# Energy of an electron

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Hi everyone,

Suppose that there's an electron at rest removed from all gravitational sources and any other fundamental particles. There's an observer who is revolving around the electron at a distance of $d$. But, due to lack of reference points, the observer cannot say with certainty that he is revolving or the electron is. He assumes that the electron is revolving. According to the Larmor's Formula, the observer will find energy being radiated out by the electron since he observes it revolving. But, how can the electron radiate out energy if it's not revolving? So, will the observer record no energy?

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All particles have a field.

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swansont    6166

Hi everyone,

Suppose that there's an electron at rest removed from all gravitational sources and any other fundamental particles. There's an observer who is revolving around the electron at a distance of $d$. But, due to lack of reference points, the observer cannot say with certainty that he is revolving or the electron is. He assumes that the electron is revolving. According to the Larmor's Formula, the observer will find energy being radiated out by the electron since he observes it revolving. But, how can the electron radiate out energy if it's not revolving? So, will the observer record no energy?

Acceleration is not relative. The electron will not be radiating.

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Sensei    599

Suppose that there's an electron at rest removed from all gravitational sources and any other fundamental particles.

Any particle with rest-mass (unlike massless particles) can be at rest in its own rest frame of reference.

https://en.wikipedia.org/wiki/Rest_frame

There is also such frame of reference, center of mass,

in which either object is moving.

https://en.wikipedia.org/wiki/Center_of_mass

https://en.wikipedia.org/wiki/Center-of-momentum_frame

Earth doesn't revolve around the Sun, but Earth revolve around center-of-mass of entire Solar System, so the same the all other planets.

Majority of the Solar system mass is in the Sun, so center-of-mass of Solar system is located close to the star core.

But in binary star system it could be not true anymore.

BTW, it's used to find out whether distant stars have planets.

https://en.wikipedia.org/wiki/Doppler_spectroscopy

Edited by Sensei
• 1

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studiot    1131

Acceleration is not relative. The electron will not be radiating.

Just to pick up on swansont's point;

You need to distinguish between translational (accelerating) motion which classically leads to radiation by a charge and rotation or (accelerating) angular motion which does not.

I say classically because with the correct boundary conditions in quantum mechanics the translational motion does not lead to radiation.

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So no energy is recorded.

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swansont    6166

Just to pick up on swansont's point;

You need to distinguish between translational (accelerating) motion which classically leads to radiation by a charge and rotation or (accelerating) angular motion which does not.

I say classically because with the correct boundary conditions in quantum mechanics the translational motion does not lead to radiation.

Angular motion does, too. Cyclotron radiation.

Of course, an electron "rotating" is a misguided notion, as it's a point particle. But send it on a curved path, and it will radiate.

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studiot    1131

Angular motion does, too. Cyclotron radiation.

Of course, an electron "rotating" is a misguided notion, as it's a point particle. But send it on a curved path, and it will radiate.

Is an electron traversing a 'curved path' translating or 'spinning on its axis'?

Edited by studiot

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swansont    6166

Is an electron traversing a 'curved path' translating or 'spinning on its axis'?

When the lines between classical and quantum are blurred like this, it's unclear what one means or how it will be interpreted.

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studiot    1131

When the lines between classical and quantum are blurred like this, it's unclear what one means or how it will be interpreted.

I can't see it.

Either something moves from A to B or it does not.

If it does then translation is involved, regardless of what else happens.

It doesn't really matter whether that something is a blurred wavelet, a quantum particle or something really esoteric.

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swansont    6166

I can't see it.

Either something moves from A to B or it does not.

If it does then translation is involved, regardless of what else happens.

It doesn't really matter whether that something is a blurred wavelet, a quantum particle or something really esoteric.

Electrons in an atom do not have defined trajectories. You can't say anything about how they got from one point to another, if you were to localize them at two different points in time. But the OP isn't talking about that. It was, however, talking about a rotating electron. How does one interpret that? And how does one make a clear answer to anyone who thinks a rotating electron isn't nonsensical? So you don't see it, because you know the subject matter, but you aren't the only one reading the answer.

