Large Hardon Collider

[Eliseos]

Hopefully just the stupid half.

[Woozie]

Hopefully just the stupid half.

Hey, conservatives deserve to live just as much as we do!

[Eliseos]

Does fiscally conservative count? Because that's what I am

[Woozie]

That statement was really aimed more at the extreme, Glen Beck/Sarah Palin worshipers. Regular conservatives don't bother me any more than regular liberals.

[zoobernut]

Does fiscally conservative count? Because that's what I am

There is no such thing in the US your label is based on your social issues. Fiscal conservatives are just weird liberals.

If you are socially liberal you are a liberal.

[Celeras]

One more delay away from 2012.

[Eliseos]

There is no such thing in the US your label is based on your social issues. Fiscal conservatives are just weird liberals.

If you are socially liberal you are a liberal.

Well then I'm a moderate.

[Lhyet]

I'm surprised that no one has yet mentioned that today is the birthday of the father to the theories of relativity; Albert Einstein. 131 days ago today.

It's amazing how much an affect one person can have on so many fields of physics.

[Mizango]

Been busy with basketball today I gave my props and well wishes this morning on my FB page if that counts.

[Lhyet]

That works! I do love my astronomy calendar, so full of useful dates. Such as Saturday 20th being the anniversary of Isaac Newtons death.

[Woozie]

That works! I do love my astronomy calendar, so full of useful dates. Such as Saturday 20th being the anniversary of Isaac Newtons death.

Edit: I'm an idiot

[Ferion]

Kind of a random question, but does anyone have a good place to start to learn Brownian motion that kind of gives a brief background of the stochastic calculus and sigma algebra needed to understand it. I can't seem to find any explanations or lecture notes online that don't assume that you're writing a dissertation on the subject. I'm more interested in the option pricing theory behind it, but even a model used to describe particle movement would be great if it's slightly simplified.

[Woozie]

Have you tried a statistical mechanics textbook? Or thermal physics? Something like this:

http://www.amazon.com/gp/product/157...der_1577666127

You should be able to find books like this at your school library or on demonoid or rapidshare or something.

Edit: http://www.amazon.com/Modern-Course-...der_3527407820

Another good one. But most Statistical Mechanics books will have something on brownian motion. I actually learned about brownian motion from a book on computational physics. I can't remember the exact book it was though.

[Ferion]

Yeah I'm on spring break so I haven't checked the library at my school yet, was just seeing if anyone knew of anything online to get me started. Thanks for the suggestions though.

[Woozie]

For internet sources I'd just go to a torrent and try to find pdf files of statistical mechanics books. But like I said, if you're good at programming, learning from a computational physics book may be a good idea. You can download those as pdf files too, but not all of them go over brownian motion. If I could remember which one I learned brownian motion from, I'd find the pdf for you.

[Eliseos]

Saw this at work today, thought it was pretty interesting

http://www.scientificamerican.com/ar...ames-webb-jwst

EDIT: URL not working right because of the = sign in it, article title is 6 Fun Facts about the James Webb Space Telescope. Neat pictures of it and the development.

[Kaylia]

What kind of space are we dealing it in relavity, and what mathematical axiom are used before we reach the s² metrics. It's never defined clearly in the book I'm using, they always jump to s² metrics without defining anything.

[Max™]

Numerous answers, differentiable manifold, pseudo-Riemannian manifold, such that the metric tensor need not be strictly positive definite.

Wait, lemme pull up the wiki, since I couldn't know this stuff on my own .

http://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold

There ya go, from matrices to that should be simple enough.

Further into the basics: http://en.wikipedia.org/wiki/Differentiable_manifold

or further down the rabbit hole: http://en.wikipedia.org/wiki/Introdu...ral_relativity

and

http://en.wikipedia.org/wiki/Mathema...ral_relativity

Believe it or not, you can do a lot more by reading through these wiki pages, and using the heavily crosslinked nature of the articles to further investigate terms you don't recognize, than simply find stuff to copy/paste to try and appear smart.




Whoops, I assumed you meant GR, not SR, if you meant SR then these are what you're after: http://en.wikipedia.org/wiki/Minkowski_space and http://en.wikipedia.org/wiki/Riemannian_manifold for further info on the positive definite Riemannian forms.

[Kaylia]

Yeah, I already read most of these.


I was simply wondering what's the difference between euclidian R^4 and the space we use in general relativity. Is the only difference the metric/pseudo metric (and it's implication), or is there something that else I'm missing?


Basically, I had an argument with a teacher, and I'm writting a follow up e-mail. I just want to be sure of my stuff before sending it.

[Max™]

Yeah, it's the mapping variations between Euclidean with it's flat metric and Pseudo-Riemannian which can have variable metrics.

I believe Euclidean is isomorphic, lemme check, ah, it is isomorphic to any n-dimensional vector space, and Riemannian is at best diffeomorphic, there can be a map produced, but it can vary depending on the space it is being mapped to/from.


tl;dr, the mapping and metric are the big differences before you start applying tensor structures and shit like that.


To further check your points: http://en.wikipedia.org/wiki/Isomorphism
http://en.wikipedia.org/wiki/Homeomorphism
http://en.wikipedia.org/wiki/Diffeomorphism

Euclidean can have diffeomorphic maps produced to pseudo-Riemannian spaces, but you can't do calculus normally on said manifold as it is.


Ah, this should be what you're trying to find:

In modern mathematics, Euclidean spaces form the prototypes for other, more complicated geometric objects. For example, a smooth manifold is a Hausdorff topological space that is locally diffeomorphic to Euclidean space. Diffeomorphism does not respect distance and angle, so these key concepts of Euclidean geometry are lost on a smooth manifold. However, if one additionally prescribes a smoothly varying inner product on the manifold's tangent spaces, then the result is what is called a Riemannian manifold. Put differently, a Riemannian manifold is a space constructed by deforming and patching together Euclidean spaces. Such a space enjoys notions of distance and angle, but they behave in a curved, non-Euclidean manner. The simplest Riemannian manifold, consisting of Rn with a constant inner product, is essentially identical to Euclidean n-space itself.

If one alters a Euclidean space so that its inner product becomes negative in one or more directions, then the result is a pseudo-Euclidean space. Smooth manifolds built from such spaces are called pseudo-Riemannian manifolds. Perhaps their most famous application is the theory of relativity, where empty spacetime with no matter is represented by the flat pseudo-Euclidean space called Minkowski space, spacetimes with matter in them form other pseudo-Riemannian manifolds, and gravity corresponds to the curvature of such a manifold.

From good old: http://en.wikipedia.org/wiki/Euclidean_space

I didn't realize you were asking literally for the defining difference between a Euclidean and Riemannian.