit. 15th ed. Vol 14, p347). This is in fact the contemporary atomic model minus the quantum theoretic add-ons following Bohr, but it was rejected on the grounds that by radiating continuously the electron would gradually lose energy and spiral into the nucleus. No electron could thus remain in any particular orbit indefinitely. This is, evidently, specious reasoning . The Earth does not lose energy by spinning around the Sun. The kinetic energy remains constant, both for the Earth around the Sun and the electron around the nucleus under normal conditions; so there is no question of energy loss. Just as the Earth does not fall into the Sun, thanks to its continuously-changing-in-direction tangential velocity, thus “falling into” the Sun from gravity as much as it “falls out” of the Sun due to its tangential velocity, thus keeping the orbital radius fixed; so does the electron does not fall into the nucleus – here instead of the gravitational force there is the electrostatic attraction between the positively charged nucleus and the electron with its continuously-changing-in-direction tangential velocity.
Had it not been for the discovery of radioactivity, we could have retained the “plum-pudding” atomic model to this day. In 1896, Henri Becquerel discovered radioactivity – rays emanating from certain minerals fogged unexposed photographic plates. His student Marie Curie discovered that only certain chemical elements gave off these rays of energy, and provided its name, radioactivity. In 1899 Ernest Rutherford discovered and named a component of radioactivity, alpha rays. It turned out that they were positively charged particles – now we know them as Helium nuclei with two protons and two neutrons.
No one knew what caused the emission of energy from minerals – that phenomenon certainly violated the law of conservation of energy, and also showed that positive charge could move upsetting previous thinking. They wondered as to how the energy from the Sun was generated – some form of radioactivity? If someone then had derived the kinetic formula relating mass and energy on a non-destructive basis, which I found in 1999, human history would have taken a very different turn for the better.
Rutherford upset the “plum pudding” atomic model in 1911, with his famous gold foil experiment which validated the Hantaro Nagaoka model. With his assistants Geiger and Marsden he beamed alpha particles through a 0.00004 cm thick gold foil and detected them as flashes on a screen. It was found that 1 in 20,000 alpha particles were deflected by an angle of 45 degrees or more, while others went straight through. The straight-through-going particles could mean that alpha particles could punch through the positive “pudding” in the Thomson atoms, or that atoms consisted of mainly empty space offering no resistance. However the deflections of the very few particles indicated that they were getting near some heavy positively charged mass, which formed the nucleus of the atom. What kept these charges together – why did they not fly apart? The accepted theory now is that there is a certain “strong force” operating entirely within the nucleus and not outside, that keeps the positive particles along with the neutral-charge neutrons together. Rutherford held that the positive particles (now known as protons, or Hydrogen nuclei) were held together by electrons. Thus according to him a Helium nuclei, or an alpha particle, is four Hydrogen nuclei (protons) held together by two electrons.
For my purpose, that is, to provide an electrostatic explanation for the force of gravity, and to deduce the new equation F=BnN/r^2 (details given earlier) this much information is enough. Later developments of the atomic model by Bohr and others are not relevant, for as of today no one seriously questions that electrons orbit a much heavier positively charged nucleus in the atom.
In the next instalment the logic and derivation for the abovementioned equation will be provided. To recapitulate; gravity is considered nothing electrostatic as it is very weak, always attractive, always steady, has nothing positive or negative relating to force-field, has everything to do with just uncharged masses, and has a very long range. I don't know what the odds will be upon me, to provide a most convincing explanation, completely iron-clad.
Arindam Banerjee, Hampton Park, Melbourne, 7 May 2020
The cause of gravity – 6
Why do atoms and molecules attract each other; why don’t they fly apart?
Obviously, there have to be plenty of good reasons, now current, relating to how atoms stick together as liquids and solids (both crystalline and amorphous). For liquids, the stick-together of atoms or molecules is called the cohesive force. For the sticking between a liquid and a solid surface, we have adhesive force. What exactly are these forces? Why do atoms in a crystal stay together in a regular formation, as electron microscopes show? Why are solids solid?
The Nagaoka-Rutherford model of the atom presents the positively charged nucleus at the centre, and the electrons orbiting around the nucleus. This is the current atomic model. Now, if there are negatively charged electrons around every atom, why do not atoms always repel each other on the electrostatic basis? All matter should be gas then!
Reality is that – in most cases - as we increase temperature solids become liquid, and then from liquid turn to gas. (In Std. 8, (1969) our Physics teacher Father Vassalo explained this to us in terms of vibration. He would shake his belly gently to show the transformation of matter from solid to liquid, and more vigorously to show the transformation from liquid to gas. I cannot forget this, the finest exposition of the basics of thermodynamics. ) Rising temperature makes the atoms vibrate more, thus decreasing the inter-atomic bond strengths, till finally the bonds are broken and then they move away from each other. But why were they together in the first place?
Let us consult the Encyclopaedia Britannica (15 ed., 1992) about this matter of inter-atomic or inter-molecular attraction. We look up on the words “adhesion” and “cohesion”. Vol 1 p97 under the heading “adhesive” tells us: “Modern research indicates that adhesion occurs on a minute and intimate molecular level. This explanation, called the adsorption theory, holds that adhesion depends on the same molecular attraction as that which binds all solid matter; any two materials can thus theoretically adhere if they are placed in close enough molecular proximity”. Okay, so let us now look up “adsorption theory”. Vol 1 p109 defines adsorption as “capability of all solid substances to attract to their surfaces molecules of gases or solutions with which they are in contact”. P110 goes on: “Adsorption refers to the collecting of molecules by the external surface or internal surface (walls of capillaries or crevices) of solids or by the surface of liquids”. Vol 1 p435 defines cohesion as “in physics, the intermolecular attractive force acting between two adjacent portions of a substance, particularly of a solid or liquid. It is this force that holds a piece of matter together. Intermolecular forces act also between two dissimilar substances in contact, a phenomenon called adhesion. These forces originate principally because of coulomb (electrical) forces. When two molecules are close together, they are repelled; when further apart, they are attracted; and when they are at an intermediate distance, their potential energy is at a minimum, requiring the expenditure of work to either approximate or separate them. Thus, work is required to pull apart tow objects in intimate contact, whether they be of the same or different material. The attractive forces of cohesion and adhesion act over a short range and vary in magnitude, depending on the substances concerned. If a piece of glass is submerged in water and then withdrawn, it will be wet – ie water will cling to it, showing that the force of adhesion between water and glass molecules is greater than the force of cohesion between water molecules”.
So from the above we learn that electrical “coulomb forces” are responsible for keeping matter together as “intermolecular attractive forces”. This is all very well, but does not explain the exact mechanism involved. How does it work, really what is happening? How is it that there is repulsion at very short ranges, and attraction at longer ranges? From the photo of the iron-sulphide shown, it is evident that there is a range (in a solid) which is optimum for a particular crystalline structure. How to make sense of it all? It would appear that for any molecule in solid form there has to be at a temperature a certain intermolecular distance responsible for the rigidity of the solid. This picture makes it very clear. Still, why does not the negative charge at the outer of the atoms/molecules simply repel each other? Are they held together by mutual repulsion, or attraction? For a solid the latter seems likely, for the liquid the former!
We now search the internet to find any recent findings about this subject, and check out the latest theories that make sense. It is necessary to do this background check before putting forward my new ideas about gravity and molecular attraction on the electrical Coulomb basis. (They would not be new if someone had already done them!)
Googling for “intermolecular forces” provides a number of sites providing explanation for intermolecular forces: the wiki reference is perhaps the most explanatory.
https://en.wikipedia.org/wiki/Intermolecular_force
The site mentions that:
Attractive intermolecular forces are categorized into the following types:
• Hydrogen bonding
• Ionic bonding
• Ion–induced dipole forces
• Ion–dipole forces
• van der Waals forces – Keesom force, Debye force, and London dispersion force
These are very involved explanations and no doubt they are correct as per their own particular areas. I do not wish to go into the details of any or all of them. Fortunately for me, they all miss out on the very subtle and basic aspect common to all intermolecular attraction, which is also the cause for gravity. That element, very fundamental, that has been missed all along will be detailed in the next instalment. The basic question remains: as the electrons – negatively charged – orbit the nucleus, why does matter stay together? Why do they NOT *always repel*? The literature makes statements like :
1. Hydrogen bonding “The hydrogen bond is often described as a strong electrostatic dipole–dipole interaction”.
2. Ionic bonding “ It is essentially due to electrostatic forces, although in aqueous medium the association is driven by entropy and often even endothermic.”
3. Dipole forces “Dipole–dipole interactions are electrostatic interactions between molecules which have permanent dipoles.”
4. Ion-dipole and ion-induced dipole forces “Ion–dipole and ion–induced dipole forces are similar to dipole–dipole and dipole–induced dipole interactions but involve ions, instead of only polar and non-polar molecules. Ion–dipole and ion–induced dipole forces are similar to dipole–dipole and dipole–induced dipole interactions but involve ions, instead of only polar and non-polar molecules.”.
5. Van der Waals forces: “The van der Waals forces arise from interaction between uncharged atoms or molecules, leading not only to such phenomena as the cohesion of condensed phases and physical absorption of gases, but also to an universal force of attraction between macroscopic bodies.”
