sup bb, wanna go integrate?  
let’s explore the area under your quartic function.  
I wanna e to the eye your pie.  
you wanna converge the sum of our sequences?  
I’ll approach your limits.  
let’s go somewhere private and determine your local maxima.  
I need to find the slope of your curves.
 
>why did I actually take calculus

@Sollace  
The kicker is special rules/restrictions on how you travel. The Alcubierre drive might have them so that it doesn’t allow causality violations. I think it does, but I can’t yet prove it, that’s what I’m working on.

@Cirrus Light  
Hm…
 
Yeah, don’t believe it would create a causality violation.
 
Going faster than light you be able to move a distance faster than it takes for your change to propagate to observers (as in they would see you arriving before they see you leave) but it would only be an illusion. You’re not actually moving back in time.
 
They can’t give you information from after you arrive to before you left either because it would take as long if not longer for that information to reach you than it took for you to travel the distance.
 
If you travel a distance faster than light, then travel back to your original starting point you would only arrive there in time to see yourself arrive at the point you just left because the distance traveled would be near identical.
 
The only stick up would be if you can travel even faster than you already were, but that’s assuming such a thing would be possible if not exponentially more difficult.

@Cirrus Light  
Yeah, It does get rather complicated, and really I don’t expect something like that to pop up within our lifetimes :P
 
But, on another matter, I’m actually working on getting an Astronomical society set up here at UA, and me and a couple other guys who are getting it together are thinking of doing something of the ilk of a supernova hunting project since we’re able to use the 16-inch at the university, being in the physics and astronomy department. Not a lot of opportunities for aspiring students in the department, and I’m working to get that changed, because if there is anything we need more of, it’s people with an interest in understanding the workings of the universe around us.

@Sollace  

 
Yes.
 
The two are equivalent.
 
It violates some of what are called energy conditions, but those are something else entirely - nothing nearly so fundamental as energy conservation.
 
The biggest issue is the possibility of causality violations…
 
I actually talk about this a bit in my reply to Firelord:
 
@FirelordofHyrule  
Deeper over-arching principles can often be expressed in ways that ruin something. For example, trying to spin a paddlewheel using the same water it pushes is obviously impossible - But it’s only obvious because we know about energy conservation.
 
Otherwise, you could spend years trying to devise clever schemes to run the water uphill, downhill, through a magnet, a cooler and a compressor or all kinds of complex nonsense to try to get the paddlewheel to power itself. You could get lost in flow, density and Bernoulli equations to the point where it could almost seem like it’s possible.
 
The discussion on Alcubierre seems to be a similar vein - except here, the drive itself is the complex water flow, and causality and time travel paradoxes may be the “energy conservation” (metaphorically - Alcubierre doesn’t present any conflicts with conservation as far as I know) - The overarching principle to make it fail.
 
One of the things I’m really interested in is questions of causality and such. By virtue of ftl travel, there’s no question it will at least appear to travel backwards in time in some frames of reference. So it appears to have tachyonic paradoxes, but I’m not so sure because nothing is traveling locally faster than light.
 
I’d have to dig a little more, but from what I’ve seen of the metric and seen written, I don’t think the drive causes anything so terrible as causality violations - or to be more precise, “closed timelike curves”. Some people think it does, but from what I’ve seen of it, I think a more careful investigation reveals that it doesn’t - But I’ll have to research a bit more to find out with enough certainty to argue, though I’m leaning that way myself (I don’t think it causes closed timelike curves).

@Cirrus Light  
Oh, well that is promising.
 
But is that a negative quantity of energy or negative energy?
 
Negative quantity sounds like it would violate one of the laws (energy can not be created or destroyed).

@Cirrus Light  
Well, I haven’t really researched much of GR, I’m just going off what bits I know from my astronomy and physics classes, but even with my meager knowledge, I know that the principles of relativity state that time and length contraction would result in the destruction of anything traveling faster than light… through space; there is nothing, however, which states that space itself cannot travel faster than light, and considering that the celestial bodies in the universe bend space around them, I don’t see how something like that couldn’t be exploited to produce faster than light travel while effectively not traveling faster than light.

@FirelordofHyrule  
Ooh. How much of GR have you researched? I’m just starting to get the Tensor stuff, myself. I can find geodesics given a metric and analyze a metric, but finding a metric from a stress-energy tensor is still a bit beyond me.
 
That may be remedied by Christmas, though.
 
@Sollace  
In a sense, so yes. But to note, it only “powers” it in the same way that dirt powers gravity. The Alcubierre drive is pretty much a gravity drive - it warps space, and that’s what gravity is; a warping of space.
 
