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tisdag 24 november 2020
Understanding "photons" from electron spin and dimensional analysis
söndag 22 november 2020
Experimental evidence of higher order electron spin?
In a previous post I made the conjecture that electrons can have spins that are any multiple of the reduced Planck's constant, and not just the two discrete values of +/- 1/2 h_bar which we have been taught. Is there any experimental evidence to back this up? I think there might be, have a look at the following image that was taken from an article in Nature:
The experiment performed is the well known double slit experiment with electrons. I have proposed that this experiment can be explained by the Stern-Gerlach phenomenon, that is, the more you widen the other slit the more you increase the inhomogeneity in the magnetic field produced by the moving electron and the electron trajectories are then split according to their spin. As you would expect, lower spins are more probable than higher order spins, although in the image I think I can spot spin up to the order of at least 9. It would not be surprising if the probability follows a binomial distribution.
tisdag 17 november 2020
On the stability of atomic orbitals and the electron spin
In the early phases in the formulation of a theory of the atom, one of the major problems that occupied the minds of its pioneers was the sudden death that the system would experience since, according to Larmor's formula, an electron that is constantly being accelerated in a circular orbit around a nucleus would, within a short period of time, radiate away its energy and eventually crash into the center. This problem is sometimes claimed to have been "solved" by quantum mechanics, but was it really?
When Bohr postulated that the electronic orbitals must have a quantized angular momentum, that was a bold and brilliant move that led to a good quantitative prediction of the hydrogen spectrum, but did it solve the problem presented by the Larmor formula? In this post I will argue, in a heuristic way, how the electron spin might be the key to solving this problem, and thereby the stability of the atom.
The starting point in a treatise of quantum mechanics is usually taken to be the wave-function (or in some cases Heisenberg's uncertainty formula). The reason for this might be the order in which these models entered the stage historically. It should be kept in mind, though, that Schrödinger's equation does not take into account electronic spin, the spin is added only later in an ad-hoc fashion. Here I invite you to for a moment take a somewhat different view.
Assume that the quantized electronic spin is the natural starting point of quantum mechanics.
More specifically we assume that the electronic spin angular momentum is quantized in units of the reduced Planck's constant:
S = n*h_bar.
Bohr's assumption when formulating his model of the hydrogen atom was that the orbital angular momentum of the electron was quantized by the same formula:
L = n*h_bar.
How can we now add these pieces together to arrive at a solution to the atomic problem? Well, what if the spin angular momentum has the opposite sign of that of the orbital angular momentum?
L = -S.
Then we have that the total angular momentum of the system is given by
L_tot = L + S = 0.
This does not provide any rigorous proof of the stability of the orbit. From purely heuristic considerations, however, it would seem plausible that a stable system that does not constantly loose energy to the environment is characterized by a zero total of angular momentum, that is
L_tot = 0.
In the case of the hydrogen atom, this is only possible if we introduce electronic spin, which by empirical observation is quantized.
This way of reasoning might put into question some common wisdom surrounding electronic spin. It is generally taught that electron spin can only take the values
S = +/- 1/2 h_bar.
Again, however, does this seem "physical" to you. Take as an example a vibrating string, its frequencies are quantized, but there is no upper limit to its values.
söndag 21 juni 2020
Electro-magnetic origin of the heavy mass?
1. Gravity and Electromagnetism both follow the inverse square law
2. Ordinary electrostatic attraction is 10^36 times greater than gravitational attraction, hence a minuscule net dislocation of charges of celestial bodies could account for gravity.
3. Having only one force is more economic
It turns out that this idea has already been elaborated on in detail. Please check out the following paper:
Deriving gravitation from electromagnetism
Can. J. Phys. 70, 330-340 (1992)