Computing the Volume of a Negative Sphere: Formula and Implementation

[PoPpAScience]

If I wanted to run a formula for the Volume of a Negitive Sphere on a computer which way would I write it?: V=(4pi/3)-r^3 or V=(4pi/3)r^(-3) or ? Has anyone else tried to run this formula on a computer? :shy:

 

[e(ho0n3]

What in the world is a negative sphere? If you have the formula for a negative sphere, just make a function to do the calculation. What is the problem?

 

[PoPpAScience]

The problem is lack of math education. The question is do I put the negitive sign in front of the r or the 3? A negative sphere can be pictured as a reverse Big Bang. Also, I am wondering what happens if this equation is run on a computer. Tks 4 your replies.

 

[e(ho0n3]

So I'm guessing a negative sphere is a sphere with negative volume!? If it is, put the negative sign in front of the r. I'm not sure what you mean by "running" the equation on a computer. You can do this on a calculator if you wanted to, so...

 

[chroot]

1) There is no such thing as a negative sphere. Radii can only be zero or positive.

2) A sphere is not a model of the big bang. It's just a sphere.

3) You don't "run an equation" on a computer. You can solve an equation with a computer, or you can use a computer to plug numbers into any formula you can dream up. That doesn't mean the results mean anything.

- Warren

 

[PoPpAScience]

Thank you for those replies. Another question if you pls. When one puts two mirrors in front of another, there seams to be an over lapping reflection, maybe into infinity. If at the moment of alining the two mirrors, the reflections take time to reflect back and forth into infinity, what would be a formula to describe this? Please be patient with my process, this is the first time I have asked any questions about my thoughts. Thks.

 

[HallsofIvy]

How about an object with constant negative curvature? Is it a closed figure? Does it have a finite volume?

 

[Entropy]

Maybe what you mean is an inverse sphere instead of a negative sphere?

 

[PoPpAScience]

Yes Entropy that sounds like a better discription. Tks.

 

[chroot]

I can't say I know what an inverse sphere is, either.

- Warren

 

[PoPpAScience]

Lets say if you take the Singularity at the beginning of the Big Bang theory, and instead of it exploding outwards into some unknown medium, it instead exploded in upon itself. What would that equation be?

 

[chroot]

There's no "equation" for such a situation.

- Warren

 

[PoPpAScience]

Tks Warren for your replies. I see I am going to have a hard time equating my thoughts on reverse expansion from a "Zero Point". The only time this can happen, is at the very beginning of our Universe. I can see it , but I can not express it. I feel the equation "(4pi/3)-r^3" would cover this, if a number generator starting at Zero is introduced to "r". This number generator can run into infinity, or have a stopping point. I have seen on tv animation where it looks as if you are falling forever into a smaller point (like a black Hole), or like my mirror example from before. This is the way I see it.

 

[humanino]

I fear for you PoPpAScience, because you say you suffer from lack of math education (well, we all do ) and you are trying to tackle problems that are so difficult. Big Bang theory requires a fairly advanced knowledge in math and physics.

 

[rgoudie]

When one puts two mirrors in front of another, there seams to be an over lapping reflection, maybe into infinity. If at the moment of alining the two mirrors, the reflections take time to reflect back and forth into infinity, what would be a formula to describe this?

Unfortunately, the light will not reflect back and forth forever as each reflection absorbs an amount of light. I remember being in an entranceway of an office building that had mirrors on all walls. As I looked at my reflections in one mirror, they repeated for what seemed like at least one hundred reflections, but eventually they faded away into darkness.

-Ray.

 

[humanino]

each reflection absorbs an amount of light

Even with pefectly reflecting mirrors, that would not work, because you need an integer number of photons with definite energy (color), as opposed to classical waves whose energy can be arbitrarily small.

But there are indeed a classical formulae to describe the wave model of light reflecting on ideal mirrors.

 

[Zurtex]

Tks Warren for your replies. I see I am going to have a hard time equating my thoughts on reverse expansion from a "Zero Point". The only time this can happen, is at the very beginning of our Universe. I can see it , but I can not express it. I feel the equation "(4pi/3)-r^3" would cover this, if a number generator starting at Zero is introduced to "r". This number generator can run into infinity, or have a stopping point. I have seen on tv animation where it looks as if you are falling forever into a smaller point (like a black Hole), or like my mirror example from before. This is the way I see it.

