Summary
This is a first attempt to reconcile Spintronics with Complex Quantum Mechanics. Spintronics is a theory at the edge of moderm research and Quantum Mechanics.
For an "Introduction to Spintronics and Spin Quantum Computation" see:
http://www.physics.umd.edu/rgroups/spin/intro.html
I now build up an argument by considering the latest research results from:
Lending an iron hand to spintronics
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Physics 2, 6 (2009) – Published January 20, 2009 |
See:
http://physics.aps.org/articles/v2/6
Introduction
I am investigating the possibility, here, of creating a basis for aligning Spintronics with Complex Quantum Mechanics (Complex QM). The results that I have seen for some Spintronics experiments defy description and so I am concentrating on two such experiments below. I shall be suggesting that spin can be associated with a mass rich particle and charge can be associated with an energy rich particle. I have stated previously that I view charge as the excess balance of energy over mass in a particle, so the previous sentence simplified this approach. Please consider this article more as a basis for discussion than a set theory.
Notation for Angular Displacement.
In the figure “Spintronics in Complex QM 1” I am using a cylinder or zylinder (complex cylinder) to describe just one complex winding.
To complete a complex winding around a sphere we need to use three adjacent zylinders.
Since there are three such cylinders with major axes along the X, Y and Z axes respectively each angle is measured three times. Thus angle a (alpha) has the three components a’ ,a’’ , and a’’’.
It is useful to use three components instead of two because this system can now be used for the point P on any surface.
Note that if we use a unit vector and restrain to keep this value for the complete winding then for the cylinder shown above the angle ?’’’ should cancel for one rotation of the red vector or winding as it will sum to 360 degrees. The same is true for all three angles if we consider a sphere.
However if the sphere is punctured or deformed this will not hold true.
The angles can also be associated with a system of resolved vectors for the point P.
Investigating Applications to Spintronics
Spintronics exploits the quantum propensity of the electrons to spin as well as making use of their charge state. The spin itself is manifested as a detectable weak magnetic energy state characterised as “spin up” or “spin down”. The two spin states can be regarded as winding or unwinding in
Complex Quantum Mechanics (Complex QM).
I am now going to propose (tentatively - all my views here are subject to later revision as I clarify issues) that the process of complex winding may be closely associated with mass to energy transformation. The two processes may not be exactly the same but this is an initial position I am taking. If this is true complex winding has to be completed in ‘shells’ completely winding for one radius before starting the next slightly larger radius shell.
The diagram (b) suggests to me that I investigate the decay/interaction that creates an hyperbolic result like this.
Obviously an exponential result (see figure Spintronics Decay 1) is not going to create a curve parallel to the to the y axis abd is not going to create a curve parallel to the X axis.
The Spin Hall experiment (taken from an online article “Lending an iron hand to spintronics” by Piers Coleman, Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA Published January 20, 2009 http://physics.aps.org/articles/v2/6) does not mention if the hyperbolic paths are for free electrons or not. I shall assume that there is a set of electrons following this path in the experiment that behave as shown previously and below.
Figure Spintronics Decay 2 is a better approximation to the result in diagram (b).
I leave these investigative comments in place to show how I have derived an explanation for these spintronics experiments. There is only a loose connection here with complex space and for the rest of this article I shall not refer to it again.
I consider the experimental behaviour to exhibit wave like characteristics (see figure Spintronics Wave 1 and 2).
At first I though this could be the F wave but now I believe that it is related to the V wave and mass to energy conversion.
In the figure “Spin Hall Effect 1” I imagine what the possible effect upon an isolated electron could be upon a waveform.
Then in the figure “Spin Hall Effect 2” I try to develop this hypothesis to a case resembling the experiment results more closely. Notice that I imagined the spins contrary to the experimental data.
The figure “Spin Hall Effect 3” comes in line with the experimental data.
