Origin of the Universe

[Chattiestspike2]

Wwhen it comes to the origin of the universe, or the singularity from which the expansion started, what is the going idea of the origin of the singularity?

When it comes to quantum fluctuations and quantum mechanics and the uncertainty principal, as far as I'm aware, particles can virtually pop into existence from nothing. I recently watched a video on Best0fScience's channel and, to my humbling, saw some scientists discussing how the universe could have came into being from that same kind of quantum fluctuation. So if this is the case, would that not mean the the universe "came from nothing?"

I don't completely buy it- that the universe "came from nothing" because I do feel that there is more that I need to know. Is there any insight that anyone would be able to share with me on this? Thanks

 

[borrofburi]

Wwhen it comes to the origin of the universe, or the singularity from which the expansion started, what is the going idea of the origin of the singularity?

Quantum foam energy stuff.

I don't completely buy it- that the universe "came from nothing" because I do feel that there is more that I need to know. Is there any insight that anyone would be able to share with me on this? Thanks

Well, when you get right down to it: either something has always existed, or something came from nothing. Both of which are very uncomfortable ideas.

 

[KuiperKitten]

Then again, when you get down to these levels, concepts like nothing, existence, time and origin don't mean a whole lot. The only way that we can get a hold of the beginning/origin of the universe until now is through mathematics and we will have to develop a whole new way of thinking and an appropriate language to interpret and talk about what the math suggests.

 

[AndromedasWake]

Wwhen it comes to the origin of the universe, or the singularity from which the expansion started, what is the going idea of the origin of the singularity?

There is no origin to a singularity, it's not physically meaningful. The popular idea of the Universe being birthed from a singularity is down to a failure of communication by scientists. A singularity is simply a region of undefined solutions in a set of equations. In the case of the BB, it's a gravitational singularity, or a singularity occurring in the mathematics of gravity (General Theory of Relativity.)

A singularity is NOT an infinitely dense object, or infinitely small volume. It has no physical meaning at all. For this reason, scientists recognise when a mathematical model encounters a singularity, as GR does in the past, it illustrates that the model is incomplete and unable to explain something. Therefore, scientists chase methods of 'singularity avoidance'. Many of these gained ground when inflation hit the scene, but recent work as shown that these models probably can't do the job on their own. As such, some kind of extension to the theory is required.

It has long be known that quantum mechanical events must play a significant role in the Universe's earliest moments, because on a small scale they are significant, and the entire scale of the Universe used to be smaller than a proton (although that's a bit of a misnomer, a proton can't really be said to have any physical extent.)

There is a growing trend for scientists to modify Einstein's formulation of GR (yep, his is still the most popular despite many others over the last 95 years) and introduce quantum effects to see how the Universe behaves when it's tiny. Remarkably, it is possible in some of these models for the Universe to be born from some kind of quantum nucleation event and rapidly expand immediately afterwards.

This says virtually nothing about the nature of the 'thing' that was there before the Universe, except that certain quantum mechanical preconditions must be place. We can't use the colloquial meaning of nothing to describe this domain - it is still something. Chaotic inflation models predict that such events can occur anywhere in the Universe under certain conditions (which arise on a probabilistic basis) which might imply that our Universe was born inside another one, with a completely different set of dimensions (in some cases, time-like dimensions don't even need to be there, the wider Universe can be eternal.)

Large numbers of Universes might be appearing all the time, each inside another. This is quite a popular hypothesis, but it's largely conjecture and speculation so don't get carried away. The scientific consensus on how the initial state of the Universe came to be is "we really don't know, we've only been looking into it for a few decades, give us a break!"

When it comes to quantum fluctuations and quantum mechanics and the uncertainty principal, as far as I'm aware, particles can virtually pop into existence from nothing. I recently watched a video on Best0fScience's channel and, to my humbling, saw some scientists discussing how the universe could have came into being from that same kind of quantum fluctuation. So if this is the case, would that not mean the the universe "came from nothing?"

