Bob_for_short

A field is nothing else but a force standing in the equation of motion of a probe particle. It cannot be explained differently. As soon as we can put our particle anywhere in the space, we may assign to the space points certain fields (forces). When our particle goes from x1 to x2, the force changes from F(x1) to F(x2). The concept of field is quite similar to the concept of space - of all possible particle positions. But is is always a certain "number" in the particle equation of motion.

Interesting... so kinetic energy varies, depending on the reference frame one is referring to... so it has "kinetic energy with respect to x reference frame"?

Yes, of course. A still body with respect to you may be moving with respect of a moving guy and may hit his head.

If photons must be laterally polarized, how can photons, exchanged along the line between two particles, explain the longitudinal "pushing" & "pulling", along that line, caused by Electrostatic forces ??

Nohow. It is not the transverse photons that act along the line. It is the electrostatic Coulomb force = the property of charges, not photons.

The Poynting vector, which tells you the direction of energy transport (and thus momentum) is E x B.

The pointing vector for electrostatic field equals zero (B=0). It makes sense only for propagating waves, not for static fileds.

What one does is calculate the observed mass of the electron, [math]m_{e}[/math] as you call it, in terms of the parameter in the action [math]m[/math], say. Formally, you can think of [math]m[/math] as being divergent. Regularisation and renormalisation allows a finite [math]m_{e}[/math] to be defined.

In order to calculate the Compton effect or e-p scattering in the first Born approximation we use m = m_e. We constructed QED with the observable m_e, m_f, and e. It is our interaction term that gives divergences, not the original parameters. So the renormalizations are modification of the interaction term jA, namely, removing the self-action effects (=corrections to masses and charges). In the end we have results of another, renormalized theory with another interaction term.

I did not want to imply that QED is an effective theory as such. To regulate it introduce a mass cutoff [math]M[/math]. What I mean is that one hopes that physics at a very high scale does not effect the physics at the scales we are interested in as we consider [math]M rightarrow infty [/math]. If so, then it stands a chance of being renormalisable, as we know QED is renormalisable.

You know, it is a too speculative reasoning about physics at short distances because we judge about it from our classical notions, namely from a point-like electron. We speak of "vacuum polarization" that "screens" too singular potential, etc. At the same time the electron is very tightly bound with the quantized electromagnetic field so it is not point-like but smeared quantum mechanically. So there is no singularity at r = 0.

A point-like nucleus bound in an atom creates a positive charge cloud with no singularity at the atomic center. You may find the corresponding effective potential in my paper in Fig. 1 and Fig. 4, see http://www.springerlink.com/content/h3414375681x8635/?p=78336560cf3d4e3f98e6fb8eac587340π=0 (available also in arXiv).

After all, as we approach the Planck scale we expect QED to not hold.

Yes, the physical predictions of QED will be different at short distances but the theory as a model does need any scale distance to be renormalizable.

One is interested in the Ward-Takahashi identities which expresses if the symmetry holds "quantum mechanically".

Again, it is a consequence of the original equations of theory which is gauge invariant by construction. WT identity is an identity, something like a = a. It's a banality, not a fundamental feature, I would say.

Isn't that what renormalistion is all about?"

Yes but for photon mass they say "it is protected" by this or that as if it was not the sequence of the theory basics. The electron mass is also "protected" then.

The "bare mass", the pole in the propagator without interactions is not the same as the pole when interactions are present. These interactions "dress" the mass.".

So what is the mass values before and after renormalizations? We do not have any other value but m_e.

Renormalisation is really the statement that we do not need to consider higher energy/momentum scales to get a handle on the theory at low scales, say at the scales of the LHC.

I do not think so. After renormalizations there is no trace of the cut-off or any other regularization parameter. QED is not an effective theory.

Renormalizations are necessary with an interaction term containing a self-action. Renormalizations remove the self-action "effects". In particular, the self-action terms contain a "perturbation" of a kinetic nature so such terms modify the original masses. If one uses the right experimental values as the original masses, the perturbatibe corrections are not necessary so they are discarded (= renormalizations).