The figure “Spin Hall Effect 4” suggests that alternative paths 3 and 4 might work in a similar manner but then the paths would not be trapped by the iron atoms that drive this process.
We are not yet ready to put forward a new interpretation. We need to establish a reason why the path in the hyperbolae follow the directions found in experiment. The figure “Spintronics Decay 3” gives an explanation based upon the geometry of the hyperbola being linked that assumes a predisposition to spin in one direction.
Now I can start to create my own interpretation. In the figures “Spin Hall Effect 5, 6 and 7” I show some possible scenarios. The diagrams are not entirely accurate but schematic. There does not need to be 75% mass for example but between, say, 50% and 75%.
The figure “Spin Hall Effect 5” is my first attempt to explain why the electrons in diagram (b) end up with reversed spins.
The figure “Spin Hall Effect 6” is an alternative attempt to explain why the electrons in diagram (b) end up with reversed spins.
The figure “Spin Hall Effect 7” is much closer to the picture that I believe explains the Spin Hall experiment. What I now believe is happening is that the electron on one side is following a V wave trough with a minima for energy at the hyperbolic cusp while the opposite side is following an inverted V wave trough with a maxima for mass at the hyperbolic cusp.
So relating this behaviour back to the iron atoms (which have a reversed spin to each other) then a single F wave around that atom would interact with the V wave patterns in this figure.
Both electrons at A and F have spin but no charge in the Spin Hall experiment so a final correction is made in figure “Spin Hall Effect 8”.
The different phases presented to the electrons following paths ABC and DEF by the iron atoms account for their different behaviour. I expect that since these paths (top picture) are both outward towards A (from C) and F (from D) and not continuous from FEDCBA (that also represents a complete wavelength) then this could be an induction factor (caused by the iron atoms having reversed spin and polarity) reversing the expected behaviour along DEF. However this is a chicken and egg scenario and I expect that the truth may well be that either circumstance (cause or effect) can be present depending upon circumstances.
Spin and Charge Currents
The original diagram (a) for the experiments is also difficult to interpret but now I have some basis for doing so.
In figure “Spin and Charge Currents” the ratios of mass to energy are schematic and not available from experimental data. However using this scheme it is possible to get the same outcome as the Spintronics experiments! For the charge current the initial electrons may have a 50%+ energy ratio to mass while for the spin current the initial electrons may have a 50%- energy ratio to mass. This seems more likely for the charge cuurent to allow the energy/charge to accumulate.
Conclusion
There is now a basis for re-interpreting Spintronics in Complex QM terms. It is far too early to comment any more comprehensively and I would appreciate comments from physicists working in this field. I am pleased that I have found some correspondence although it could be argued it lies more in Mass to Energy conversion than in Complex QM terms.
I have previously considered charge as a surfeit of energy over mass. Spin can be considered as the reverse and seems to act in a similar manner to a skater who pulls in their arms and legs to revolve faster. This is not to automatically equate a smaller mass radius with increased angular momentum but to suggest that there is a link.
I am beginning to see that when I stated that that spin can be associated with a mass rich particle and charge can be associated with an energy rich particle. I was nearly correct. I am believe that angular momentum can be associated with a mass rich particle or energy to mass transfer and magnetic momentum can be associated with an energy rich particle or a mass to energy transfer. So at present a more complicated picture seems to be emerging and perhaps this may be clouding the issue but some correspondence could exist and I mention the possibility here. I expect that spin generally will not change in an electron unless it is subject to outside forces. So we can still associate spin with the amount of mass present in the electron while charge can be with the amount of energy present in the electron. However if we accept that the mass to energy transference is defined by the V wave then spin and charge must vary (ay least slightly).
When we consider this alongside angular momentum and magnetic momentum a more complicated picture emerges that still needs clarifying.
Perhaps spin and charge may hold constant (as a combined dynamic system) because angular momentum and magnetic momentum maintain a constant magnetic field resulting in no observable difference?
