There is a scale comparison that is always made when comparing Newton and Coulomb, The motive of gravity is assumed to inhere within the quantity of matter, which we have become slack in calling mass, distinguishing it from the density and the volume of space. We then experimentally determine the unit charge mass
without pausing we have found a relative quantity that is undefined in Newton's system. Newton uses the quantity of matter concept, thus we require the electron volume and the electron density.Newtonian density is an undefined concept.
Re: What is the volume (spacial region) of an electron?
Date: Mon Mar 22 13:55:10 1999
Posted By: Michael Ford, Staff, Radiation Safety/Health Physics/Plutonium/Nuke Weapons, Battelle Pantex, Pantex Plant
Area of science: Physics
As far as I have been able to determine, the volume of an electron
has not been determined. One might be able to deduce the volume
of an electron from the effective radius of the Bohr hydrogen atom of
0.53 A or 0.53 x 1E -10 meters. Since the hydrogen atom is made up
of one proton and one electron, one could assume a uniform
density of subatomic particles throughout the volume (for
argument's sake) where,
density (H atom) = (1.0079 AMU)/[(4/3)*PI*(0.53e-10 m)^3]
density (H atom) = 1.62 e30 AMU/m^3
Assume density (H atom) = density (e-), then
density (e-) = (5.49 e-4 AMU)/ e- Volume
and substituting and solving for the e- Volume, we find
e- Volume = (5.49 e-4 AMU)/(1.62 e30 AMU/m^3)
e- Volume = 3.4 e-34 m^3
or about 1800 times smaller than the volume of the Bohr hydrogen
atom which is consistent with the mass differences between the
proton and the electron. Dependant upon your assumptions, the
same process could be used for other subatomic particles.
However, due to the homogenizations involved, those calculations
would also be plagued by the same inaccuracies.
My best guess. 'Hope this helps!
[Moderator note: Another approach is to equate the rest mass of the electron
with the energy of a spherical distribution of an amount of charge equal to that
of the electron. Doing this allows you to solve for the radius of the
As you can see, we do not have a concept of the density of an electron.
Newton’s definition of density
Newton’s definition 1 in the Principia:
Quantity of matter is a measure of matter that arises from its density and volume jointly.
In Definition 1 Newton uses Kepler’s rule to define density in a cryptic way. He labels the constant of density R03/T02 ”mass” and neglects to clarify that 1/T2 is frequency.
This is Newton’s greatest discovery. He was the first person to realize the fundamental nature of Kepler’s rule.
In order to brand Kepler’s rule as his own discovery Newton associated it with two superfluous terms: force and mass. If Newton were to use Kepler’s rule as is with only radius and period he would have glorified Kepler and reduced himself to a mere astronomer. As a marketing genius and a megalomaniacal worlbuilder Newton chose to brand Kepler’s rule as Newton’s laws and made it the foundation of his System of the World.
Force and mass are decorative terms Newton superimposed on Kepler’s rule and are not supported by observations. They do not exist in operational formulas. Observations reject the existence of mass (matter) but in order to save Newton’s authority physicists — instead of dropping the word mass – invented the concept of zero mass, e.g., the photon.
Force too is redundant. Einstein showed that force is unphysical. Once again, in order to save Newton’s sacred authority physicists do not let go of Newton’s occult force. They keep writing ”F” in their derivations in order to cancel it in the next line.
Based on the above I propose the following propositions. Please let me know what you think in order to prove or eliminate these propositions:
1. Kepler’s Rule is fundamental
1.1. discovered in a database of observations
1.2. proven to work in the solar system
1.3. proven to work in binary stars and other systems
1.4. takes only two terms — radius and period of an orbit
1.5. is independent of any laws and theories, such as Newtonism
2. Kepler’s rule is the definition of density
2.1. For a given frequency and volume density is constant
3. Newtonism is a branding of Kepler’s Rule
3.1. newtonian mechanics is kepler’s rule written with standard units and constants
3.2. mathematical formalisms of newtonian mechanics – Lagrange, Hamilton – are Kepler’s rule expressed with calculus notation
It is worth looking at this alternative view, not because it is what i want to convey, but because many, myself included have not read Newton, and so can lean toward fanciful aspersions against him. Yet this is nothing new to Newton then or now, and is reputation really only becpmes greater because it is always found to be misinformed to comment without reading.
