- #36
anorlunda
Staff Emeritus
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It's obvious that there are desires for mental models of electric conductivity that involve electrons behaving like ball bearings, and which sit somewhere between circuit analysts and Maxwell's equations. But nature is not compelled to provide us all the simplifications we crave.
Free electrons accelerate in an electric field, but they also collide with atoms and the mean-free-path is very short. The Drude Model attempts to capture that (as in the above picture). But consider those red dots like the circular bumpers in a pinball machine. The bumpers do more than bump, they add kinetic energy to the balls. @Drakkith mentioned thermal excitation of electrons and energetic pinball bumpers can be compared to that.
We know that the pinball machine is tilted down, and that we can add new balls at the top, and that some balls will come out at the bottom, but what happens in the middle is quite chaotic and impossible to describe except statistically. Start thinking statistical mechanics.
But the Drude model is old and deprecated. The modern version is the free electron model. It considers the distribution of energies, the statistics of fermions and other quantum effects. (the muffin-tin-approximation is fun to read about) Now it sounds even more like statistical mechanics. Indeed, the models of resistivity in bulk materials can be compared to Boltzman's reasoning in deriving the perfect gas law. Each begins not with individual electrons (electric) or molecules (gas) but rather with assumptions about energy distributions in bulk.
Perhaps a good analogy of current in a wire, is the flow of energy from the core of a star to the surface of the star. I read (sorry can't remember the link) that because the mean-free-path of a photon in the core is so short, that it takes an average of one week for a photon to complete it's voyage to the surface. From a bulk thermodynamics view it is trivially obvious that the energy released in the core must reach the surface, but explaining that in terms of the time evolution of individual photons is hopeless.
That leads me to a conclusion that I know will be unsatisfying and likely to produce protests. I say that (other than the statistical mechanics approach), there should be no attempt to explain resistivity or current in a wire using visualizations of electrons behaving like ball bearings. All the analogies and all the verbalizations that don't begin with energy distribution statistics are wrong. They can't begin to explain things like the relationship between thermal conductivity and electric conductivity, or the change of resistance with temperature. Perhaps putting those attempts on the PF forbidden topics list is too strong, but they should be discouraged.
We are fortunate to have QED, Maxwell's Equations, and Circuit Analysis frameworks. Each of those is a safe harbor, correct (within its frame of assumptions) and self-consistent I call those levels 1, 2 and 3. Anyone who wants to study fractional levels and thinks that they can be made simple, intuitive, and describable without math, is acting foolishly.
Free electrons accelerate in an electric field, but they also collide with atoms and the mean-free-path is very short. The Drude Model attempts to capture that (as in the above picture). But consider those red dots like the circular bumpers in a pinball machine. The bumpers do more than bump, they add kinetic energy to the balls. @Drakkith mentioned thermal excitation of electrons and energetic pinball bumpers can be compared to that.
We know that the pinball machine is tilted down, and that we can add new balls at the top, and that some balls will come out at the bottom, but what happens in the middle is quite chaotic and impossible to describe except statistically. Start thinking statistical mechanics.
But the Drude model is old and deprecated. The modern version is the free electron model. It considers the distribution of energies, the statistics of fermions and other quantum effects. (the muffin-tin-approximation is fun to read about) Now it sounds even more like statistical mechanics. Indeed, the models of resistivity in bulk materials can be compared to Boltzman's reasoning in deriving the perfect gas law. Each begins not with individual electrons (electric) or molecules (gas) but rather with assumptions about energy distributions in bulk.
Perhaps a good analogy of current in a wire, is the flow of energy from the core of a star to the surface of the star. I read (sorry can't remember the link) that because the mean-free-path of a photon in the core is so short, that it takes an average of one week for a photon to complete it's voyage to the surface. From a bulk thermodynamics view it is trivially obvious that the energy released in the core must reach the surface, but explaining that in terms of the time evolution of individual photons is hopeless.
That leads me to a conclusion that I know will be unsatisfying and likely to produce protests. I say that (other than the statistical mechanics approach), there should be no attempt to explain resistivity or current in a wire using visualizations of electrons behaving like ball bearings. All the analogies and all the verbalizations that don't begin with energy distribution statistics are wrong. They can't begin to explain things like the relationship between thermal conductivity and electric conductivity, or the change of resistance with temperature. Perhaps putting those attempts on the PF forbidden topics list is too strong, but they should be discouraged.
We are fortunate to have QED, Maxwell's Equations, and Circuit Analysis frameworks. Each of those is a safe harbor, correct (within its frame of assumptions) and self-consistent I call those levels 1, 2 and 3. Anyone who wants to study fractional levels and thinks that they can be made simple, intuitive, and describable without math, is acting foolishly.
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