# Attempting to Understand Alcubierre

1. May 10, 2006

### McC

I apologize tremendously if this is in the wrong spot -- I couldn't decide between here and the "Beyond the Standard Model" subforum.

Background (Not terribly relevant)
I'm a "hobbyist" when it comes to physics. For me, it's one of those things that, had circumstances been different, I would've devoted life to studying. Instead, I'm an animator, which is where my heart ultimately ended up leading me. However, I still maintain an avid interest in physics of all sorts, but particularly with respect to "sci-fi" technologies that hold the promise of losing their fictional aspect.

To that end, I was very intrigued when I first read about Alcubierre's metric on the BPP website, but dismayed to find the paper unavailable at the time. Recently, as part of an animation-related project I'm pursuing, it's come to the forefront of my thought again. Fortunately, arxiv.org is around now and his paper, along with many others, are now available to everyone.

The Problem
The trouble is, I barely understand the equations I'm looking at. The papers assume a certain level of expertise and variable recognition that I simply lack. Beyond a purely academic interest in the topic, I'm interested in developing an understanding of the Alcubierre equation(s) that I can use to plug in a radius for a warp bubble, a desired "speed," and provide an "power requirement" as a result.

As I understand it, the initial paper was refined by Chris Van Den Broeck, and then refined further such that the quantity of negative energy required was on the order of about -10 kg (though I've no idea what this -10kg will "get you" as far as the size and speed of the bubble go, nor if it's actually representative of anything approaching a "power requirement").

So, what I'm looking for specifically is a watered-down version of the metric that I can use to plug in two values (speed and radius) and produce a third (energy/power requirement). However, in the more global sense, I would love it if someone could guide me through a sort of "Alcubierre for dummies," explaining what the equations all mean.

Thanks a bunch! This is a fantastic forum you've got here, and I look forward to learning a lot here.

2. May 10, 2006

### scott1

Your an non-physicst trying to understand a advance physical equation. I'am not sure if it will be easy for anyone to explain it in a "the Warp drive for dummies" without having to remove all the equations form it.

I'am pretty sure you already have a basic understanding on how the Alcubierre drive(a.k.a warpdrive) works but if you don't:
The Alcubierre drive works by contracting the space in fornt of you and expanding the space in fornt which causes you to travel faster then light.

3. May 10, 2006

### JesseM

According to section 5 of this paper, there are some unphysical aspects of the Alcubierre solution, because in order for the "warp bubble" to move faster than light it seems to be a requirement that the exotic matter be able to locally move faster than light:

Last edited: May 10, 2006
4. May 11, 2006

### McC

The equations are the very things I seek explanations for, so any explanation removing the equations is ultimately meaningless and not useful to me. If I understand the framing of the equation, the equation itself falls into place easily for me. When I first looked at the Alcubierre metric, I was stymied by what "s" was in the very first equation. When someone explained the s was a distance in Minkowski space, expressed by three spatial coordinates and one time coordinate, it made plenty of sense.

I'm mostly looking for a Rosetta stone. The math itself isn't the hold-up, nor is the concept (I understand, or with a bit of very light research can look-up and understand, the text portions of the papers just fine). It's the assumptions the papers make about the readers having foreknowledge of what each symbol represents that catch me up. For instance, equation 6 has a variable expressed as $$\sigma$$. I have no idea what this is supposed to represent. It's said after it's introduced that it's an arbitary parameter. But an arbitrary parameter representing what?

An explanation of the variables is more or less what I'm seeking when I refer to a "warp drive for dummies."

Does this problem extend to the refinements on the Alcubierre metric postulated in the other papers I linked in my first post?

5. May 11, 2006

### pervect

Staff Emeritus
I suspect that the difficulties are deeper than you realize. As the text states, $\sigma$ is just an arbitrary parameter. It's whole purpose is to make f(rs) appear to look like the top-hat function in 7) for large $\sigma$.

The top-hat function in 7 is not used directly because it's not differentiable. So one needs a parameter that makes a differentiable function approach the desired function as the parameter takes on large values. This is $\sigma$.

The exact form of 6) was chosen to make the math easier, from what I can tell.

The "expansion" is where all the action is. As the text states, space is being shrunk (negative expansion parameter $\theta$) in front of the object, and re-expanded (positive expansion parameter) in back of the ship.

I don't see how you are going to be able to understand much more than that without a lot of math you don't have.

I had to look up the math relating to the "expansion" myself (Wald, General Relativity pg 216), and I'm finding it a bit hard to follow myself.