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..).
Not an expert in QM/QFT but the Aharonov–Bohm effect certainly illustrates that the EM vector A exists and is physically relevant.
https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect
Try this. Plot the spacetime diagram; the stationary "reference" frame has a spacelike gap whose edges move forward in time. Project them forward. Now do the same thing for the moving hole and you can see how they can intersect. But in the "reference" you must make sure the "simultaneous"...
Okay, this thread has convinced me: one can not just talk about "mass", "force", etc... without the mathematics (and in my case associated diagrams). The Lorentz Energy-Momentum vector, the associated rest mass as an invarient, and the unitary Lorentz transform/matrix. On the other hand, the...
What about?
"
Professor Mika Sillanpää of the Department of Applied Physics and O.V. Lounasmaa laboratory at Aalto University is carrying out basic research on micromechanical resonators measured at ultralow temperatures.
Read more at...
I have been reading Walter Isaacson's "Leanardo De Vinci". Chapters 10, 11, 12 contain a delineation of various concepts Leanardo concluded from experiment and reasoning. Yes he could have revolutionized physics, and probably mathematics, but there was no "ecosystem" for these ideas; beyond a...
You have to be more modest in your immediate goals. First, start with Special Relativity and answer _all_ the exercises. In order to do this, you will have to learn about "Linear Algebra"; which at a crude level is Matrices. This is reachable in almost any math curriculum before the 12th...
Actually, the using the differential notation/antisymmetric tensor form reduces the symbolic clutter a lot. You can fit rotations and velocity changes on one line. Actually, the physics fit's on four lines of crisp geometric objects and then everything else is Minkowski geometry. Simple...
For the Schwarzschild case, I would just
1)look at Flamm's Paraboloid and then
2) pick/find your starting position,
3) Decide what coordinate system to use (I would use the local Schwarzschild coordinates but there are a lot more)
3) select the spatial direction for r , theta, phi in normal...
Worked fine for me. I do have one complaint about the comments beyond Eq: 32. I think it is misleading since a loop of wire in a time-varying magnetic field certainly does demonstrate a curl-type electric field; i.e. a transformer. It's true that the original source might be electric but the...
Okay, I understand.
Now if somebody could show me the mathematical derivation in terms of Maxwell's equations and/or the electromagnetic two-form, I would appreciate it. It would save me some trouble and thinking. Preferably with very few words.
I don't know what "reference frame" means but in GR, coordinate systems using null geodesics are used for certain purposes. Photons, in GR, have "direction" and an associated foliation.