Does a Static Charge in a Classical Field Constantly Lose Energy?

[Bobhawke]

The field gives the force a unit charged particle would feel when placed in the field of another charged particle. The field exists at every point in spacetime (for long range fields). I always think of a field as being like the disturbance created by throwing a rock into a pond, which propagates through the water. But if the field exists everywhere in spacetime, doesn't this mean for a classical field a static charge is constantly and forever losing energy in the form of the field? Going back to the analogy of the water waves, to create a field at every point in spacetime, one would have to have something osciallting for eternity in the water creating new disturbances, which would take an infinite amount of energy. How can this be?

In the quantum theory, the particle undergoes quantum fluctuations due to the uncertainty principle. Could this infinite vacuum energy be the source of the infinite energy of the field?

 

[pmb_phy]

The field gives the force a unit charged particle would feel when placed in the field of another charged particle. The field exists at every point in spacetime (for long range fields). I always think of a field as being like the disturbance created by throwing a rock into a pond, which propagates through the water.

A field doesn't need to be a distrubance in order for it to exist. The case of a stationary charged particle is just such an example of a field with no distrubance.

But if the field exists everywhere in spacetime, doesn't this mean for a classical field a static charge is constantly and forever losing energy in the form of the field?

No. The field is static and there is no flow of energy and therefore it is not loosing energy.

Going back to the analogy of the water waves, to create a field at every point in spacetime, one would have to have something osciallting for eternity in the water creating new disturbances, which would take an infinite amount of energy. How can this be?

It can be because there is nothing oscillating in a static field. I recommend doing away with that visualization because it will get you into trouble. For instance there can be a field with energy flow even for static fields. So long as the Poynting vector, which is proportional to the cross product of the electric field and the magnetic field. is non-zero there will be no energy flow. However if there is a static magnetic field and a static electric field for which the cross product is non-zero then there will be energy flow. Even then there is no problem with energy conservation. Consider a spherical magnetic with a uniform magnitization which has a charge uniformly distributed over its surface. Even though such a field is static the Poynting vector is non-zero. It points in a direction around the sphere. The energy flows in circles so that the energy never flows away, it merely flows around the sphere never leaving! I find that pretty nifty since its not intuitivley obvious!

Pete

 

[Bobhawke]

ok so let's stick with the example of the single static charge. If i suddenly place a charge anywhere in the field, it experiences a force with a delay equal to how long it takes light to get there from the initial charge. This suggests to me that the first charge must be constantly throwing out an inifinite number of photons in order to guarantee that a charge placed anyhwere within its field gets 'hit' by a photon. Infinite number of photons = infinite energy.

Otherwise the first charge must somehow 'know' the precise location of any charge that suddenly appears in its field without ever having interacted with it, so it can send a photon to it, which can't be.

 

[zonde]

Could this infinite vacuum energy be the source of the infinite energy of the field?

As I understand quantum mechanics can describe interactions of particles but can be of little help with description of vacuum energy itself.
I came to this forum with the same question but have not sorted it out clearly.
Maybe fields can be thought as structured vacuum energy (structure is changed from random perturbations to some systematic perturbations) and so it will not require any energy flow at distance? Then virtual photons would be kind of description for that structure.

 

[pmb_phy]

ok so let's stick with the example of the single static charge. If i suddenly place a charge anywhere in the field, it experiences a force with a delay equal to how long it takes light to get there from the initial charge. This suggests to me that the first charge must be constantly throwing out an inifinite number of photons in order to guarantee that a charge placed anyhwere within its field gets 'hit' by a photon. Infinite number of photons = infinite energy.

Otherwise the first charge must somehow 'know' the precise location of any charge that suddenly appears in its field without ever having interacted with it, so it can send a photon to it, which can't be.

The problem here is that you're assuming that the photons are the same kind of photons that are in a beam of light. They are not. The photons which mediate the electric field are virtual photons. There is an FAQ on this at

http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html

See the section labeled Do they violate energy conservation?

