The Gravitational Seebeck Effect

Today, I will discuss a concept which I am not the first to think of, but hope to be one of first to write down the equations and derivations for such an effect. It involves a generalization of the thermoelectric effect to also include gravity. I don’t know what to call it, so the “gravitational Seebeck effect” will suffice for now. The thermoelectric effect includes the Seebeck effect, which states that a temperature gradient across a metal will cause the creation of an electric potential gradient. This effect has been exploited for years and describe how thermocouples can be used as thermometers after proper calibration.

After discussions with Prof. Fronsdal, it seems that there is experimental evidence which suggests that the typical Seebeck effect is non-linear. The typical equation is dV = -SdT, where dT is the temperature difference applied and dV is the potential difference produced. S is the Seebeck coefficient, which is dependent on the metal. The non-linearity presents itself by shifting the equation by a constant which is equivalent to a microvolt.

If gravity is included into this equation, it could fix this non-linearity seen in experiment. Furthermore, the weakness of gravity motivates why this would only cause a shift in the electric potential by a microvolt. So right now, I have written down an equation for the current density j, which is similar to Ohm’s law, but also includes a coupling to temperature and the gravitational potential \Phi.

{\bf j} = -\sigma\nabla V - A\nabla T - B\nabla\Phi

j is the current density. A is a constant related to the Seebeck coefficient by A = \sigma S. Also, B is a new constant which I have introduced. There are quantum mechanical and statistical mechanical derivations of A, so I figure learning these may give incite on how to derive B.

Some questions I have include does B depend on the material properties? Perhaps the mass density. Does this effect treat solids and gases differently? A solid is made up of microscopic massive constituents which cannot move, while a gas’s constituents can move. Insulators do not have free electrons and therefore do not show the Seebeck effect. Does this mean that solids will not have the gravitational effect, but gases will?

Tomorrow, I will meet with Prof. Fronsdal and see what he has to say about these thoughts and questions. I may learn that there are other people which have already been developing this theory. I am not sure how much other people have thought about this idea. I couldn’t find any similar explanation on the internet. If it is true, then Roderich Graeff’s experiments could confirm the validity of the generalized equation.

Furthermore, it seems that this electric potential (and perhaps gravitational potential) must contribute entropy to the system. This seems to be the only way to keep the second law of thermodynamics and have the entropy always be equal or increase as time progresses. Perhaps the true total entropy cannot decrease, but the way it is currently calculated can… I retract all statements made about total entropy spontaneously decrease. This seems to be the only way to resolve the controversy of D’Abramo’s thermocharged capacitor.


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