5.1 Keesom interaction: “These forces originate from the attraction between permanent dipoles (dipolar molecules) and are temperature dependent.[8]
5.2 Debye forces: “arising from interactions between rotating permanent dipoles and from the polarizability of atoms and molecules (induced dipoles).”
5.3 London dispersion force: “The third and dominant contribution is the dispersion or London force (fluctuating dipole–induced dipole), which arises due to the non-zero instantaneous dipole moments of all atoms and molecules.”
It is evident that a great deal of work has been done by the physics community to research this important and intricate area. While terms like “electrostatic force” and “dipole forces” are used, they do not satisfy my query above, that is, why does not matter fling apart because of the outer negative charges for the atoms/molecules repelling each other. How on earth does matter stick together as solids and liquids if the basic tendency is repulsion due to the outer electrons of the atoms/molecules?
My insight relating to the electrostatic explanation for gravity is by contrast extraordinarily simple. I hope that it may help researchers in this area of intermolecular forces to further develop their work. I will talk on this aspect in brief in the next instalment. For the moment, I once again rejoice in that my insight into the electrostatic nature of gravity has not been foreshadowed by anyone.
Arindam Banerjee
Melbourne, 18 May 2020
https://www.facebook.com/photo/?fbid=3592305034130601&set=a.506922209335581
This is the photo of iron sulphide atoms in a crystalline structure.
It is taken from p156 the book
"Physics of the Atom" by Wehr and Richards, Addison-Wesley, 1964
19 May, 2020
The cause of gravity – 7
What is gravity, and the derivation of F=K.N1.N2/D^2 as the attractive force between atoms at any distance D between uncharged masses with N1 and N2 protons/electrons
This is the seventh instalment of my essay on the cause of gravity, the weak but sure force that holds the parts of the universe together. To recapitulate in brief: Signor Leonardo da Vinci’s definition of force, which forms the basis of the Newtonian laws of motion, is random, violent; and being self-defeating, vanishes. This contrasts with the sure and constant force of gravity (attraction between masses) as found by Sir Isaac Newton, and used to prove beyond doubt that the Earth moves around the Sun. (If the Earth did not move around the Sun, it would fall into the Sun. As much as the Earth “falls into the Sun” from the gravitational pull, so much, every instant, it “falls out” due to the tangential motion.) Thus there is a contradiction – one kind of force “defeats itself” and the other kind is always there, always constant. How can that be? Also, as we now know, the formula for universal gravitation cannot account for the (charged) ionic masses streaming away from the Sun? Why does not the enormous gravity of the Sun pull those charged masses back?
Electrostatic force was once surmised to be related to gravity as there were many similarities, such as being equal to the product of charges and being inversely proportional to the square of the distance between the charged masses. However electrostatic force is much stronger than gravity; there has to be charge creating an electric field for its formation; it has much lesser range. There did not seem any link between the forces of gravity and electrostatics.
The finite, indivisible, structure of the atom led to the surmise that charge could be composed of discrete, indivisible components. From experimental work it was found that there is a very small negatively charged mass which was discrete and indivisible – it is known as the electron. Experiments also indicated that within each atom there is a core, or nucleus, of positive charge. The modern notion prevalent in Chemistry is that the negative charges (known as electrons) orbit the positively charged nucleus. In physics the quantum theory would have it that these electrons are “standing waves”, or charged matter which acts not like a particle but as a “wave. Nevertheless, it is not denied that the electrons (whether as particles or as waves) have negative charge; nor is it denied that the nucleus has a positive charge: and finally in a normal atom there are as many electrons around the nucleus as there are protons in the nucleus. Since there is a balance of charge within the atom (with as many protons as there are electrons) the net charge is zero.
So how do we go on from here? It would seem a total no-hoper to try to show that gravity is a weak form of electrostatic force. If nothing else, it would appear that the negative charged cloak of the atom would repel other atoms that too have negatively charged cloaks. And yet, this does not happen. As shown in the last instalment there exist strong inter-atomic forces of adhesion and cohesion. The reason for the existence of such forces is held to be electrostatic fundamentally, but exactly how, whether there is a common factor behind the various explanations presented, is not yet known. (Rather to my relief!)
Well then… time to start the show! First, a brief discussion about zero, and what it means in this context. Let us talk money now, what everyone understands! Consider my zero dollar company, HTN Research. And I ask, why should it be worth zero dollars? I say, it should be worth a trillion dollars. Everybody laughs. Then I add, okay, let us see what are the negative factors preventing it from being a trillion dollars. I remove all those negative factors, that make it a zero dollar company, and hey, my company becomes worth a trillion dollars! (Not instantly, though.)
To talk physics now, consider a flat plate, let it sink to the bottom of the ocean, and then lift it up. It will look the same. For contrast take a closed box, not too strong, and do the same function. It will rise up completely squashed. In the first case, for the steel plate, there was equal water pressure, immense though it was, on either side so the forces cancelled out leaving no net force acting on the plate. In the case of the closed box, there was low pressure inside the box so the much higher pressures around squashed the box. The point I am trying to make it is that the fact of anything being zero does not mean that there are no equal positives or negatives – of any sort - that make it zero. Whether money, or pressure, or partner for life… Take out the positive out from anything in life, you get the negative. Take out the negative, and you get the positive.
Let us apply the notion of zero to a single normal atom. It has a net zero electric field around it. I submit that this zero electric field is the net result of the positive electric field from the positively charged nucleus and the negative electric field. However this does not mean that they do not exist separately. Just that, at any point somewhat distant from the atom, the fields add up to zero, so we say that there is a zero electric field around an atom.
In Figure 1, we consider only the negative electric field arising out of the negative charge from the electrons of other atoms, acting upon the electron E at position A. (We do not consider the positive field at this stage – just remember, once again, the subtle and undeniable point that the zero electric field is the sum of the negative electric field and the positive electric field). Now the negative electric field will cause a repelling force F to act upon the electron E at position A. If this force is very strong, the electron will be knocked out of orbit and the atom will become charged, or ionised. Let us say this does not happen. What then will happen is that the electron E at A will get acceleration, or move faster. As it does not quit orbiting, it will come to position B which is on the other side of the atom. At this point the same repelling force F will cause it to brake, thus to reduce its velocity. Thus the same force accelerates it, and then brakes or decelerates it, so there is no net effect upon the electron in terms of force. Now when we consider that there is matter all around this atom, doing just this thing, it will become clear that the repelling force caused by the electrons around the nucleus of atoms do NOT cause repulsion among atoms. This is a very important point, and I present this as a breakthrough in science. To repeat, the negative charges around the nucleus of atoms, when seen as orbiting electrons, cannot cause repulsion among the atoms. To add, the lines of force involved in this repulsion process rarely go through the centre of the atom, the nucleus that is. All of which means, the atom is essentially untouched by the negative electrostatic forces caused by the negatively charged orbiting electrons.
We can now provide the proof of the electrostatic formulation of the universal formula for gravitations, that is F=K.N1.N2/D^2 superseding F=G.M1.M2/D^2 , where N1 and N2 are the numbers of protons/electrons in the uncharged masses M1 and M2 respectively, distance of separation of nuclei/centres_of_mass being D.
In Figure 2 we show two hydrogen atoms, A and B, separated by the distance D. A hydrogen atom has a single positive charge q as the nucleus (a proton) with an electron of charge –q orbiting the nucleus. We now work out the forces of attraction and repulsion following the venerable Coulomb’s law for electrostatic attraction and repulsion.
The forces of attraction are: Electron of A with proton of B = k.q1.q2/D^2, and electron of B with proton of A = k.q1.q2/D^2; so the total attractive force is 2k.q1.q2/D^2.
The forces of repulsion are: Proton of A with proton of B = k.q1.q2/D^2 ; and electron of A with electron of B which is also k.q1.q2/D^2 . We note that the force of repulsion between the electron of A and the electron of B is tangential thus does not act through the nuclei; it acts as a ripple effect upon the electron orbital movement around the nucleus with equal acceleration and deceleration; and thus does not create any net repulsive force upon the atom.
Thus the net force between the atoms A and B is an attractive one, which is equal to
F=k.q1.q2/D^2. Now, q1=q2=q which is the electronic charge, a fixed value. So
F= K.N1.N2/D^2 where K = kq^2 and N1=N2=1, that being the number of electrons/protons in the atoms A and B.
Thus is demonstrated, the most basic derivation of the updated formula for universal gravitation on the electrostatic basis.
It will be immediately observed that it is valid only for uncharged masses. Thus, the ions do stream out of the Sun, as they are charged, and thus beyond the scope of the Sun’s gravitational pull which is valid only for uncharged masses.
This formula also explains the attraction between all atoms, all material. It underlines as a common feature all the theories relating to intermolecular forces. The rise of fluid in capillary tubes owes to such electrostatic attraction. How does water from the ground rise up in plants? Through capillary tubes within the plants: the fluid adheres to the walls of the capillaries in the plants, pulling itself up by the electrostatic forces between the atoms of the fluid and the atoms in the wall linings.
In Figure 3, we extend the derivation of the updated gravitational formula for a hydrogen atom and a helium atom, and two helium atoms. In Fig. 3 we do not draw the electron-to-electron interactions, just the proton to electron and proton to proton interactions.