There’s some other tricks to it. In most understandings of it, it requires negative mass-energy (remember e = mc ² , in relativity, energy and mass are equivalent), but a more recent investigation shows that the negative energy may be a result of it working, not something you need to make it. That’s promising.

@FirelordofHyrule  
Is the Alcubierre drive the one I’m thinking of that would require matter with a negative mass to power it?

@Cirrus Light  
Heh, I’ve built a couple fighter jets and other such nonsense many a time :P
 
But, yeah, alternative propulsion is practically an obsession of mine (that is, aside from Roman culture and history); The physics behind the Alcubierre drive are sound, taking General Relativity into account, how to produce such a distortion in space is another matter entirely, though.

@FirelordofHyrule  
Ever try the realism overhaul mods?
 
Funny you should mention KSP since I haven’t touched it in months, but just today tried a few airplane designs with little success, but successfully rendevouzed and docked Rainbow and Twilight in LEO in small Gemini-like crafts (imagine the Mercury capsule outfitted with an equipment section like a miniaturized version of Gemini’s).
 
I spent many years completely obsessed with aerospace - still love the heck out of it, but feel a little less obsessed just because there doesn’t seem to be anything new for me to discover about it >.<
 
So now I’m enthralled with curved spacetimes of general relativity and field propulsion concepts like the Alcubierre Drive.

@Cirrus Light  
I’ve always been fascinated with exoplanetary systems, especially those with the possibility of harboring extraterrestrial life, and also the possible future of space exploration. I do admit, sci-fi and Kerbal Space Program have played a pretty major role in the development of that interest XD

@FirelordofHyrule  
Lol! I live in ‘Bama but I’m going way out of state tomorrow as the university starts up again for Fall semester. Somewhat ironic.
 
Anything really particular you’re interested in? Neutron stars? Red Dwarves? Dust cloud dynamics and effects? Planet hunting?

@Cirrus Light  
Yeah, second year Astro Major at Alabama, though I’m just now getting into Cal 2 and Electromagnetism :p

@FirelordofHyrule  
Oh, really? Sweet. I’m in “Physics-Astronomy” right now, but might switch to just “physics” since I’m looking at theoretical physics - specifically/especially general relativity.

@Barhandar  
I’d rather just get a nice, stable, boring office job. ‘^’

@Background Human  
Oh, trust me, as an astrophysics major, I know the pain.

@Keith Mowz  
Jock is opposite of a nerd.
 
Also, you’re welcome to invent adjustable wrench. Both mathematics and physicists would LOVE it.

@Barhandar  
Again, no, accountant. Or maybe banker, dunno, depends where I can get a job. And what I was referring to was mostly in regards to math when physics is involved, where you don’t have a screwdriver, you have an entire shop class worth of tools, each set of which has a dozen or so different sizes and models. I like my metaphorical assembly projects to use the basics because trying to use the metaphorical allen wrench set drives me up a wall when I have to consult my metaphorical instruction manual to figure out which of the twenty of them fit for this problem because otherwise I’m going to metaphorically end up stripping out the bolts when trying to work it together.

This is quickly becoming one of my favourite discussions to follow.

@Keith Mowz  
Except math DOES work reliably, or else no sort of algorithmic solution’d be possible.
 
Saying it doesn’t is like saying you should be able to drive nail in with a screwdriver. Different tool required, but a consistent one for specific kind of problem.
 
@Keith Mowz  
JOOOOOCK

@Cirrus Light  
Head tilt
 
Yeah this is why I stopped pursuing engineering. :T

@FirelordofHyrule  
@Sollace  
See, that’s what I’m talking about. The problem looks so simple and unassuming, then the solution blows up in your face.
 
@Cirrus Light  
Similarly, you can approximate an integral as the sum of rectangular slices under a function, f(y) tall and delta-y wide. As delta-y decreases the approximation becomes more accurate, and the limit as delta-y becomes infinitely small is the integral itself. Hence the notation S( f(y) dy ).

@Cirrus Light  
Indeed.
 
And indeed. Was having trouble figuring out how I would explain dy to him.

@Sollace  
UV Voodoo is the devil. You think it will help you, but like any other kind of voodoo, it’s just evil Xp
 
Naw, it’s a powerful tool, but darn it makes things complex, sometimes.
 
 
@Keith Mowz  
dy =/= d*y.  
d isn’t a variable, it’s an “operator” - it means a “zero but not really zero” increment in whatever comes after it. It’s a differential - sort of like the limit as delta-y approaches zero.
 
It’s kind of like a really really tiny change in y with certain specific properties.
 
Specifically, it’s defined as:  
(replacing y with x)