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studiot    1131

Electrons in an atom do not have defined trajectories. You can't say anything about how they got from one point to another, if you were to localize them at two different points in time. But the OP isn't talking about that. It was, however, talking about a rotating electron. How does one interpret that? And how does one make a clear answer to anyone who thinks a rotating electron isn't nonsensical? So you don't see it, because you know the subject matter, but you aren't the only one reading the answer.

Upon re-reading the OP I find the same interpretation as I originally made viz heliocentric v geocentric motion argument applied to the electron/observer system, clearly considered as a miniature Earth/Sun system.

This is why I replied as in post#5 clearly identifying and underlining a classical response, but drawing the distinction between this and a quantum response.

As a matter of interest do you think a quantum electron changing its energy level by tunneling in a semiconductor without changing its position in the lattice emits EM radiation?

Edited by studiot

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Sensei    599

Electron bound in atom is pretty specific case,

hard to make experiment,

but free electron emitted by electron gun,

fired at target, has significant velocity and kinetic energy..

If we pass free electrons through hole in electron gun's positive charged electrode, they will fly freely..

Then their trajectories can be bend,

by electric or magnetic fields.

So one can put there electromagnets on the top, bottom, left and right, of vacuum chamber..

And bend electrons trajectories,

and call it CRT.

Electrons accelerated to significant velocity/kinetic energy have to lost their energy (decelerate) prior riching "out frame of reference", and release their energy by emitting photons with appropriate energy.

Edited by Sensei

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zztop    11

Electrons accelerated to significant velocity/kinetic energy have to lost their energy (decelerate) prior riching "out frame of reference", and release their energy by emitting photons with appropriate energy.

Electrons do not emit photons, the atoms of phosphorus coating the CRT do.

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Electron transition releases energy.

$E_2 - E_1 = hf$

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StringJunky    1485

Electron transition releases energy.

$E_2 - E_1 = hf$

Photons.

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Yes. Energy in the form of photons.

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zztop    11

Electron transition releases energy.

$E_2 - E_1 = hf$

These are the electrons transitioning between the energy levels WITHIN the atoms of phosphorus coating the CRT screen. NOT the electrons coming from the electron gun as "Sensei" incorrectly posted.

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MigL    491

Either or, makes little difference to the OP.

The OP inquired about the equivalence ( ? ) between an observer revolving around a stationary electron, versus a spinning electron with a stationary observer.

Aside from the fact that the revolving observer is undergoing acceleration and there can be no equivalence between the two cases, the notion of a spinning, POINT particle is non-sensical ( or at least ill-defined ).

Swansont has already mentioned this a few times.

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swansont    6166

If we ignore the quantum contradiction here and instead assume we had a microscopic ball on which charges were placed, the ball would radiate if it were rotating.

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zztop    11

Hi everyone,

Suppose that there's an electron at rest removed from all gravitational sources and any other fundamental particles. There's an observer who is revolving around the electron at a distance of $d$. But, due to lack of reference points, the observer cannot say with certainty that he is revolving or the electron is.

Rotation is absolute. As such, observer rotating around an electron is NOT equivalent with electron rotating around the observer. The premise of your OP is false.

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StringJunky    1485

Rotation is absolute. As such, observer rotating around an electron is NOT equivalent with electron rotating around the observer. The premise of your OP is false.

The observer would feel an acceleration wouldn't they?

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zztop    11

The observer would feel an acceleration wouldn't they?

Yes, if the observer is rotating, he will feel the acceleration.

If the electron is rotating, then the observer will feel no acceleration.

This is why rotation is absolute (it can be detected with an accelerometer )

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StringJunky    1485

Yes, if the observer is rotating, he will feel the acceleration.

If the electron is rotating, then the observer will feel no acceleration.

This is why rotation is absolute (it can be detected with an accelerometer )

Thought so, cheers.