Are Phonons "optical" phenomena ??

[Widdekind]

When atoms in a crystalline lattice interact, vibrationally, via phonons, do they exchange virtual photons (making the interaction, ultimately, an "optical", electromagnetic phenomena) ??

 

[swansont]

Yes, the nature of the interaction is electromagnetic.

[Bob_for_short]

Yes, the nature of the interaction is electromagnetic.

 

Keeping in mind quantum electromagnetic, with a stable medium.

Edited September 1, 2010 by Bob_for_short

[Widdekind]

Keeping in mind quantum electromagnetic, with a stable medium.

 

(thanks again for the replies)

 

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 ?

[Bob_for_short]

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.

[Widdekind]

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.

 

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

 

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 ?

[Bob_for_short]

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.

Edited September 2, 2010 by Bob_for_short

[Widdekind]

(thanks for the response)

 

Just noting patterns, from the Classical Electron Radius (R_c), to Compton Wavelength ([math]\Lambda_C[/math]), to Bohr Radius (a_B):

 

[math]R_c \propto e^2[/math]

[math]\Lambda_C \propto 1[/math]

[math]a_B \propto 1/e^2[/math]

 

[math]R_c \propto 1[/math]

[math]\Lambda_C \propto \hbar[/math]

[math]a_B \propto \hbar^2[/math]

Of course, this is merely a restatement of the previously proferred pattern. 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 (?).

[Widdekind]

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.

 

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 ?

 

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 ?

Edited September 3, 2010 by Widdekind

[Bob_for_short]

... 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.

[Widdekind]

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 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 ?

[Bob_for_short]

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.

[Widdekind]

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 clarification & confirmation.