@vanhees71
I'm not sure I understand. The beam splitters do not change polarization here, polarization comes into it only in situation 3 and 4 where I explicitly added the filters. That is why i simply added the appropriate H and V to the states in the 3rd equation.
I totally agree that there is...
@vanhees71
I now tried to calculate things explicitly and believe my idea above to be incorrect. (Calculation follows below, I'd be very grateful for someone to check it.)
However, I do see a problem with causality if my idea were correct:
Image we set up the light source to send one photon per...
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...
@vanhees71
Thanks. I was just confused because my sources never mentioned that there would be alternative ways of doing it - some used the asymmetric beam splitters, some used symmetric ones, but none mentioned that both exist.
@Aidyan and Cthugha
Funnily, the references you both provided on first sight again seemed to contradict each other - Zetie talking about 180° phase shift on reflection, Cthugha explaining that the shift is 90°
But thanks to the reference by Henault, I finally understand it: There are symmetric...
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...
@PeterDonis
Thanks a lot.
I assume the same is true for the case of the expanding hole.
I find this somewhat surprising - the black hole expands and the photon moves "outwards" - but that's probably simply a consequence of using global coordinates. OTOH, it shows that Penrose diagrams are...
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...
@atyy
Thanks. Yes, I suspect you're right and that this is what is more or less implied by the qualifier "local OPF", but at least to me it is not very clearly stated.
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...
@Dale Absolutely great, that was exactly what I was looking for.
PS: Would be great if you published/posted that calculation with the different constants somewhere.
It seems I was phrasing things very badly. So if I understand things correctly, the correct way of stating things would be to look at all dimensionless constants and instead of talking about "changing c" I should talk about changing these constants. So instead of saying, "let's increase c by...
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...
So, finally I can answer my own question at least partly:
The metric inside of a mass is related to the "excess radius" (how much longer is the way through a sphere than expected from its circumference), and this is directly related to the 00-component of the Einstein-tensor. (See Feynman...
@Paul Arveson
Thanks. Yes, and this means that if a particle flying in one direction is accelerated to the right, a particle flying in the opposite direction is also accelerated to the right.
Actually, I think I found the problem: I looked only at the deflection of the orbit in GRorbits - but I...
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...
So, after thinking a bit more about it, I think I finally understand it:
Consider the lower side of the rectangle and replace it with a parabola to make it a geodesic.
The vertical line on the left has to be parallel transported along this geodesic.
The geodesic starts with a vector that points...
@Orodruin
Thanks, I wil have to think about that.
I'm not quite sure why making the Feynman rectangle infinitesimally small would change anything and how exactly the transport of vectors along the geodesics would change the picture (After all, both the vertical spacelike geodesics and the two...
@Orodruin
I don't think Feynman supposes to lift anything - he says that we have two objects and follow the worldline of each of them.
And yes, as I said in my previous comments, to make to horizontal lines geodesics, we should and could use a parabola. If the waiting time is, for example 2...
@Orodruin
You are right, at least for the horizontal lines (the vertical lines are straight lines from one height to another, so they are spacelike geodesics in the Schwarzschild metric, are they not?). The horizontal lines connect two points at the same height and different times. If I replace...
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...
@Peter
Thanks for that.
@George Jones
I do not think this answers the question, because the same argument would apply to the tt-component of the metric which cannot be written in closed form without explicit pressure dependence. The A(r) relation is actually universal and holds for any matter...
@PeterDonis
I agree that the pressure dependence should not cancel in other r-coordinates.
However, I'm not totally sure I see how the purely geometrical fact that I define the r-coordinate using the surface relation (as done by Schwarzschild) causes the vanishing pressure term.
I suspect it is...
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}...
@Orodruin
Sorry for not having a clue, but could you explain (or link to some explanation) what the differences are between
the different Gammas (with tilde and overbars)?
@All
Thanks a lot. So I confused a coordinate-based quantity (the coordinate acceleration on a geodesic) with a physical quantity (four-acceleration). Seems I keep making this mistake...
Sorry, yes, I garbled up on the left side, it should have been
\frac{dv^\mu}{d\tau}
For a force-free particle that moves on a geodesic (as stated in the OP), the covariant derivative is zero, isn't it?
But still, in any coordinate system, the equation
\frac{dv^\mu}{d\tau} v_\mu
should hold, or...