Design notes

Last update: December 01, 2007

 

Basic idea

The idea is predicated on the supposition that particle mass, in this case of the electron, is maintained and mediated by a classical background EM field (CBF). That is, the mass would be zero if the fields were absent. The direct-action theory points in this direction, but is still immature. Therefore, at this stage some of the predictions necessary to perform an experiment are no more than guesses. It is not known if the relevant part of the CBF field is quasi-monochromatic at the electron Compton frequency. It may for example be that the field energy density matches that of the Dirac electron-hole ‘sea’ without requiring that it be monochromatic. A finite (renormalized) ZPF is not out of the question either.

The proposal here is to modulate the electron mass electromagnetically – thereby demonstrating the electromagnetic fungibility of mass. The input is that mass is maintained by a CBF, but without having to commit to a particular spectrum. More specifically, under the hypothesis that mass is electromagnetically maintained, dynamic changes in the effective mass imply corresponding dynamic changes in the CBF, which could, in principle, be detected as a propagating signal – in practice as a depletion or excess of the steady-state CBF required to maintain mass elsewhere.

Effective Mass

One possibility is to make use of mass modulation (effective mass) as it already occurs for example in a semiconductor lattice, and modulate that through some exterior (eg magnetic) field. Let us call the apparatus in which the effective mass is being modulated as the generator (rather than transmitter), call the outgoing depletion or excess of the alleged background field the signal, and call the test apparatus designed to pick up the signal via sympathetic modulation of the electron masses therein the detector.

The above arguments suggest that we require the generator and detector have overlapping characteristics. Ideally therefore, they should be the same material. In the generator, modulate the (effective) electron mass, and look for sympathetic fluctuations of effective electron mass in a detector – light speed delayed. We need to look for is a material with means of modulating effective mass of electrons by a large amount. Once we have that, the appropriate means of detection will probably suggest itself.
 

Pressure

I prefer modulating the effective mass m* by mechanical means since it protects against the possibility that the energy for the change is acquired not from a background EM field but from the modulation source itself. You will see from the paper by Lange et al that we need to be able to modulate by around 23 thousand atmospheres in order to see a 1% change in effective mass in GaAs.

Bearing in mind we will want to modulate the pressure (under computer control) piezo seems a good method. I am hoping these pressures can be achieved with a piezo transducer with a little geometric focusing, whereby the force from the piezo is delivered to the GaAs by a tapered truncated cone.

More here on piezo pressure transducers::
http://www.physikinstrumente.com/en/products/prdetail.php?sortnr=400600.40

Material

The material may be important: it seems at first reading of the Lange paper that the sensitivity of m* to pressure in GaAs is a consequence of a strong non-quadratic term in energy versus momentum in this particular semiconductor.

Effective Mass measurement

The Lange method employed some S. de Hass technique (don't know what it is) to measure m*. Important for us is that the measurement involves a rate of change with temperature, which is incompatible with our requirements that modulation and measurement proceed dynamically at some reasonable clip. I suggest therefore we consider cyclotron resonance instead. A description of Cyclotron Resonance (CR) as a method of measuring m* in semiconductors is given in the book by Ashcroft & Mermin 'Solid State Physics', chapter 28 (page 570 in my copy). Dresselhaus has described the CR technique applied to Si and Ge.

Temperature

Liquid He temperatures were used in the Lange experiment. This is for whatever reason associated with the S. de Hass technique.

Cyclotron Resonance measurement of m* requires that the cyclotron frequency is much greater than the collision frequency which is a strong function of temperature. In the Ashcroft & Mermin data the CR at 24GHz was measured at T=4K, so it looks as if low temperatures will also be required if we adopt this method. (The DC magnetic fields were of the order of kGauss.) Perhaps a way forward is an initial investigative phase wherein we find out the precision with which one can identify a 'collective' m* at various temperatures, starting at 293K and going down from there, to 77K, but to 4K only if necessary.

Absorption cross section of the mass modulation signal

This is angle dependent. At this stage, and very speculatively, I think we will be able to use the classical Thomson value for the scattering cross-section of the signal. This is σ ~ re2 where re is the classical electron radius ~ 3 x 10-15 m so σ ~ 10-29 . Hence the extinction coefficient k (exponential loss per unit radial length away from generator) will be of order σ times the density of free electrons participating in the measurement. For solid volume number density (of protons and electrons) rho, one has

k = f rho σ

where f is the fraction of electrons available for participation in the measurement (nominally the conduction band occupancy). Typical solid volume density is rho ~ 1023 / m3 . Then

k ~ 10-5f

In a semiconductor, f is of the order of the Boltzmann coefficient (ignoring degeneracy) for the band gap Eg in question:

f ~ exp(-Eg/kbT)

This factor is exp(-3000) at T = 4K, and therefore kills off any possibility of measurement unless we work at relatively elevated temperatures, and / or artificially excite carriers through, say, a pulse of optical radiation. The problem with the latter is that it restricts carriers to the surface, so we loose out on the bulk absorption.

Let us consider first the maximum possible temperature. 1eV photon energy is the highest possible at which semiconductors are relatively transparent. If CR can be performed at this frequency (a big if), then this gives a maximum allowable collision frequency of order 1014 Hz.

Energy relaxation time as a function of electron temperature Tn: Comparison of the model and data for GaAs at several lattice temperatures, from the web pages of Palankovski.

It appears that the relaxation time is not an incredibly strong function of temperature and is always much longer than 10-14 s. Therefore, provided CR at such frequencies is possible, there should be no problem operating at elevated temperatures. 

The Boltzmann factor for T = 300 K for a 1eV band gap is around 10-17, which is still a show-stopper. Even at T = 500 K the factor is around 10-10. This gives k ~ 10-15 which is still bad news.

In short, we do not seem to be able to get the conduction density up high enough to be able to make a measurement. 

Doped GaAs
We could try working with doped GaAs to bring f close to 1, and hope that the doping leaves more or less intact the sensitivity of m* to pressure. Probably the very best we could hope for would be a 1% of number density contribution to the conduction band, giving k ~ 10-7

This presents a daunting task: we will be looking for fluctuations in the effective mass in the detector material of order

where Omega is the solid angle of captured radiation in the source, and L is the optical depth of the source.

 

 

 

Procedure

1. In the first phase we demonstrate effective, and precisely repeatable m* modulation (at whatever temperature turns out to be necessary).

2. In the second phase we have two pieces of GaAsAl, both with cyclotron frequency m* detectors. In one, the pressure is modulated by piezo at some frequency well below the cyclotron frequency, and we look for correlated fluctuations of m* in the other.