# Tag Info

24

Maxwellian electrodynamics fails when quantum mechanical phenomena are involved, in the same way that Newtonian mechanics needs to be replaced in that regime by quantum mechanics. Maxwell's equations don't really "fail", as there is still an equivalent version in QM, it's just the mechanics itself that changes. Let me elaborate on that one for a bit. In ...

20

It is a standard exercise in quantum electrodynamics to find the angular dependence of the differential cross section. Which more or less means how probable it is for the photons to scatter at a certain angle, given the energy of the incident particles. So assuming the spins of the electron-positron pair is averaged, and that you don't care about the photon ...

13

But what we never seem to see is why the electron and positron move the way that they do. Saying "they move like they do because of the force on them" doesn't explain anything at all. It's a non-answer. The equation of motion for charge particle (electron,positron) in magnetic field is $$m\frac{d}{dt}\left(\frac{\mathbf ... 12 Absolutely. If Compton scattering occurred in first order in e, the only contributing diagram would be the obvious one. Say we're in a frame with the electron initially at rest and an incoming photon in the z direction. Then the electron 4-momentum is$$p^\mu_{\text{in}} = (m,0,0,0)$$while the photon 4-momentum is$$k^\mu_{\text{in}} = ...

11

It is not a good idea to see a Feynman diagram as some sort of collision process really happening. The diagram is just a term in the perturbative expansion of a quantum mechanical transition amplitude (in other words, a nice "graphical" way to represent a bunch of integrals). The only actual observed objects are two incoming photons with a certain energy, ...

10

After the hypothetical split, 2 photons with the same energy would be propagating at an angle ok with momentum conservation. Then there would be a rest frame where the angle is 180 degrees. Now if you stay in this restframe and go back in time before the split, your single photon would be at rest. However, that is not possible: According to relativity, speed ...

9

Virtual particles are not real. They come, as I've said in many answers on this site, from a naive interpretation of Feynman diagrams which should not be taken as an actual, exact description of how the physics works. The actual description of an interaction in the quantum field theory is more complicated than "photons are exchanged". In particular, ...

9

Would you dig a ditch with a surgeons scalpel? Yes, quantum mechanics ultimately underlies all physical observations but the mathematical expressions for large dimensions with respect to $\hbar$ become cumbersome and are replaced by the simplest ones for the appropriate study. Thermodynamics, for the study of bulk matter, blends smoothly with quantum ...

8

A photon is an elementary particle. As much elementary and as much particle as the electron . A single elementary particle has a fixed mass and cannot emit another particle without violating energy conservation, because its mass is fixed. In the center of mass of a massive elementary particle, electron, there is no energy for an emission , for a ...

7

The binding energy of the electrons in a silver atom is far less than the rest energy of an electron, so there is no ambiguity about the number of electrons in a silver atom. That makes adding up the spins a straightforward business. By contrast, the combined mass of the two up and one down quarks in a proton is about 10MeV (it isn't precisely known) but ...

6

This might not be quite the answer you are looking for, but one useful way to think about it is: the accelerating electron emits photons because nothing forbids it from doing so. By definition, because an electron has electric charge it is coupled to the electromagnetic field, and is able to produce excitations in this field which we can call photons. This ...

6

This comes from classical electrodynamics, there is no need to go to Standard model theory or quantum electrodynamics for this. The simple answer is that electric potentials, like electric fields, are just a way of characterizing the way charged particles interact with each other. So, charged objects create voltage analogous to the way that they create ...

5

There are very strict limits on the mass of the photon already, so it would only affect our understanding of physics on the largest scales. The cosmologists would have some hard thinking to do, for instance. However, contrary to a comment, it would not affect relativity beyond requiring us to reconsider the usual name for $c$: not "the speed of light" but ...

5

Regardless of renormalizability, the term that you wrote down $(gA_\mu A^\mu \phi)$ does not describe photons because it is not gauge invariant. This would be a theory of a massless vector boson with three dynamical propagating degrees of freedom (two transverse and one longitudinal), which is inconsistent with Lorentz invariance and irrelevant to ...

5

It's a mixture of $c_\infty = c_0 = c$ and "the question doesn't make sense". So, first, how it does not make sense: What's the "speed" of a quantum object? It has, in general, no well-defined position, so $v = \frac{\mathrm{d}x}{\mathrm{d}t}$ is rather ill-defined. Instead, we should probably look at the mass of the photon, since all massless objects ...

