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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.


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