Bob_for_short

Being a student, I heard of Maxwell multi-poles. For example, you take two opposite-sign charges Q at some distance R. Their dipole moment is Q*R. Then you decrease the distance R and increase the charge values so that the dipole moment does not change. In the limit R = 0 you have an electric dipole with practically closed lines.

Could you give an example? All the cases I can think of of electric dipoles are made of two or more electric monopoles and would have an inverted field between the poles as compared to the outside field.

A dielectric bar, like a magnet bar but charged with rho(x) = k*(|x|-L)*sgn(x), -L < x < L.

Magnets come in dipoles, there is no magnetic pole for the field line to end at. In one side out the other.

 

Electric dipoles on the other hand have two poles and so their field looks kind of like that of a fundamental dipole except for in the space between the two poles where it is the opposite direction.

So a "fundamental" dipole is different from an electric dipole? An electric dipole can also be made with continuous charge distribution, without a gap.

OK, Is it possible to construct a ball like the OP asked?

I think we can take a ball, cut it in 8 equal parts with three mutually perpendicular planes, magnetize each piece along its axis of symmetry (from the center to the surface) and make them stick together with a glue.

The magnetic field lines will always form closed loops.

Magnetic field lines are the same as electric dipole lines: they start at one pole and finish at another one.

if someone were to melt down the ore that is used to make magnets into a sphere, is it possible to make all the negative poles pointed toward the center and create a monopole on the outside? ( I know that the negative poles would repel each other, but if some thing had a strong enough pull, could it result in a monopole?)

No, the magnetic field in such a configuration will be confined within the body. It is just like two equal electrical charges, one at the center, the other one is on the sphere. No field outside the body. However the magnetic field inside will be radial. I think it is well possible to make.

John von Neumann carefully distinguished between the two types of quantum evolution processes (Type 1 "quantum jumps" = "wave function collapse"; Type 2 SWE). Now, the probability amplitude, for a "quantum jump", is equal to the overlap integral ([math]< \Phi | \Psi >[/math]), between the quantum particle's current state ([math]\Psi[/math]), and the available end state ([math]\Phi[/math]). (The probability is the squared modulus of the probability amplitude.)

Projection [math]< \Phi | \Psi >[/math] or the amplitude measurement is not an evolution or a collapse.

Roughly speaking, an Electro-dynamic potential, [math]\vec{A}[/math], can generate both [math]\vec{E}[/math] & [math]\vec{B}[/math], from [math]\vec{E} \approx \frac{\partial \vec{A}}{\partial t}[/math] & [math]\vec{B} = \nabla \times \vec{A}[/math]. Thus, an EDP, oscillating up & down along a single axis, would generate both the electric & magnetic fields, of a light wave. Is, then, the direction of [math]\vec{A}[/math] the polarization axis of light ?

Yes, that is right. A(x,t) is not a constant vector in space and time so both E and B may be different from zero. In particular, if A(x,t) = a⋅exp(ikx-iωt), you have a plane EMW.

I suggested as alternative to make a 'closet' with the clothes hanging and force fan-air flow, no heat added. It would take much longer time, but...

A little wind without closet will do.

Steven Hawking has Science at his hand to explain everything, so we don't need other scientists.

I understand, that the SWE, on its own, also does not predict the electron's spin projections -- it must be augmented by the Pauli Spin Matrices. Could you not do essentially the same, w/ the KGWE as well ?

It is not the SWE that should predict the projections but the angular momentum operator. SWE still holds if the interaction does not depend on spin variables. The Pauli equation is reduced to SWE if there is no magnetic field, for example. Each spinor component obeys SWE then. The same statement is valid for KGWE.

(thanks for the replies)

 

If w.h.t. (1) F = dp/dt; (2) F = -dV/dx; then could you consider, that the "electro-static potential (V)", which an electron "emits", and whose gradient defines the electro-static force-field emanating from said electron, as a "cloud" of virtual photons, of varying spatial density, so that their "electro-magnetic pressure" (P ~ dp/dt) generates the "push" associated with the electro-static potential (V) ?? In symbols, can you equate -dV/dx = dp/dt (of the virtual photon "cloud") ??

