# The Naked Scientists Forum

### Author Topic: How big is protons force field and electrons?  (Read 2494 times)

#### jccc

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##### How big is protons force field and electrons?
« on: 16/07/2014 06:34:47 »
Is a proton on Earth attracts an electron on the moon? According to  F=kx1x1/r^2, the answer is yes?

If so, is charged particles has infinity radius force field?

If so isn't the universe is connected by EM field?

#### PmbPhy

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##### Re: How big is protons force field and electrons?
« Reply #1 on: 16/07/2014 13:12:41 »
Quote from: jccc
Is a proton on Earth attracts an electron on the moon? According to  F=kx1x1/r^2, the answer is yes?
You're thinking classically, not using quantum field theory (QFT) which is what needed in this case. Unfortunately I don't know QFT so I can't help. However I suspect that the field is too small to be defined at that distance.

#### Bill S

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##### Re: How big is protons force field and electrons?
« Reply #2 on: 16/07/2014 13:49:33 »
Matt Strassler describes a field as something that: “…is present everywhere in space and time, can be, on average, zero or not zero….”

This does suggest that, in principle, fields are infinite in extent.  Obviously, we are limited in the degree to which we can detect a field with increasing distance – as with gravity – but presumably it is still there?   Possibly that’s what you meant by: “…the field is too small to be defined at that distance.”

#### JP

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##### Re: How big is protons force field and electrons?
« Reply #3 on: 16/07/2014 14:29:07 »
In quantum field theory, fields are things that permeate all space and time.  The "electromagnetic field generated by an electron" is described by the electron coupling to this background electromagnetic field and changing it.  The electron doesn't create the field, but rather creates a disturbance in the field that we call "the electromagnetic field of the electron."

You can think of it loosely like boats on an ocean: the ocean is the background field and would exist even in the absence of boats.  The boats are like particles, which interact with the ocean and can disturb it.  The boats don't generate the ocean, but they do generate particular disturbances on the ocean.

#### PmbPhy

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##### Re: How big is protons force field and electrons?
« Reply #4 on: 16/07/2014 15:01:47 »
Quote from: Bill S
Possibly that’s what you meant by: “…the field is too small to be defined at that distance.”
Yes. Exactly. Also there are uncertainty relations with regard to the components of the fields that have to be taken into account too.

Think about how you'd measure such a field. In classical electrodynamics you choose what's called a test charge which is a charge you use to determine the value of the field at a given point and you make much much smaller than the charge which whose field you're measuring. You can't do that with a proton since the electron has the same charge. Then you'd have to precisely measure the location of the source charge and the test charge which can't be done due to the uncertaintly principle, especially since you want to measure the force on the charge and force. And force is not an observable in quantum mechanics so all you can do is find the expectation value of it and <f> = d<p>/dt. Since there's some uncertainty in p this means that there is some uncertainty in <f> and therefore the proton's electric field. So the field can be so small as to be measured to be zero if the uncertainty is too large.

But this is too complicated for me to determine myself. Perhaps JP can do the calculations? What do you say JP? :)
« Last Edit: 16/07/2014 15:16:49 by PmbPhy »

#### jccc

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##### Re: How big is protons force field and electrons?
« Reply #5 on: 16/07/2014 15:24:22 »
In quantum field theory, fields are things that permeate all space and time.  The "electromagnetic field generated by an electron" is described by the electron coupling to this background electromagnetic field and changing it.  The electron doesn't create the field, but rather creates a disturbance in the field that we call "the electromagnetic field of the electron."

You can think of it loosely like boats on an ocean: the ocean is the background field and would exist even in the absence of boats.  The boats are like particles, which interact with the ocean and can disturb it.  The boats don't generate the ocean, but they do generate particular disturbances on the ocean.

JP, I never read that before, so happy to learn it, and I totally agree with it so far.

Tell me more about the ocean please, its nature, property, is it made of negative charged particle?

I give you all my weed!

#### JP

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##### Re: How big is protons force field and electrons?
« Reply #6 on: 16/07/2014 17:03:10 »
Quote from: Bill S
Possibly that’s what you meant by: “…the field is too small to be defined at that distance.”
Yes. Exactly. Also there are uncertainty relations with regard to the components of the fields that have to be taken into account too.

Think about how you'd measure such a field. In classical electrodynamics you choose what's called a test charge which is a charge you use to determine the value of the field at a given point and you make much much smaller than the charge which whose field you're measuring. You can't do that with a proton since the electron has the same charge. Then you'd have to precisely measure the location of the source charge and the test charge which can't be done due to the uncertaintly principle, especially since you want to measure the force on the charge and force. And force is not an observable in quantum mechanics so all you can do is find the expectation value of it and <f> = d<p>/dt. Since there's some uncertainty in p this means that there is some uncertainty in <f> and therefore the proton's electric field. So the field can be so small as to be measured to be zero if the uncertainty is too large.

But this is too complicated for me to determine myself. Perhaps JP can do the calculations? What do you say JP? :)

Excellent explanation, but I'm afraid it's too complicated for me as well.  It could be done and this is precisely what quantum electrodynamics can do, but the calculations tend to be monstrous, even for simple problems, so its often attacked with computer simulation.

#### jccc

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##### Re: How big is protons force field and electrons?
« Reply #7 on: 17/07/2014 02:30:13 »
In quantum field theory, fields are things that permeate all space and time.  The "electromagnetic field generated by an electron" is described by the electron coupling to this background electromagnetic field and changing it.  The electron doesn't create the field, but rather creates a disturbance in the field that we call "the electromagnetic field of the electron."

You can think of it loosely like boats on an ocean: the ocean is the background field and would exist even in the absence of boats.  The boats are like particles, which interact with the ocean and can disturb it.  The boats don't generate the ocean, but they do generate particular disturbances on the ocean.

Is the field charged? Is the disturbances generated by electron called EM wave/photon?  What's light speed in this ocean/field?

#### The Naked Scientists Forum

##### Re: How big is protons force field and electrons?
« Reply #7 on: 17/07/2014 02:30:13 »