I'll just quote wikipedia:
"Any period of ten years is a decade, and there is no 'official' legal nor administrative start or end point,[1][2] so it can be any arbitrary span of ten years. "
"The frequently used method to refer to decades is the cardinal method, which groups years based on...
Eh, the delineation of a "decade" is somewhat arbitrary anyways. Since most people refer to the decade as 10-19 inclusive (the 2010's) then I think I'm good :D
"Solved" is maybe too strong a word for that paper... DNN's are trained to approximate the functions produced by numerical integrators. This leads to a constant-computational cost approximate solution. As far as I can tell anyways...
A lot of negativity on the internet suggesting this is not the case...(but I have no idea about the statistics - just remarking on what I see around on the internets these days)
My impression, and I could certainly be totally wrong on this, is that the OP was asking for a mathematical derivation that says that Maxwell is consistent with relativity (i.e. starting from Maxwell's equations, derive that they give a constant speed ##c## for EM waves in all inertial reference...
Although I agree with your conclusion, I don't think this answers OP's question. Unless I'm misreading, this statement simply assumes Maxwell's equations agree with experimental fact, which they do, but the OP is asking why they do.
Sometimes, if you are referring to very old texts (e.g. Bohr) you might notice a big difference between the language and frameworks used there and that used in modern physics. A lot has changed in the last 100 years. There's not just concepts which were proven wrong (e.g. the Bohr atom), but...
1. This is easily google-able, see here: https://earthsky.org/space/does-our-sun-reside-in-a-spiral-arm-of-the-milky-way-galaxy
2. In between the galaxies is mostly just empty space. The inter-galactic medium exists (a very diffuse gas), there are dwarf galaxies, and there could be a few stars...
There's no general answer to this question...##\partial_\beta T_{\mu\nu}## depends on the stress energy tensor and the coordinates you chose...it's like asking "what's ##d\vec{v}/dt##?" without specifying anything about ##\vec{v}##. It's hard to figure out what you're trying to get at.
At most...
Can you explain where the quote "Light doesn't lose energy as it ascends. It was emitted with less energy at a lower elevation." comes from? Is that your own hypothesis, or did you read it in a book or lecture somewhere? On the face of it, that statement appears to be simply false - but I might...
I think in a more advanced treatment of SR/GR, that would not be a helpful way to think about proper time, but in elementary treatments (like Serway), this treatment is pretty common. I think it mostly stems from the Newtonian bias of treating coordinate time as a legitimate measure of time...
I think you are confusing the statement that a "geodesic between two events measures maximum proper time" with OP's statement about "shortest measurement of time for two given events". There are many ways one could travel from event A to event B - if one travels along a geodesic then the proper...
Don't get into the "John will see David's clock...and David will see John's clock..." kind of arguments - they will just serve to confuse the issue. The two events in this scenario are "David leaves Earth" and "David arrives on the Moon". For John, the two events happen at two different places...
The minimum of the function is obviously at (0,0)...not sure that's a great goal... :P
I don't know if I agree with the (0,0) origin though...It seems a lot of people who have 0 experience in a field nevertheless think they are experts.
Are you referring to a specific paper in which the equation in the form ##m=E/c^2## appears? If so, please cite the paper so we understand the context. Otherwise, I'm sure Einstein used the equation in both forms regularly.
Doesn't Apple use Google for its cloud services anyways though? If you store your information on the Apple Cloud...you're really just using the Google Cloud aren't you?
I put my PhD in a nice frame...now it's on top of a bookshelf at my mom's house along with all my other diplomas and her diplomas...currently running out of room because my mom likes to frame all the diplomas (even a C.Phil) lol. But you do you; you should display it however you like.
Many fields of astronomy use QM or GR frequently. The use of modern physics is very prevalent in astrophysics.
Some examples:
1. All of cosmology is heavily GR dependent.
2. Astroparticle physics (e.g. simulating/detecting neutrinos from astrophysical sources) is heavily QM dependent.
3...
For this part of the question, use the relativistic velocity addition formula. However, 100ft/s is so small compared to 0.86c that the answer would essentially be 0.86c up to rounding.
Ah yeah, I think there some errors in my interpretation as well. I thought OP was asking like OP is racing the light so OP would have to return to the starting point as well.
Your friend would measure 20 seconds with his clock, you would measure a shorter time on your clock. See the twin paradox for more explanation.
More realistically, you would die due to acceleration when you were trying to change directions near instantaneously when you reach the mirror.
The "affine" part of the connection refers to the type of data that is being connected. In that case, the tangent spaces (which are affine spaces) at different points on a manifold are connected and thus you get an "affine connection". You can have non-affine connections which identify...
To just expand on fresh_42 a little, I quote from wikipedia:
Since this question was posed in the physics (SR/GR) sub-forum, I will specify that generally we consider only a "pure manifold" when doing physics. This is because if you have a disjoint union of two sets as your "manifold", then...