Negative volume, that's unpossible!- Ralph Wiggum

 

"There's no such thing as negative area"

Au contraire, mon frere. I can certainly make a graph of the movement of a thing, and put the horizontal axis where I want. If I graph the speed of the thing against time, it is certainly possible that the area of the graph under the x-axis is greater than the area above it, making for a total negative area. That area is merely data on a graph, it has no real-life counterpart. On a graph of speed vs. time, the area is the displacement, so it does represent a real-life value, and if the distance travelled is mostly in a negative direction, the graph is definitely going to show a negative overall area. If you put the x-axis near the top of a piece of paper, you can claim the paper has a negative overall area, but it is not meaningful in that context. We typically measure the area of a surface starting at one edge, not somewhere in the middle, when the surface area being measured is something like a board or piece of paper. If you need to know how much paint will cover a wall, it would not be useful to go to the store and give the salesperson a negative value. Context is everything.

 

[QUOTE=no_really,Dec 4 2005, 10:47 AM] "There's no such thing as negative area"

Au contraire, mon frere.

 

[QUOTE=magician,Dec 4 2005, 01:26 PM] Geometry is the study of the properties of figures that remain unchanged when the figures undergo what are known as "rigid transformations": translations and rotations, as opposed to expansions, contractions, or distortions.

Area is a geometric property; it is unchanged by rigid transformations.

 

No, it isn't.

The definite integral of velocity is displacement, which can be positive or negative. The area between the graph of the velocity function and the x-axis is the integral of the absolute value of the velocity, which is nonnegative.

Look at any calculus text: area is not defined as the integral of f(x); it is defined as the integral of |f(x)|. The area between the graph of y = sin(x) and the x-axis for one period of sin(x) is 4, not 0.

Of course we're talking about physics here. But to say that we're not talking about geometry is wrong: physics relies on geometry, and on algebra, and on calculus as the language in which to formulate its rules.

Area is nonnegative. In geometry, and in physics.

 

What he said. I think I said positive or negative, but it's really positive, negative, or zero .

 

I guess there are a couple different ways black holes are formed, but the most general case is the implosion of a supermassive star. If the imploded star has less than a certain mass, it will explode into a supernova. If the imploded star has more than that certain mass, it will collapse to an infinitesimally small point, a black hole.

The gravity of this black hole pulls in everything, even light, and as more mass and energy are pulled into this infinitesimally small point, it becomes denser and denser, yielding a greater and greater gravitational pull.

There are two laws that come to mind when discussing black holes. The Law of Conservation of Mass, and the Law of Conservation of Energy. These two laws are pretty straight forward, they basically say that neither mass or energy can simply "disappear". The Law of Conservation of Mass isn't actually true, because mass can be converted to energy during a reaction, such as when liquid gasoline is converted into rotational energy and heat within a combustion engine. The Law of Conservation of Energy does hold true though, at least as far as conventional physics are concerned.

The question that arises from these laws, in pertinence to black holes, is basically "What happens to all of this mass and energy at this infinitesimally small point?"

This is basically the point at which the generally accepted theory ends, and the multitude of possibilities begins. There are many theories as to what happens, from "white holes" at the other end which basically do the opposite of black holes, to the idea that black holes might be used as time portals. It gets all crazy and stuff...

As far as negative volume goes, it would indeed be logical to say that the volume is never negative, but simply "infinitesimally small". Another possibility, reaching into the realm of theoretical quantum physics, deals with the concept of anti-matter (or dark matter). If you vest confidence in the concept of anti-matter, then it would seem possible for there to be anti-volume. But from there it gets insane, cool, but insane.

I think I'll stick to the engineering and leave the physics as a hobby, haha.

 

Isn't negative volume about the amount of space we allow a spammer on here?

 

Actually, the current theories regarding black holes place a singularity at the center, which has no volume and infinite density. This can happen because the intense gravity warps space-time into an infinate curvature. (Actually space and time cease to exist as defined by conventional physics at this point, including General Relativity.)

Now there is a volume within the black hole if you define the edge of the "hole" as the Schwarzschild radius, which is where the gravitational pull creates an escape velocity that is equal to the speed of light (also known as the event horizon, or point of no return).

 

I'm pretty sure that a plane travelling on a conveyor belt creates a negative volume beneath it's wheels