The question now is, what is this constant K and what does it really represent? Further, what new insights into the universe can we get from the new electrostatic representation of the formula for universal gravity? That will be discussed in the next instalment on this topic: the cause of gravity.
Arindam Banerjee
Hampton Park, Melbourne, 25/05/2020
The figures mentioned in the article are to be found in my facebook time, links are
Figure 1:
https://www.facebook.com/photo?fbid=3609632575731180&set=pcb.3609639489063822
Figure 2:
https://www.facebook.com/photo?fbid=3609633399064431&set=pcb.3609639489063822
Figure 3:
https://www.facebook.com/photo?fbid=3609634162397688&set=pcb.3609639489063822
Cheers,
Arindam Banerjee, 26 May 2020
The cause of gravity – 8
Finding the value for the constant K in the updated equation for gravitation involving electrostatics
Consider two isolated Helium atoms separated by a distance of one meter in free space. They each have the mass of 6.6464731*10^-27 Kgs. We make the note that the Helium atom as having equal numbers of protons and neutrons in the nucleus is more suited than say the hydrogen atom (having just the one proton in the nucleus) to represent masses in general.
According to the law of universal gravitation, the gravitational force between two equal masses, each called m, is
F=Gm^2/d^2, where d is the distance between the masses and G is the universal gravitational constant with the value of 6.674*10^-11 MKS units. (Note: when we use a physics formula, we have to adopt a particular set of fundamental units. MKS means Meter Kilogram Second. It is thus different from the CGS units of Centimeter Gram Second.)
The attractive gravitational force between two Helium atoms separated by 1 meter will the be:
F=6.674*10^-11*(6.6464731*10^-27)^2/(1)^2, or
F=6.674*6.6464731^2*10^(-11-27-27), or
F = 294.828*10^-65, or
F=2.94828*10^-63 Newtons.
The force for the electrostatic/gravitational attraction between two helium atoms separated by one meter is from the formula
F=k*q^2*N1*N2/D^2 , where D is one meter, N1=N2=2 (there being 2 protons/electrons in each atom) and q is 1.6021*10^-19 coulombs (a MKS unit) is
F=k*(1.6021*10^-19)^2*2*2/(1)^2, or
F=k*2.56672441*10^-38*4, or
F=k*10.26689764*10^-38, or
F=k*1.026689764*10-37 Newtons and this value has to be equal to 2.94828*10^-63 Newtons found above from the older formula.
Thus k*1.026689764*10-37 = 2.94828*10^-63 from where we get the value of k as
k= 2.87163669*10^-26 MKS units.
The new upgraded formula for gravitational attraction for uncharged masses with N1 and N2 protons/electrons in each; where the number of protons and neutrons in the nucleus are roughly similar; and separated by distance D meters is
F=2.87163669*10^-26*N1*N2/D^2 Newtons
Arindam Banerjee
Melbourne, 28 May 2020
The cause of gravity – 1
Brief:
The formula for universal gravitation is well known to be, as the force F acting between two masses m and M, parted by a distance r from their centres of mass, as F=GmM/r^2, where G is the gravitational constant found by experiment. Recently the author has updated this formula to F=BnN/r^2 where B is a constant, and n and N are the number of protons or electrons in the masses m and M. It is obvious that as n and N are proportional to m and M, this is essentially the same formula with the difference that instead of masses, the new formula involves charges. Thus the gravitational force is expressed electrostatically, as a manifestation of electrostatic force. In other words, there is no difference between electrostatic force and gravitational force.
As such, there should be, among reasonable people, no quarrel with the new electrostatic representation of gravity, as on the surface it is a re-statement of the earlier statement. The curious may well be satisfied that an electrostatic representation of gravity may somehow explain what is so far unexplained and not understood about the manifestations of Nature: such as capillary action in plants and narrow tubes where fluid rises up defying gravity and the law of conservation of energy; and how charged winds streaming from the Sun can be formed despite the Sun’s huge gravity.
But, as presented – so far - without supporting logic as to its derivation, the new formula seems to be a trivial form of the existing formula, imparting no new knowledge. It may also seem preposterous as uncharged masses, by definition, do not emit any measurable electric field. Finally, the electrostatic forces are estimated to be as per physics literature to be some 10^39 times stronger than the gravitational force. For all these reasons, the gravitational force has been held to be something entirely independent, yet similar to the electrostatic force.
It is my purpose, in the following articles, to show that despite the above sound objections arising from the existing scientific viewpoints, indeed the gravitational force is a manifestation of electrostatic force.
Instead of the just the physics community, I will make my appeal primarily to the intelligent lay public, who are innocent of whatever passes for modern physics. For that purpose, prior to making my new points, I will try to impart a crash course in the fundamentals of electrostatics, as simply as possible. Furthermore, I will as my target audience have my old school friends, whose loyalty and faith in my abilities I most deeply cherish. My sole request to them – and all my other friends in Facebook and beyond in the online world - is to tell me, as bluntly as possible, exactly what they do not understand about what I will be writing, in further instalments on my Facebook timeline. (I will post my writings in the Usenet newsgroup sci.physics as well).
Cheers,
Arindam Banerjee, 21/4/2020
The cause of gravity – 2
Historical background:
Sir Isaac Newton, in his great work known as the “Principia”, primarily stressed upon two factors; the role of geometry in modelling reality, and the use of mathematics to make correct and accurate predictions in idealised environments, like say a body in free space surrounded by nothing. Let us have this in mind when we discuss how he managed to discover gravity, from the general level of the scientific thinking in his time
.
The scientific thinking of his time was Aristotleian. For many hundreds of years, it was believed that the Sun went around the Earth – exactly as we can all see for ourselves. The stars were the openings to Heaven, sending down heavenly light. They moved in crystal spheres that too revolved around the fixed Earth. The Christian Church devoutly followed the Aristotleian model, for it was perfectly, obviously, correct with the stars being proof of Heaven and the need to be religious and dutiful to get there, via the Church of course. Let us not forget, no one had a clue about gravity, or even force as a scientific measurement construct, for that matter.
So the ancients did their science in their own way, basically through empirical methods as they lacked the theory and the resulting mathematical modeling. To the extent they were practical, following geometry, they got good results. As an example, let us see how the Greeks calculated the distance to the Moon. They used parallax. This means that when one points to an object at one point, there is a certain angle with respect to a common plane. From another point on the same plane, there is a different angle. To experiment (P.S. try this), point at anything a bit distant with a finger or scale with just one eye. Then shut it and open the other eye. The object will have “moved” but it is just the parallax effect. You will have to shift the finger or the scale to the original object to find the angle of parallax. From the distance between your eyes, and the angle, the distance to the object can be found.
Hipparchus of Nicaea (190-120 BC) used the parallax method to get the distance to the Moon with reasonable accuracy. The ancients may not have known about force and gravity the way we do, but they did know about parallax, geometry - and Hipparachus himself is also credited with inventing trigonometry! Incidentally, the parallax method is still used to this day to find the distance of stars and galaxies from our planet.
Thus Isaac Newton was heir to the great Greek scientific traditions. He had been further influenced by Copernicus and Galileo. About these two, now: let us also get in touch with dates, we are doing some history after all!
Copernicus (1473-1543) is credited with discovering (in the West that is) the heliocentric system, that is, the Sun is fixed and the planets revolve around it. He did it without a telescope, just his naked eye with some pointing tools. And that was enough. What he found was that the angular positions of heavenly bodies (stars, planets) changed the most every six months, constantly. The same old parallax system is at work, this time instead of the space between two eyes from our earlier example, twice the distance of the Earth from the Sun! Copernicus concluded that the dominant and hallowed geometric system (Sun and planets and stars going around the Earth each in its own crystal sphere) was wrong. The explanation, to account for this anomaly, was that the Earth was revolving around the Sun. It was a perilous explanation, for it went against the doctrines of the Church. Galileo (1564-1642) was persecuted in 1633 for supporting Copernicus, by the famous Church Inquisition where he was forced to recant, and say that Copernicus was wrong and Aristotle was right. He was more fortunate than Giordano Bruno, the talented Dominican friar who was burned at the stake on 17 Feb 1600 for upholding the Copernican heliocentric view, and further stating that the universe was infinite and that other solar systems also existed.
Back to Isaac Newton (1642 – 1737). It should be obvious from the mood of his time (as presented above) that the geocentric model was absolutely dominant – all the churches expounded it, the universities taught it, all rich and important people believed it utterly. Exactly as they believe in special and general relativity, quantum theory, big bang, expanding universe, black holes, quarks, bosons, string theories, neutrinos, photons, fusion, e=mcc, spacetime, nothing can go faster than light, etc. etc. etc. these days, following Einstein, Feynman and Hawking. Newton was evidently too smart to fall for the geocentric model – but how could that make him popular with the powers that were in his time? Newton had a miserable time as a student, and did his best work when he was on his own, away from the mediocre professors professing the Aristotleian geocentric model. But, he did not have anything really substantial to smash the geocentric model. The angular differences in the positions of the heavenly bodies could be dismissed with airy hand-waving, along with some spurious explanation like wobble in the crystal spheres, as a devil’s prank to confuse the faithful.
