Take a look at how Finite element analysis software works; the differential equations govern how adjacent cells interact. Stitching the cells together, and obeying the differential relations, allows you to see how a source can propagate out into the surroundings; and go on and on. All without...
It's not true that you can't communicate or have to wait till the end of time; the detection of gravity waves indicate that one could probe a black hole with disturbances and detect the resulting gravity waves. A little presumptuous in terms of technology but when has that stopped dreaming?
Yes, but if the model, GR, is broken inside and somebody came up with an alternative, I would expect that the alternative would be testable in gravity wave signatures. I realize our detection is primitive so far, but one can hope for future experiments. Gravity probe B; that took a long..long...
Due to an egregious error in an earlier posting, I have been studying Kerr metrics. It appears (although I have doubts) that the mathematics of spinning black holes has: escapes clauses, something similar to negative energy (repulsive regions), and closed time-like orbits/areas/curves. To me...
I'm thinking of the holograms on credit cards; where you see different pictures depending upon angle. Take two pictures
1) One a mirror
2) A black plate.
and place them in place of the "pictures".
I realize that this isn't quite what was asked but perhaps some variation? My knowledge of...
I think the direct equation you want is div(curl(V))=0; for instance, https://math.stackexchange.com/questions/26854/what-is-an-intuitive-explanation-for-operatornamediv-operatornamecurl-f
Now reasoning backward's from div(V)= 0 to integration and proving the conditions for V=curl(R) escapes me...
Is it generally possible to get a copy? I would be interested in other opinions (I think I disagree with a lot of them) on what is "real"; but I am always interested in the reasoning behind various viewpoints.
Not dogmatic: just critical :)
Given your application, I think you should start doing Multiphysics modeling on any measurement method. I like Comsol (because it's flexible and is user-friendly (so to speak); but it's expensive (as are the commercial alternatives). There is a free program I tried and it seems to work: Elmer...
Remember that these equations are a description of "real" things. It turns out this description is a little complicated, but very accurately describes what we observe in intermediate range physics: colliding stars, black holes....
This is not truly a direct answer but I would recommend something along the lines of reading the eighth chapter in
Davis "Interpolation and approximation ";
https://www.amazon.com/dp/0486624951/?tag=pfamazon01-20&tag=pfamazon01-20
Which is my favorite goto although I am sure that there are...
Yes, I have always said the past is as uncertain as the future in QM; a radical oversimplification. But taking a Bayesian attitude, information allows future certainty. Otherwise, when we take measurements we are destroying knowledge of the past; sort of a squishy conserved thing that disturbs...
Well, my model is simple, if I use a fluorescent screen and see an electron light up a spot I can then determine where the electron was at that moment and with careful measurement probably the energy. So I have gained information that affects all my future calculations; i.e. I have filtered my...
Apparently disagreeing with others (perhaps more knowledgeable); I think information is gained after a measurement. We are going from uncertainty to certainty. I don't know how others define "information" but I would take that as an increase in information. I think any form of Shannon's...
Yes, Minkowsky diagrams with light cones. Since the light paths are invariant pick any two coordinate systems "moving" and "stationary" and compare "events"; where the cones intercept world lines. You get wave crests (that start at different times) or clock ticks or whatever (birthdays..).