Another problematic aspect of Descartes’ physics vis a vis Newton’s universal gravitation is the Cartesian identification of volume with mass, which is unavoidable given Descartes’ identification of spatial extent with material substance. He cannot contemplate variations in density, because the very concept of density entails a distinction between space and matter. If matter is less dense in some regions of space than in others, we can hardly claim that the idea of a region of space with arbitrarily low density – or even zero density – is unintelligible. Thus his rejection of the vacuum and insistence on continuous substance obliged Descartes to make the mechanical properties of bodies, including both their inertial resistance to acceleration and the force of gravity propelling them toward the Earth, strictly dependent on their volumes. This was recognized as a shortcoming of Descartes’ physics, even among his followers. When they began to seek a mechanistic explanation for Newtonian gravity, this was among the first problems they needed to resolve. To do this, there was little choice but to reject the identification of matter with extent, so most mechanical philosophers departed from Descartes by adopting the ancient belief in particles (atoms) moving in a void.
The earliest proponents (that we know about) of the atomistic view were the ancient Greek philosophers Leucippus and Democritus, followed by Epicurus. Most of our knowledge of the teachings of these men comes to us second-hand through the Roman poet Lucretius, who wrote an account of the atomistic philosophy in the form of a monumental poem entitled De Rerum Natura (“On the Nature of Things”). We know almost nothing about Lucretius himself, except that he supposedly went mad as a result of drinking a love potion, and killed himself at the age of forty-four. By adopting the atomistic view, it was possible to rehabilitate Descartes’ mechanical model of gravity, and make it at least nominally consistent with the quantitative dynamical aspects of Newton’s universal gravitation……
The difference between the theories of Huygens and Fatio is that Huygens was still strongly under the influence of Descartes, and persisted in thinking of vortices circling the earth at orbital speeds, tending to compell ordinary static bodies downward due to a gradient in their density, similar to a fluid pressure. In contrast, Fatio had seen the Newtonian light, and rejected Cartesian vortices as “an empty fiction”. His model assumed a purely isotropic omni-directional flux of particles. To account for the net force of attraction between two “coarse bodies” immersed in this bath of ethereal particles, Fatio assumed that the flux particles are entirely reflected, but with some diminished speed. In other words, the incident particles strike the body at a very high speed, but rebound with a slightly lower speed…….
During the years from 1689 to 1693 Fatio enjoyed an extremely close personal relationship with Isaac Newton, and for some time they planned to produce a second edition of the Principia together. Fatio evidently first met Newton on the occasion of Huygens’s visit to the Royal Society, when Huygens read his treatise on light along with an appendix on “the cause of gravity”. This was another mechanistic model for universal gravitation, based on fluidic action, quite distinct from Fatio’s model. In private correspondence Huygens critiqued Fatio’s model on the grounds that the rebounding flux particles, being slower, would necessarily be closer together, so (Huygens suggested) the density of the flux would increase in the vicinity of a massive body, and hence produce a repulsive rather than an attractive force. Fatio says he himself was “detained” by this objection for three years, but eventually convinced himself that the momentum flux of the rebounding particles would be lower than of the incident flux, because of the lower speed, despite the increased spatial density. Huygens conceded the point. (More than once in Fatio’s treatise he reports that “I had fully satisfied him of that objection”, and “I answered all objections that were made to me”, and so on.)
I find therefore that density is an undefined concept, or rather a concept that is well understood among those who adopt a particle theory of matter, in which density simply refers to the quantity(count) of particles in a defined volume.
This is certainly how Newton used it as if he had any different meaning he would have said so in his definitions.
However, we have completely misunderstood his subtley in our definition of density. Our only hope is to return to Avagadros number in its definition, and to recognise the effect of the tautology on our comparison of gravitational and electrostatic forces!.
The scale difference disappears.