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.
Arindam Banerjee
Hampton Park, Melbourne, 25/05/2020

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