Pete

 

[Bobhawke]

So there is no problem for quantum fields, but there is for classical fields. What about back in the day when people didnt know about quantum mechanics and there was only classical fields - didnt my question come up at some point? Didnt anyone ever tell Maxwell he was wrong?

 

[pmb_phy]

So there is no problem for quantum fields, but there is for classical fields. What about back in the day when people didnt know about quantum mechanics and there was only classical fields - didnt my question come up at some point? Didnt anyone ever tell Maxwell he was wrong?

In classical mechanics there are no photons so there is no need to consider a flow of energy. It is said that a charged particle generates an electric field and it is the field which acts on charges placed in the field. One charge does not act on another charge in this sense.

There is a problem in that in classical EM a charged particle must have a finite size since if it was a point charge (zero radius) the energy of the field would be infinite. Something similar happens in QFT and is corrected for by a process known as renormalization. There are problems in QFT regarding infinities and I don't think that's been worked out completely yet. I think that this is not a problem because the math predicts precisely what is observed.

Pete

 

[Bobhawke]

sorry to revive this topic but I have one or two more questions:

First for the classical field, if a disturbance is not necessary for it to exist, then what 'kicks' a particle when it enters the field of another? Its like the field propagates through space telling every point it passes how much force to exert if a charge is placed there, but there is nothing there to actually provide that force.

Second, how do particles that are separated by large distances interact through virtual particles? They can only exists for a very short time due to the energy time uncertainty, so if 2 charges are separated by a large enough distance spatially there wouldn't be enough time for a photon to travel the distance as a virtual particle. But the electromagnetic force is long range, every charge must feel the field eventually no matter how far away it is.

Also, I should say thankyou for being good enough to answer my questions.

 

[AhmedEzz]

I'm no expert but I *think* I can answer your first question

What 'kicks' the particle is the force resultant from the field itself and the other particle's field. However, the response differs depending on the charged particle that enters the field.
However, this does not mean that the field needs disturbance to exist.

 

[pmb_phy]

sorry to revive this topic but I have one or two more questions:

First for the classical field, if a disturbance is not necessary for it to exist, then what 'kicks' a particle when it enters the field of another? Its like the field propagates through space telling every point it passes how much force to exert if a charge is placed there, but there is nothing there to actually provide that force.

First of all the field exists through all of space so a particle never enters the field. It is always in it. Second, the field itself is at the same position that the particle so nothing has to propagate from source to field point. Its already there.

Second, how do particles that are separated by large distances interact through virtual particles?

Since that is a question regarding quantum field theory you might get a better reponse if you post this in the quantum mechanics forum. There may be people there who can help that don't frequent this forum. I think Hans is good in this area. I hear that vanesch is an expert in this field. I hear very good things about him.

They can only exists for a very short time due to the energy time uncertainty, so if 2 charge

I'd use caution when you use this kind of arguement. The exact interpretation of the time-energy uncertainty relation can be difficult and is often stated incorrectly.

Also, I should say thankyou for being good enough to answer my questions.

You're welcome. We're here to please!

Pete

 

[zonde]

First of all the field exists through all of space so a particle never enters the field. It is always in it.

Field exists through all of space and time but not with the same intensity. You are just splitting hairs.

Second, the field itself is at the same position that the particle so nothing has to propagate from source to field point. Its already there.

Properties of field depend from nearby charges so at least information has to propagate from charge to field point not speaking about say virtual photons.

 

[pmb_phy]

Field exists through all of space and time but not with the same intensity. You are just splitting hairs.

I'm being precise.

 

[Bobhawke]

First of all the field exists through all of space so a particle never enters the field. It is always in it. Second, the field itself is at the same position that the particle so nothing has to propagate from source to field point. Its already there.

Since that is a question regarding quantum field theory you might get a better reponse if you post this in the quantum mechanics forum. There may be people there who can help that don't frequent this forum. I think Hans is good in this area. I hear that vanesch is an expert in this field. I hear very good things about him.

I'd use caution when you use this kind of arguement. The exact interpretation of the time-energy uncertainty relation can be difficult and is often stated incorrectly.

You're welcome. We're here to please!