It is said that in 1666 (that is, when Newton was 24 and Galileo had been forced to recant his views only 33 years ago) that the famous apple fell on Newton’s head, or on the ground before him. Why did it fall to the ground? A simple question, but no one had asked it before. Why was it moving faster and faster (accelerating) as it fell? Newton thought that there had to be an attractive force between the mass of the Earth and the apple, which caused it to fall. It was moving faster and faster because till it fell, the force was working constantly upon it, causing acceleration. Newton then theorised that all bodies with mass are attracted to each other. The apple falls to the Earth, but the Earth is also influenced – the Earth also moves towards the apple, but as the Earth is too big, and there are many other falls all over, the Earth’s movement is not discernible.
Newton theorized that the attractive force was proportional to the multiplicative product of the two masses attracting each other, and inversely proportional to the square of the distance separating them. This directly leads to the present formula, F=GmM/r^2. However let us not forget that the gravitational constant G was not known until Cavendish measured it in 1797-98, some 131 years after Newton had his famous insight, which had so far eluded everyone else.
If masses did attract one another, just as the Earth attracts the falling apple, then why does not the Earth fall into the Sun, like the apple falling to the ground? Either gravity operated only on Earth (thus the Earth and the Sun did not attract each other) or the sun being very small (like say Apollo’s chariot) revolved around the Earth; or - and this was supported by astronomical findings supporting Copernican model of the rotating Earth revolving around the Sun - the Earth actually moved around the Sun.
It was obvious that the Sun was far bigger than the Earth, from the phenomena of eclipses and the knowledge of the Moon’s dimensions. It is still not known 100% that gravitation works for heavenly system, the way it does for the apple-Earth system, thus the universal theory of gravitation remains a theory, although one of the most powerful theories known, like the atomic theory. It is still a theory, for it cannot explain why ionised masses escape from the Sun’s extraordinary gravitational pull.
The Earth then has to move tangentially, always, for ever, to escape falling into the Sun. It certainly would do so if a giant hand stopped its motion! What Newton with his geometry and maths explained, clearly, was that the Earth is in fact always “falling into” the Sun, but because of its tangential velocity, “falling out” by more or less the same amount. (The” more or less” accounts for the elliptic orbit, that is, not purely circular, as Kepler (1571-1639) had worked out before Newton.)
The earlier point is worth pondering about, for a few minutes. It explains the motion of all satellites. The tangential motion allows the satellites to not fall back to the Earth, and keep constantly revolving unless the tangential speed is reduced by drag of some kind, including rocketry.
Another point about gravity – the gravitational force simply depends upon the existence of mass. It never changes for that mass. It is constant, always there. This mass always attracts, thus its force never changes, it is exerted all around in all angles. Always, always…. Such is the fundamental design of the Universe. Can we probe a bit deeper into its cause, now? I think some more groundwork is necessary.
22/04/2020
The cause of gravity – 3
The conception of force
Force is the central issue in physics – or at least, it should be the central issue in physics. It is from force that all things move, or stay put. Force moved over distance is work, and work has the same units as energy. Energy, then, is expended when a force moves over a distance. There is a vast difference between force and energy – as I see it, force is for the physicists to better understand the workings of the Universe; and energy is for the businessmen to make money. So it is, that as far as possible, to understand the fundamentals of Nature, I avoid the use of the energy concept.
The difference between force and energy is tricky. It is easy to confuse one for the other, and most people untrained in physics may do so. Force must have direction – it is thus called a vector. Because forces have direction, two separate forces operating in the same direction add up to one double-force. In opposite directions, they cancel out to zero. But energy has no direction. It is thus called a scalar quantity. Energy is usually defined as the capacity of a body to do work. It is further postulated that energy is always conserved. Its form however changes: when we drop a ball to the ground, the potential energy of the ball at the start changes to the maximum kinetic energy just near the point of impact. After this, though, the thinking is not that clear. After impact, the kinetic energy is converted to heat energy. Instead of saying that this energy is lost, we say, as per classical physics, that the entropy, a mathematical concept about the state of disorder in the universe, has increased. I have never been happy with this explanation – it seems to me pretty self-evident that energy is continuously getting created by the Sun and Earth, being used for various purposes, before being radiated out for destruction into deep space. Thus, energy is pretty slippery. It is always getting used up. We need money to use energy, if we cannot make use of the natural sources like the Sun and wind and water and geothermal.
Is force equally slippery?
As far as I can see, Leonardo da Vinci (1452-1519), in his Notes, made the first-ever proper description of force with the following statements:
“Force I define as a spiritual power, incorporeal and invisible, which with brief life is produced in those bodies which as the result of accidental violence are brought out of their natural state and condition. I have said spiritual because in this force there is an active, incorporeal life; and I call it invisible because the body in which it is created does not increase in weight or in size; and of brief duration because it desires perpetually to subdue its cause, and when this is subdued it kills itself.”
Such a definition of force is slippery indeed! From da Vinci’s definition, secularized, force is the “result of accidental violence” brought out “natural state and condition”. Thus it is random and violent. It is “brief in duration”, meaning it is transient, certainly nothing permanent. A perpetual desire to “subdue its cause” means that it is revolutionary. When successful in that “it kills itself” so is suicidal. This appears as quite a statement of the violent political mood of his times, based upon sneaky opportunisms, as elaborated upon by his contemporary Machiavelli (1469-1527)!
It will not be difficult to see how much da Vinci’s conception of force - which in his day had to be purely mechanical - influencing later scientists like Galileo, led to the formulation of the well-known Newtonian laws of motion. The phrase “natural state and condition” is known as inertia, formulated in the first law of motion. “Result of accidental violence” refers to acceleration, and is formulated in the second law of motion. The statement “when this is subdued it kills itself”, refers to the third law of motion which states that to every action there is an equal and opposite reaction.
From the above discussion we find that the conception of mechanical force is not just slippery; it is random, violent, transient and suicidal. Nothing constant about force! And yet, with such conception of force, formed from the greatest minds in the West, all the wonderful works in engineering have been done, from locomotives to jet engine airplanes; from muskets to missiles; small cars to huge ships! As force is slippery, so energy too is slippery. Energy mutates from one form to another. Just like force, its magnitude depends upon the frame of reference with respect to any observer. Thus two jet airplanes flying side by side may gently nudge each other, with minimal force or expenditure of energy involved. But if they collide, meaning the reference frames are opposite now, the forces involved and the energy spent in the disaster is enormous.
The above conception of force, so widely accepted because it was correct, makes Isaac Newton’s discovery of gravity all the more remarkable. For gravity is not slippery, nor random, nor violent, transient and suicidal. It is the very opposite. It is constant, spreading out in all directions, relatively very gentle, and permanent. Being all that, it is gravity which holds us all together on this planet; and it is gravity that makes the entire universe a permanent moving system composed of unlimited quantities of matter. Gravity, thus, is an entirely different kind of force. As we shall see, it is a much muted form of electrostatic force. Till now, despite their basic similarity, gravity and electrostatic forces are held to be independent: one is not the manifestation of the other.
A few more points: the random nature of mechanical force had led Leonardo da Vinci to conclude that a device that would perennially give out energy (a perpetual motion machine) was impossible. Even when gravity was discovered as a constant force, this was found to be true. This inability to construct a perpetual motion machine was a factor in the definition of the law of conservation of energy, that energy could neither be created nor destroyed. Certainly this law is much appreciated by the fossil fuel industries!
Researching Leonardo da Vinci’s comment on the nature of force, this time with a more modern mindset, we note the words “I have said spiritual because in this force there is an active, incorporeal life”. Now concentrate on the words “in this force” and “life”. Da Vinci is not talking of force as an expression of the inanimate – for him all forces relate to life and spring from some unknown higher purpose, thus blurring the line between physics and metaphysics.
“Life force” thus is essentially internal. It comes from within, but is related to without. Going by da Vinci’s perception, it is inherently random and self-destructing. But what if it can be made to act otherwise, with the purpose of steady movement in one direction? What if instead of being pushed around by external forces, bodies can push themselves with internal “life force”? We all know that this is a dream monetized by science fiction. Can this fiction become fact? Can we overcome the effects of gravity with internal force?
For over twenty years, I have wrestled with the above issues. My work has been presented online. In 2000 I published in my “adda” website my book “To the Stars!”. It attracted minimal interest, till in 2003 an article by myself was published in the Science Section of Outlook Magazine, in India. I got fiercely hostile reactions to my article, which surprised me before I got disgusted with the low quality of scientific temper, from low personal attacks. For example, one Garg, a junior scientist in the employ of the Govt. of India, offered gratuitous abuse.
The link for that article is at https://www.outlookindia.com/magazine/story/newt-is-old-hat/220728
I now believe, that the editors thought that I was attacking Newton with my new ideas, and that was the reason for its publication!
