@Prometheus labs CEO  
It is, yes - or rather, the curvature is caused by the energy density distribution in spacetime.
 
But the equations that predict the Casimr Cavity have no contribution from gravity, but are entirely from quantum EM equations, afaik. That last part might not be precisely accurate, but I’m really, really sure that the Casimir effect is not a gravitational effect, at least.

@Cirrus Light  
Mayb the cashmere effevt is caused by the gravity rot the two plates stretching spacetime by a minuscule amount in between them, reducing the amount of vacuum energy in between them. Isn’t vacuum energy density related to spacetime curvature and density? If not please correct me

@Prometheus labs CEO  
It’s an inevitable consequence of the uncertainty principle in a vacuum - though that is subject to some averaged conditions that probably rule it out.
 
Another case of it that I’m not sure if is ruled out or not is Casimr cavities.
 
In the last decade or two some papers by Dr. Harold White suggest the negative energy density may be a result of the “warp bubble”, though, rather than the cause of it. I’m not sure how you ascertain that in General Relativity, other than the stress-energy tensor is typically the cause of the spacetime metric, which then influences the behavior of the mass-energy distribution described by the stress-energy tensor.
 
So it’s a weird relationship, but the matter causes the curvature of spacetime.
 
But curvature can cause curvature, too, since gravity waves exist.
 
Then again, that interpretation of the curvature causing the negative energy density may be based on certain cosmological models outside the scope of canonical GR.

@Cirrus Light  
Still might take awhile considering we have yet to find true negative mass

@Prometheus labs CEO  
That was the original modification to the metric. But later revisions showed it could be done with arbitrarily small amounts of negative mass depending on the field configuration. Revisions I wish I knew the math to understand better :q

Okay now we just need a piece of negative mass the size of Jupiter… this might take a while

@dyanamicwarfare  
Physics is the models we use to try to understand the universe. We make models - mental pictures and rules with which to apply certain equations - to try to be able to predict phenomenon.
 
In some sense, it’s not just a huge impact on everything that makes the world and universe work, it is everything in the world and universe. It’s all physics.
 
But in another sense, reality itself isn’t those equations, those equations are just something we use to try to understand reality. It works amazingly - even shockingly well, and it does deepen our understanding of the universe, but it’s not the universe itself.
 
You’ll understand that better as you study it more.
 

 
As for my earlier comment, eh, well, it should make sense after you take Algebra. Algebra is pretty fundamental and important. But don’t worry if it’s hard at first - that’s not unusual, and you’ll get plenty of practice as time goes on because everything is algebra, heh. You never really stop using it, you just learn new things to use on top of it, and it gets easier as you do more.

@Cirrus Light  
quite a mouthful there :P
 
physics are very interesting and they have a huge impact on everything that makes the world and universe work i have no clue how 70% of it works but i know that it is a very important study and i hope one day i will understand it better
 
i hate to say it but you are talking to a coming freshman who really wished he paid attention in math and science but i have worked with variables and understand some concepts of basic algebra because i have worked with computer programming as a planned future job so i hope i can understand you comment a bit better (if it will stil exist) when i am a bit older
 
thanks for the lesson and i hope you can change the world with that knowledge it has great value these days.

@dyanamicwarfare  
They’re kind of variables.
 
It depends on which ones you’re talking about.
 
So, later on, you’ll learn calculus, which will open up the whole world of differential equations.
 
the (dx)’s, (dy)’s, and all the other d-somethings, with the curly d’s and the regular d’s, represent a tiny change in something. It’s this kind of idea that if you took a video of a flying arrow, and slowed it down until it stopped, it would still be moving, but infinitely slowly. You’ll learn more exactly how this works when you learn calculus - it’s really awesome, and calculus is really a fundamental for all of physics.
 
As for other things - sometimes it’s useful to store “tables” of information, and they have certain relationships so things work better this way - I won’t get into those now (unless you want me to! But if you haven’t used variables yet it might be a bit hard for me to not go too fast) - but here’s an example of one of those things.
 
It’s a special kind of “table” of information called a Tensor, which means some important things about how it works. This is the “metric tensor”
 

 
So if I write
 
g _ij = 2 * T _ij  
(the aterisk * is used to denote multiplication sometimes, especially in equations with variables),
 
Then I’m actually describing 9 equations at once.
 
g _ij = 2 * T _ij is really
 
g ₁₁ = 2 * T ₁₁  
g ₁₂ = 2 * T ₁₂  
g ₁₃ = 2 * T ₁₃  
g ₂₁ = 2 * T ₂₁  
g ₂₂ = 2 * T ₂₂  
g ₂₃ = 2 * T ₂₃  
g ₃₁ = 2 * T ₃₁  
g ₃₂ = 2 * T ₃₂  
g ₃₃ = 2 * T ₃₃
 
And whether those are written above or below has a special meaning to do with higher mathematics;
 
g _ij is a completely different thing from g ^ij (though they are related in a very important way!).
 
And the neat thing is, you can kind of change the physics behind the problem and say “i and j can go to 4” or “i and j can go to 10” and the math is still true.
 
i’s and j’s are called “indices”. And the author I originally took those equations from (back when I didn’t understand them) seemed to have decided to use greek letters for all the indices. So all the little greek letters are indices like that.
 
It’s a smart thing to do, so they don’t get confused with exponents and subscripts.
 
Exponents just mean something is multiplied by itself that number of times.  
2 ¹ = 2,  
2 ² = 2 * 2,  
2 ³ = 2 * 2 * 2,  
2 ⁴ = 2 * 2 * 2 * 2,  
4 ² = 4 * 4,  
so on and so forth.
 
