/sci/ - Science & Math

If your mom has a particle with electrical charge <span class="math">q[/spoiler] resting at position <span class="math">r_M[/spoiler], say 5000 miles from you, then it's electrical field goes as <span class="math">\propto\frac{1}{|r-r_M|^2}[/spoiler].

Now if your mom accelerates the charge further away from you, i.e. <span class="math">r_q(t)[/spoiler] changes its value with time, then, from your perspective, it has a velocity <span class="math">v_q:=r_q'(t)\neq 0[/spoiler], and so there is a current <span class="math">j=q·v_q[/spoiler].

The fact that she moves the charge isn't instantaneously clear to you though: the light of that event first has to travel to youfor you to see it, and also the field doesn't change instantaneously. In particular, what happens is that the Maxwell equations
<span class="math">(d/dx)B\sim j+(d/dt)E[/spoiler]
go "oh shit, there is a moving charge/current! It's time to radiate and change the electrical field."
The electromagnetic wave propagates everywhere and soon your <span class="math">\propto\frac{1}{|r-r_M|^2}[/spoiler] will be corrected accordingly. If your mom moves away, the field will go down.

Now gravity also goes like <span class="math">\propto\frac{1}{|r-r_M|^2}[/spoiler], but there were no Maxwell equations of gravity.
Here, if your mom throws a book through the room, and it's position <span class="math">r_B(t)[/spoiler] changes, then the force follows it as <span class="math">\propto\frac{1}{|r-r_B(t)|^2}[/spoiler]. There are no sophisticated gravitational waves. Once the book movies, it gravitational force on you chances in that same moment.
The above doesn't matter for Newton and his absolute space.

But Einstein had special relativity in 1905, and it said (muh Interstellar twin paradox etc.) that if someone moves, his axis of "now" tilts. Everybody has its own "now".
In particular, if someone moves a book away from you AND by moving stuff is able to affect things in his new frame instantaneously, then he would actually affect not you but your past you.
See http://en.wikipedia.org/wiki/Tachyonic_antitelephone

To answer your question, Einstein wanted a more dynamical gravity.

>>6877092
The bridge is literally Feynmans PhD thesis

http://en.wikipedia.org/wiki/Wheeler%E2%80%93Feynman_absorber_theory

>>6877040
My advise to learn it (and this is also the advice I give w.r.t phenomenological thermodynamics, where many people never become friends with concepts like enthalpy etc.) is to take a piece of paper and write down what the physical observables, in the end, actually are - what the theory is supposed to produce. Then take the spacetime concept as given and try to figure out the chain of mathematical concepts and expression from experimental input to theoretical output. That's not as easy or funny as it sounds - and you develope a positivist attiture.
If you simply try to learn what's in front of you, then you get confused where or why one does things. It's true that one has to spent far to long with passing from the definition of the path integral, through all the tricks, down to some Z[\phi] which seemingly mysteriously knows the answers to the poser questions..
An (even more) generic suggestion: Consult different resources. What do you work with?
If you're crying about renormalization and regularization in particular, do it on the grid or in statistical physics - that will clear up a big lot.

>>6877131
I'm pretty certain leaning GR is much simpler if you do it in the context of physics lectures. The math, you can literally imagine geometrically (maybe apart from the diffeomorphism group)

I learned a lot from Simpsons online lecture notes and I read part of Subsystems of Second Order Arithmetic, which I believe to be a core book of the Reverse Mathematics program.

I think it's a clear and interesting topic for a masters. But to answer the question requires more information on what your general outlook is, in particular where you see yourself after doing a PhD.
There are people out there, like
http://math.stackexchange.com/users/622/asaf-karagila
who baffle me a little. A guy who's academic outlook is to study the Axiom of Choice and it's variant in standard models of set theory. The crazy thing (to me) is that people like this effectively decide to become experts in a niece (where the basics have been laid out close to 100 years ago) without any chance for recognition by people knowledgeable in any other field.

The subject matter that Reverse Mathematics is furiously and deeply trying to understand will not collapse. It's "solved" and my opinion (which is completely naive) is that it will not matter in the future. Even the related computability issues I came to associate with the general realm of topics will not matter much, as approached by the logicians.

What I want to get at is this: If you want to understand logical foundations and plan and later don't necessarily aim for developing stuff anybody else will want to use, then do it. Otherwise, step into the light of reality and learn something you'll use later.