Arindam Banerjee
25 April 2020
The cause of gravity – 4
Measuring fundamental constants (G) and the meaning of research
(start rant)
Today the entire field of physics is thoroughly institutionalised, with standardised thinking dedicated to perpetuating the established orthodoxies, like any religion. These high priests – in the field of what is called “modern physics” involving the theories of relativity, publish their weird notions, with amazing smoke screens of mathematical gibberish to confuse the most intelligent lay persons, in select journals and conferences, to maintain their high prestige. Their efforts are very expensively funded by the Governments and various rich parties, blindly supporting the high priests ensconced in universities and Govt. laboratories. Amateurs or hobbyists have no place in this closed system. The best they can do is to publish their work online; in social media, email, etc. unless they spend thousands of dollars for publication in some vague journal which will be automatically derided by the establishment because of its low ratings. In this system success is measured in terms of the money squeezed out from the higher powers for some “output”. Like gravity waves, quarks, red shift, big bang, string theory, black holes, bosons, neutrinos… you name it, there will always be more coming!
So much is this notion prevalent, that only the expenditure of millions or billions of dollars involving vast projects such as making black holes, or fusion energy, is considered solely necessary to finding something new and wonderful – which, however hardly ever happens. Anything revolutionary in physics, involving low budgets and lone endeavour is automatically discarded as cranky or plain wrong if it goes against the grain of the orthodoxies.
(end rant)
The greatest advances in physics did not require huge investments in money and manpower. What was needed was insight, dedication, patience, skill, tenacity… of the talented amateur, working with minimal help. Sir Isaac Newton is the best known example, as the discoverer of the force of gravity. But his discovery in 1666 was far from complete. He could only indicate that the gravitational force between two masses was proportional to the product of the two masses, and inversely proportional to the square of the distance between their centres of gravity. Newton did not know what the proportionality constant was. We now know it as the gravitational constant G.
It was only in 1798 (that is 135 years after Newton’s discovery) that the Gravitational Constant was found from measurement, by Henry Cavendish. The experiment was painstakingly done by Cavendish, but the apparatus itself was simple. A recent attempt to recreate a model of the original apparatus is shown in the Youtube video film
Cavendish’s experiment was conducted in a large sealed room, to prevent air currents. Two lead balls, spaced widely apart were joined by a thin light rod. A fine string suspended these two balls from their centre of mass, from the ceiling. Two heavy lead balls were placed near the suspended balls, such that they could each attract the suspended ball in the same direction so as to produce the maximum twisting effect (torque) upon the string. How much the string would twist, could be found out by the angular displacement of a very light long strip connected to the twisting string. The movement of the edge of this strip could be tracked from its initial position to find the angular displacement.
So much (from above) I have got from the literature, and the rest is my own construction, relating to the necessary calibration and measurement. The gravitational force is very small. And yet, it can be measured correctly with proper application. The main issue is calibration, for any measurement.
What we have to know is how much the thread twists for a certain torque (twisting action). Let us say that the length of the suspended rod with its attached balls is ten meters. Torque is equal to the force F multiplied by the distance r to the point of twist. Or T=F*r. With equal force from the other end it is T=F*r + F*r = 2Fr or F.d. The torque motion will be resisted by the material in the string – it cannot twist indefinitely - after a certain angle (depending upon the quality) the string will no longer twist as a result of the torque. Thus T= k.theta, where theta is the angle of twist and k is a constant depending upon the quality of the string. F.d=k.theta then; now we need to find k.
The issue of calibration now comes in. Let us see how it can be done. From about 10 cm from the centre of the suspending string, tie a fine thread to the rod on both sides. Slide it over a pulley to a suspended mass of say 1 gram, on both sides. A continuous torque now acts on the suspended string. It will twist by a certain angle, then stop twisting. Measure that angle. Now make more experiments with increasing or decreasing weights, and changing the distances involved, to get many values of theta, and from F, d and theta, so many values of k which should all be more or less the same for a given torque applied with various values of F and d. Numerous experiments average out the experimental error, statistically, to get k.
The rest of the experiment is simple. Just get the very heavy balls of lead near to the suspended balls, at right angles and as near as possible without touching. The small balls will be attracted by this extra mass near them, and the torque will be created till the suspended string twists by an angle theta. Knowing k and theta, the torque T is known. Knowing the torque T and the distance d, the gravitational force F between the suspended ball of mass m and the heavy ball of mass M is known. Various values of F can be found with increasing or decreasing the static balls; that is fro. Now at the end position, the distance between the centres of gravity of the suspended ball of mass m and the heavy ball M is found. This is r. So now we have all that is needed to find the gravitational constant G from the formula
G = F*r*r/(m*M)
With this formula, Cavendish could work out the mass of the Earth, knowing g, the acceleration due to gravity. Every apple of mass m falls to the Earth with mass M, by the law of universal gravitation (it is assumed now that as per Newton not just lead balls in an experiment are attracted with the constant G, but all bodies in the universe) it falls with a force F which by Newton’s second law is equal to m.g
The above equation can be written as M=F*r*r/(G.m) With F=mg, it is M=r*r*g/G
For the fun of it, let us put in the values to get the mass of the Earth! r is the Earth’s radius which is 6371 Km or 6371000 m. g on the surface is 9.8 m/sec/sec. G is found to be 6.674*10^-11 in MKS units. The calculator result is that the mass of the Earth is 5.96 *10^24 Kg. How nice! Knowing the mass of the Earth we can also find the mass of the Sun, Moon and so on. In the practical sense, we can know how much force is exerted by the Earth on distant objects like satellites or space vehicles.
**** NEW ****
So far we have been dealing with the known. Research to most means looking things up, but as a professional researcher I do not call that research; I call that search. Research (re-search or search again and again and again…) means looking at an established search in a new way each time, with a slightly different angle, with the knowledge of relevant new knowledge and finally with special insight (from the Divine, in my case and with all my heroes in science: Plato, da Vinci, Newton, Maxwell, Tesla, my great-uncle Sir U N Brahmachari) for its own sake, or for some practical purpose.
Applying that notion of research to the notion of the gravitational constant G, what do we find?
**** INSIGHT ****
We find that none of the masses involved in the experiment were charged with electricity.
*****************
Which amounts to, the law of universal gravitation may or may not apply to charged masses. This explains why ions stream out of the Sun, despite the Sun’s huge gravitational force. However up till now, we had assumed that charged masses were subject to gravitational forces, so the ion streaming from the Sun is a mystery.
But what is charge? Sir Isaac Newton had no idea about charge, no clue about electricity. Cavendish may have had some idea, for his apparatus was a large torsion balance, used to measure electrostatic forces. We will go into the details of electrostatics in the next instalment. That will be the prelude to expressing the equation of universal gravitation in electrostatic terms.
Arindam Banerjee
29 April 2020
Further comments in my facebook post: 29 April 2020
understand this, that the Gravitational Constant was measured only with masses with no charge in them. Both were uncharged. This is a small but vital point. It shows that assuming that the law of universal gravitation is valid for charged masses is an assumption. It is the job of the researcher, that is, one who searches old stuff with new eyes, to point this out. And that is what I have done. And will be doing, in later instalments.
With the measurement of the slightest twist of a string, one may thus weigh the Earth, Sun, Moon and the planets! Direct the course of spaceships! Such is the power of the correct theory. Or rather, the more correct theory. Science is always provisional, that is, in for change.
Thus I wonder, how much mad those around the likes of da Vinci, Galileo, Newton, Cavendish, Franklin, Faraday thought them to be! They would not have had the faintest clue of what was going on. They would stoutly believe in established notions expounded from some pulpit or altar. Things have not changed, have they!?
The cause of gravity – 5
The fundamentals of electrostatic attraction leading to the structure of the atom
To recapitulate the thesis: “The formula for universal gravitation is well known to be, as the force F acting between two masses m and M, parted by a distance r from their centres of mass, as F=GmM/r^2, where G is the gravitational constant found by experiment. Recently the author has updated this formula to F=BnN/r^2 where B is a constant, and n and N are the number of protons or electrons in the masses m and M. It is obvious that as n and N are proportional to m and M, this is essentially the same formula with the difference that instead of masses, the new formula involves charges. Thus the gravitational force is expressed electrostatically, as a manifestation of electrostatic force. In other words, there is no difference between electrostatic force and gravitational force.”
We have dealt with the development of gravitational force at some length, in the earlier instalments. To validate the thesis that there is no difference between electrostatic force and gravitational force, let us see how the electrostatic force was developed to the point where it could be seen as being deeply involved in the basic elements of matter, that is, atoms.
From the second volume of the revered Halliday and Resnick, we learn that Thales of Miletus, in 600 BC, knew that a rubbed piece of amber will attract bits of straw. This results from electrostatic forces. Prior to this, it was known that certain naturally occurring “stones” (magnetite) will attract iron. This is magnetism. These two sciences developed quite separately until 1820, when Hans Christian Oersted (1777-1851) observed that an electric current in a wire can affect a magnetic compass needle. This discovery led to the entire new science of electromagnetism.
For our purpose, to show that there is no difference between electrostatic force and gravitational force, the sciences of magnetism and electromagnetism are not relevant. We will concentrate upon electrostatics, first by presenting the historical background.
If we suspend a glass rod, and rub it with silk, remove the silk stuck to it, then bring near it a second glass rod also rubbed with silk, we will find that the rods repel each other. The American Benjamin Franklin (1706-1790) was the first to distinguish between positive and negative charges. The former related to the kind of charge on the rod; the latter to the kind of charge on the silk. In its normal or neutral state, all matter (that is, what is measured as mass) contains equal amounts of positive and negative charges. When material bodies like glass and silk, or rubber and fur, are rubbed together, a small amount of charge is transferred from one to the other, upsetting the electric neutrality of each.