No! A charge does not emit any potential V( r )! V( r ) is a potential energy of interaction of two charges and r is their relative distance. There is no other meaning of the potential energy.

If energy can not be created or destroyed then what happens to the energy of 2 photons when they destructively interfere with each other?

The interference picture is not destructive in all the space. In some regions the fields cancels each other, in other they add. The energy of EMF is an integral over the whole space from the energy density (E² + B²). It remains constant despite the bright and dark region may travel in space.

...Electrons are always surrounded by a swarm of virtual photons...

 

...If we provide the necessary energy, for a virtual photon to become a real photon w/o violating the conservation law of mass-energy, it does just that. That is why an excited electron emits a real photon... The jettisoned photon is one of the electron's virtual photons, that suddenly finds itself with enough energy to keep going, w/o violating the conservation law of mass-energy, and it does. In other words, one of the electron's virtual photons suddenly is "promoted" to real photon...

 

This strongly suggests, that photon absorption represents the "demotion", of an incident real photon, into a "bound" or "hang-around" virtual photon. Perhaps an electron's cloud of virtual photons is the repository housing all the incident photons it has ever absorbed ??...

In my pet theory this bla-bla about virtual photons surrounding an electron is represented in a concrete formula (solution): the electron is a part of quantum oscillators. The whole system is called an "electronium". When you push the electron, the state of oscillators change - they get excited that corresponds to appearing real photons.

On the other hand I need a Coulomb interaction term too. It is another, independent property of charges (apart from emitting photons) and is not reduced to exchange of "virtual" photons. I my model each electronium has its own oscillators, like each atom has its own electrons and energetic levels. So the charge attraction/repulsion is another feature of charges.

In the standard QED this question is quite vague due to initially decoupling the "mechanical" and electromagnetic properties of a change and considering the coupling by the perturbation theory. Factually nobody has written the solution for a real electron surrounded by the virtual photons. Such a solution has to include the "mechanical" and the "wave" variables. I advances such a solution from physical and mathematical reasoning as an ansatz in http://arxiv.org/abs/0811.4416 and http://arxiv.org/abs/0806.2635

Case 3:-

Mass A accelerates away from stationary observer and mass B.

Observer detects electric+magnetic fields and also sees photons emitted from A, while only electric field is detected from B.

 

If observer accelerates at same acceleration as A, magnetic field and photons disappear and only electric field is detected from A, while mass B now produces electric+magnetic fields and Photons.

Photons from A do not disappear in an accelerated reference frame. The radiated EMF energy density is positive and cannot be canceled with a variable change. The emitted photons can be "registered" by a photomultiplier or reflected by a mirror, so their presence is easily visible in an accelerated RF.

People are saying gamma ray come from decaying nucleus and is different from X-ray of same frequency.

But after all its em ray, not a particle stream.

Then theoretically if you go on increasing the quanta of energy of photon, can't you make gamma ray?

Yes, we can and we make. By increasing the projectile energy in the Bremsstrahlung, for example.

A regular, visible light becomes gamma-ray flux in a fast-moving reference frame due to Doppler shift (increase) of frequency.

But normally nuclear gamma-rays sources in laboratories emit much less photons than there is in a visible light. So gamma-rays consist of rare "particles" (hard photons).

... I thought that [math]\Lambda_C[/math] was the characteristic amount by which electrons lengthen the wavelengths of incident photons, sort of the "inertial impact" of electrons on photons (?).

This interpretation is much better because it treats the electron classically and photon quantum-mechanically. Yes, [math]\Lambda_C[/math] determines the energy loss of the incident photon (which leads to increasing its wavelength).

