# do electrons have inertia

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If electrons do not move in classical-mechanical lines of continuous gradations of velocity. I.e. if they don't accelerate and decelerate in a linear sense, how can they be said to have inertia? Does a free electron moving from A to B have the capacity to travel at different speeds according to the amount of force that pushed it? If not, what basis is there for regarding electrons as having mass. I.e. why not just call them a massless particle similar to photons except with charge and unique forms of transit?

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It takes energy to accelerate an electron, thus electrons have mass. If electrons were massless they would always travel at the speed of light.

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It takes energy to accelerate an electron, thus electrons have mass. If electrons were massless they would always travel at the speed of light.

I'm aware of that reasoning, but I was wondering how they can be measured as changing speed since they supposedly don't move linearly but pop-around randomly within probability curves and things like that.

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You question is how do we understand the mass (or inertia) quantum mechanically?

The usual methods of non-relativistic quantum mechanics do not use forces or velocities but rather Hamiltonians. You can then apply canonical methods of quantisation.

The point is that in a classical limit electrons will obey the Lorenz force law where we can replace the position and velocity by their expectation values. We assume that the electromagnetic field is not quantised.

$m \frac{d \langle \mathbf{v }\rangle}{d t }= q \mathbf{E} + q \langle \mathbf{v}\rangle \times \mathbf{B}$.

In this limit the mass and electric charge appear as "classical parameters" to be measured.

Quantising the electromagnetic field also leads to quantum electrodynamics.

Edited by ajb
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Not having a well-determined momentum or position does not correspond to not having any momentum or position at all. $\Delta{x}\Delta{p} = \frac{\hbar}{2}$

The QM effects become important on the scales where the deBroglie wavelength (h/p) is large. If you put a 1 kV potential on an electron, you will accelerate to have 1 keV of energy (ignoring any other effects) and the speed to which that corresponds, within the uncertainty that QM dictates.

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Not having a well-determined momentum or position does not correspond to not having any momentum or position at all. $\Delta{x}\Delta{p} = \frac{\hbar}{2}$

The QM effects become important on the scales where the deBroglie wavelength (h/p) is large. If you put a 1 kV potential on an electron, you will accelerate to have 1 keV of energy (ignoring any other effects) and the speed to which that corresponds, within the uncertainty that QM dictates.

So electrons are observed to accelerate and decelerate? Still, how can they decelerate if they don't have anything smaller than themselves to transfer momentum to? Can a particle collide with something with the same or greater mass and still lose speed? What would you do if you wanted to slow down an electron? Pull the emergency brake?

Edited by lemur
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I have personally accelerated and decelerated electrons through an electric field and observed the effects of their varying velocities and wavelengths, so yes, that can be observed.

They can transfer their momentum to other atoms in elastic collisions, although the large mass of atoms means the atom ends up with only a small fraction of the electron's energy and the electron bounces along on its merry way.

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I have personally accelerated and decelerated electrons through an electric field and observed the effects of their varying velocities and wavelengths, so yes, that can be observed.

They can transfer their momentum to other atoms in elastic collisions, although the large mass of atoms means the atom ends up with only a small fraction of the electron's energy and the electron bounces along on its merry way.

Here's what I don't get: why is an electron going through an electric field different than a photon going through a field of atoms? Doesn't the photon slow down due to the electrostatic force of the electrons/atoms as it passes through the glass, water, plastic, or whatever?

Ok, as far as the electrons slowing due to momentum-transfers, here's the scenario I'm imagining: a cold liquid is charged with electrons until it begins to boil and expand. In that case, would the electrons decelerate as the gas is expanding because the average momentum of the atoms would be getting translated into expansion and thus the electrons would lose speed together with the atoms they were colliding with?

Edited by lemur
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Photon's can't slow down, because they're massless. They can only be absorbed or emitted.

Electrons have electric charge, so they experience a Coulomb force in the electric field and are accelerated or decelerated.

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Photon's can't slow down, because they're massless. They can only be absorbed or emitted.

Why is C less in a medium then?

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Here's what I don't get: why is an electron going through an electric field different than a photon going through a field of atoms? Doesn't the photon slow down due to the electrostatic force of the electrons/atoms as it passes through the glass, water, plastic, or whatever?

A photon carries no electric charge. It does not interact with the electromagnetic field. This is despite the fact that the electromagnetic field is a bunch of photons. Photons do not interact directly with other photons.

