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What is a singularity?

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When talking about the origin of the universe and the big bang what does a singularity mean?Is it an event,an object.....

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Don't quote me on this, Gerry but I think Gravitational Singularities (as opposed to the notion of Artifical Inteligence Singularities) are predicted by Einstein's theory of general relativity. That if you compress a body of a given mass down to a sphere of radius which is smaller than its Schwarzschild Radius, effectively creating a situation where all the mass of the given object is compressed within that sphere, then the escape velocity of such a body (the speed needed to break free from its gravitational attraction) would exceed that of the speed of light. By all accounts, Black Holes and the Big Bang have this property. Whether this can be emprically tested or not is an open question, for although our best and well tested theories point in the existence of singularities, the very nature of a black hole, for example, means that we may never actually observe such a singularity due to not being able to see past the event horizon where information in the form of light cannot escape.

Hopefully, someone with more knowledge on this will come along.

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When talking about the origin of the universe and the big bang what does a singularity mean?Is it an event,an object.....

No-one really knows. General relativity breaks down and gives an 'infinite' result. The simplest treatment of singularities is to think of them as regions of zero  volume and hence infinite density. This prescriptive description is unlikely to be physically meaningful and is at variance with a quantum mechanical view of the universe.

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While black hole (gravitational) singularities get the most press, they actually crop up in other areas of physics. A mathematical singularity is a point where the maths breaks down, in the case of physics this is thought to happen because the theory is only an approximation of reality.

To take a simple example, imaging water spiralling down a drain. The closer the water is to the centre the faster it is swirling, its speed being inversely proportional to the radius of the whirlpool. This results in a singularity, as the radius approaches zero the speed of the water approaches infinity. The real world doesn't behave like this - this means our simple theory of drains is not applicable for very small radii.

There have been attempts to solve the black hole problem using quantum physics. For example, the string theory treatment is called a Fuzzball, and has no singularity. However, it's very difficult to verify whether this description is correct - from a distance, a Fuzzball would look just like a classical black hole.

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To give a slightly different insight when physicist talk about singularities. Think of singularities as situations where equations show undefined behaviour.  For example in special relativity you have terms like 1 / sqrt(1 - (v/c)^")  as v approaches the value of c, the speed of light, you can see you get a divide by zero condition, in infinitely big number that is not defined.

A fairly simple video, seeing black holes were mentioned, with a very elegant but simple mathematical walkthrough can be seen here

Taking a step aside and thinking of something simple,  the classic example I  would always give back in tutoring days is a function like y =  1 / x. Draw this graph in the interval {-1, 1). to show why it breaks down.

See what happens when you draw the graph starting from the left point on the negative side of the x axis, you'll see that y tends towards - infinity, it just gets bigger and bigger, but in the negative direction !. Now perform the same exercise drawing the graph starting from the postive side for  x > 0. In this case as x goes towards 0 y tends to + infinity. 

How can that be, at zero you can even get two answers + or - infinity. this is a singualrtiy of an even worse kind compared to the special realtivity case above.  In any case, in both situations we get garbage, the rules break down. The only thing we can say about this system is that at the point 0 there is no meaningful answer/number.  

On a sidenote, A mathematician would even argue that writing in this case 

lim x -> 0 for  y = 1 / x = inifinity

is a sin.  Writing something like lim x -> 0+ for y = 1 / x = +inifinity and similarly for the negative side is a better way to state the problem in this situation.

Edited by AlexB67
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Thanks for the great info.Very interesting to think of a singularity in terms of where the math breaks down at some point,I've always thought of one like Qualia's info does (excellent,new info for me in there-thanks).Are there cosmological singularites that don't involve a Shwarzschilds Radius?Is it is possible for energy to "create" matter under the right circumstances in "space" or a "space vacuum"?

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To give a slightly different insight when physicist talk about singularities. Think of singularities as situations where equations show undefined behaviour.  For example in special relativity you have terms like 1 / sqrt(1 - (v/c)^")  as v approaches the value of c, the speed of light, you can see you get a divide by zero condition, in infinitely big number that is not defined.

