Explaining Singularity: A Beginner's Guide

[woz]

I have been wondering for some time what a Singularity is, I have read it in various places around this forum but I don't understand. Could someone be so kind to explain that me?

Forgive my ignorance, English is not my first language and I am new in all this.

 

[marcus]

I have been wondering for some time what a Singularity...

other people may want to answer in greater detail. here is a "bare-bones" simple example


think about the function f(x) = 1/x

it has a singularity at x = 0

the function will not compute at the point x = 0


if you start with x negative and move towards zero the function
value goes towards minus infinity

if you start with x positive and move towards zero it goes to plus infinity

there is no way you can "patch" or "fix" the function to give it a value at zero in such a way that it will be smooth-----it just has a bad spot at
x = 0 that you have to live with

------------
general relativity, the geometric theory of gravity which Einstein handed us in 1915, has some bad spots where it won't compute-----these can be points or lines or regions, depending.

it's a theory of how matter bends space and how curved space guides the flow of matter and it works remarkably well, but solutions to the equations can have regions where the theory breaks down and does not give sensible results---it gives infinite densities or curvatures----and these regions (which don't necessarily have to be pointlike or even bounded) are called singularities.

 

[phreak]

Or if you're less educated than that, we could just say that a singularity is an infinitely small point in space-time.

 

[marcus]

Phreak, you have a great bulk of English usage to support what you say, but I am trying to get a minority point of view heard

Education is not the issue---it's not a snob/reverse snob business.

Singularities really do appear (in General relativity) as rings and infinite volume hypersurfaces, that is to say regions and it really makes it hard for people to understand basics of current bigbang cosmology if they get stuck on the idea that a singularity has to be a point.

One person who gets this right---and who addresses a wide popular audience----is the "Ask the Astronomer" guy, he sells a lot of
Astronomy FAQ books and has extensive samples on the web

check this out:
http://www.astronomycafe.net/qadir/ask/a11717.html

----exerpt---
In an infinite universe...which has always been infinite in its 3-d spatial volume even at the big bang...as you run this collapse back to moments after the big bang, you are still left with an infinite volume to 3-d space, but the density of matter and energy in the neighborhood of each point, becomes infinite. So, unlike the nearly point-like initial 3-d state of the closed universe with its nearly point-like initial singularity, for an infinite universe you end up with an infinite surface which has an infinite density of energy and mass at each point...
---end quote---

my boldface emphasis
he is talking "infinite volume singularity" ----"singular hypersurface"


As for black holes, nearly every black hole in nature must likely have
some degree of rotation and we know that the singularity inside a rotating black hole is not a point

the point singularity is only in the rare case of a perfectly non-rotating hole

so we can say that probably no (or almost no) point singularities exist in nature, in the black hole department

as far as General Rel goes, the point singularity is something ideal in our imagination, not out there in the real world

this is just my point of view on it, there's plenty of room for different takes
and you are welcome to believe that all singularities are mathematical points of infinite smallness if you choose

 

[mathman]

There are solutionsof the equations of General Relativity which are singular, for example inside a black hole. However, on physical grounds (quantum theory) most physicists believe that this (singularity) is unphysical, that is General Relativity is wrong in this extreme case.

 

[ArmoSkater87]

The singularity is very hypothetical. Honestly, i don't think we will ever know if it exists and any of its properties. Since nothing, not even electromagnetic radiation can escape from the singularity...we will not know anything about it. The only thing we can do is hypothesize about what is it and how it behaves.

 

[Dovekie]

Singularity, apparently, can be explained by observing the spinning patterns of a round coin/disk. I found this site that might interest you. Here is the contents below...

Old problem, new spin

Have you ever noticed what happens when you spin a coin on a table? As the coin starts to fall over and roll on its edge, its spin gets faster and faster until it suddenly stops altogether.

This behaviour has posed a longstanding puzzle for mathematicians and physicists. However, Professor Keith Moffatt from the Isaac Newton Institute has come up with a new model that may both explain the spinning coin, and have implications for fields as diverse as aircraft design and meteorology.

Rather than an actual coin, Professor Moffatt used a heavy spinning disk known as Euler's disk as his model. He showed that a thin layer of air between the disk (or coin) and the table is responsible for the accelerating spin. As the disk tips over and begins to settle, it loses energy. However, rather than slowing down it actually speeds up as the energy dissipates.

Theoretically, the disk should spin faster and faster as its energy decreases. Eventually, it would spin infinitely fast as it reached an infinite point known as a singularity.

However, in practice singularities are not known to exist anywhere in our universe except inside black holes. Instead of spinning forever, the disk will suddenly halt.

"The key to it is internal friction in the air. We call it viscosity," said Professor Moffat. "In that final stage as the disc is vibrating above the table, there is a thin cushion of air trapped in there. That's why there is a lot of dissipation of energy and it suddenly stops."

In a paper in the journal Nature, Professor Moffat describes the spinning disk effect as a "finite-time singularity". He believes that his research may be useful in studying turbulence, where finite-time singularities may also occur. Improvements in our understanding of turbulence could help us with a number of tasks, including building better-performing aircraft and more accurately predicting the weather.

"There is a lot of numerical evidence from very high-powered computation that certain quantities become infinite. This is why there is a great deal of interest in this phenomenon in the turbulence community.

"Any fundamental new understanding of turbulence would help improve the predictability of systems. This applies not only to aerodynamics and aircraft design, but also to atmospheric dynamics and weather forecasting."

 

[Dovekie]

Reading back on that article I posted above, I started wondering about the paragraph -- "However, in practice singularities are not known to exist anywhere in our universe except inside black holes. Instead of spinning forever, the disk will suddenly halt."

Instead of spinning forever, the disk will suddenly halt. As these experiments concerning singularity have been conducted on Earth, wouldn't this be due to the pull of gravity? Or does the viscosity of the air underneath the disc somehow resist the pull of gravity, and the only reason it stops spinning is because it runs out of "energy".