That's the first thing I thought when he specified GR.
There was a discussion here a few months ago on vanishing Ricci tensors and what it says about "flat" spacetime in n-dimensions in comparison to a vanishing/non-vanishing Curvature tensor that (I think) led to some discussion on...
Data is plural, so it is "Data were consistent with," etc.
I've always felt that data "fit" better in the singular however. I think it can be technically considered correct either way if the "many data" is considered to be the singular object that contains all of the data.
I'm not an...
I've always wondered why quaternions aren't/haven't been taught very much.
Perhaps there has been more investigation into their use than I'm aware of, but it seems like the choice of Gibbs' vector calc (IIRC developed from his study of quaternions) was the rather arbitrary result of Gibbs'...
Because there is no \theta or \phi dependence.
Just wanted to clarify because I've seen students make the conclusion that the laplacian is always
(\frac{\partial^2}{\partial r^2},0,0)
after doing their first "make use of the spherical symmetry" lapacian in spherical...
I know a number of people with PhD's who say they only have a BS on their resume so that they can get a better paying job.
Some have even asked their grad schools if there is any way to get a PhD rescinded so that they won't have to worry about their employer ever finding out about said PhD.
I'm in the process of getting my application to grad school completed and have a number of "5000" level classes that I'm not exactly sure how to classify on my my applications.
Is it appropriate/acceptable to list ALL of them as "graduate" classes that I've taken as an undergraduate....even...
Well, this thread has me feeling even more anxious about next semester than I already was....
I'm a physics major who is taking topology next semester...who also hasn't had analysis or abstract algebra.
I'm hoping my interest and prior self-study in differential geometry (for general...
The problem with that is that many professors don't like reading "novels." In my experience, you have to be as terse as possible when emailing a professor with a question.
If you write too much (even when you feel it is necessary information), you often get one of two "responses."
1) A...
This thread is in the relativity section, and according to GR, "light" does produce gravity.
If you looked at a completely "empty" Universe that was void of any form of energy, matter, radiation, etc., in a 4 dimensional spacetime where
\mathbf{R(X,Y)Z}=R^{a}_{\ bcd}X^{c}Y^{d}Z^{b}=0=R_{bd}...
I wish I had something more comforting to say, but the truth of the matter is that you're pretty much d.o.n.e as far as academia is concerned.
My early years showed promise for intellectual success until I ruined it all at age 16. I ended up really pushing my limits my junior year of H.S. and...
It probably should bother you that the major theories of the world have definite areas where they can't agree.
But don't let the word "force" be too much of a factor in that.
Force is just the word given to describe a particular mathematical act.
One theory has gravity being sent out...
Sorry...misread the OP's post
Saying that a tensor is of type (r,s) means that it has r number of contravariant indices and s number of covariant indices.
Contravariant and covariant vectors transform slightly different under coordinate transformations.
A contravariant vector...
My understanding of differential forms is that, given the map
\phi : V \to V^{*}
If f \in V^{*} is a 0-form (a real-valued function on V^{*} ), then \phi defines the function \phi^{*} f on V
where \phi^{*}: F^{0}(V^{*}) \to F^{0}(V)
as the function such that...
You'll first need to get an Bachelor's in an appropriate field. I would assume something like a bio-physics major with some kind of "Physiology" focused minor.
Then you'll need to go on to graduate school in an appropriate field. I believe there is research on neural physiology in many...
Exactly. I wish there were some sort of standard "WARNING: HAND-WAIVING NON-MATHEMATICAL ANALOGY AHEAD" for situations like this.
It seems that the vast majority of posts in this forum are clearing up the confusion that comes from misinterpreting "worded" analogies that were meant to...
That sounds more like a personal philosophy. I don't need a worded definition for space in order for it to be complete. I'd actually prefer that it be defined by the mathematics so as to avoid the semantics and possible ambiguity of defining it with words as well.
What do you mean by this...
It depends on what theory you're using.
General Relativity doesn't consider gravity as a force. Massive objects create a space-time geometry with a "curvature" described by the curvature tensor. There is no actual "force" of gravity, just the curvature of space-time that is created by...
It's the opposite of this.
GR says that geometry of space is due to gravity, not that gravity is due to the geometry.
If it were symmetric then geometry would create gravity as well, but GR (I believe) doesn't include this. It only allows for gravity to create geometry.
That's a good idea. I seem to like learning the differential geometry more than the actual physics of GR so far.
I know I've heard Isham's book mentioned before too....I'll look for it at the library today.
Thanks again for the help!
Thanks for the replies. I know that the tangent space at the point P (from my first post) is a vector space, I wasn't sure when/how they differed.
So, if I'm following this correctly......then the following statements are correct (at least in their usage of "vector space" and "tangent...
I'm not sure I fully understand the difference between these two terms when used in differential geometry/general relativity.
If I were to describe covariant differentiation to someone, I would say something like this:
"On a curved manifold (imagine a basketball), you could assume a tangent...
There are some 256,000 words in the English language. Most of those are archaic forms that have fallen out of favor, so the "actual" number is much less.
Giving worded analogies of what the mathematics is saying is always a slippery slope. Use the idea of a "fabric" as a vague basis to...
Re-reading my post...I don't know that I worded myself well.
I was curious if it was just "me" or if studying GR was more "standard" in the UK.
My own feeling from seeing the curriculum of various schools (from looking online myself, visiting sites like this, and searching for GR...
Why are there so few research groups that focus on relativity and gravity in the US?
It may be only my perception, but it seems that studying general relativity is rather "standard" in the UK. The schools I've looked at all seem to have a few classes on relativity at the undergraduate level...