5

In our modern understanding, every electron is thought to be a localized excitation of the electron (or Dirac) (spinor) field $\Psi(x^\mu)$, while every photon is considered to be an excitation of the photon (vector) field $A^\nu(x^\mu)$, which is the quantum field-theoretic counterpart of the classical four-potential. Thus, the answer to your questions ...

5

Classical electromagnetic waves emerge from the underlying quantum electrodynamic description in a smooth and consistent manner. The quantum framework means that the classical waves are built out of photons, and the only time one has to worry about more detail than what Maxwell's equations provide is at the level of particle physics and wherever quantization ...

5

Anna V is wrong when she says Maxwell's equations are inconsistent with black body radiation. In quantum mechanics, even if you ignore radiation there is a charge density which you can calculate (in principle) from Schroedinger's Equation. In a warm body, this charge density is fluctuating by random thermal motion. If you track the time evolution of the ...

5

I cannot answer to all the questions but would like to stress something regarding what the Casimir effect tells us and what it doesn't. If you look at how it is derived for the usual EM interaction, an experimental verification of the standard Casimir effect tells us that: the EM field can have standing waves between two plates and outside them There ...

5

Feynman diagrams are most definitely not a representation of what's going on between the particles. Feynman diagrams are simply a tool to help you remember formulas: if you want to calculate the probability that two electrons will scatter off each other in so-and-so angle, you draw all possible diagrams with two incoming electrons and two outgoing electrons ...

5

I believe it would be incorrect to term this as "photon-splitting". What is really happening is that a photon is being annihilated and subsequently two new photons are created by means of a non-linear optical process. Such a process that is routinely harnessed in quantum optics laboratories is spontaneous parametric downconversion (SPDC). The reason why ...

5

Virtual particles are not real. A virtual particle is essentially defined by being associated to a propagator. It is, formally, nothing more than such a propagator. The idea of "virtual particle" doesn't even exist before you notice that you can draw pretty Feynman diagrams as a succinct representation of the way QFT amplitudes are calculated. This is ...

5

First of all, note that different authors disagree what should be the Coulomb potential $V$ in $d$ spatial$^1$ dimensions. Here we will assume that it satisfies Gauss's law, i.e. $$\tag{1} V(r)~\propto~\left\{\begin{array}{rcl} r^{2-d} &\text{for}& d~\neq~ 2, \\ \ln(r)&\text{for}& d~=~2. \end{array}\right.$$ Here we will only discuss the ...

4

There are two factors at play here. The Lorentz force which causes the paths to bend with a radius proportional to the particles velocity and with a sense that dependent on both the particles charge and the direction of the particles velocity. In high energy (compared to $m_e$ events) such as the one pictured, the particles are nearly co-linear at the ...

4

So how is it possible to have a quantized outcome from a symmetric continuous event? Easily. So easily that I'll describe the easiest example to me. Which is to describe what happens when a Stern-Gerlach device interacts with a spin 1/2 particle. You could have a particle with any spin whatsoever, but no matter what single particle state you pick it ...

4

Quantum electrodynamics is needed to describe Nature instead of classical electrodynamics because quantum phenomena are observed – and have been observed at least since 1900 – which prove that classical physics in general and classical electrodynamics in particular is incorrect as a description of Nature and a better theory is needed. The quantum phenomena ...

4

It fails when the photon number is small. Since the electromagnetic field can never be zero because of the third law of thermodynamics this automatically couples the temperature, the effective volume and the photon number to each other. As a result it is experimentally impossible to do experiments with single photons at low frequencies because we can't ...

4

.Your title asks about the electric field. The content is about the electromagnetic waves, two different entities. Electromagnetic waves emerge from an innumerable number of single photons. As one cannot have water waves with just a few molecules but need of the order of $10^{23}$ (avogadros number) one cannot measure electromagnetic waves if the photons ...

4

There are two things to consider: What does the potential look like? Is the wave function of the qubit narrow in the flux or charge basis? Potential shape The Hamiltonian of the transmon (a junction in parallel with a capacitor) is $$H_{\text{charge qubit}} = - E_J \cos(\phi) + \frac{(-2en)^2}{2C}$$ where $E_J\equiv I_c \Phi_0 / 2\pi$, $I_c$ is the ...

3

Schwartz is simply noting that the $\beta$-function has a generic expansion in QED of the form (29) where $\beta_{0,1,2}$ are some numbers that can be computed by explicitly calculating the various Feynman diagrams. For instance the leading $\epsilon/2$ is the tree-level result in $d=4-\epsilon$ dimensions. This can be easily seen as follows. In ...

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