With a potential interaction term no corrections to the masses arise and no renormalizations are necessary, in my opinion.

You can think of the gauge invariance as fixing the mass of the photon to zero. Any quantum effects cannot "push it" away from zero. It is protected.

The photon mass is zero because of Maxwell equations for the field strengths E and B. Of course it is so in terms of four-vector potential too.

Do "quantum effects" (you mean interaction) push the electron mass? It is numerically m_e in any order of perturbation theory, isn't it?

In QED you still have wave function renormalisation of A. (I'd need to re-read my QFT books to say much more.)

It is a coefficient, not a photon feature.

Yes, please, think it over. I need your insight.

By the way, does your answer mean that the electron mass is "not protected"?

I was told recently that there is no photon mass renormalization. It brings up an interesting question: what is then renormalized in photon? Which of photon features? (What is wrong in the bare photon that needs redefining?)

Can m-theory explain the birth of the universe ? If yes ,how ?

No, it cannot since currently m=11 and our universe is 3-dimensional. We need a better m-theory - with m=3.

So, what is a magnetic field then?

Magnetic field is a field determining the magnetic force in the equation of motion of a charge ((q/c)[vxB]) or in equation of motion of a neutral magnet (dipole interaction force).

It can be measured and given experimentally or calculated from a given current/magnet data.

It is an inter-charge interaction force, if you like. No propagating photons are necessary to explain it.

But isn't the photons used to describe what the magnetic field is as well as describe how it attracts?

No. It is virtual photons, not real. Real propagate, virtual do not. That is why many avoid employing the term "virtual photons". The good and unambiguous term is a "variable magnetic near-field", not a "virtual photon".

So, we explain magnets with photons, which are themselves electromagnetic wave packets, isn't that kinda of navigating around the problem?

No. Virtual photons are "attached" to charges. They are not propagating to infinity unlike real photons (wave packets). They are rather different because they are electric and magnetic quasi-static charge interaction terms in the Hamiltonian. They are known also as a "near" field.

Does the same explanation for the interaction between charged particles, that QED offers, apply to the magnetic field? Is the magnetic field explained as the overlapping of virtual particles.

Your question is not clear. If you mean static magnetic fields, they are classical and do not need any particles to be explained. A classical static magnetic field B is a solution of a static equation with a known current j: B = B(j). It determines the field distribution in space.

If you speak of variable magnetic fields that is calculated from QED equations, they are automatically taken into account when one considers charge interaction. It may be "explained" as due to virtual particle exchange. This "explanation" is similar to the Coulomb time-dependent interaction "interpretation" in terms of virtual photons.

Factually, however, the magnetic and Coulomb time-dependent interaction terms can be separated from radiation and be still considered as properties of charges rather than virtual photons. This is achieved in the so called Coulomb gauge. It is the charge wave-functions that overlap, not virtual particles.

As for the size of an electron, it depends what you mean.

I mean the same thing as an atomic size - the electron elastic form-factor determining the charge distribution in space for ealstic scattering. When we write 1/r, we mean a point-like electron with Coulomb law. In QED the charge is in permanent interaction with the quantized electromagnetic field that smears the charge over space. I wonder - what size of charge smearing does QED predict for a real electron? In order to calculate the corresponding cross section (expressed via elastic form-factor), one has to add the quantized EMF in the electron equation.

I agree with this. Having an elegant mathematical description in which calculations are very clear is desirable, but if we were to loose all contact with the real word then it is not clear if we still doing "physics".

Yes, I also speak of a physical theory with physical predictions. Currently, however, the theory operates with "bare" stuff, "counterterms", etc., and the final results are not really clear to most of researchers.

For example, the size of a real (or dressed) electron, what is it according to QED? I mean theoretical estimation in terms of e, m, h-bar (not an experimental one).