Pete

I should have said in my head I was imagining magicking a particle into existence in the field of another.
Everything is not always in the field - the field propogates with a finite speed so there can be things that haven't felt it yet. I don't think you answered the question of how the field can exert a force on a particle if the field is not a disturbance of some sort.

Also, I thought this was the quantum mechanics forum?

thanks again

 

[vanesch]

First of all, one should make a distinction between quantum fields and classical fields: they are different beasts, and although it can sometimes be helpful to switch between them, it is a tricky business which often leads to inconsistencies.

Classical fields are dynamical entities which are defined over spacetime, and often they are coupled to ANOTHER dynamical entity, which is a (set of) particle(s). Usually, classical fields obey some conservation principles, like the conservation of energy, and then it is obvious that static fields shouldn't "radiate away" energy. These conservation laws often follow from specific parts of the dynamics, which also stop you from setting up "paradoxial" situations. For instance, from the Maxwell equations (the dynamics of classical electrodynamics) follows charge conservation. As such, it is impossible, within a field that obeys the Maxwell equations, to have a charge "suddenly appear out of nowhere". If you want to do that, then the Maxwell equations cannot be universally valid, and in that case, there's no guarantee for energy conservation anymore either. What is important to note, again, is that in classical fields, the particles are a separate dynamical entity. They are IN the same spacetime, but particles are not "part of" the fields. They just happen to be defined over the same spacetime.

Quantum fields are different beasts. You can introduce them in different ways, but quantum fields are quantum systems, which have a (Hilbert) state space and so on. The only quantum fields we kind of understand well are free fields, and we apply perturbative couplings between free fields as approximations to "real, interacting" quantum fields. So let us look at free fields first. Free quantum fields can appear in different energy eigenstates (as any quantum system), and it turns out that the ground state is (usually) a unique state, which we call "the vacuum". There are excited states of quantum fields, and we call those excited states: particles ! For the (free) Quantum Electrodynamic field, the excited states are called photons. Or better, we call photons, the differences between successive excited states, and an excited state is a single or many photon state. So photons are to the quantum electrodynamical field what excited orbitals are to the hydrogen atom: they are states of excitation.

Note that this time, particles are not an "outside" dynamical system: they are genuinly part of the dynamical description (in fact, they emerge from it) of the quantum dynamics of free fields.

Electrons, for instance, are states of excitation of the (electron) Dirac field. A state with a single electron is a specific excited state of that field, and a state with 5 electrons and 3 positrons is yet another excited state of that same quantum field.

If we have several fields, they can *couple* dynamically (just as classical mechanical systems can couple). If that happens, we don't know anymore exactly what goes on, but we can look upon it as free fields with a perturbation. That perturbation then manifests itself as "transitions between the excited states" of the free fields, which, in the corresponding particle view, is seen as particles "colliding", "creation", "annihilation" etc...
In fact, it is just excited free field states changing through the "interaction perturbation".

The precise bookkeeping of how these excited free field states change, can be handled surprisingly enough by a set of diagrams which derive from the free field description and the interaction description: the so-called Feynman diagrams. They determine how "incoming" excited states can transform into other, intermediate excited states, and finally to "outgoing" excited states, through a set of precise calculational rules. One calls the particle description of the intermediate excited states: "virtual particles". So on one hand, virtual particles are just a concept in a calculational technique ; on the other hand, they are highly intuitively suggestive. But it would be an error to consider them as a kind of classical particles, for several reasons:
- particles are not independent dynamical entities in quantum field theory, as they were in classical field theory. They are emerging quantum states of the fields themselves.
- in as much as the "particles" of free quantum field theory share some properties with classical particles, this is much less obvious in non-free quantum field theory ; it is only in their asymptotically free states that the ressemblance re-emerges, and that we can talk about "incoming" and "outcoming" particles.
- virtual particles are calculational elements which help us to find out how free quantum fields can be used as an approximation to interacting quantum fields ; at no point they are asymptotically free states themselves. So it is not clear in how much they relate to those free states, and in how much they are just a calculational aid.
- virtual particles have "impossible" dynamical properties if we force them into the picture of a genuine particle, such as imaginary mass.