ZPF Absorption Rate in Magnetization of Electrons

[Green Destiny]

Homework Statement

Just basically want to see if my algebra is ok.

Homework Equations

All are relevent.

The Attempt at a Solution

Calculating Rates in Magnetic Moments to Predict Period Interaction Between a Fermion and the Zero-Point Field

First we must identify the net magnetization $$\vec{M}$$ as the sum of individual magnetic moments [1],

1. $$\vec{M}= \sum^{N}_{i=1} \vec{\mu}_i$$

The magnetic moment $$\vec{\mu}_i$$ is a magnitude of the constant expression of $$\frac{e \hbar}{2Mc}$$. If these equations where pertaining to a spinor field $$\psi$$ (or simply an electron) then the electron in a certain magnitude of magnetic moments act like a clock to potentially absorb a photon at an energy of $$\frac{e^2 h}{4Mc}$$ [2] from the ZPF (zero-point field) which would imply an interaction term. Using the algebra of a limiting vector on the classical vector component $$\vec{\mu}_i$$ then we would find the upper bound at the squared value of $$15MeV$$.

Taking the dot product between the magnetic moment (the sum of the magnetization field $$\vec{M}$$ which should not be mistaken for a mass, or the magnetic moment identity in the equation $$F= \nabla(M \cdot B)$$ where here $$M$$ is the magnetic moment) and the magnetic field $$B$$ of Equation 1. we have:

2. $$F= \nabla(\vec{M} \cdot B)= \nabla(\sum^{N}_{i=1} \vec{\mu}_i \cdot B)$$

which implies also that

3. $$\nabla(\sum^{N}_{i=1} \vec{\mu}_i \cdot B)= \nabla(MBcos \theta)$$

The force here can now be viewed in terms of a Lorentz force where the charge is seen in terms of magnetism. This can be seen in a simple substitution:

4. $$\nabla(\sum^{N}_{i=1} (\vec{\mu}_i \cdot B)= (\oint (B -\mu_0M) \cdot \partial \mathbf{A})v \times B$$

where $$\mu_0$$ is the permeability.

$$= q_Mv \times B$$

Which would imply a force due to magnetism $$F_M$$, where $$q_M$$ is the magnetic charge. Since the sum of magnetic moments calculate the exact absorption rate of photons when electrons have an energy of $$\frac{e^2h}{4Mc}$$ then the magnetization can be seen as giving rise to the interaction between the electron and the zero point field - remember, the magnetization is the sum of the magnetic moments, and the magnetic moment is a magnitude of one half less than that required for zero-point energy absorption. The rate in which an electron may obtain an upper bound of energy at $$hf=15MeV$$ and their respective Magnetizations should be investigated as possible co-roles.

The magnetization field has an energy, as do all quantum fields in a vacuum, and small perturbations as would be expected from a model of an electron with an absorption rate for photon in the ZPF-connection can be seen in terms of the work of the field and the H-Field as $$\delta W= H \cdot \delta B$$, so trivially substituting this into our equations we can have:

$$\delta W = H \cdot \delta B = \nabla(\sum^{N}_{i=1} \vec{\mu}_i \cdot B)vt$$

Where we have multiplied the quantity of $$vt$$ on both sides to give the appropriate dimensions.


Ref.

http://www.pma.caltech.edu/~ph77/labs/nmr.pdf

http://books.google.co.uk/books?id=...t energy contribute to a hamiltonian?&f=false

 

[Green Destiny]

I haven't received a reply on this topic, and think this may be partly due to perhaps not understanding the topic's queeries, or rather I have not explained the properties expected very well. So without further adue, my friend John posited some questions to me the other day, and they were good questions, so to clear any ''misconceptions'' I hoped to post them here to make the OP clearer... of course this still depends on whether my algebra is correct which I may still need guidance on.

What do you mean by an electron acting like a clock? Ordinarily when an electron absorbs a partial photon it's via Compton scattering, and as a result the electron moves.

Well, in light of magnetization (which is simply the sum of magnetic moments in an electron) one can find a specific quantity i.e $$\frac{e \hbar}{2Mc}$$ and this quantity is just one magntitude lower than an absorption energy (which can be found in the last reference I think). Usually these equations will permit to electron charge clusters and investigates the rate in which absorption could be measured like a clock. Adding energy photons is directly equivalent to adding a photon or by a relativistic increase of energy. Magnetization similarly increases in energy with the electron, so magnetiudes of magnetic moments are magnitudes of an internal energy, and a specific magnitude of that energy can create the phenomenon of the electron absorbing vacuum energy.

There is a demonstrable interaction, but in free space where we might detect say the Casimir effect, the motion would surely be minor and random, akin to Brownian motion?

Maybe. I question how random this would be, but I don't question how minor the results are if not under the correct conditions. Whenever an electron absorbs a photon it obtains an energy of $$\frac{e^2 h}{4Mc}$$ which may be in direct correlation with their respective magnetization energies. If so, then measuring such magnetic moments could be used as a clock to measure the rate in which they are receiving an energy from the vacuum.

Can you elaborate on the upper bound of 15MeV? That's a lot of energy.

I'm afraid not. I just assume its a matter of experimentation http://books.google.co.uk/books?id=...t energy contribute to a hamiltonian?&f=false

No problem re a force, but how can charge be seen in terms of magnetism rather than electromagnetism?

That's a very good question. It reminds me when I first learned about Gravitomagnetism. However, just as Gravitomagnetism is analgous to Gravito-electro-magneto-interaction equations, as is magnetic charge analogous to an electromagnetic charge. It vaguely focuses on the magnetization part of the charge rather than focusing on the whole thing http://www.britannica.com/EBchecked/topic/357015/magnetic-charge - the link basically varifies it is analogous, but the nature of the charge will become more obvious when reading on the monopole, which most of us will have come to know by now as a fundamental charge of magnetism.

In similar vein you mention a magnetization field. Wouldn't this just be an electromagnetic field where you have circular relative motion? A magnet is a magnet because the motion of interior electrons shares a common orientation.

There are electromagnetic moments as far as I am aware - I think this involves the electromagnetic inertia idea of Feyman. But it may be best not to mix the two as magnetization is simple the sum of the magnetic moments experienced by any single electron which is a phenomenon which is known rather well. If a unification of the magnetic force and the electric forces where to be investigated in the equations presented, I would not imagine it too difficult to unify them. I suppose the equations like to focus of the magnetic phenomenon of magnetic moments, and how certain energy levels of an electron could be hinting at ZPF-interaction coupled with magnetic moments acting like a counter to those effects. For instance, how many magnetic moments for an electron are required at an energy of $$\frac{e^2 h}{4Mc}$$? We know that under conditions of electron charge clusters that this energy is what is obtained from the vacuum, but equally internal to the electron, the energy fascits certain magnetic moments which an electron can also experience.