When you say "(4pi/3)-r^3" do you mean (4\pi/3)(-r^3) or 4\pi/3 - r^3? The first one doesn't make any sense as all 3D geometrical objects have a positive volume and radius is also always positive. The 2nd one seem to be applicable for a situation where you have a hollow sphere with radius one r represents the radius of the space inside the sphere.

The idea of the big bang unfortunately uses more than Euclidean geometrical shapes and requires a much greater understanding of physics and mathematics to model. However (and I don't have the knowledge in this area) I don't believe the universe is even close to a sphere.

I believe a misconception of black holes is that the centre mass is infinitely small, this is not so (although you'd need to ask a physicist).

 

[humanino]

I don't believe the universe is even close to a sphere.

The current paradigm is that the expansion of the universe accelerates. That indeed implies an open universe with negative curvature. The fate of this universe would be a death due to dilution of energy.

a misconception of black holes is that the centre mass is infinitely small, this is not so

As far as I understand "center of mass", this is mathematically defined as the barycenter point with respect to mass density weighting : this is a single well-defined spot. But the "center" of the black-hole is the singularity of spacetime, where the 4-curvature becomes infinite. This is classically a point where the General Relativity failure occurs. It is know strongly likely that QM theory of gravitation will somehow "blurry" the singularity, either through extended objects (strings) or due to granular spacetime (like in Loop Gravity) for instance.

 

[ahrkron]

It looks as if you were trying to describe the beginning of the universe as the "implosion" of an initial mass.

The first problem that comes to mind is the origin of that initial mass. Then, a more serious problem, from GR, is the fact that there is plenty of evidence for the current model of the evolution of the universe some time after the BB. This means that there was an expansion at least at some point after your "initial mass" was just hanging around. As a result, you would need to explain how is it that GR "kicked in", and why it had not before.

In any case, it is good that you are thinking about this problems. If you seriously want to pursue them, there is a lot of learning that you need to do. Just getting a "negative sphere formula" won't cut it.

Just to give you an idea of what seems lacking:

Newtonian mechanics (for which you need to learn calculus, which requires in turn approx 1yr of hard work) describes the motion of cars, projectiles, stars, planets and many others to maybe 1 part in a million. That means that a new model for things should have at least that precision.

General Relativity (for which you need lots of other math, maybe 1 more year of work) gets the last digits right. Let me elaborate: in some cases, Newtonian methods fail by more than 1 in a million, more like 1 in a hundred, or even 50%. In those cases you need a better model, and GR provides it. It gets right the last digits. In very special situations, those "last digits" are noticeable, or experimentally visible. However, in the rest of situations, the new theory (in this case, GR) still gives results that are compatible with both the old theory and experiment (within the experimental resolution).

Your idea of the "negative sphere" sounds interesting, but it cannot go any further without a solid link to physics (i.e., experiment) and a much wider framework. The BB model is not a concoction made out of a nice sounding phrase. Instead, it is the result of the following process:

Out from a lot of (gravitational) experimental data, a set of "basic laws", plus a method to obtain predictions from them, was found (Newton's mechanics).
From electromagnetic and optical experiments, a modification of the idea of space and time came along (Special Relativity, or SR).
Trying to extend SR, a new, more accurate, theory of gravity was obtained (General Relativity, or GR),
Then, with a solidly supported set of "basic laws" for the behavior of gravity, people investigated what those laws say about the beginning of the universe.
What they say is what people know as the "Big Bang model". It is not only an idea. It also makes various predictions (among them, the precise energy composition of the cosmic microwave background radiation, and the relative abundance of many elements in the universe), and they were confirmed with an excellent precision.

There are still many open questions in the model, for which it would be great to have new people come and contribute their efforts. However, in order to get to a point where you can contribute, you need to invest some serious time in math and physics. It is a fascinating enterprise though, worth the time and work.

 

[PoPpAScience]

Ahrkron thanks for your reply, I agree whole heartedly with what you say. I have more to say onwhat is replied here, but I am away from home and have to wait for home to have time to reply. So looking forward to conversing in this forum I feel good intentions here. Thanks All.