[Petrochemicals (OP)]

In a black hole there is a singularity, what exactly is it?

[William Hardy]

singularity definition can be as:
a point in space where the quantities used to quantify the gravitational field become infinite in a way that is independent of the coordinate system.

[evan_au]

In a black hole there is a singularity, what exactly is it?

It is a place where you end up with infinities.

Einstein interpreted infinities as indicating that the equations break down, and it needs a more advanced theory.

There are mathematical tricks that have successfully dispatched many infinities in quantum theory.
- But when it comes to gravity and black holes, the infinities remain stubbornly obnoxious. (in technical terms, the results are not "renormalizable")
- Most physicists believe that we are still looking for a better theory, which can unite General Relativity and Quantum Theory.
See: https://en.wikipedia.org/wiki/Renormalization

[Eternal Student]

Hi Petrochemicals.

  You've had two good answers but they both mention "a place" or "a point in space".
It doesn't need to be a real point or place in the universe.  It's just a point in a more abstract mathematical space.

   The Theory of General Relativity works with objects called "manifolds".   The manifold together with a mathematical object defined on it ("the metirc") is our model of spacetime.   A singularity of the type described by William (above) cannot be included in any manifold,  so to say that another way - it cannot be included in any model of spacetime.

   This leads to two reasonable possibilities:
(i)  The model is limited.
,or else,
(ii)  The singularity is not a real place or point in the universe anyway.

Most physicists go for option (i) believing the singularity must be a real place in the universe but the model breaks down there.   However option (ii) is perfectly reasonable and has to be considered.
    The centre of a blackhole can be identified as a singularity as described by William (above) and therefore it CANNOT be identified as any "point" or "place" in our model of spacetime.
   
- - - - - - - - - -
     

(in technical terms, the results are not "renormalizable")

      Re-normalisation is a very general term that applies to many processes and theories in physics.  There is a better term that specifically refers to removing the singular nature of the metric at some points.  A singularity is said to be "removable" if there exists co-ordinates in which the singular nature of the metirc can been removed.   The centre of a black hole is a non-removable singularity - no choice of co-ordinates can remove the singular behaviour of the metirc here.

More than one singularity:
     Using the most conventional co-ordinates to describe a simple (Schwarzschild) black hole produces a metric that we call the conventional Schwarzschild metric.  These co-ordinates feel quite natural and intuitively seem like spherical co-ordinates centred around the black hole.  This leads us to believe the centre of the black hole would have co-ordinates r=0  and that there is another interesting region called the event horizon which appears to be the surface of a sphere around the black hole with radius r_s.  These co-ordinates are most often used to produce the diagrams and descriptions that you've probably already heard and read about.  The thing is that using these co-ordinates, the metric actually has multiple singularities.  There is the singularity at the centre but the metric is also singular at all points along the event horizon.
    The singular nature of the Schwarzschild metric at the event horison is removable, we can find alternative co-ordinates (for example, Kruskall co-ordinates) where this singular nature is removed.
    When we talk about "the singularity" for a black hole it is taken forgranted that we are talking about the non-removable one.  However, mathematicians will happily call any point where the metric becomes singular, "a singularity", so depending on the co-ordinates you are using there can be multiple singularities for a Black Hole.

[Zer0]

Singularity defines Infinites of What exactly?
🤔
Space & Time?
Speed & Acceleration?
Mass & Volume?

P.S. - Are ECOs & MECOs Real?
(Only Theoretically or in Reality)

[charles1948]

Could a singularity be only a mathematical idea, useful in doing calculations,  but having no physical reality. 

Rather like decimal points. Which serve a useful purpose in distinguishing between, say 75 and 7.5.

But surely no-one would think, that there are actual physical "decimal points" in the Universe.

[Eternal Student]

Hi Zero.

Singularity defines Infinites of What exactly?

    In mathematics, a function is singular at a point if it stops being well behaved at a point.  This applies to any function.
The type of "bad behaviour" being considered here (concerning black holes and the OP question) is that of a function diverging to infinity.
There are several functions that are of relevance here.  We could be considering the metric (which is a tensor valued function), or just a few components of the metric (which are just conventional real valued functions).  I have discussed the situation where such function(s) become singular  - it always happens at (what is thought of as) the centre of blackhole but it can also happen at the event horizon  etc.
William's answer seemed to involve the Riemann curvature tensor (which is another, more complicated tensor valued function defined on spacetime).