From the point of view of electrostatics, matter is of two types – conductors and insulators. A conductor – usually a metal – is what will not develop a charge when rubbed, unless it is attached to an insulator like glass or rubber, and the conductor is not touched by the hands in the rubbing process. Metals, the human body, the Earth are conductors of electricity as the charges can move in such conductive matter. Charges cannot move in insulators like glass, hard rubber, plastic, mica.
The Hall effect shows that only negative charges are free to move in conductors, but in electrolytes both positive and negative charges can move. It is now known that the actual charge carriers in metals are free electrons, but this was not known to the early experimenters, who had no clue even about atoms let alone electrons. What they knew was that if an insulated conductor was contacted with a charged insulator, then the charge would be transferred to the insulated conductor and spread all over the surface evenly. They knew that the charge would be passed on, and halved if an equal sized uncharged conductor would be touched by a charged conductor (both being insulated!). It is with such a background that the torsion balance was devised to measure the quality and quantity of the electrostatic forces by Charles Augustin de Coulomb (1736-1806). (We have already seen how Cavendish used a much enlarged torsion balance to find the gravitational constant G in 1797-98.) Thanks to Internet, we can easily get details from such sites as:
http://ffden-2.phys.uaf.edu/104_2012_web_projects/cicely_shankle/Page%202%20-%20Coulomb%27s%20Experiment.html
which explain and extol the ground-breaking work he did in 1785. Coulomb’s first experimental results show that the force between charges is inversely proportional to the square of the distance between them, that is F ∞ 1/r^2. These forces act as per Newton’s third law, that is, act on the line joining them but pointing in opposite directions. Further he showed that the force was proportional to the quantities of charge q1 and q2 on the charged spheres such that overall the formula for force, known now as Coulomb’s law, is F∞ q1*q2/r^2. With a proportionality constant k, this becomes
F=k*q1*q2/r^2, and is the fundamental formula for electrostatics.
It is immediately clear that this formula is structurally similar to F=G*m1*m2/r^2, the law of universal gravitation, which by 1785 was more than 100 years old. However it was also noted that the force of gravitation was much weaker, and always attractive. In other words, the attraction between two masses, with charge, would vary with design – but in the case for gravity, the attraction would always be the same. This realisation placed gravity as an entirely separate force, and to this day this remains the standard scientific standpoint.
Before I prove my thesis in the next instalment, let us study the development of atomic structure from an electrostatic point of view. John Dalton proposed his atomic theory in 1803, a fair while after Coulomb’s experiments. Not being chemical in nature, the atomic theory was irrelevant to the development of electrostatics and its possible relationship with the force of gravity. However, its impact led to the realisation that charge, like atoms, could also be indivisible and finite and thus a group (when static) or flow (when moving) of “corpuscular” particles as found by J J Thomson in 1897. The term we use today for Thomson’s corpuscle is electron. It had been coined by G. J. Stoney in 1891, to denote the unit of charge relating to passing electric current through chemicals. Thomson’s colleague Joseph Larmor also used that term, in his theory that the electron was an aetheric component – not a part of an atom (for that would mean violation of the atomic theory which held that atoms could not be further divided). (Aether is the fundamental component of the universe, supporting all radiation from all sources as the medium for electromagnetic waves, being an infinitely fine, infinitely elastic solid through which all matter flows without resistance. – my definition, following 19th century natural philsophers.)
The site https://history.aip.org/history/exhibits/electron/jjelectr.htm gives details about J J Thomson’s experiments with cathode rays in cathode ray tubes. In brief, a cathode ray tube is just a glass tube with electrodes at both ends. When a high voltage difference is applied to the electrodes, and the gas in the tube taken out (like any light bulb) there is a glow in the tube, following from a flow of current which meant that charge was flowing through the near-vacuum, causing picturesque effects. The general consensus was that these “cathode rays” were like light rays propagating through aether. However, the cathode rays could be deflected by magnetic fields, unlike light rays. The rays also passed through very thin foil – unlike light. Scientists Perrin, Wiechert and Lenard found out respectively in 1896-1897 that the cathode rays carried a negative charge; the ratio of their mass to charge was over a thousand times smaller than the hydrogen ion; if the rays were particles they were extremely small as they had a good range despite material obstructions.
Thomson made his breakthrough when he made a near perfect vacuum for the cathode ray tube. Previous experiments had failed to bend the cathode rays in an electric field, which raised the suspicion that they were not charged particles after all. He surmised that the remaining gas is the tube was being made conductive by the cathode rays; so acting as a sheath to the cathode rays. Charged particles do not bend to an electric field when they are enclosed in a conductive sheath. After evacuating the gases from the tube, Thomson found that indeed the electric field was bending the cathode rays (incidentally this is the science behind the old television sets). This was the final proof – negatively charged “corpuscles”, very small in size, constituted the cathode rays. Thomson stated that as his first hypothesis; the second was that these corpuscles are constituents of the atom; the third was that the corpuscles are the only constituents of the atom.
The second and third hypotheses met with scepticism. While the second hypothesis has been accepted (with difficulty by the scientists of his time, for it violated the atomic theory – it was easier to visualise massless fluid charges associated with indivisible atoms) the third has not been accepted. How could atoms be built up from these “corpuscles”? Where was the positive charge? Thomson co-proposed an atomic model, known as the “plum pudding” or “raisin cake model”: thousands of tiny, negatively charged corpuscles swarm inside a cloud of massless positive charge. In insulators, these corpuscles were more or less stuck unless rubbed off. In conductors, they moved. Under electric voltage (in evacuated tubes) they moved in free space. The massless positive charge (the pudding or cake) never moved, of course. When the corpuscles were squeezed out, by physical pressure or electric potential, the atoms showed their positive charge; which remained so until the absorption of the missing corpuscles to regain charge neutrality. In this way, the natural phenomena relating to electrostatics were adequately explained. For this atomic model, J J Thomson got the powerful support of another Thomson, Lord Kelvin, the venerable scientist after whom the Kelvin temperature scale is named. It was Lord Kelvin who had proposed the “plum pudding” atomic structure in 1902. J J Thomson worked on substantiating this model from 1903 to 1907.
The Japanese physicist Hantaro Nagaoka proposed an alternative model in 1904 – here the atom resembled the solar system or the planet Saturn, with rings of electrons surrounding a concentrated positive charge. (Ency. Brit. 15th ed. Vol 14, p347). This is in fact the contemporary atomic model minus the quantum theoretic add-ons following Bohr, but it was rejected on the grounds that by radiating continuously the electron would gradually lose energy and spiral into the nucleus. No electron could thus remain in any particular orbit indefinitely. This is, evidently, specious reasoning . The Earth does not lose energy by spinning around the Sun. The kinetic energy remains constant, both for the Earth around the Sun and the electron around the nucleus under normal conditions; so there is no question of energy loss. Just as the Earth does not fall into the Sun, thanks to its continuously-changing-in-direction tangential velocity, thus “falling into” the Sun from gravity as much as it “falls out” of the Sun due to its tangential velocity, thus keeping the orbital radius fixed; so does the electron does not fall into the nucleus – here instead of the gravitational force there is the electrostatic attraction between the positively charged nucleus and the electron with its continuously-changing-in-direction tangential velocity.
Had it not been for the discovery of radioactivity, we could have retained the “plum-pudding” atomic model to this day. In 1896, Henri Becquerel discovered radioactivity – rays emanating from certain minerals fogged unexposed photographic plates. His student Marie Curie discovered that only certain chemical elements gave off these rays of energy, and provided its name, radioactivity. In 1899 Ernest Rutherford discovered and named a component of radioactivity, alpha rays. It turned out that they were positively charged particles – now we know them as Helium nuclei with two protons and two neutrons.
No one knew what caused the emission of energy from minerals – that phenomenon certainly violated the law of conservation of energy, and also showed that positive charge could move upsetting previous thinking. They wondered as to how the energy from the Sun was generated – some form of radioactivity? If someone then had derived the kinetic formula relating mass and energy on a non-destructive basis, which I found in 1999, human history would have taken a very different turn for the better.
Rutherford upset the “plum pudding” atomic model in 1911, with his famous gold foil experiment which validated the Hantaro Nagaoka model. With his assistants Geiger and Marsden he beamed alpha particles through a 0.00004 cm thick gold foil and detected them as flashes on a screen. It was found that 1 in 20,000 alpha particles were deflected by an angle of 45 degrees or more, while others went straight through. The straight-through-going particles could mean that alpha particles could punch through the positive “pudding” in the Thomson atoms, or that atoms consisted of mainly empty space offering no resistance. However the deflections of the very few particles indicated that they were getting near some heavy positively charged mass, which formed the nucleus of the atom. What kept these charges together – why did they not fly apart? The accepted theory now is that there is a certain “strong force” operating entirely within the nucleus and not outside, that keeps the positive particles along with the neutral-charge neutrons together. Rutherford held that the positive particles (now known as protons, or Hydrogen nuclei) were held together by electrons. Thus according to him a Helium nuclei, or an alpha particle, is four Hydrogen nuclei (protons) held together by two electrons.