It is reasonably believable in normal quantum mechanics if you have a finite range force. In QFT it is more problematic since even your vacuum state changes when an interaction is present, so the effects can never be isolated.

Thus it is clearly a "difficulty" of the present theory.

I would view it on a more pragmatic level. We make predictions with QFT with this sort of difficulty in mind, and are surprised that our QFTs do so incredibly well at predicting the outcomes of our experiments.

It is not the only difficulty, unfortunately.

My second question is whether it is desirable to have a theory without any conceptual and mathematical difficulties, just in the spirit of QM?

Can you give me references, if any, to the justification of adiabatic hypothesis in QFT? Why should we switch off the interaction in asymptotic states? Because we cannot solve coupled equations?

Can you back that up?

Yes, I can.

The initial state in this thought experiment is an electron and a photon, while the final state is a single electron. Have you ever observed something in between, which is neither initial nor final state?

I am not an experimentalist but I think any radio-wave attenuation in a conducting medium is a simple example of that. A photon has a finite wave-train to be more or less of certain frequency (10^4 oscillations, for example) so its absorption time is finite.

This might get a bit technical. A quantum state at one time evolves into a new quantum state at a different time according to something called the time-evolution-operator.

 

For the electron, the time evolution operator contains objects known as creation and annihilation operators. A creation operator creates a particle in the system and an annihilation operator destroys a particle. Which creation and annihilation operators live in the time evolution operator depends on the physical laws of the system. [...]

 

So in some sense, the electron does not absorb the photon at all - it is destroyed, along with the photon, and a new electron is created.

Apart form this language (creation-annihilation operators) there is another, more appropriate one: the state amplitude depending smoothly on time. While absorbing the photon wave the old state amplitude fade and the excited atomic state amplitude grows up. In the end there is not the initial states but the final only. Similarly for scattering a photon. The state populations depending on time is more physical since there is no instant creation or destroying states in reality.

I am not sure if the electron in higher orbits moves faster.

Okay, how does a electron absorb a photon? Can anyone explain this to me, or is it one of those things in physics that can't be broken down into laymen terms? Or is their even a mathematical explanation of this phenomena?

A photon is a long wave-train propagating is space. An atom is a compound system also existing in space as a de Broglie wave. When two waves meet, the photon wave starts to push and pull the atomic electron. If the resonance conditions are approximately satisfied, the atom may get excited in the end and the photon energy is thus spent on increasing the atomic internal motion energy. The quantum mechanics is a wave mechanics so this works as I have just described.

Wait, this just sunk in -- my book defines m=m1+m2. Wouldn't that make m=-3/2, -1, -1/2, 0, 1/2, 1, 3/2 ?

No, for example, 3/2 + 1 = 5/2.

I have no idea about it.

All of you guys are perfectly right. My question however, was, in instance of the explanation of the charges, how the charges interact with each other when there's no physical contact between them.

I always say that charges are "long-handed". One can consider them as overlapping. Point-likeness of a charge means a simple dependence of the force from distance. But the force is a long-range one. Charges are quite different from neutral atoms that need close contact to interact. Charges are long-handed and sticky.

According to what I've read about magnetic fields, all they're described as are imaginary lines around the magnet that depict the area where the magnet has effects upon. What exactly is a magnetic field? And how is the attraction caused?

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Okay, since no one's replying to this thinking this as something amateurish, let me rephrase it.

I need someone to explain how the attraction is caused by magnets. What is the 'field'?

We think of magnetic fields as imaginary lines of force (let's say I think of it that way). How is this force caused around the magnet?

In order to explain it to you, I have to know what you understand, what does not cause questions to you.

A magnetic field is a quantitative notion. It stands in the charge motion equations and determines the force on a moving charge. It also stands in the magnetic dipole motion equations and determines the external magnetic force.

Magnetic fields are created with magnets and currents. You may safely understand it as an interaction of moving but rather neurtalized charges so the Coulomb interaction is not the main part of the charge interaction.