The Riemann curvature tensor is derived from the metric tensor, so I will just indicate what the metric tensor is or does.
The metric tensor serves many purposes but one of the easiest to understand is that it tells us how proper distances are measured in spacetime.  The Riemann tensor uses this information to tell us something about the curvature of the spacetime.  Both are therefore telling us something about the geometry of the spacetime.
So when you ask "infinities of what exactly?"  I could offer an answer that it is all about geometry.  At a singularity, there are infinities in some key quantities that describe the geometry.   For this reason a spacetime that includes a singularity cannot be modelled as a manifold under the General Theory of relativity because there is no geometry that could be applied.

  I hope that helps a bit.

[Eternal Student]

@charles1948
    Yes, that's pretty much the idea.
A singularity is a mathematical term, it's describing something about the behaviour of functions.  Physicist's have stolen it and now some people use the term "singularity" as if it's a real place or thing in the universe.

   When mathematician's say "there's a singularity here" they are telling you how functions behave in that region.

   When Physicist's say "there's a singularity here" there are always people who think it's a thing or a place you can find.

[charles1948]

@charles1948
    Yes, that's pretty much the idea.
A singularity is a mathematical term, it's describing something about the behaviour of functions.  Physicist's have stolen it and now some people use the term "singularity" as if it's a real place or thing in the universe.

   When mathematician's say "there's a singularity here" they are telling you how functions behave in that region.

   When Physicist's say "there's a singularity here" there are always people who think it's a thing or a place you can find.

Yes, I think you're right.  Modern physics is getting increasingly led away from physical reality,  into mere mathematical abstractions.  Which look good on paper, but contradict actual experience.

I think this started with Einstein.  His ideas don't make sense as a rational explanation.

[Kryptid]

Which look good on paper, but contradict actual experience.

Example?

I think this started with Einstein.  His ideas don't make sense as a rational explanation.

Just because they don't make sense to you doesn't mean they don't make sense. Experiments and observations have overwhelmingly supported relativity. Something defying common sense does not mean that it is wrong.

[Eternal Student]

Hi Charles.   I hope all is well.
   I can go along with some of what you've said in that last post but not all of it.

     You said -

Modern physics is getting increasingly led away from physical reality,  into mere mathematical abstractions.

    Well that may be true of modern theoretical physics but I shouldn't worry about it.  It's not that practical physics is being lost or forgotten, just that it's getting new names.  New areas and fields of science are developing to take up the ground that is being left behind while the theoretical physicist's do their thing.   We now have well developed fields of study that are called things like "Quantum Information Science" and "photonic systems engineering",  while in the past there were just scientists some of which declared an interest in these areas.

I think this started with Einstein.  His ideas don't make sense as a rational explanation.

   I don't think it (GR) is meant to describe the universe in ways a human being would generally choose to understand it.  However, GR has made many predicitions that have been tested and verified.  It all depends on what you mean by "rational explanation".  It's a luxury if a piece of theoretical physics fits comfortably with how we (human beings) imagine things or seems sensible but it doesn't have to be the only aim.

[evan_au]

Singularity defines Infinites of What exactly?

The singularity can be anything - it depends on what you are measuring (and how).

- In simple theories of aerodynamics, air resistance approaches infinity as you approach the speed of sound.
     - So, in these theories, the speed of sound is a singularity
     - In fact, some guns can fire bullets faster than the speed of sound, so scientists knew it was not a true singularity
     - And eventually, they managed to break the speed of sound in a manned rocket
     - And Concorde became a (loss-making) commercial supersonic service, for quite a while

In special relativity, mass, energy and momentum approach infinity as you approach the speed of light.
     - Our most powerful particle accelerators can get to within a smidgeon of the speed of light, and these quantities do seem to approach infinity as you get closer to c
     - So, to the best of our knowledge, this is a true singularity (Einstein scores 100% again)
     - But a singularity we can never reach, even if we had the energy of a whole galaxy to play with

In current theories of quantum gravity, the energy of empty space approaches infinity near the event horizon of a black hole
     - In my simplistic understanding, these theories attempt to model the virtual gravitons around the black hole, typically in 11 dimensions. But gravitons have a (tiny) energy, and a (tiny) equivalent mass; but there are lots of them.
     - When you add up the gravitational effects of all these virtual gravitons, you end up with a patch of empty space that has infinite mass, which doesn't seem intuitive at all.
     - Physicists are convinced that this is not a true singularity, and there must be an improved theory that doesn't suffer from this fatal flaw.
 

[Zer0]

Hello E.S.!
😊

Thanks Alot for the deep detailed explanations.
👍

Must say, Your grasp on physics is quite Firm.
💪
You are definitely a wonderful addition to the TNS Forum.
😇
Hope & Wish your pleasureable presence here continues uninterrupted.




