What is singularity?

[Dillinger4]

I was watching a show on black holes and they mentioned that
once an object is grabbed by the gravitational forces of a black hole there is no escape. As the object proceeds towards the center of the hole singularity is achieved. What does this actually mean? I know it has somthing to do with light not being able to escape from a black hole or somthing. Any ideas?

[NotLKH]

It is unfortunate that The currently accepted laws of physics break down
under the immense gravitational pull acheived by "Black Holes".
Einstein, Hawking, et al. of course only presented theories that "could" be applied, but neither one have presented anything that categorically occurs. Does an object "Keep Falling"?, does it "Break free"? and enter a different realm?


Ultimately, we'll never know.
Maybe our kids.

[Dillinger4]

Yes it is quite exciting and confusing at the same time. Does an object enter a parallel universe? Maybe.

[Dillinger4]

You actually zipped the WTC thread? That's funny. Yes there was a lot of heat in that one.

[Guv]

Singularities exist in mathematics, but many claim (with good reason) that they do not occur in nature.

A mathematical singularity usually involves some value growing without bound, although it sometimes refers to a situation in which a coordinate system or function has an undefined or anomalous value.

The North & South poles of a sphere are sometimes referred to as singular points because longitude has no meaning (there is no East/West direction), and the tangent of latitude (involved in some equations) grows without bound as the latitude approaches either Pole. Physically, there is no problem at the poles of a sphere, but some equations have a problem there. The problem relates to the choice of coordinate system rather than the actual location. If you choose a different coordinate system, the current North and South Poles cease to be a problem, although the problem might move to other points.

Functions like 1 / (x^2 - 1) are said to have singularities at both x = 1 and at x = -1,
while 1 / (x^3 - 1) has three singularities, two of which are at complex values of x. As you approach any of these singular points, the value of the function grows without bound. Some say that the value of these functions become infinite (although mathematicians avoid such statements).

Physicists refer to a singularity at the center of a black hole because the mathematics of relativity theory breaks down there. The following is from the site mentioned in the Post by ThinkTank.

The general theory of relativity could be regarded as the law that confirms the development of time in bent three-dimensional space. But having bent space to a certain point it must inevitably reach a singular point (where time and space become indefinable). This is known as the Penrose-Hawking singularity theorem. It explains the destruction of space-time by gravity, and black holes are singular points enclosed by an "event horizon".

When objects are sucked into black holes, they continue falling for an unlimited period of space and time. At a central point, gravity becomes infinite, time and space are bent, and concepts of time and space, as we know them, become irrelevant. Such an occurrence happened when the Universe was formed, and this is also known as a singular point. Objects sucked into singular points disappear from our Universe without a trace.

I have bolded parts of that quote, because I do not believe there is any experimental justification for them. They could be valid statements, but they are based on the extrapolation of equations into situations that cannot be tested.

The mathematics of relativity breaks down at the center of a black hole, indicating a singularity. There is no reason to be certain that the mathematics is applicable there, except for the fact that it is applicable almost everywhere else. Note that the mathematics of classical physics correctly described gravity and mechanics for all known situations prior to about 1880, but broke down when scientists were able to perform experiments not possible prior to the end of the 19th century. Similarly, future developments might discover that different mathematics is required to describe what happens at or near the center of a black hole. It could be that the equations of relativity are no longer applicable at or near the center of a black hole.

[STT]

yup, Guv is totally right.. black holes are theoritical and are only proven to exist mathematically..

[Dillinger4]

I have yet to read guv's post due to the large amount of data presented but if they are only proven to exist mathematically this must be false becuase they do infact exist. Do you mean the concept of singularity has only been proven to exist mathmatically?

[thinktank]

Well..what do you think about the electrons then ??

An electron is a theoretical object. It 's not a miniature round ball as you see in various illustrations.

[Dillinger4]

Well..what do you think about the electrons then ??

An electron is a theoretical object. It 's not a miniature round ball as you see in various illustrations.

But an electron does exist does it not?

[Guv]

I did not mean to imply that black holes do not exist, only that we have no observational or experimental knowledge of what occurs beyond the Event Horizon. There is a lot of observational evidence for their existence.

The mathematics of General (not special) Relativity Theory indicates that gravitational force compresses all matter in the black hole to a dimensionless point. There is zero volume, huge amounts of mass (usually ten or more solar masses), and incredible gravitational force (1 / Distance^2 grows without bound as you approach the point at the center). General Relativity treats both space and time dimensions in ways counterintuitive to our common notions: At the center of a black hole, it predicts extreme spatial curvature and no time dimension or actions take an incredible amount of time or something else weird about time measurments.

Note that if you approached the center of an ordinary object like the Earth or a star, you would be surrounded by matter. The gravitational force on you would decrease as you approached the center because of the outward pull of the matter between you and the surface. As you approach the center of a black hole, all of the matter is always between you and the center. Then is never any matter exerting an outward pull. The (1 / Distance^2) term in the Force equation grows without bound.

Since we cannot observe anything beyond the Event Horizon, there is no way to be certain that the mathematics is valid there. I think there is reason to believe that the mathematics is valid for at least some distance beyond the Event Horizon.

Perhaps there is some phenomena that results in the mathematics not being applicable at distances exremely close to the center. Maybe rotational effects counteract gravity, preventing the matter from collapsing into a point. Perhaps there is some non zero quantum theory limit beyond which space measurements no longer apply. If space is quantized like energy, there is a smallest amount of space that is bigger than a dimensionless point. Perhaps there is somethiong else that makes the mathematical model inappropriate.

There are a lot of weird counterintuitive phenomena relating to black holes.