A fairly simple video, seeing black holes were mentioned, with a very elegant but simple mathematical walkthrough can be seen here

Taking a step aside and thinking of something simple,  the classic example I  would always give back in tutoring days is a function like y =  1 / x. Draw this graph in the interval {-1, 1). to show why it breaks down.

See what happens when you draw the graph starting from the left point on the negative side of the x axis, you'll see that y tends towards - infinity, it just gets bigger and bigger, but in the negative direction !. Now perform the same exercise drawing the graph starting from the postive side for  x > 0. In this case as x goes towards 0 y tends to + infinity. 

How can that be, at zero you can even get two answers + or - infinity. this is a singualrtiy of an even worse kind compared to the special realtivity case above.  In any case, in both situations we get garbage, the rules break down. The only thing we can say about this system is that at the point 0 there is no meaningful answer/number.  

On a sidenote, A mathematician would even argue that writing in this case 

lim x -> 0 for  y = 1 / x = inifinity

is a sin.  Writing something like lim x -> 0+ for y = 1 / x = +inifinity and similarly for the negative side is a better way to state the problem in this situation.

Alex thanks for taking the time on this,when I have time I will watch this and go through the math to get a better handle on mathematical singularities-this sheds a very new light on this subject for me.

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I am not sure that there is a completely accepted technical definition of "spacetime singularity". There is, however, a reasonably generic definition of "singular spacetime". Singular spacetimes have "edges".

Roughly, a spacetime is singular if there is a path that a rocket with a finite amount of fuel could traverse that is either inextandable  at some finite (wristwatch) time in the or at some finite (wristwatch) time in the past.

Inextendable in the future. because the rocket falls "over the edge and off of spacetime" and "into the singularity", e.g., inside a black hole.

Inextandable in the past, because the rocket materializes "over the edge and onto spacetime" and "off of the singularity", e.g., "at" the Big Bang.

By the Penrose-Hawking singularity theorems, many "reasonable" classical spacetimes must be singular. Very roughly, in any "reasonable" classical spacetime, gravity is so stong that the fabric of spacetime gets ripped, thus creating an "edge".

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I can only assume a big bang singularity and a standard black hole singularity must be quite different? .. otherwise nothing could have escaped a big bang singularity?

Although not knowing where the universe came from or how it came about before the bang (for lack of a better word) I would think means we can't really say it began with a singularity?

Edited by Cath

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I can only assume a big bang singularity and a standard black hole singularity must be quite different? .. otherwise nothing could have escaped a big bang singularity?

Yes. A black hole singularity is in the future, and is clothed by an event horizon. The Big Bang singularity is in the past, and is naked.

Although not knowing where the universe came from or how it came about before the bang (for lack of a better word) I would think means we can't really say it began with a singularity?

Singularities really represent our provisional state of knowledge. Our theories break down "at" spacetime singularities. Better theories might not break down at these "places and times", but they will still likely breakdown somewhere, i.e., new theories should apply to all the situations covered by present theories, and to situations that our present theories can't handle, but not to all situations. The British astrophysicist John Barrow wrote

"Time and time again, the development of our most powerful theories has followed this path: ... then something unexpected happens. The theory predicts that it cannot predict: it tells us that there are things that it cannot tell us. Curiously, it is only our most powerful theories that seem to possess this self-critical feature. ... I believe that we can expect to find more of these deep results which limit what can be known."

I take the optimistic view that this means that progress can always be made.

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A singularity means a point where some property is infinite. For example, at the center of a black hole, according to classical theory, the density is infinite (because a finite mass is compressed to a zero volume). Hence it is a singularity. Similarly, if you extrapolate the properties of the universe to the instant of the Big Bang, you will find that both the density and the temperature go to infinity, and so that also is a singularity. It must be stated that these come due to the breaking down of the classical theory. As yet, there is no theory of quantum gravity, but it is entirely possible that the singularities may be avoided with a theory of quantum gravity.

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The replies are really helping me understand what a singularity is or can be,I honestly never realized what they are-I had a rigid model in my mind that I knew must be flawed.The explanation of the math involved has shown me how the theories "break down" at some point,which for me adds logic to a subject composed of so many theories.I do give much credit to those developing and interpreting such theories-they (you?) obviously understand the math involved,but not all of us do.Thanks again for helping me understand.....

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