For my purpose, that is, to provide an electrostatic explanation for the force of gravity, and to deduce the new equation F=BnN/r^2 (details given earlier) this much information is enough. Later developments of the atomic model by Bohr and others are not relevant, for as of today no one seriously questions that electrons orbit a much heavier positively charged nucleus in the atom.
In the next instalment the logic and derivation for the abovementioned equation will be provided. To recapitulate; gravity is considered nothing electrostatic as it is very weak, always attractive, always steady, has nothing positive or negative relating to force-field, has everything to do with just uncharged masses, and has a very long range. I don't know what the odds will be upon me, to provide a most convincing explanation, completely iron-clad.
Arindam Banerjee, Hampton Park, Melbourne, 7 May 2020
The cause of gravity – 6
Why do atoms and molecules attract each other; why don’t they fly apart?
Obviously, there have to be plenty of good reasons, now current, relating to how atoms stick together as liquids and solids (both crystalline and amorphous). For liquids, the stick-together of atoms or molecules is called the cohesive force. For the sticking between a liquid and a solid surface, we have adhesive force. What exactly are these forces? Why do atoms in a crystal stay together in a regular formation, as electron microscopes show? Why are solids solid?
The Nagaoka-Rutherford model of the atom presents the positively charged nucleus at the centre, and the electrons orbiting around the nucleus. This is the current atomic model. Now, if there are negatively charged electrons around every atom, why do not atoms always repel each other on the electrostatic basis? All matter should be gas then!
Reality is that – in most cases - as we increase temperature solids become liquid, and then from liquid turn to gas. (In Std. 8, (1969) our Physics teacher Father Vassalo explained this to us in terms of vibration. He would shake his belly gently to show the transformation of matter from solid to liquid, and more vigorously to show the transformation from liquid to gas. I cannot forget this, the finest exposition of the basics of thermodynamics. ) Rising temperature makes the atoms vibrate more, thus decreasing the inter-atomic bond strengths, till finally the bonds are broken and then they move away from each other. But why were they together in the first place?
Let us consult the Encyclopaedia Britannica (15 ed., 1992) about this matter of inter-atomic or inter-molecular attraction. We look up on the words “adhesion” and “cohesion”. Vol 1 p97 under the heading “adhesive” tells us: “Modern research indicates that adhesion occurs on a minute and intimate molecular level. This explanation, called the adsorption theory, holds that adhesion depends on the same molecular attraction as that which binds all solid matter; any two materials can thus theoretically adhere if they are placed in close enough molecular proximity”. Okay, so let us now look up “adsorption theory”. Vol 1 p109 defines adsorption as “capability of all solid substances to attract to their surfaces molecules of gases or solutions with which they are in contact”. P110 goes on: “Adsorption refers to the collecting of molecules by the external surface or internal surface (walls of capillaries or crevices) of solids or by the surface of liquids”. Vol 1 p435 defines cohesion as “in physics, the intermolecular attractive force acting between two adjacent portions of a substance, particularly of a solid or liquid. It is this force that holds a piece of matter together. Intermolecular forces act also between two dissimilar substances in contact, a phenomenon called adhesion. These forces originate principally because of coulomb (electrical) forces. When two molecules are close together, they are repelled; when further apart, they are attracted; and when they are at an intermediate distance, their potential energy is at a minimum, requiring the expenditure of work to either approximate or separate them. Thus, work is required to pull apart tow objects in intimate contact, whether they be of the same or different material. The attractive forces of cohesion and adhesion act over a short range and vary in magnitude, depending on the substances concerned. If a piece of glass is submerged in water and then withdrawn, it will be wet – ie water will cling to it, showing that the force of adhesion between water and glass molecules is greater than the force of cohesion between water molecules”.
So from the above we learn that electrical “coulomb forces” are responsible for keeping matter together as “intermolecular attractive forces”. This is all very well, but does not explain the exact mechanism involved. How does it work, really what is happening? How is it that there is repulsion at very short ranges, and attraction at longer ranges? From the photo of the iron-sulphide shown, it is evident that there is a range (in a solid) which is optimum for a particular crystalline structure. How to make sense of it all? It would appear that for any molecule in solid form there has to be at a temperature a certain intermolecular distance responsible for the rigidity of the solid. This picture makes it very clear. Still, why does not the negative charge at the outer of the atoms/molecules simply repel each other? Are they held together by mutual repulsion, or attraction? For a solid the latter seems likely, for the liquid the former!
We now search the internet to find any recent findings about this subject, and check out the latest theories that make sense. It is necessary to do this background check before putting forward my new ideas about gravity and molecular attraction on the electrical Coulomb basis. (They would not be new if someone had already done them!)
Googling for “intermolecular forces” provides a number of sites providing explanation for intermolecular forces: the wiki reference is perhaps the most explanatory.
https://en.wikipedia.org/wiki/Intermolecular_force
The site mentions that:
Attractive intermolecular forces are categorized into the following types:
• Hydrogen bonding
• Ionic bonding
• Ion–induced dipole forces
• Ion–dipole forces
• van der Waals forces – Keesom force, Debye force, and London dispersion force
These are very involved explanations and no doubt they are correct as per their own particular areas. I do not wish to go into the details of any or all of them. Fortunately for me, they all miss out on the very subtle and basic aspect common to all intermolecular attraction, which is also the cause for gravity. That element, very fundamental, that has been missed all along will be detailed in the next instalment. The basic question remains: as the electrons – negatively charged – orbit the nucleus, why does matter stay together? Why do they NOT *always repel*? The literature makes statements like :
1. Hydrogen bonding “The hydrogen bond is often described as a strong electrostatic dipole–dipole interaction”.
2. Ionic bonding “ It is essentially due to electrostatic forces, although in aqueous medium the association is driven by entropy and often even endothermic.”
3. Dipole forces “Dipole–dipole interactions are electrostatic interactions between molecules which have permanent dipoles.”
4. Ion-dipole and ion-induced dipole forces “Ion–dipole and ion–induced dipole forces are similar to dipole–dipole and dipole–induced dipole interactions but involve ions, instead of only polar and non-polar molecules. Ion–dipole and ion–induced dipole forces are similar to dipole–dipole and dipole–induced dipole interactions but involve ions, instead of only polar and non-polar molecules.”.
5. Van der Waals forces: “The van der Waals forces arise from interaction between uncharged atoms or molecules, leading not only to such phenomena as the cohesion of condensed phases and physical absorption of gases, but also to an universal force of attraction between macroscopic bodies.”
5.1 Keesom interaction: “These forces originate from the attraction between permanent dipoles (dipolar molecules) and are temperature dependent.[8]
5.2 Debye forces: “arising from interactions between rotating permanent dipoles and from the polarizability of atoms and molecules (induced dipoles).”
5.3 London dispersion force: “The third and dominant contribution is the dispersion or London force (fluctuating dipole–induced dipole), which arises due to the non-zero instantaneous dipole moments of all atoms and molecules.”
It is evident that a great deal of work has been done by the physics community to research this important and intricate area. While terms like “electrostatic force” and “dipole forces” are used, they do not satisfy my query above, that is, why does not matter fling apart because of the outer negative charges for the atoms/molecules repelling each other. How on earth does matter stick together as solids and liquids if the basic tendency is repulsion due to the outer electrons of the atoms/molecules?
My insight relating to the electrostatic explanation for gravity is by contrast extraordinarily simple. I hope that it may help researchers in this area of intermolecular forces to further develop their work. I will talk on this aspect in brief in the next instalment. For the moment, I once again rejoice in that my insight into the electrostatic nature of gravity has not been foreshadowed by anyone.
Arindam Banerjee
Melbourne, 18 May 2020
https://www.facebook.com/photo/?fbid=3592305034130601&set=a.506922209335581
This is the photo of iron sulphide atoms in a crystalline structure.
It is taken from p156 the book
"Physics of the Atom" by Wehr and Richards, Addison-Wesley, 1964
19 May, 2020
The cause of gravity – 7
What is gravity, and the derivation of F=K.N1.N2/D^2 as the attractive force between atoms at any distance D between uncharged masses with N1 and N2 protons/electrons
This is the seventh instalment of my essay on the cause of gravity, the weak but sure force that holds the parts of the universe together. To recapitulate in brief: Signor Leonardo da Vinci’s definition of force, which forms the basis of the Newtonian laws of motion, is random, violent; and being self-defeating, vanishes. This contrasts with the sure and constant force of gravity (attraction between masses) as found by Sir Isaac Newton, and used to prove beyond doubt that the Earth moves around the Sun. (If the Earth did not move around the Sun, it would fall into the Sun. As much as the Earth “falls into the Sun” from the gravitational pull, so much, every instant, it “falls out” due to the tangential motion.) Thus there is a contradiction – one kind of force “defeats itself” and the other kind is always there, always constant. How can that be? Also, as we now know, the formula for universal gravitation cannot account for the (charged) ionic masses streaming away from the Sun? Why does not the enormous gravity of the Sun pull those charged masses back?
Electrostatic force was once surmised to be related to gravity as there were many similarities, such as being equal to the product of charges and being inversely proportional to the square of the distance between the charged masses. However electrostatic force is much stronger than gravity; there has to be charge creating an electric field for its formation; it has much lesser range. There did not seem any link between the forces of gravity and electrostatics.
