I have a question on how exactly polarizing filters would influence interference in a Mach-Zehnder interferometer.
To explain, I'll show some configurations and what I would expect to happen - please tell me if I am incorrect anywhere.
Here is the standard MZI configuration with no filters and...
I'm confused by the phase shifts in a Mach-Zehnder interferometer because I keep finding two different explanations.
One explanation (for example, given on Wikipedia, but also elsewhere) states that on each reflection, the phase shift is 180 degrees, but only, if light is reflected from the...
Dear all,
I have a question on Penrose diagrams. Consider a collapsing star that forms a black hole with a Schwarzschild radius normalized to 1. What happens in the Penrose diagram when additional matter falls in? I suspect the diagram then has to look like this :
When the outer shell (second...
Dear experts,
I'm currently working my way through the paper Masanes, Galley, Müller, https://arxiv.org/abs/1811.11060.
On page 3, they define what they call a bi-local measurement: If we have two systems a and b and we define an outcome probability function for some measurement f on system a...
If the speed of light would change in the universe without any other natural constant changing, would all clocks be affected in the same way by this?
This is implied by Einstein in this paper on page 368
http://myweb.rz.uni-augsburg.de/~eckern/adp/history/einstein-papers/1912_38_355-369.pdf...
I have the following question considering frame dragging:
A test mass starting at rest near a rotating mass or with an initial velocity pointing towards the center of the rotating mass will be deflected in such a way that it begins to move around the mass in the rotational direction. This is...
In the Feynman Lectures on Physics, Feynman explains the curvature of spacetime by drawing a rectangle in spacetime, see
http://www.feynmanlectures.caltech.edu/II_42.html Fig. 42.18
First waiting 100 sec and then moving 100 feet in height on earth's surface results in a different situation...
I'm looking influence of pressure on the general interior Schwarzschild metric (see for example the book by Weinberg, eq. 11.1.11 and 11.1.16.
The radial component of the metric (usually called A(r)) depends only on the mass included up to radius r
A(r) = \left(1-\frac{ 2G M(r)}{r}\right)^{-1}...
Consider a force-free particle moving on a geodesic with four-velocity v^\nu.
The formula for the four-acceleration in any coordinate system is
\frac{dx^\mu}{d\tau} = - \Gamma^\mu_{\nu\lambda} v^\nu v^\lambda
Since the four-acceleration on the left side is orthogonal to the four-velocity, this...
In his book Gravitation and cosmology, Weinberg derives the perihelion precession of Mercury in the Robertson expansion. The final formula is
\Delta\phi =\frac{6\pi M G}{L} \frac{2+2\gamma-\beta}{3}
The second term is one for GR (β=γ=1).
I have two questions regarding this formula:
1. The...
One way to see that spacetime is curved is to try and draw a "rectangle" in spacetime (see the figure in the Feynman lectures, ch 42.7): If I wait for 100 seconds and then move upwards on earth, I end up at a different point in spacetime than when I first move upwards and then wait for 100...
I've thought of a new way (at least I never read it anywhere) of counting the independent components of the Riemann tensor, but I am not sure whether my arguments are valid, so I would like to ask whether my argument is sound or total bonkers.
The Riemann tensor gives the deviation of a vector A...
I'm trtying to get a better understanding of the spatial part of the energy-momentum tensor, and although similar questions have been asked here, I think the point I do not fully grasp has not been covered so far.
The stress tensor can be considered as "momentum flux density" tensor.
If I...
I am a bit confused by the fact that in GP-coordinates
https://en.wikipedia.org/wiki/Gullstrand%E2%80%93Painlev%C3%A9_coordinates
the spatial part is flat.
I try to imagine the following experiment:
First create two rigid shells at two coordinates r1 and r2 outside of the event horizon.
The...
I was always a bit puzzled by the Heisenberg picture (not mathematically, I'm fine with that, but conceptually) - if a "state" describes a system, how can it not be time-dependent, if the system changes?
I just found an alternative way of looking at it which seems to make sense to me, but I'm...
IIUC, there are two different interpretations of GR - either as curvature of space time (as in Misner Thorne Wheeler) or as a (spin-2)field that influences all matter (as in the books by Weinberg or in the Feynman Lectures on Gravitation) and that leads to the underlying Minkowski metric being...
I have a question concerning the paper "Quantum imaging with undetected photons".
http://arxiv.org/abs/1401.4318
In the schematic (Fig. 1) a photon (idler) is created at NL1 and passing the object at O to be reflected further to NL2.
It is then stated in the paper
"By reflection at dichroic...
I'm a bit puzzled by the dynamics of things falling into a black hole. If I start with a test mass at infinity, it will fall freely into the black hole and reach the speed of light at the event horizon.
What happens if I throw something towards the black hole? Will it already reach the speed of...
If I understand everything correctly, space near (but outside) a mass is curved negatively, so that if I create a triangle with, for example, rigid rods and the mass in its center, the angles would sum up to less than 180°. (If I am mistaken, please correct me.)
On the other hand, the typical...
Light bending in the "hot plate" model of curvature
In the Feynman lectures, feynman describes the hot plate model of space curvature and shows that light is bent around the center of the plate, see Fig. 42-6
http://www.feynmanlectures.caltech.edu/II_42.html#Ch42-S1
However, the hot plate...
Looking at the Einstein equation, stresses can cause a deformation of space time.
This link here
https://twitter.com/anilananth/status/339030628181868544
gives a value for the elastic modulus ("stiffness") of spacetime.
I think that the value of 10^24GPa must be related to Einstein's...
The Wikipedia page on the graviton
http://en.wikipedia.org/wiki/Graviton
contains the following sentence:
"Additionally, it can be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 field must couple to (interact...
Consider a monatomic gas of hydrogen (just to make the example as simple as possible) at a temperature T. If I use Boltzmann statistics, I would say that the probability of finding any arbitrary atom at energy E should be proportional to
##g_i e^{-E_i/(k_BT)} / Z(T)##
where ##g_i## is the...
Consider the Sommerfeld-model of a metal. We have a discrete but very large number of possible states, bounded by the Fermi energy.
Since the distance between the levels in a potential well scales as 1/L^2, for a very small specimen the number of states becomes small as well. Taking the...
I'm a bit confused by vacuum "fluctuations" (I know there is nothing fluctuating since vacuum is lorentz invariant) and their interpretation/representation by Feynman diagrams.
In a normal Feynman diagram, you have energy conservation at each vertex, so overall energy conservation is ensured...
In ch 30-7 of the Lectures, Feynman explains that the field of a plane of oscillating charges at a point P is proportional to the velocity of the charges, considered at the appropriate retarded time (retarded by the vertical distance from the point P).
Feynman derives this formula only for...
If I understand things correctly, the coherent state of a laser beam implies that the photon quantum field is a superposition of states with different particle numbers.
This also implies that a laser beam is not in an energy eigenstate.
To get energy conservation, I assume that this...
In QFT of a real Klein-Gordon-Field, the field operator
\phi(x) is an observable.
Mathematically, this is the case because it is a sum (over all k) of a and a^\dagger and this yields a Hermitian operator.
Physically, I can understand this because this equation would describe, for example, a...
I'm currently trying to make some intuitive sense out of Quantum field theory, but I'm not really understanding the vacuum.
Consider a real (or complex, with + in the right places) scalar
particle (a Klein-Gordon field).
Now consider the propagator (or correlation function)
G(x-y)=...