• There is a distance at which the velocity of light is exactly what is required for a circular orbit. While impossible in practice, you could imagine a torus shaped space station surrounding the black hole at that distance. An astronaut in that space station with powerful binoculars could see the back of his head. To the astronaut, the donut shaped space station would look like a long straight cylinder.
  
• I have seen claims that you cannot observe anything falling beyond the Event Horizon. It is claimed that gravity red shifts light more and more as you approach the Event Horizon, making objects dimmer and dimmer as they approach the Horizon.
  
• It is claimed that time slows down as an object approaches the Event Horizon. There is a Scifi story about telepathic identical twins, one of whom falls into a black hole. In the story, the twin who falls in experiences his life ending rather quicky. His twin goes crazy and commits suicide because he is aware of his brother’s terror for years and years. According to Relativity Theory, the intense gravity does something weird with time, causing different time scales to be applicable to the brothers.

In real life, I believe that nothing ever falls through the Event Horizon. I think that the Event Horizon expands to engulf matter that is nearby. My idea is as follows.

Imagine that an Event Horizon has radius R, and lots of matter is falling toward it. At some point in time, There is enough matter inside a sphere or radius (R + x) to sustain a black hole whose Event Horizon radius is radius (R + x). The matter never fell though the Event Horizon at radius R, the radius of the Event Horizon increased.

The above seems to avoid the counterintuitive notion of requiring an indefinite amount of time for an object to fall past the Event horizon. In the twin brother story, the Event Horizon would grow in a reasonable amount to time, engulfing the unfortunate twin and preventing any further communication between the brothers, thus allowing the surviving twin to stop sensing his brother’s terror.

[STT]

We will not know the true behavoir of a black hole until we unite general relativity with quantum mechanics...

[boscord]

Am I right in saying (theoritically) that black holes are defined to be a paradox: Meaning that they basically (yeah, right!) are in 0 dimensions, thus allowing them to both exist and not exist (by our standards) and allow them to be in two places at once (in a sense).

Like: Our world is defined in 3 dimensions, so when it comes to black holes (0 dimensions) it is the equivalent of:

Enters here ---> | Universal Space Vacuum | <--- Exits here

This is just what I was told though, so dont be too hard!

Anyway, I believe that this follows along the theory of antimatter.

Anyway, Im starting to get a headache reading all of the black hole posts so im heading out.

Adios!

[CornedBee]

As far as I know, our world is defined in 4 dimensions. 3 space and 1 time.

[boscord]

Ahh..nice

I forgot about that one

Oh well, anyway...

[[Digital-X-Treme]]

Some information here on the mathematical side of singularities... may be of interest: http://mathworld.wolfram.com/Singularity.html

[STT]

Actually, in the super string theory, there are more than 4 dimensions (3 dimensions + 1 for time), but they are tightly curled up so they are hidden from our eyes. The need for these extra dimensions is because the superstring theory needs these extra dimensions in order for the string to exist. It is a pretty nice theory, there is loads of information on the net about it...

[mlewis]

Time is not a dimension; it is a phenomena.

Proof?

Think of each dimension as an axis of a graph. In order for a dimension to "Exist", a point on that graph has to be able to move along that axis.

Now any dimension is a subset of the dimensions above it (for example, dimension 1, a line, is a subset of a plane. dimension 2, a plane, is a subset of dimension 3, space. etc.)

So if time is a dimension, it must be a subset of some other controlling factor.


There is no other factor, but there are dimensions higher than 4, thus time is not a dimension.

Also, if time began, then time cannot be a dimension because a dimension must be infinite in all directions.

[kedaman]

Dimensions are mathematical tools, none of them actually exists, they have been defined as models, not been interpreted.

[mlewis]

And thus time cannot be a dimension, cuz it sure as heck exists

[kedaman]

Unless it's an illusion

[mlewis]

I want proof that its an illusion

[Guv]

M Lewis: Time is certainly not equivalent to a spatial dimension, but when used to locate an event, it seems to function as one coordinate of what looks like a position vector.

In discussing Relativity Theory, Einstein once said that any statement about space without time is geometry, while any statement about time without space is philosophy. Any statement in physics refers to both time and space. Thus, an event is fundamental to physics.

For many purposes of physics, it is handy to use 4D notation which looks very much like geometry or vector analysis. (X, Y, Z, T) are the coordinates of an event, while (DeltaX, DeltaY, DeltaZ, DeltaT) is a vector specifying the interval between two events. Instead of equations describing particle motion, you have the geometry of the World Line of the particle.

Note that there are other coordinates systems for which one dimension is not specified by a distance. In Polar, Cylindrical, & Spherical coordinates one or more measurements are angles instead of distances, and must be treated differently from the distances. When you think about such coordinates systems, time as a coordinate or a dimension does not seem so strange.

Note also that mathematics deals with finite as well as infinite spaces. The surface of a sphere (or torus) is a finite 2D space. There are analogous finite 3D spaces. A dimension does not have to be unbounded. In fact, a cylinder is a 2D space with one finite and one unbounded dimension.

[kedaman]

In other words a green elephant is two dimensional.

[mlewis]

hmm...

food for thought

[Guv]

A blue elephant is two dimensional. Green elephants are 3D.

[mlewis]

What dimension is a white elephant?

[kedaman]

Nope, that's not my point. A colored animal has two dimensions, color and animal type, even if it's not directly mathematical. I'm in the middle of developing a library of dynamically dimensioned entities in C++, and the green elephant being my favourite analogy

[mlewis]

hehe ok then

So I assume a white elephant is 2d as well?

[NotLKH]

Hmm,
Doesn't a color itself have 3 dimensions? RBGWise, that is!

[CornedBee]

BTW, the superstring theory proposes a 11-dimensional world...