The finite, indivisible, structure of the atom led to the surmise that charge could be composed of discrete, indivisible components. From experimental work it was found that there is a very small negatively charged mass which was discrete and indivisible – it is known as the electron. Experiments also indicated that within each atom there is a core, or nucleus, of positive charge. The modern notion prevalent in Chemistry is that the negative charges (known as electrons) orbit the positively charged nucleus. In physics the quantum theory would have it that these electrons are “standing waves”, or charged matter which acts not like a particle but as a “wave. Nevertheless, it is not denied that the electrons (whether as particles or as waves) have negative charge; nor is it denied that the nucleus has a positive charge: and finally in a normal atom there are as many electrons around the nucleus as there are protons in the nucleus. Since there is a balance of charge within the atom (with as many protons as there are electrons) the net charge is zero.
So how do we go on from here? It would seem a total no-hoper to try to show that gravity is a weak form of electrostatic force. If nothing else, it would appear that the negative charged cloak of the atom would repel other atoms that too have negatively charged cloaks. And yet, this does not happen. As shown in the last instalment there exist strong inter-atomic forces of adhesion and cohesion. The reason for the existence of such forces is held to be electrostatic fundamentally, but exactly how, whether there is a common factor behind the various explanations presented, is not yet known. (Rather to my relief!)
Well then… time to start the show! First, a brief discussion about zero, and what it means in this context. Let us talk money now, what everyone understands! Consider my zero dollar company, HTN Research. And I ask, why should it be worth zero dollars? I say, it should be worth a trillion dollars. Everybody laughs. Then I add, okay, let us see what are the negative factors preventing it from being a trillion dollars. I remove all those negative factors, that make it a zero dollar company, and hey, my company becomes worth a trillion dollars! (Not instantly, though.)
To talk physics now, consider a flat plate, let it sink to the bottom of the ocean, and then lift it up. It will look the same. For contrast take a closed box, not too strong, and do the same function. It will rise up completely squashed. In the first case, for the steel plate, there was equal water pressure, immense though it was, on either side so the forces cancelled out leaving no net force acting on the plate. In the case of the closed box, there was low pressure inside the box so the much higher pressures around squashed the box. The point I am trying to make it is that the fact of anything being zero does not mean that there are no equal positives or negatives – of any sort - that make it zero. Whether money, or pressure, or partner for life… Take out the positive out from anything in life, you get the negative. Take out the negative, and you get the positive.
Let us apply the notion of zero to a single normal atom. It has a net zero electric field around it. I submit that this zero electric field is the net result of the positive electric field from the positively charged nucleus and the negative electric field. However this does not mean that they do not exist separately. Just that, at any point somewhat distant from the atom, the fields add up to zero, so we say that there is a zero electric field around an atom.
In Figure 1, we consider only the negative electric field arising out of the negative charge from the electrons of other atoms, acting upon the electron E at position A. (We do not consider the positive field at this stage – just remember, once again, the subtle and undeniable point that the zero electric field is the sum of the negative electric field and the positive electric field). Now the negative electric field will cause a repelling force F to act upon the electron E at position A. If this force is very strong, the electron will be knocked out of orbit and the atom will become charged, or ionised. Let us say this does not happen. What then will happen is that the electron E at A will get acceleration, or move faster. As it does not quit orbiting, it will come to position B which is on the other side of the atom. At this point the same repelling force F will cause it to brake, thus to reduce its velocity. Thus the same force accelerates it, and then brakes or decelerates it, so there is no net effect upon the electron in terms of force. Now when we consider that there is matter all around this atom, doing just this thing, it will become clear that the repelling force caused by the electrons around the nucleus of atoms do NOT cause repulsion among atoms. This is a very important point, and I present this as a breakthrough in science. To repeat, the negative charges around the nucleus of atoms, when seen as orbiting electrons, cannot cause repulsion among the atoms. To add, the lines of force involved in this repulsion process rarely go through the centre of the atom, the nucleus that is. All of which means, the atom is essentially untouched by the negative electrostatic forces caused by the negatively charged orbiting electrons.
We can now provide the proof of the electrostatic formulation of the universal formula for gravitations, that is F=K.N1.N2/D^2 superseding F=G.M1.M2/D^2 , where N1 and N2 are the numbers of protons/electrons in the uncharged masses M1 and M2 respectively, distance of separation of nuclei/centres_of_mass being D.
In Figure 2 we show two hydrogen atoms, A and B, separated by the distance D. A hydrogen atom has a single positive charge q as the nucleus (a proton) with an electron of charge –q orbiting the nucleus. We now work out the forces of attraction and repulsion following the venerable Coulomb’s law for electrostatic attraction and repulsion.
The forces of attraction are: Electron of A with proton of B = k.q1.q2/D^2, and electron of B with proton of A = k.q1.q2/D^2; so the total attractive force is 2k.q1.q2/D^2.
The forces of repulsion are: Proton of A with proton of B = k.q1.q2/D^2 ; and electron of A with electron of B which is also k.q1.q2/D^2 . We note that the force of repulsion between the electron of A and the electron of B is tangential thus does not act through the nuclei; it acts as a ripple effect upon the electron orbital movement around the nucleus with equal acceleration and deceleration; and thus does not create any net repulsive force upon the atom.
Thus the net force between the atoms A and B is an attractive one, which is equal to
F=k.q1.q2/D^2. Now, q1=q2=q which is the electronic charge, a fixed value. So
F= K.N1.N2/D^2 where K = kq^2 and N1=N2=1, that being the number of electrons/protons in the atoms A and B.
Thus is demonstrated, the most basic derivation of the updated formula for universal gravitation on the electrostatic basis.
It will be immediately observed that it is valid only for uncharged masses. Thus, the ions do stream out of the Sun, as they are charged, and thus beyond the scope of the Sun’s gravitational pull which is valid only for uncharged masses.
This formula also explains the attraction between all atoms, all material. It underlines as a common feature all the theories relating to intermolecular forces. The rise of fluid in capillary tubes owes to such electrostatic attraction. How does water from the ground rise up in plants? Through capillary tubes within the plants: the fluid adheres to the walls of the capillaries in the plants, pulling itself up by the electrostatic forces between the atoms of the fluid and the atoms in the wall linings.
In Figure 3, we extend the derivation of the updated gravitational formula for a hydrogen atom and a helium atom, and two helium atoms. In Fig. 3 we do not draw the electron-to-electron interactions, just the proton to electron and proton to proton interactions.
The question now is, what is this constant K and what does it really represent? Further, what new insights into the universe can we get from the new electrostatic representation of the formula for universal gravity? That will be discussed in the next instalment on this topic: the cause of gravity.
Arindam Banerjee
Hampton Park, Melbourne, 25/05/2020
The figures mentioned in the article are to be found in my facebook time, links are
Figure 1:
https://www.facebook.com/photo?fbid=3609632575731180&set=pcb.3609639489063822
Figure 2:
https://www.facebook.com/photo?fbid=3609633399064431&set=pcb.3609639489063822
Figure 3:
https://www.facebook.com/photo?fbid=3609634162397688&set=pcb.3609639489063822
Cheers,
Arindam Banerjee, 26 May 2020
The cause of gravity – 8
Finding the value for the constant K in the updated equation for gravitation involving electrostatics
Consider two isolated Helium atoms separated by a distance of one meter in free space. They each have the mass of 6.6464731*10^-27 Kgs. We make the note that the Helium atom as having equal numbers of protons and neutrons in the nucleus is more suited than say the hydrogen atom (having just the one proton in the nucleus) to represent masses in general.
According to the law of universal gravitation, the gravitational force between two equal masses, each called m, is
F=Gm^2/d^2, where d is the distance between the masses and G is the universal gravitational constant with the value of 6.674*10^-11 MKS units. (Note: when we use a physics formula, we have to adopt a particular set of fundamental units. MKS means Meter Kilogram Second. It is thus different from the CGS units of Centimeter Gram Second.)
The attractive gravitational force between two Helium atoms separated by 1 meter will the be:
F=6.674*10^-11*(6.6464731*10^-27)^2/(1)^2, or
F=6.674*6.6464731^2*10^(-11-27-27), or
F = 294.828*10^-65, or
F=2.94828*10^-63 Newtons.
The force for the electrostatic/gravitational attraction between two helium atoms separated by one meter is from the formula
F=k*q^2*N1*N2/D^2 , where D is one meter, N1=N2=2 (there being 2 protons/electrons in each atom) and q is 1.6021*10^-19 coulombs (a MKS unit) is
F=k*(1.6021*10^-19)^2*2*2/(1)^2, or
F=k*2.56672441*10^-38*4, or
F=k*10.26689764*10^-38, or
F=k*1.026689764*10-37 Newtons and this value has to be equal to 2.94828*10^-63 Newtons found above from the older formula.
Thus k*1.026689764*10-37 = 2.94828*10^-63 from where we get the value of k as
k= 2.87163669*10^-26 MKS units.
The new upgraded formula for gravitational attraction for uncharged masses with N1 and N2 protons/electrons in each; where the number of protons and neutrons in the nucleus are roughly similar; and separated by distance D meters is
F=2.87163669*10^-26*N1*N2/D^2 Newtons
Arindam Banerjee
Melbourne, 28 May 2020