Archive for the 'Quantum Mechanics' Category

Nov 14 2021

Greatest Lower Bound

One would guess that the particle physicists and quantum field theorists may like a 1.3335 x 10-15 m diameter of a free electron, because it is closer to a point particle than many estimates of the diameter.  It is possible that 1.3335 x 10-15 m is also the limit inferior of the sequence S137 to Sn in an atomic orbital.

The maximum diameter, on the other hand, will depend on the element and on the orbital.  At a spin flip, electrons in all orbitals may reduce to 1.3335 x 10-15 m, before taking off on a new trajectory and increasing in diameter again.  We cannot speak of a limit superior of the sequence of diameters of the electron in an atomic orbital nevertheless.  That will depend on the direction of electron travel, and on whether the atom is at the surface of the earth, or at some other planet.  For the latter, it depends on the density of the gravitational field.

We may also ask whether 1.3335 x 10-15 m is the greatest lower bound at all locations in the universe.  This raises the question of whether the fine structure constant is a universal constant, or whether or not the Coulomb gauge is the same everywhere.

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Sep 28 2021

Diameter of the Electron

Published by under Quantum Mechanics

It has been surmised that with conjugate wave gravitons, the number of gravitons in a free electron in the earth’s locale may be the reciprocal of the fine structure constant.  We may then use this number to determine a possible diameter of the electron.

First, start with the energy:

(5.011 x 10-11 J) x 137 = 6.8651 x 10-9 J

Then use the electron’s spin angular momentum:

ħ/2 = (½) mvr = (½) mr2ω

Rearranging:

ω = ħ / (mr2)

Considering rotational kinetic energy, we have:

Ek = (½) [Iω2] = (½) [ (½) mr2 ] ω2 = 6.8651 x 10-9 J

Substituting ω from above:

Ek = (½) [ (½) mr2 ] [ħ / (mr2]2 = (½) (½) [ħ2 / (mr2)]

1/r2 = [(4) (6.8651 x 10-9 J) (9.1095 x 10-31 kg)] / ħ2

r = 6.6676 x 10-16 m

D = 2r = 1.3335 x 10-15 m

ω = ħ / (mr2) = 2.6040 x 1026 rad/sec

This angular velocity is fictitious, though it can be used in calculations due to Green’s Theorem (see April 2007 paper).

Of course the number of gravitons in an electron in an atomic orbital varies, and thus the electron diameter would vary also.

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Jan 25 2021

Final Mediator

Going back to the April 2007 paper once again: “… and the same Coulomb force being the final mediator of the gravitational force as proposed, the mass energy of the proton appears to be integral to gravitational field action.”, we can go further back in history to examine the path of how we arrived at this place.

In the scientific community, the cause of gravity is by many still considered as unknown.  As Hughes-Hallett et al. puts it in relation to the gravitational force: “How does acceleration come about?  How does the velocity change?  Through the action of forces.  Newton placed a new emphasis on the importance of forces.  Newton’s laws of motion do not say what a force is, they say how it acts.” 1

Newton himself says in The Principia: “…considering in this treatise not the species of forces and their physical qualities but their quantities and mathematical proportions, as I have explained in the definitions.” 2  In Definition 8 Newton says: “This concept is purely mathematical, for I am not now considering the physical causes and sites of forces.” 3

Roger Cotes, Plumian Professor of Astronomy and Experimental Philosophy at Cambridge University wrote in his Editor’s Preface to the Second Edition of The Principia: “But will gravity be called an occult cause and be cast out of natural philosophy on the grounds that the cause of gravity itself is occult and not yet found?” 4  Electromagnetic waves were not yet discovered in 1713 when Cotes wrote this, so it is difficult to imagine how anyone could have discovered the cause of gravity back then.

1  Hughes-Hallet, Gleason, McCallum et al., Calculus, John Wiley & Sons, Inc., 2005, p.304

2  Cohen, Whitman, Isaac Newton, The Principia, Mathematical Principles of Natural Philosophy, University of California Press, 1999, p. 588

3  Ibid., p. 407

4  Ibid,. p. 392

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Dec 04 2019

Electric and Magnetic Fields

Jon Rogawski has a cool diagram and calculation using Faraday’s Law on page 979 of his Multivariable Calculus book*. The magnetic field around the straight wire with an alternating current flowing in it produces a voltage in an adjacent looped wire with no conventional energy applied except that from the other wire.

Of course this magnetic field, and likewise for electric fields, must have a pervasive field in which to transmit. One may say it transmits through the air, however Faraday’s law also applies in space.

These E and B fields transmit by turning and bending the E and B fields of the dense gamma rays.

* Rogawski, Jon, Multivariable Calculus, W. H. Freeman and Company, c. 2008

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Aug 19 2019

The News

Published by under Astrophysics,Quantum Mechanics

News again says that the moon is glowing in gamma rays in the MeV range, and if people go back to the moon they will have to be shielded from the gamma rays. Of course scientists came up with a reason for the gamma rays, other than gravity, because they had to.

