Attempting to Understand Alcubierre

[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 http://www.arxiv.org/PS_cache/gr-qc/pdf/0009/0009013.pdf 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").

Please help
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.

 

[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.

 

[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:

The most problematic feature of the warp drive geometry is the behaviour of the negative energy densities in the warp bubble wall [2, 5]. If the Alcubierre spacetime is taken literally, part of the exotic matter will have to move superluminally with respect to the local lightcone. It is easy to see that all exotic matter outside some surface surrounding the center (let us call this the critical surface), will move in a spacelike direction. For vs > 1, there has to be exotic matter outside the critical surface, since the function f must reach the value 0 for some rs (which, of course, can be infinity), and the negative energy density is proportional to (df/drs)^2 for an ‘Eulerian observer’ [1]. As noted in [5], the Alcubierre spacetime is an example of what can happen when the Einstein equations are run in the ‘wrong’ direction, first specifying a metric, then calculating the associated energy–momentum tensor.

The problem of tachyonic motion can be interpreted as meaning that part of the necessary exotic matter is not able to keep up with the rest of the bubble: if one would try to make a warp bubble go superluminal, the outer shell would be left behind, destroying the warp effect.

It is conceivable that the problem can be circumvented, for example by letting the distribution of exotic matter expand into a ‘tail’ in the back. It may be possible to do this in a way compatible with both the QI and the Quantum Interest Conjecture introduced in [13], which states that a pulse of negative energy must always be followed by a larger pulse of positive energy. However, it is unlikely that one can get rid of tachyonic motion of the exotic matter without introducing a naked curvature singularity in the front of the bubble [14].

 

[McC]

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.

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."

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

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

 

[pervect]

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.