Hello Evan!
😊
Thank You for clearing out the confusion by providing various examples.
🙏
(Hey! Why'd you stop with the ' Fun Facts '...yours are entertaining & educative)




I did have a follow-up Query...i Always do!
🤭
But it's Unrealistic & a Fictional Fantasy.
Hence, i shall be a good boy n keep quite.
🤫
Anyways, i do Not want P.C.s OP to be moved to ' New Theories ' or
 ' Just Chat '...that would be very unfair n unjust on my part.
✌️
(*Please Note* - i am a layman science enthusiast, i am very poor on technical scientific jargons, hence I'd Request everyone to Not spend Alot of time answering my queries. I'm adapting & learning slowly & shall be at par within a decade. Until then just a few simple words shall suffice, TY!)
🙏



Charles...
Did You Observe how these Gentlemen above gently & eloquently mentioned in a polite manner that " Science " does Not Claim it Knows All!

I feel that's the Beauty of Scientists...they are Bold enough to Accept things, that they are speculative about.


P.S. - " WE do Not know, what We do Not Know "....
Is Prejudice only in the sermonic perspective of Religion..
But in the Reference Frame of Science, it's Pride!

[Eternal Student]

Hi Zero and thank you.

   Sadly, I'm not sure about any long term plans.  I'm still trying to work out what it is that a forum does and what makes people use it (and especially why they keep coming back to it regularly).

    Very briefly (let's not take up the whole thread and hijack the OP), why are you a regular here and why do you spend so much time putting emoticons into everything and appearing to at least glance at everything anyone has written?   Don't say anything that may jeopardise your online safety and of course, you don't to say anything at all.

Best wishes to you.

[Colin2B]

A singularity is a mathematical term, it's describing something about the behaviour of functions.  Physicist's have stolen it and now some people use the term "singularity" as if it's a real place or thing in the universe.

When talking about music B.B. King said "I don't think anybody steals anything; all of us borrow” 

Could a singularity be only a mathematical idea, useful in doing calculations,  but having no physical reality. 

Rather like decimal points. Which serve a useful purpose in distinguishing between, say 75 and 7.5.

But surely no-one would think, that there are actual physical "decimal points" in the Universe.

Science uses maths and so borrows a lot of ‘idealised’ concepts from it. Yes, they are useful for doing calculations, but often they are there because they genuinely describe how something behaves.
Take the earth-moon system. Under Newtonian gravitational theory both the earth and moon behave as point sources of gravitational field and very accurate calculations can be done on that basis. True, no one would think that either is actually a dimensionless point, but they behave as if they are under that model.
(That’s an easy one to understand, but there are examples in GR and QM where people take an interpretation used for calculating and assume it represents something it was never intended to).
Most of physics is based on models and we can describe an electron (in one model) as a point particle, meaning that its mass and charge seem to originate from a point. So, a point is just a mathematical construct/concept, but does that mean the electron doesn’t exist in ‘reality’ - as you often seem to doubt?
To me something is real if it has a consistent, repeatable, predictable effect, whether or not that effect is on our direct sensors or on mechanical/electrical devices.

Yes, I think you're right.  Modern physics is getting increasingly led away from physical reality,  into mere mathematical abstractions.  Which look good on paper, but contradict actual experience.

I think this started with Einstein.  His ideas don't make sense as a rational explanation.

When you talk of rational explanation (or often, the common sense view) you are talking about things which are rarely what they seem.
What about the rational explanation that the sun goes around the earth? Seems rational and common sense so why do these idiot scientists go on about the earth going round the sun? Surely that can’t be true?
The important thing to remember about Einstein is that if you take the trouble to understand what his theories really say, you will find that they are very rational. These are not just ‘look good on paper’, they are also shown to be more accurate than Newton’s theories, by measurement. Just because they don’t line up with our daily experiences doesn’t mean they don’t make sense - but you do have to make the effort to find out rather than dismiss at a cursory glance.

PS:
When mathematician's say "there's a singularity here" they are telling you how functions behave in that region.
When Physicist's say "there's a singularity here" they are telling you how a ‘thing’ behaves (or is thought to behave) in that region.

[jeffreyH]

One apple picker, picks 10 apples. You have ten pickers. Each picks the same amount. Therefore 10 pickers times 10 apples each equals 100 total apples. Now you have an unlimited number of apple pickers. Each successive picker picks one more apple than the last. Since the number of pickers unlimited there are infinite pickers. This leads to an infinite series of apple pickers and an infinite sum that diverges to infinity. Here we have a singularity.

