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Infinite Force of an Electron?

Perpetual Student

Illuminator
Perpetual Student
Joined
Jul 8, 2008
Messages
4,852
Is the following a genuine puzzle or is there a simple explanation?
As far as we know an electron has no spacial dimensions other than location -- i.e. it is considered to be a point particle. Now, the resulting force of the electric charge is related to distance from the electron in accordance with an inverse square relationship. Is the force therefore infinite at the point of the electron? Does that make that point some kind of singularity -- an electrical singularity?
 
Perpetual Student said:
Is the following a genuine puzzle or is there a simple explanation?
As far as we know an electron has no spacial dimensions other than location -- i.e. it is considered to be a point particle. Now, the resulting force of the electric charge is related to distance from the electron in accordance with an inverse square relationship. Is the force therefore infinite at the point of the electron? Does that make that point some kind of singularity -- an electrical singularity?
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The inverse-square law is only valid at large distances. As you get closer to the electron, higher-order QED corrections kick in and modify the electrostatic force law; go closer still and you run into different forces altogether (weak, Higgs, ?).

Solving these sorts of equations is complicated, and in some cases you get apparently-infinite components, when turn out (thanks to renormalization theory) to disappear when you try to calculate anything observable. So, yeah, there are "singularities" in there, but they're not quite the one you're thinking of.
 
Perpetual Student said:
Is the following a genuine puzzle or is there a simple explanation?
As far as we know an electron has no spacial dimensions other than location -- i.e. it is considered to be a point particle. Now, the resulting force of the electric charge is related to distance from the electron in accordance with an inverse square relationship. Is the force therefore infinite at the point of the electron? Does that make that point some kind of singularity -- an electrical singularity?
Click to expand...

Aside from the points made above, I'd also like to mention that force, as an independent quantity, doesn't really make an appearance in standard quantum mechanics. There is an expectation value for the gradient of the potential for a particle, and that is equal to the time derivative of the momentum (so it's analogous to Newton's 2nd law), but because the wave function for even a pointlike particle is not a delta function, that quantity doesn't diverge. That's why you can solve the hydrogen atom, even assuming BOTH protons and electrons are pointlike and without bothering with the QED corrections. In fact, it's far easier to solve it without those corrections - not quite as accurate, but much simpler to work with, and good enough for most applications.
 
Ziggurat said:
Aside from the points made above, I'd also like to mention that force, as an independent quantity, doesn't really make an appearance in standard quantum mechanics. ...
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What does that mean? Quantum mechanics is an incomplete theory in that it does not take into account or deal with force? Is there some sort of transition theory to the macro world where force manifests itself?
 
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Perpetual Student said:
What does that mean? Quantum mechanics is an incomplete theory in that it does not take into account or deal with force?
Click to expand...

No, I'm saying you don't need force in quantum mechanics. There is something analogous to force (the expectation value of the gradient of the potential), but even in cases where the gradient of the potential diverges (such as for a 1/r potential), the expectation value of the potential gradient (found by integrating the wave function squared times that gradient over all space) does not.

Now, classically speaking, force is the gradient of the potential. But there's no expectation values involved, so questions like "what is the force between two charges at distance r" make sense in a way that they simply don't in quantum mechanics. The larger and more massive your system, the more like classical force the quantity I mentioned above will behave.
 
Perpetual Student said:
What does that mean? Quantum mechanics is an incomplete theory in that it does not take into account or deal with force? Is there some sort of transition theory to the macro world where force manifests itself?
Click to expand...

Force is defined by acceleration, which in turn requires knowing the position of something (so you can measure its change with time). In QM you don't have a position - you have a probability density for position. So force, while it can be defined in various ways, is not so useful a concept when QM uncertainties are important.
 
Thanks for the responses; as usual, when it comes to QM, more questions were created than solved for me. QM is frustrating! So many aspects of it cannot be visualized and are even downright counter-intuitive, but I'm not giving up. I have found many helpful sources that will help me explore your comments further....

-- no wonder Einstein never bought into QM!
 
Here's a little article where I "bless" the electron with an awareness or consciousness, ala panpsychism.
Which came first, motion or growth, or better, energy or mass?
by Ted Erikson

Time does not really exist for light (electromagnetism). But light cannot validate itself without creating, that iis "sparking" mass to gain a surface from which to reflect, absorb, diffract, refract, etc. Any particle of mass will do but mass itself needs time to validate its existence. So let us place panpsychism in perspective by stating that such that an awareness, or consciousness, for any particle of mass recognizes that is must be of a greater size, i.e. larger, bigger, or more complex to gain more time of "life".

This idea is verified from biological studies, i.e., life spans increase as size of many species vary from bacteria to whales. Extrapolating this verifiable information down to the size of the ubiquitous electron carrying a charge suggest "lifetimes" must be of orders less than attoseconds, i.,e., extremely small since it appears and reappears about an atom. Quantum probabilities are required to localize regions where it may be found.

Light controls motion and mass controls evolutional growth, but light "needs" mass and mass "needs" time. This is the real philosophical question of which came first. Panpsychism, an ancient idea of consciousness in ALL things is a most sensible answer.
 
SdogV said:
Here's a little article where I "bless" the electron with an awareness or consciousness, ala panpsychism.
Which came first, motion or growth, or better, energy or mass?
by Ted Erikson

Time does not really exist for light (electromagnetism). But light cannot validate itself without creating, that iis "sparking" mass to gain a surface from which to reflect, absorb, diffract, refract, etc. Any particle of mass will do but mass itself needs time to validate its existence. So let us place panpsychism in perspective by stating that such that an awareness, or consciousness, for any particle of mass recognizes that is must be of a greater size, i.e. larger, bigger, or more complex to gain more time of "life".

This idea is verified from biological studies, i.e., life spans increase as size of many species vary from bacteria to whales. Extrapolating this verifiable information down to the size of the ubiquitous electron carrying a charge suggest "lifetimes" must be of orders less than attoseconds, i.,e., extremely small since it appears and reappears about an atom. Quantum probabilities are required to localize regions where it may be found.

Light controls motion and mass controls evolutional growth, but light "needs" mass and mass "needs" time. This is the real philosophical question of which came first. Panpsychism, an ancient idea of consciousness in ALL things is a most sensible answer.
Click to expand...
Not really. But, thanks for playing!!:)*






*this is a duplicate of my post to your duplicate of your post in another thread.
Just curious, are you planning to post this in every thread on electrons/particles/light/QM?:confused::jaw-dropp
 
Re: fuel air" *this is a duplicate of my post to your duplicate of your post in another thread.
Just curious, are you planning to post this in every thread on electrons/particles/light/QM?

Sorry, just trying to find where I can fit with intelligent people.
 
SdogV said:
Re: fuel air" *this is a duplicate of my post to your duplicate of your post in another thread.
Just curious, are you planning to post this in every thread on electrons/particles/light/QM?

Sorry, just trying to find where I can fit with intelligent people.
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Only if you a planning to post that same wrong statement. If not, no.

At this point, I have to suggest as their server at McDonalds though.
 
SdogV said:
Sorry, just trying to find where I can fit with intelligent people.
Click to expand...

If that's the case, I'd recommend posting things that actually make sense. Your previous post was complete nonsense.
 
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