Where does the energy possessed by a free electron come from

[Mr Virtual]

Hi
We say that the probability of finding an electron anywhere in vacuum is 100%. This means an electron is constantly moving from place to place. Where does this energy come from? Why doesn't this source of energy never get exhausted? Does this mean an electron has infinite energy? Or is this energy drawn due to interaction with the quantum particles present in the vacuum? If this is the case, then is the principle of conservation of energy followed here?

regards
Mr V

 

[strangerep]

We say that the probability of finding an
electron anywhere in vacuum is 100%.

What? No, we don't say that. Did you perhaps mean "...the probability
of finding an electron somewhere in space..."?
If you meant that, let us know and I'll try to say something more helpful.

- strangerep.

 

[Mr Virtual]

What? No, we don't say that. Did you perhaps mean "...the probability
of finding an electron somewhere in space..."?
If you meant that, let us know and I'll try to say something more helpful.

No,no. I mean what I say. Until you actually observe the electron, it has 100% probability of being present anywhere in vacuum. You don't know where it is, until you "see" it. You obviously know it is "somewhere in space" , but not exactly where. And seeing it means hitting it with a photon. When that happens, you can see its latest position possible, though again you won't know its exact location after a short time.
I maybe wrongly stating what I mean, or maybe I don't know exactly what is happening. But that is beside the point. What I actually wanted to know was : where does a free electron get its energy from? Because in my knowldge, an electron possesses some energy even in its free state.

regards
Mr V

 

[Anonym]

What? No, we don't say that. Did you perhaps mean "...the probability of finding an electron somewhere in space..."?
If you meant that, let us know and I'll try to say something more helpful.

Somewhere is undefined notion which belong to the poetry and not to the physics. Mr. Virtual expression “the probability of finding an electron anywhere in vacuum is 100%” is precise verbal formulation of unitarity. Express your opinion only in case when you know what you are talking about.

You obviously know it is "somewhere in space", but not exactly where.

No. As you said above Anywhere = Everywhere. The measurement violates the unitary evolution law but do not violate unitarity.

Where does this energy come from? Why doesn't this source of energy never get exhausted? Does this mean an electron has infinite energy? Or is this energy drawn due to interaction with the quantum particles present in the vacuum? If this is the case, then is the principle of conservation of energy followed here?

“Where does this energy come from?” It defined by the initial conditions which is the state of the physical system at arbitrary chosen point in time. It in turn presents the accumulated history of the system.

“Why doesn't this source of energy never get exhausted?” We assume that the motion of free electron in vacuum as well as any other physical system is described by the physical law. That is the same law as yesterday or tomorrow(otherwise it is not a law), that is invariant under time translations. Then the energy must be conserved quantity.

“Does this mean an electron has infinite energy?” No. E=mc^2. Everything is finite.

“Or is this energy drawn due to interaction with the quantum particles present in the vacuum?” Yes. The system you suggest to consider is the free electron and vacuum.

“If this is the case, then is the principle of conservation of energy followed here?” Yes, see above.

Regards, Dany.

 

[Iamu]

I don't want to hijack this thread of yours, too... but like I said in your other thread, the problem here lies in thinking of the electron as something like a billiard ball with inertia.

The electron will never naturally come to absolute rest through collisions. It would be natural for a hard ball to do this, but it takes energy to press the electron particle/wave thingy into a hard ball in the first place. (Actually, though, generally not even the hard ball would come to absolute rest through collisions unless we factor in inelastic collisions and friction--otherwise, if we plug the pockets and set a few pool balls rolling on a frictionless surface, the chances of anyone of them stopping due to a collision is tiny, and then it generally wouldn't stay put for long before another ball collided with it. The total momentum will be conserved. See Anonym's post above.)

If you shut the electron wave/particle thingy into a box, it's wave will bounce back and forth off the walls, and this produces a pressure inside the box. If you made the box smaller, it would bounce faster and there would be more pressure. If it were to ever come to absolute rest (or close), we'd have to squeeze it and hold it there. Unlike a hard ball, for the wave/particle thingy, zero momentum is not the state of least kinetic energy; in fact the more we localize it, the more it tries to break free.

Now, we take the same wave/particle thingy in a very tiny box, and release it into an infinite vacuum. It'll spread forever. Let's say it's been spreading for a year and we build a gigantic box around it at this point. The pressure on the walls of this box would be infinitesimal compared to the pressure on the walls of the the original small box. Eventually, the electron will spread so thin, it will be indistinguishable from the vacuum fluctuations; it "decoheres" (or we could say it becomes coherent with the vacuum environment).

The free electron's lowest natural energy state isn't standing still; it's spreading out to the point of nonexistance.

 

[strangerep]

Somewhere is undefined notion which belong to the poetry and not to the physics. Mr. Virtual expression “the probability of finding an electron anywhere in vacuum is 100%” is precise verbal formulation of unitarity. Express your opinion only in case when you know what you are talking about.

Well, I've obviously upset you inadvertently. So I'll just say that I was
only trying to clarify what was being asked. "I" am included in "we", so
that bit was probably ambiguous. The "somewhere" bit was in my question
to the OP, so that wasn't an opinion.

I won't attempt any further answers to this thread, since it's way too
easy to offend people unintentionally.