The classical electron radius assumes that the electron's mass arises from electro-static self energy. This is an assumption, and need not be physically accurate at all. Is there is any evidence that the c.e.r. is physically meaningful ?

No, only problems with such an interpretations (runaway exact solutions).

Intriguingly, the Compton wavelength is the radius an electron would have to have, were it limbs spinning at the speed of light, in order to account for its spin angular momentum. Solely to order-of-magnitude:

 

[math]\hbar \approx (m r^2) \omega \approx (m c^2) / \omega[/math]

 

[math]\hbar \omega \approx m c^2[/math]

This is the "baseline" phase frequency, of electrons, according to the Klein-Gordon Equation. Is this physically significant ?

No, because it does not predict the discrete spin projections.

If you take into account the magnetic field energy (together with electrostatic), you may arrive at larger "classical" electron radius proportional to the Compton length.

I meant to say, manipulate the phase factors, of various paths, by manipulating [math]\vec{A}[/math] along those paths. You yourself said that "the phase factors do [depend on [math]\vec{A}[/math]]". So, by suitably manipulating [math]\vec{A}[/math], you could manipulate the phase, and hence action, associated with those paths. Wouldn't that, then, affect the particle's dynamics, via the principle of least action (action minimization) ?

Of course, it would. Accelerators are designed in a way to get the desired beam path. It is exactly A who is "manipulated".

Electro-dynamic potentials ([math]\vec{p} \rightarrow \vec{p} - e \vec{A}[/math]) affect particle momentum, and hence (path integrated) phase, yes?

 

With suitably sophisticated micro-manipulation, of electromagnetic fields, then, one could -- conceivably, if but barely so -- "micro-manage" the phases, of all those paths passing through one's "territory". Since, as you said, most far-out paths are "good zeros anyway", then such "coherent phase manipulation" could conceivably create a "united voting block", which could exert unexpectedly profound influence, on remote events, non-locally, yes (like a small symphony being "heard" over a cacophonous babbling din) ??

The paths in the integral do not depend on A. The phase factors do. You cannot manipulate with paths because they are given. You cannot change the integral value because it is unique, like 1 + 2 = 1 +1 + 1. You always hear the sum = 3.

Wow, what about coherent light, like lasers ? Can CED describe lasers, or is QM required, for such BE condensates ?

Yes, CED describes lasers in the sense of emitting and propagating the EMF. However it does not deal with photons. The number of photons in a coherent beam is uncertain anyway. What is certain is the wave phase. If you read QED, you may find a chapter "Radiation of a classical current" or so (see QED by Akhiezer, Berestetski or other sources with coherent light description).

The Bohr Radius ([math]\hbar^2 c^2 / (e^2/4 \pi \epsilon_0) m_e c^2[/math]), Electron Compton Wavelength ([math]\hbar / m_e c[/math]), & Classical Electron Radius ([math]e^2 / 4 \pi \epsilon_0 m_e c^2[/math]), all increase by factors of the Fine Structure Constant (so that the Compton Wavelength is the geometric mean of the other two). Is this significant ?

No. The classical electron radius is a dimensional parameter appearing, for example, in the Tompson formula. The other its meanings are misleading.

The electron Compton wave-length, appeared first in the Compton formula, has nothing to do with the electron size. Remember, in the Compton formula derivation the electron is considered as a classical relativistic particle with mass m. The h-bar comes from the photon property E = h-bar*omega (different from the energy of a classical EMW). After recombining the dimensional parameters to get the Compton length, you characterize the photon as a classical wave with a classical wavelength (no h-bar involved) which was not the initial assumption. Photon is not characterized with a wavelength (but energy) and the electron is not quantum in this problem.

Bohr radius is meaningful and includes the electron charge. This is a real size amongst three of them, if you like.

From the value of the Fine Structure Constant, we know that:

 

[math]\hbar c \gg e^2 / 4 \pi \epsilon_0[/math]

by over two orders of magnitude. So, does that tell us, that electro-magnetic phenomena are "fully quantum" phenomena, "well inside" or "well under" the scope of the quantum scale ?