Electrons outside of the atom -- free electrons are accurately described classically and they interact with the electromagnetic field according to classical mechanics under the Lorentz force with the handbook value for electron mass. Back in the dark ages (say prior to qbout 2005) many television and computer displays used cathode ray tubes -- which are based on controlling electron trajectories using an electromagnetic field. Ditto for oscilloscopes.

BTW the energy and position operators have both a discrete and a continuous spectrum. Free electrons can take on a continuum of values for both position and energy. Only confined electrons have only discrete values for thse quantities.

Edited by DrRocket
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Why is C less in a medium then?

A simplistic explanation would be to say that photons traveling through a medium are absorbed and re-emitted with a small delay while traveling through the medium, so that the individual photons always travel at c but the overall net effect is that the light pulse is slower than c.

(By the way, c usually represents the speed of light in vacuum, and is a physical constant, so it never changes. The phase velocity and group velocity of light can change, however.)

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A simplistic explanation would be to say that photons traveling through a medium are absorbed and re-emitted with a small delay while traveling through the medium, so that the individual photons always travel at c but the overall net effect is that the light pulse is slower than c.

(By the way, c usually represents the speed of light in vacuum, and is a physical constant, so it never changes. The phase velocity and group velocity of light can change, however.)

So when light goes through a clear medium like glass or water the photons are being absorbed and re-emitted by the electrons of the substance as they pass through it? I thought the particles just didn't absorb the light and thus it could pass through without interference. I guess that's impossible, though, since the light obviously bends but how can it get absorbed and re-emitted without any scattering? That's a divergent question, I know, but it seems like the photons slow down because they interact with the electrons without actually getting absorbed/re-emitted, in which case I don't see why photons affected by electrostatic charge would be so different from electrons affected by an electric field.

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The more correct explanation of my post is available here:

http://physicsforums...393&postcount=4

That was a great read. Materials are transparent to photons where the connective lattice of their atoms are not capable of absorbing the frequency of the light. Then it says, however, that the lattice still has the effect of slowing down the photons a bit without explaining how that would be caused. My guess would be that because electron lattices vary between black-bodies capable of emitting and absorbing all frequencies to "clear-bodies" emitting and absorbing none, that there is some degree of electrostatic force that the photons encounter that fails to absorb them completely, yet still exerts some force on them as they pass. Sorry to speculate, and I hope someone corrects me with better information, but would that not be very similar to the effect of an electric field on free electrons? I suppose the odd thing about photons would be that they would immediately move at a higher C the moment they transcend one medium for another. Can electrons slow down in an electric field and maintain that speed after the electric field is no longer acting on them?

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The post discussed this

On the other hand, if a photon has an energy beyond the phonon spectrum, then while it can still cause a disturbance of the lattice ions, the solid cannot sustain this vibration, because the phonon mode isn't available. This is similar to trying to oscillate something at a different frequency than the resonance frequency. So the lattice does not absorb this photon and it is re-emitted but with a very slight delay. This, naively, is the origin of the apparent slowdown of the light speed in the material. The emitted photon may encounter other lattice ions as it makes its way through the material and this accumulate the delay.

I disagree with the observation that atomic absorption does not take place; AFAIK it proceeds just as described above — it is an attempted excitation of a mode that is not allowed. The phonon model does not explain the slowdown in a gas, for example, but light slows down in a gas.

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I disagree with the observation that atomic absorption does not take place; AFAIK it proceeds just as described above — it is an attempted excitation of a mode that is not allowed. The phonon model does not explain the slowdown in a gas, for example, but light slows down in a gas.

Is there knowledge about what photons do when they encounter electrons not configured to accept their frequency? May they still be influenced in some way without being absorbed? If so, how?

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Is there knowledge about what photons do when they encounter electrons not configured to accept their frequency? May they still be influenced in some way without being absorbed? If so, how?

I am not aware of any way of testing this, owing to the Heisenberg Uncertainty Principle.

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I am not aware of any way of testing this, owing to the Heisenberg Uncertainty Principle.

Could the wave-function behavior indicate it in some way? Sorry if this is a naive question. I understand nothing about the relationship between "wave functions" and empirical observations/measurements.

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Could the wave-function behavior indicate it in some way? Sorry if this is a naive question. I understand nothing about the relationship between "wave functions" and empirical observations/measurements.

No.

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