@EmilioPisanty Actually it's the least contrived one inasmuch as it's the only one out there AFAIK. Presumably one can concoct a truly bizarre one but there seems to be no universal way of doing this.
There aren't separate parts to the time dilation: a gravitational part and a motion part. The time dilation cannot be divided up like that that. There is just the proper time along some curve. In this case that curve is a circukar orbit.
@JohnRennie That certainly makes sense, but it seems to disagree with that text from Wikipedia, and the graph, which claims that at a certain altitude the gravitational time dilation exactly cancels the velocity time dilation, so that the time rate is in sync with time at the Earth's surface. I don't see how we can get that cancellation effect from your formula.
We know that for a GPS we need to make a correction for both general and special relativity: general relativity predicts that clocks go slower in a higher gravitational field (the clock aboard a GPS satellite moves faster than a clock down on Earth), while special Relativity predicts that a movin...
Consider a Mass on earth. The time dilation on the surface of Earth is
$$T' = T \sqrt{1 - \frac{2GM}{rc^2}}$$
Now if the mass is moving around the earth at velocity of v w.r.t Earth, what will be the time dilation within the mass as seen from the Earth? The object could be in free fall, orbit o...
Oh wait. That first question asks for an orbit where the time dilation of the orbiting observer matches the time dilation of the observer stationary on the Earth's surface.
And yes, there is such an orbit. What I'm saying is that there is no orbit where the time dilation is zero relative to an observer far from the black hole.
@JohnRennie I agree with that. I've just been skimming through the PDF by Neil Ashby, linked in this answer physics.stackexchange.com/a/390402/123208 It looks quite good, and even though it's fairly short it has derivations for most of the stuff it uses.
I gave a partial answer to a homework questions here and was firmly told in comments that even partial answers to homework questions are not allowed. Is that correct ? As far as I can see, the guidelines on homework questions only prohibits complete answers.
Follow up question: if any answer at ...
Why is $\varepsilon_{ab} \, ^{d}S_{cde} = \frac{1}{2} \eta_{bc} \varepsilon_a \, ^{pq} S_{pq e} $ for $S$ anti-symmetric in all indices in 3D Minkowski space $(t,x,y)$
Hmm, using $\varepsilon_{ab} \, ^d = \delta_{ab3}^{12d}$?
I want to just say $\varepsilon_{ab} \, ^d S_{cde} = \eta_{bc} \varepsilon_a \, ^{cd}S_{cde}$ but then adding the $1/2$ because you sum over things twice but it's clearly breaking math
I can't be bothered to analyze whether they're just a minority that's being loudly reported by the system or a sizable majority
@JohnRennie I don't much, either
it separates "signatures_by_country" from "signatures_by_constituency"
presumably the former goes in the bin, and the latter gets tallied up
I suspect it's just loudly-reported cruft
it shows some 10k signatures from Germany and some 10k signatures from Edinburgh East
(and also, the signature page explicitly asks whether you're a British citizen or a British resident, so the presence of foreign countries probably doesn't matter much.)
@Slereah Ick. Even dealing with spherical polygons (a subject that just keeps coming up in my current project) is nasty compared to the equivalent planar problems.
Single photon interferometric experiments are a things (indeed, people had to learn how to do those before they could do all the spiffy delayed choice experiments and Bell's inequality experiments that drive discussions of entanglement). Townsend's QM book has a bunch of references in the first few chapters but my copy is in another state. — dmckee ♦46 mins ago
@dmckee gaseous, I imagine?
I can't quite see how you liquefy a book, but then again, you never know
@EmilioPisanty I'm not going to respond to that. If the readers want to argue over unrealistic interpretations of what I wrote, then they're welcome to do that. I'm not getting involved :-)
@ACuriousMind well, at least XML schemas don't have all the verbs at the end.
I'm going to write a paper where all the periods are replaced with commas, and then all the verbs are included in order, separated with spaces, at the end
with the aim of being as intelligible as possible to German readers
Though on the matter of asking for native speakers, I have observed several times that really fluent non-native speakers usually have a more precise grasp of the formal grammar.
Many native speakers, including this one, basically blew off a lot of their formal instruction in grammar because (a) that stuff requires thinking and (b) feeling that they already know how to talk.
@EmilioPisanty That's a transformation that's rather easy to reverse algorithmically, so you're really only making it unintellegible to everyone not willing to write something to transform it back!
sorry if I sound bitter, btw. I'm staying at an institute guesthouse at the Garching Forschungszentrum, and I'm having to deal with the one true nightmare of living in Germany
I am not familiar with any notation used in physics. The paper "Non-hermitian random matrix theory: Method of hermitian reduction" by
Joshua Feinberg and A. Zee (Nuclear Physics B, 1997) states:
A basic tool in studying hermitian random matrices $\phi$ (henceforth all matrices will
be take...
Consider a Mass on earth. The time dilation on the surface of Earth is
$$T' = T \sqrt{1 - \frac{2GM}{rc^2}}$$
Now if the mass is moving around the earth at velocity of v w.r.t Earth, what will be the time dilation within the mass as seen from the Earth? The object could be in free fall, orbit o...
I am not familiar with any notation used in physics. The paper "Non-hermitian random matrix theory: Method of hermitian reduction" by
Joshua Feinberg and A. Zee (Nuclear Physics B, 1997) states:
A basic tool in studying hermitian random matrices $\phi$ (henceforth all matrices will
be take...
