That's indeed an interesting book. It shows why there was no Nobel prize for Einstein for his general relativty, namely because of Bergson's completely philosophical objections against Einstein's notion of time, which Bergson obviously didn't understand.
It's bit confusing, but if your lecturers insist on the opposite naming of the spinors then it must also be changed in the mode decomposition, which then must read
$$\psi(x)=\sum_{\sigma=\pm 1/2} \int_{\mathbb{R}^3} \frac{\mathrm{d}^3 p}{\sqrt{(2 \pi)^2 2 E(\vec{p})}} [v_{\sigma}(\vec{p})...
You have to read Feynman diagrams with Dirac-fermion lines "against" the sense of the arrows on the lines. If this sense of the arrows is the same as the direction of the three-momentum, it's an electron (and you have to use the spinors ##u_{\sigma}(\vec{p})## for the ingoing line and...
Sure, there's a huge unnecessary confusion in the (theoretical) literature. There's a long debate, how it works with energy and momentum conservation and all that. The solution is of course just using QFT.
Put in terms of Feynman diagrams the solution of these quibbles is very simple: You have...
I think they simply mean within the cavity not within its walls. At least this would make sense and corresponds to what's calculated.
What I didn't understand is the remark about the positron. Here they seem to rather consider a single positron close to a practically infinite conducting...
But also at constant ##Q## the force on the lower plate is in ##\vec{e}_z## that of the upper plate is ##-\vec{e}_z## (setup of the coordinates as in #7) . The calculation is the same. With approach (b) the analysis is as follows. With constant ##Q## you have
$$\vec{E}=\frac{Q}{\epsilon_0 A}.$$...
It's the other way around: In the weak interaction neutrino flavor eigenstates are produced (electron, muon, tau indicate flavor not mass eigenstates). The flavor eigenstates are superpositions of mass eigenstates and that's why the neutrinos we observe "oscillate" between different flavors...
The MS case is a special case of a mass-independent renormalization (MIR) scheme. I've discussed this in my QFT manuscript (Sect. 5.11, p188ff):
https://itp.uni-frankfurt.de/~hees/publ/lect.pdf
The strength of dimensional regularization is its mathematical simplicity in the sense that it preserves Poincare symmetry (of course for (d+1)-dimensional Minkowski space with ##d \in \mathbb{N}##) and, even more important, local gauge symmetries. In addition it's mass-independent and thus can...
That's obvious a very good description. The one thing I learnt in this thread is that this point has been a very long heated debate in the physics community as well as the philosophy-of-science community. In the latter context it's related to the hole argument...
Let's use two plates and lets use the usual approximation, neglecting the fringe fields, i.e., we make the distance of the plates, ##d## small compared to the extension of the plates. Let's put the positively charged plate in the ##xy## plane at ##z=0## and the negatively charged plate parallel...
In reality the nucleus is not point like and you must integrate over its volume to get the multipole moments from the charge distribution. For atomic physics you can then approximate the nucleus as point like using the formula in #24. Note that I corrected it, because I fogot to put the...
A static electric field is always conservative, because you have ##\vec{\nabla} \times \vec{E}=0## everywhere.
The Helmholtz decomposition theorem is not a good tool to understand the physics in the general case of time-dependent fields, because they look as if there are non-local interactions...
I can agree with almost anything except 2), and this is a very important point.
A physical setup of "clocks and rulers" defines one and only one reference frame. Of course you can use different coordinates and different tetrads to "map it", but the physical observables are independent of this...
Of course, in Newtonian mechanics and special relativity all inertial reference frames are equivalent, and that's a physical symmetry, formally described as the invariance of the physical laws under Galilei or Lorentz transformations.
To check this assumption experimentally you have to realize...
Well, that seems to be the source of our apparent disagreement. For me a reference frame is first a real thing in the lab, a satellite measuring all kinds of astronomical observables, the gravitational-wave detectors of the LIGO/VIRGO collaboration. Then we have a mathematical formalism...
Have you read a textbook on classical electrodynamics and how physical electromagnetic waves really look like? I recommend to start with studying the Hertzian dipole radiation in any good textbook on electromagnetism (Griffiths, Jackson, Sommerfeld,...).
No! Pointlike doesn't mean to restrict yourself to the monopole term, which indeed is a point-charge when you neglect the finite extension of the nucleus.
You just go on describing the charge distribution with the entire set of multipole-moments,
$$\rho_{\ell,m}=\int_V \mathrm{d}^3 r' r^{\prime...
I don't say that it is limited to actual physical constructions but that for any measurement there must be established a reference frame to be able to give positions and time of any (local) observer. Otherwise you couldn't use all your formalism to do physics and to establish that to a high...
That's the very point! I don't think that our mutual misunderstanding is about the math. That's standard, how to define a pseudo-Riemannian (Lorentzian) manifold introducing maps and atlasses, the corresponding coordinate bases for the tangent and cotangent spaces and all this.
It's really...
That's also a standard solution of the problem, but it needs the curl of ##\vec{B}##. The idea behind this is to use the ansatz
$$\vec{B}=\vec{\nabla} \times \vec{A},$$
because of
$$\vec{\nabla} \cdot \vec{B}=0.$$
Then
$$\vec{\nabla} \times \vec{B}=\vec{\nabla} (\vec{\nabla} \cdot...
So do you agree to my statements in #43 or not? Your statement is far from being clear let alone a clear definition of what you accept a frame of reference to be.
As is clear from my statements in #43, a reference point of a reference frame in the there given sense, it's clear that it must be...
I can easily accept that, but my problem is that they never give a clear definition to begin with. I'll see whether, I can check the mentioned book as soon as possible.
I already admitted that time slicing/foliation seems to narrow to give a general definition of a reference frame. I only wanted a clear stated what's wrong with my much simpler standard definition I know from all GR textbooks of a reference frame using (local) coordinates as exemplified with...
Please give a clear definition of what a reference frame is in your definition. If you don't accept the standard definition as quoted from Wikipedia, I don't understand 1) at all, and 2) doesn't make any sense to me. Is there a textbook or paper, which describes what you understand as a...
Ok, for me to understand this issue with the reference frames better, let's discuss Born coordinates and in which sense they can be used to define a reference frame. Let's use Cartesian coordinates. Then there are no coordinate singularities.
Let ##(t',x',y',z')## be "Galilean coordinates"...