Subscripts are kind of usually like variables. Like, v is usually the variable that denotes speed (though it’s often used for a few other things in physics). v _s is something like speed that’s basically speed but measured in a different way, so, really it’s a whole different variable, and he could’ve just called it, say, “k”, but by calling it v _s it’s a little reminder that this thing is very similar to “v” and has some kind of relationship with v.
 
So if you see, say, T ^a _bc , how are you supposed to know if a is an index or an exponent? Or if b or c are indices or subscripts? Well, the author of those equations wrote all the indices as greek letters, so you have that there. But in general, you kind of just learn the context and can figure it out from there.
 

 
And in case you feel daunted - don’t worry, when I originally made that image - just a few years ago - I didn’t understand any of that! Well, I knew about exponents and variables and calculus, but I didn’t know why some of the d’s were curly, I had no idea what the indices were, and I had never seen an upper-case gamma used in an equation in my life, and it was such a strange symbol it scared the heck out of me, lol.
 
And here’s something else, too - I’m actually really slow at math. In fact, I’m like one of the slowest people I know at a lot of things, and my grades - they’re not great. And I struggled like heck with some of the stuff in Algebra II. So really, never think you’re not smart enough, because I honestly think the only difference in-between smart people and not is the desire to learn. Now, I am quite smart, heh, but it just takes me a while to work things. But don’t feel like you’ll never get this far if you struggle with Algebra I - I actually had a very hard time first learning fractions, and some concepts in Algebra II were just nightmares for me to work at, and are still kind of hard for me to this day, hah. So finding Algebra hard doesn’t mean you can’t go as far as you want. And in time, you get better, and it’s okay if that takes many years. It did for me.
 
Anyways, I tried to make sense about all that, but if I just made it more confusing that’s more my fault than yours, so don’t feel overwhelmed by it, just be excited that one day you’ll understand it all if you keep going.
 
I explained so much just because it’s so exciting to me, and to say “some are variables, some are kind of like variables, some are other things - subscripts, exponents, and indices”.
 
Do you have any interest in becoming a scientist of some kind? Perhaps even a physicist?

So I am just a random guy from on here who is just going to start algebra 1 this fall. exactly what do the letters represent are they variables? or do they serve some other purpose

@Background Pony #10E2  
Kind of, actually. We haven’t for sure found out how to make a warp drive, and a lot of people think it impossible, but warping space is the name of the game in general relativity.
 
Well, curving spacetime, but it’s basically the same thing :q

@Cirrus Light  
You know how to Star Trek now? O_O
 
I’m kidding XD

It’s… Kind of nice, to see this old thing get re-uploaded here by someone.
 
You know, I first made this so many years ago… At the time, I had no idea what any of that was.
 
But now I know it… Almost all of it. Well, actually, kinda all of it! It’s been a really rough night, and it’s incredibly nice to look back and see something I’m proud of and happy about… After all these years I actually know that stuff!

@Background Pony #4767  
Not sure about the answer to the last question - I doubt anyone knows that with any real certainty.
 
But your two quotations are on a wholly different level than the alcubierre drive. Maybe not for Alcubierre’s original paper, but in the latest incarnation it’s far more plausible (Paper io9 article ). While the Alcubierre drive itself goes back to 1994, the latest incarnation of it is far more recent. And just because many solutions have failed to give us practical FTL travel, doesn’t mean it’s impossible any more than a bullet failing to reach sufficient velocity for Lunar Orbit Insertion means it’s impossible to go there.
 
And this is all to say nothing about the EmDrive. Months ago, I would’ve labelled it as pretty far “out there,” but given the latest successful vacuum tests by NASA and the White-Juday warp field Interferometer detecting an actual warp bubble with a reasonable level of certainty, I’m honestly a little sad I may have been beaten to my hopes of discovering/inventing such a thing.

@Cirrus Light  
I wish you well with it, though of course so much about the Alcubierre models still seems to me to be dependent upon engineering impossibilities, like matter with “negative mass,” whatever that even means in this context.
 
“time travel is easy, we just need to put all the mass in the universe into a narrow electrically charged cylinder of neutronium of infinite length and make it rotate at relativistic speeds.”
 
“time travel is easy, we just need to take a black hole, reshape it into a torus, and make it rotate at just under the speed of light…”
 
some of these mathematical concepts have been around since the 1930s–if you’re in physics I’m sure I don’t have to tell you about the Godel Metric, or the van Stockum dust problem. Can closed timelike curves exist in the real universe, or are they pathological artifacts of an incomplete mathematical model of reality?

The numbers, Sparkle. What do they mean?!

@Ascendant 2.0
 
#1: The Casimir effect can fulfill the negative York Time requirement (York Time being a measure of the compression/expansion of space resulting from the placement of mass/energy).
 
#2: The results of a recent rethink of the Alcubierre drive seem to indicate that the negative spacetime curvature is actually a result of the warp drive, rather than the driving phenomenon. The paper pulls up a simile: you can think of the “warp bubble” as a solid object moving through a fluid. The hydrostatic pressure in front of the object is greater than the fluid’s average at that depth, and the pressure behind the object is less. Likewise, the warp bubble moving through spacetime causes space to “pile up” in front and “stretch out” behind.
 
To create the “warp bubble,” you create a torus-shaped field of mass-energy placement, where the direction of travel is normal to the plane of the torus. As you generate this field, any initial velocity is multiplied by a “boost factor” to create your new “apparent velocity”.

Good luck getting rid of that negative mass requirement. :/

Eww… math

I think it’s more horrifying I recognized most of that.

“Why yes I do this in my sleep. Don’t you solve partial differential equations in your sleep?” - Twilight Sparkle.