[Eternal Student]

Hi JeffreyH.

   It just sounds so sad the way you say it.   Apples and infinite sums not working. 
What we need are places where algebra breaks down,  maybe places where the metric tensor changes it's signature,  functions like      that do amazing things like chase off to positive infinity only to re-appear from  the negative infinty direction.
   Come on, you've got to sell this stuff.  This is Maths not Physics,  we don't have   pew pew lasers or things like that,  just a hope that people can bend their minds to consider that +infinity is no distance away from - infinity.

[evan_au]

I don't think anybody steals anything; all of us borrow

A somewhat more metaphorical borrowing of "singularity" is in discussing Artificial Intelligence.

This is the hypothesis that AI systems could one day be smart enough to (successfully) reprogram themselves to make themselves "smarter". Then the smarter AI could work out how to make itself even smarter, leading to a runaway explosion of AI capabilities that humans could not possibly understand or control. This comes with the fear that such an AI may wipe out humans without a thought, just like a human might step on an ant without even noticing it.

We today are becoming more familiar with exponential growth in semiconductor chips and pandemics.
- But a true singularity grows far faster than exponential growth - a singularity reaches infinity in a finite time; unconstrained exponential growth reaches infinity, but it takes forever to get there...
- There are finite limits to the efficiency of computation, so a computer with a finite power supply can't really reach infinite computation speed
- But it is possible that an AI could become so powerful that we have no way of comprehending or measuring it; so, metaphorically, it may as well be infinite...

See: https://en.wikipedia.org/wiki/Technological_singularity

[Eternal Student]

Hi evan-au.

   The AI singularity would actually fit quite well into another discussion,  "Do we have enough safeguards for the advancement of science"   https://www.thenakedscientists.com/forum/index.php?topic=79672.0.   ^{(For which the answer is obviously no).}
    Anyway, it is an interesting use of the term "singularity" and I've seen and read snippets of information that there are supposed to be some "agreed" restrictions on what can be done with AI systems.  "Agreed" in the same sort of way that there are international agreements about pollution that always work well.

[Zer0]

Hello P.C.!
🙏
Sorry I'm having a lil personal talk in your OP which isn't in anyway related to the subject.
E.S. & i have tried contributing positively, hence Please do not mind & let this message pass as a one time favour.
Thank You!
🙏
(Will not continue this)

Hi Zero and thank you.
Hi again E.S.!
🙋
& You are most Welcome.


   Sadly, I'm not sure about any long term plans.  I'm still trying to work out what it is that a forum does and what makes people use it (and especially why they keep coming back to it regularly).
hmm... perhaps brainstorming, collective thinking, or simply learning something new & sharpening one's intellect.
🌪️🧠🌪️


    Very briefly (let's not take up the whole thread and hijack the OP),
totally agree!
🏴‍☠️
Hope P.C. doesn't make Us walk the plank in here.


why are you a regular here
cuz i simply LuV this place. It seems like a school, without Teachers...complete Freedom to learn any subject of your choice, no fees, recess anytime & No grades.
🏰


and

why do you spend so much time putting emoticons into everything
cuz i really Like doin it.
🙃
I'm not entirely sure why thou.
🤔
My E.Q. is waay too high, overshadows my I.Q.
🤭
(U know, thru my frame of reference, i kinda wonder why noone does that)


and

appearing to at least glance at everything anyone has written?   
yaa...i read almost everything in here. Just sheer curiosity.
🧐
Perhaps when one takes one's curiosity to extremes, then it bcums like a disease, to know et al.
Uncontrolled curiosity is sheer madness.
👻

Don't say anything that may jeopardise your online safety and of course, you don't to say anything at all.
online safety...ha ha!
No system is hack proof.
Nobody is safe.
It's just a matter of time.
I'm not bothered much, cuz I've hardly got anything to lose.
👍
(Just last week i was at the loo suspecting my landlady has set up a wifi eye piece inside an empty bulb holder.
After finishing my business, i got a stool & stood up n checked the damm holder, good thing i didn't get shocked... physically nor mentally.
Now whenever i go, i think bout it, n giggle...i mean even if she really had, what the heck would she have recorded anyways, me taking a dump...lol...surely that's not an entertaining or pleasureable site.)
🚽
 

Best wishes to you.
Best Regards,
0.

p.s. - this is another disease or mental disorder. The ps thing.
Perhaps, any repeated Action turns into a Habit.
Keep at it & it turns into an Addiction!
🖖