Thomas Seebeck found that if two ends of a metal were at different temperatures, an electric current would flow through it. Could we expect the same to happen when the wire ends are placed at two different gravitational potentials? Does gravity couple to electricity, particularly in a place where gravity is so strong (black hole)?
There are a couple of factors here to be taken into account:
- In the wire there are free charges, and under the gravitatational attraction would act on them downwards.
- But the electrical force from the part of the positive ions would tend to bring them back. So, the distribution of the electrons would be according to the resulting force.
- A strong gravitational force may distort (compress) the wire itself, because it would act on the ions in the metal structure.
- The electrical repulsion between positive ions should oppose the gravitational attraction, and the question is which one of the forces is greater.
Thus, the answer is not unique, it depends on the numerical data.
In order to have a current flow, there must be a complete circuit and there cannot be a difference in gravitational potential around a closed loop.
To make the question meaningful, you might ask if there would be a difference in electrostatic potential between the ends of a single wire, however it is not easy to see how that could be measured for the same reason as above, you need a second wire to provide a return reference.
If two ends of a thermocouple are kept at different temperature only then the current flows but if the single wire hangs with its ends at two different temperature, the thermo-couple will not be formed and circuit will not be completed. Similarly, we can not expect any current in a hanging wire with its ends at two different gravitational potentials .
To answer a somewhat different question: I believe an overall neutral plasma, placed in a gravity field, may develop a small internal electric field, provided the charge carriers have different mass. But it is a matter of doing some statistical mechanical calculations (or find some already carried out) to verify/disprove this belief.
There can be quite strong electric fields in the atmosphere, but they is most likely caused by non-equilibrium processes.
Currents in the accelerated bodies are quite known. Since one cannot distinguish between acceleration and gravity, the answer is obvious yes.
An accelerated uncharged particle does not carry any electric current. How can we expect a hanging wire with its ends at different gravitational potentials to carry an electric current similar to that in a thermo-couple?
This question really belongs to the field of cross effects in transport theory, for which a study of the https://en.wikipedia.org/wiki/Onsager_reciprocal_relations is a good starting point. There are many interesting and complex phenomena related to cross effects, like the https://en.wikipedia.org/wiki/Rayleigh–Taylor_instability. An application of the Onsager theory to describe the behaviour of ionic (plasma) flows in the atmosphere may be very interesting and useful.
Metallic conductors are not good systems for the study of electric-gravitational cross effects, if the studies are to be taken serious by experimentalists. In this context, all ideas about esoteric objects like black holes, and the theories of relativity, can safely be stored in the basement until the basic properties of cross effects are well understood.
Igor> Currents in the accelerated bodies are quite known.
What about currents in bodies under constant acceleration? With resistivity? Where does the dissipated energy in a body in a constant gravitational field come from, if answers to the former is yes and the equivalence principle is valid?
There is a similar much studied question regarding radiation from a charge under constant acceleration, by the equivalence principle with the same behaviour as a charge at rest in the constant gravity.
Dear Arbab,
No. There are no possibility of having an electric current produced by a difference of gravitational potentials and less if you think in a kind of Seebeck effect there must be also associated a gradient of temperature to such electric current. Notice that a superconductor, with a supercurrent is not a thermoelectric at all because this coupling doesn't exits.
@Ales
Your experiences are interesting, and in agreement with my gut expectations. The only known long range forces are electromagnetic and gravitational ones. However, the gravitational force is too weak to have any dynamical influence in earthly systems: it only acts as an external imposed force. Hence, the electromagnetic forces should --- at least post factum --- be expected to screen out all gravitational ones. At least for small systems.
The situation is different in large systems like our atmosphere, which always must be described as a plasma (hence introducing an electric screening length of importance). Unfortunately, it is not easy to make controlled experiments with the atmosphere or equivalent systems. But I expect much work, which I don't know about, has been done on such systems anyway.
A quick answer to the original question will be in the negative since acceleration due to gravity is same for ions and electrons (due to equivalence principle). However, in a conductor having non-zero temperature there are other effects like phonons interacting with ions (that are heavier than electrons) and electrons. So, if due to gravity and phonon interactions, there is a net drift velocity of electrons with respect to the ions, there can result a small electric current.
Net drift velocities of electrons and ions under the combined effect of phonon interaction and gravitational acceleration will be the same and consequently a hanging wire with its ends at different gravitational potentials does not carry any electric current, not even infinitesimally small.
One gravitational field (or potential) doesn't act on an electric charge and therefore never can produce an electric current. Thermal energy can change the kinetic energy of each charge and if you have an special material where the gradient of temperature can be associated to the gradient of the potential, this means that you have a Seebeck coefficient which would be impossible to have only using gravitation interaction. The gravitation interaction besides to be too weak respect to electric one, the problem is that it didn't changed the entropy per every electric charge and also the difference of the gradient for this hypothetical gradient of gravitational potentials, would need an enormous material (thermoelectric) which is absolutely out of any reality.
@Kåre Olaussen
I meant there is such a contribution to a current. But other contributions like drift current and diffusive currents are there also. The net current is subject to an equilibrium and should be zero. This is like Hall current, for example. It exists but in the finite sample the drift current due to the voltage balances it. Or a p-n-junction. The procedure is: add gravitational contribution to the chemical potential beside the elecrtic part , for example mgz + eV. Find V(z).
My answer was misleading.
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