If astronauts were shielded completely from gamma rays, that would be trouble. Biological matter needs gamma rays at and close to 312.76 MeV to stay alive.

It should be noted, nevertheless, that there are lots of bare nuclei in the solar wind. The effects of constant exposure to the nuclei, and other non-gravity radiation, need to be looked at by qualified professionals.

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Aug 04 2019

Gamma Ray Field

It has been alluded to before on this website that the thick gamma ray field in which we reside is reminiscent of the aether.  A good book on the subject was written by Joseph Larmor.  Here is a sample:

“The basis of the present scientific procedure thus rests on the view, derivable as a consequence of general philosophical ideas, that the master-key to a complete unravelling of the general dynamical and physical relations of matter lies in the fact that it is constituted as a discrete molecular aggregate existing in the aether.” *

In the same paragraph, Larmor refers to “the properties of a continuum in space,”.

* Larmor, Joseph, AETHER AND MATTER, CAMBRIDGE AT THE UNIVERSITY PRESS, 1900, p. 78

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Feb 09 2017

E = mc^2

It occurred to me in January or February 2008, during my first foray into Quantum Mechanics, that the reason there is no 1/2 factor in front of mc^2 in Einstein’s formula E=mc^2, – like there is in the Newtonian formula for kinetic energy K. E. = (1/2)mv^2, is that there are gravitons inside a fundamental particle that are bouncing back and forth against gravitational pressure on the outside, which doubles the energy.

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Feb 24 2016

Johnson–Fruechte Experiment

Produce a multiple layer wire wound coil around a roughly 2 inch diameter iron core, maybe 8 feet long. Set the cardboard tube from a roll of paper towels, on end, up on a shelf. Get as much capacitance as you can hooked up to the coil and charge up the capacitance. Aim the device at the top half of the cardboard tube, making sure the other end ‘sees’ terrestrial earth, and dump the capacitance all at once to produce a high value of current. Gravitons like to follow magnetic field lines, so one would see if the cardboard tube can be pulled over.

A software engineer across the hall from me, Jeff Johnson, who I have worked with for many years, came up with the idea of loading a lot of capacitance, and producing a high current by dumping it with one switch. The wire gauge would have to be figured out based on the current that would be produced.

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Dec 23 2015

Adhesion

Published by under Quantum Mechanics

Go to an adhesion seminar, like I did years ago with a fellow engineer, and the speaker may or may not tell you that the main component of adhesion is due to the most fundamental of van der Waals forces, that being dipole-dipole electrostatic attraction, which force falls off at a rate proportional to one over distance to the fourth power. The seminar leader is likely to tell you nevertheless that the surfaces should be clean and dry.

Obviously adhesion can also, and usually does, have a mechanical component. This is especially true in the shear direction when a surface is course, or purposely roughed up first. Pressure is often applied when adhering surfaces to force the adhesive into crevices, for the mechanical component to grab better, and to bring molecules in closer contact for the electrostatic component. If the instructions for the adhesive say to hold the pressure for a certain amount of time at room temperature, that is to let the molecules creep into crevices and to allow the dipoles to move themselves into positions that increase the number of potential energy wells that relate to movement and positioning of the dipoles.

The electrostatic component is strongest in the first 3 or 4 molecular layers of relatively complex adhesive molecules, so this makes it easier to see why pressure helps. The ‘dry’ rule is mostly because water does not make a good adhesive. The ‘clean’ rule is a little more complex. Chemists have made adhesives good at inducing dipoles into relatively non-polar material, but it is best if the material being bonded to has consistent isotropic structure. When the dipoles are setting up the energy wells, it is more efficient when dipoles of a locale ‘see’ a uniform structure across a hemispherical view. Nature prefers mathematical order. Also, an adhesive may stick to a piece of debris, but the piece of debris will probably not stick to the substrate.

Some of the strongest adhesives are solidified by heat curing, when cross linking occurs. If the dipole positions end up more rigid, they can maintain strength under high strain.

For a good description of dipole-dipole bonding, see:

Tipler, Paul A. and Llewellyn, Ralph A., Modern Physics, Sixth Edition, W. H. Freeman and Company, New York, c. 2012, pgs. 387-388

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Nov 17 2014

The Pion

Published by under Quantum Mechanics

As an example of one of the several particles that must stay, the pion “has a range of 1 Fermi”.  This is a compression factor of close to 4 compared to a graviton.  It is NOT a graviton, even though it probably was one at an earlier point in time.

The pion is a “mediator of nuclear force.” *

 

*  R. Shankar, Principles of Quantum Mechanics, Springer Science+Business Media, LLC, c. 1994, pg 366

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