The value of alpha has nothing to do with your question because in radiative processes the "small" parameter is alpha*ln(omega/m) or so. For soft radiation it may be large. Another important thing is the number of photons. Classical Electrodynamics describes well such cases. There exists a CED in media, with phenomenological epsilon and mu.

Generally, CED describes average values, and as long as the number of photons is large (the fluctuations are relatively small), one can use CED.

Yes, the nature of the interaction is electromagnetic.

Keeping in mind quantum electromagnetic, with a stable medium.

A proton is a bound-state, of a system, of 3 quarks. Roughly speaking, we can decompose the wave function, into a [math]\Psi_{CM}[/math] and [math]\Psi_{rel}[/math]. And, the [math]\Psi_{rel}[/math] is the standard nucleon wave function, producing a probability "cloud" ~1 fm across. But, then, that relative wave function can be "sliced", and "spread", a little like smearing around a deck of cards. Each "card / slice" represents a whole & complete, but only partially probable, nucleon, centered at a given CM coordinate. (If the proton is certainly centered at some CM coordinate, that's a little like "telescoping" the deck of cards, back into a single stack.) So, the proton can enter a "spatial super-position state", where the whole proton, is partially probable, at many spatial locations simultaneously.

 

If you could prepare two opposing proton beams, each of which produced protons in such de-localized states, they could "reach out", and have at some positive, if partial, probability, of interacting, w/ other protons, which otherwise would miss each other by a wide margin. Presumably, high energy p-p reactions, would cause both proton's to "collapse" into some pair of particular, punctiform, point-particle like states, which would react "normally", and scatter. But perhaps you would get, overall, more p-p (i.e., potentially fusing) reactions.

For a health reason, I cannot follow your reasoning about protons. Atoms are also compound systems. Atom-atomic collisions may be approximately described with a potential interaction. The cross section is given in http://arxiv.org/abs/0806.2635, formula (11).

"Preferencing" wave function collapse ??

 

The work functions, or inner potentials, of various materials, range from 10-30 eV (Tomonura. Quantum World Unveiled by Electron Waves, pg. 61) What would happen, if you did a Double-Slit experiment, with a macroscopic detector array (D), composed of two types of micro-detectors (d), which had dramatically different inner potentials? For example, although the apparatus would remain electrically neutral, so as not to alter the evolution of the electron [math]\Psi[/math], the incident electrons could minimize their energy by another < 20 eV, if they "chose" to "collapse" on one side of the screen (say).

 

Would the "goal", of energy minimization, "preference" or "optimize" the electron's behavior, such that more than half of the hits might be on one side of the macro-detector vs. the other, even though their wave functions were not altered in any way?

I did not get the point but the interference pattern will remain the same in my opinion. If the screens, slits, and detectors are some boundary conditions, then the material properties do not matter.

Is it possible, to put protons, into de-localized spatial superpositions ([math]\Psi_R[/math]), yet at high energy ?

Quantum mechanics answers these questions. If I knew what you want to know...

Someone inserted an interesting post about David Deutsch, and I spent some time reading about quantum computation & the Multiverse.

In some wiki page about the Many Worlds Interpretation, I found this from the "Common objections and misconceptions" list:

 

Objection: Conservation of energy is grossly violated if at every instant near-infinite amounts of new matter are generated to create the new universes.

MWI response: Conservation of energy is not violated since the energy of each branch has to be weighted by its probability, according to the standard formula for the conservation of energy in quantum theory. This results in the total energy of the multiverse being conserved.

from http://en.wikipedia.org/wiki/Many-worlds_interpretation#Common_objections_and_misconceptions

 

Is there anyone here who could explain somehow better this response: This results in the total energy of the multiverse being conserved. ?

The energy emitted by my emitter is entirely absorbed by my absorber so no energy is left to create other universes.

So what is the question? Of course, an atom recoils while radiating.