Spacetime geodesics (I).

Math, again, people!

A couple of posts ago I introduced myself to geodesics as free fall trajectories in curved spacetime. The problem with this description -one of them- is it's saying not enough. What I've learned since then about geodesics it's still not enough, but it's a step forward, so better than nothing.

This post was intended to solve geodesic equation for an easy case and show that spacetime nature depends on 4 coordinates -3 in space and 1 in time. The problem is the answer is not as straightforward as I expected. Let's see it anyway.

A geodesic is a curve. And like any curve, it can be described mathematically. General, index form is:

Leonard Susskind's GR lectures at Stanford.

I discovered Leonard Susskind because of the book "The black hole war". It was interesting and funny and the fact I was not able to grasp the last part of it -that holographic metaphore is disturbing-, didn't make me dislike it at all. I started to look at physicists more like human beings thanks to it. And that's saying a lot.

Before that, my only contact with physicists were close related hate-filled-relationships due to the fact engineering physics in Spain -the time I studied it, at least- were intended more to make an IQ selection than teaching actual interesting physics. I can blame no one for that. It's a consequence -one of the bad ones- of having a public university model. Good ones outnumbered bad ones, by the way. In the future, who knows.

 

Leonard Susskind a couple of years ago. From Stanford web.

What is happening at JSC?

Sorry for abandoning Math so soon. It is temporary, I promise. For the moment, I have to discuss another -possible- dead end. Which maybe it is not. I don't know yet. Media hype? Likely.

JSC stands for Johnson Space Center, which is one out of the 17 centers NASA has in the States.

I have heard some noise in the internet since September in sites like Gizmodo and Space.com about a JSC's scientist who claim feasibility of warping spacetime under certain specifications. Reliable science news, unfortunately, doesn't come from news sources, so I decided to wait a little before start looking for info.

Aerial view of JSC in 1989 -a long time ago, I know-. (Source: wikipedia)

Rotating superconductors. A dead end?

First time I heard about these, was back in 2006. And it seemed promising. It is a simple concept: Einstein says energy or matter warps spacetime. Why don't we modify matter in order to alter somehow spacetime?

Obviously, harvesting energy as I have pointed out previously is not going to be enough.

So, is it possible to have a "weird" state of matter which gives us more juice for warping porpuses? The idea is quite attractive, because Einstein was an open enemy of quantum theory, and this branch of physics has evolved a lot since Einstein's first days.

 

Experimental ARC Seibersdorf 2006 setup (photo from ESA web)

A massive quantity of energy.

Before talking about coordinate systems, tensors, and other cool stuff I need to know better, let's have an engineering look at the equations, specially at energy numbers.

I said before that G thing stands for describing curvature through several mathematical tools we'll see later. Let's focus, for the moment, in the T thing.

The T summarizes something called stress-energy tensor and can be descomposed as:

 

An interesting video from MIT: EFE, introductory level.

Next post was intended to be an estimation of energy needed for warping spacetime, but its going to take a little more of time since I have to do some checkup on math -and procedure.

So, in the mean time... :)

... I've already said I'm not very fond of hearing classes. In general it is quite truth, but in my quest for understanding spacetime, several internet searches have leaded me to actual videos of classes. Which is a little ironic, I guess...

Geodesics: a way to grasp curvature.

I'll go deeper with time in several concepts I'm starting to relate here, please be patient. I'm reading Misner, Thorne and Wheeler's "Gravitation" with the objective in mind of making a summary in the first "Books" post, but for now, the content of this post is an interpretation about I've already read and understood regarding geodesics.

Allow me to start with Einstein field equation -the "easy" one.

Sorry about using an image. I've tryed to use third parties LaTEX renderers, but no results. I'll improve my blogging skills in the future.

So, the equation states -for the moment-, there's a G thing, which corresponds to a T thing multiplied by a fancy constant. Well, these things are tensors, and they're pretty serious stuff because this simple equation gives us a partial diferential equation system, with 10 coupled equations. Too fast, too soon. You have to believe for the moment the G thing is were we are watching the curvature, while the T thing is a way to tell how energy is distributed. Energy distribution in space, by the way, is the responsible for that curvature.

But this post is about geodesics. Why I'm giving you all this crap?

So... Why did you say spacetime, again?

Too many post about intentions, not enough about the subject. Sorry.

It's important to fix things in order to stablish a shitty order worth of changing in the future.

As an engineer, I said previously physics -and math models about physics involved in a phenomena- were the key to design and construct cool stuff. For instance, we want to have water from a tap. We know water moves easily -as a fluid- by differences in pressure, so it seems a good idea to pressurize water in order to move it along tubes and conductions. You can fill bottles of water and transport them from a place to another but, is that practical? 

Sometimes it is, but when you want to carry a lot of water from a place to another... Man, you better attack the problem in its Achilles heel, which usually is the fundamental physical principle which gives Nature its "nature". In water, it is differences of pressure -there are actually more ways if you look closely to NS conservation of momentum equation for a fluid, but difference of pressure is quite a good choice.

The same applies to rockets and satellites. 

Let's get it on... A strategy.

As far as I learn how to working out a blog, I expect to expand and improve all subjetcs aborded. For now, the initial strategy for dealing with spacetime problem will be divided in 4 branches:

1. Real old-fashioned-book-hitting research.
2. Real physics and online paper research.
3. General views about what I'm learning along the way.
4. Dealing with dead ends.

Tired of waiting.

So, this blog goes about knowing a little more about spacetime and studying possibilities to warp it. Quite a task. Quite a pretentious big-head-smart-ass blogger, right?

When I told a classmate I was writting a blog, he was pretty impressed about my ability to talk about my exciting experiences in our university's computer center.

As an engineering student with no special fonding in hearing classes, and no classes to attend to neither, computer center is the place I've been into for a couple of months since the beginning of semester. And a lot of things happen here, yeah, but none of them worth of being described in a blog in my opinion.

In my defense I must say I'm working in a couple of projects -studying spacetime is one of them- and an internet conection has been proved to be a better tool than a library chair. And I'm hooked on reddit -first step is to admit it.

There was something, nevertheless, my classmate was right about when we talk seriously about the blog: I'm an engineer, not a physicist.

First Post: What is this all about?

Space, the final frontier... You know the rest, no reason to go on.

I like space. That's the reason I started studying aerospace engineering. Five years -that's a degree and a master, I guess- for finding and answer I already knew when I started: space I would like to be in, simply doesn't exist. There's no a StarFleet. There are no chances of pumping the Falcon into hyperspace. Space travel and exploration today is about probes, rovers, satellites and ISS.

Expectations... (source: Wikipedia)