I don't completely buy it- that the universe "came from nothing" because I do feel that there is more that I need to know. Is there any insight that anyone would be able to share with me on this? Thanks

When these physicists talk about nothing, they are talking about something. Nothing isn't nothing at all in physics. Indeed, there is no scientific definition of nothing. It's part sloppy language, and part an attempt to impress the public. See above, the Universe can be born from almost nothing, but certain conditions must be in place. In physics, energy, the laws of physics, quantum preconditions have no known origin. They are effectively treated as being eternal. Even though scientists frequently talk about a finite universe with a finite age, they all recognise the agnostic nature of physics toward the origin of reality itself. Reality is considered to be eternal and that serves scientific enquiry perfectly well.

You can do all the philosophy you want on the origin of reality, using metaphysics, but it's largely pointless and isn't going to convince most people of anything unless they have a need to justify a belief (see William Lane Craig and his followers.)

Here's something to bear in mind. Physics is the study of the observable world. Metaphysics is the philosophy of the intuitive nature of reality. We already know from physics that some very real things are completely counter-intuitive, so why would anyone put so much faith in metaphysics, which is limited by our intuition?

 

[Chattiestspike2]

Thanks AndramedasWake. This is a bit more englightening. Since I came across that video, I also watched a video by Lawrence Krauss where he does in fact explain things to full detail mentioning the very ideas that you put forth in your post.

A quote from him that stuck with me is "as long as you have nothing while quantum mechanics is applied, you will always get something." This isn't verbatem but close enough. And in light of this, the idea of the universe coming from "nothing," which isn't exactly the same kind of nothingness that the average person percieves (based on how Krauss explains it), it does tend to make more sense in my mind. Appearently, I also had a flawed interpretation of the singularity. It can't be infinitely dense because there is a finite amount of matter and energy in the universe. I remember from, I think it was your first CRAP Debunked video, that you said that it started at zero volume. This idea is hard to wrap my mind around because it does sound like essentially "nothing" but it is "something" which is taking up no space.... "space" being used in a very light sense because I understand that real space was also inside the singularity.

Thanks for clearing that up for me. I'm bound to have more questions in the VERY near future, but as of now, I'm satisfied.

 

[Master_Ghost_Knight]

I do agree, the term sigularity is extremely poorly understood, I have the impression that many people erroneously believe that a singularity is actualy a physical object, it isn't, it is mathematical object to describe a particular proprety with the equations.
It think it would help nail this issue by presenting other examples of singularities. For instance an electron can be described as a singularity in the analysis of electrical fields (a point with an undefined value on the field equation). Or for instance using a controler (like a autopilot) with a state space model can be analysed in terms of stability or even response to a certain interference by the positions of the sigularities of the transfer function (popular academic myth: give me the transfer function of the universe and I will calculate everything you want to know about it on the back of my hand). You can isolate the effects of each by the residue theorem. Let me give you a mathematical formula and show you how it looks like.
Ex.

Defined in the complex plane.
The singularities in this case are the points that makes the function undefined. For instance the point zero is a singularity in this equantion, because if you make Z=0 you get something of the sort 1/0 which is undefined. This function has an infinity of singularities for the points in 2pi*k*i (imaginary for k interger).
which makes the term (1-e^Z) zero. Every other point in that function you can get a value, you can calculate and say "in this point this function worts this", on the singularities you can't do that, you simply can't get value.
This singularity is know as a pole type singularity, this singularties have a particular relations to another construct of similar kind called "Zeros" (but zeros are points that have a defined value zero prety straigh forward) which is also important in describing how the function behave, if you have a system that allows you locate the positions of the zeros you can even cancel out the singularities and simply remove them altogheter. There are other types of singularities that doesn't tend to infinit in the vicinity (and as a residue of zero), and even tough they are undefined and doesn't realy have a atributable value directly from the equation, you can use the proposition of continuity to remove them altogheter and be able to atribute a concrete value to them without any issue (also known as removable singularities).

I can not tell you what type of singularity the equation for the big bang present since I am not an expert on the subject (i just know the math of what is a singularity and how they work), and neither I am able to tell if they use a continuos model equations or quatum equations (because depending of the cases the problems maybe dramatically different or not).
Any speculationf what it is is unfounded not only because there is a tremendous missunderstanding of what a singularity is but also because a singularity is simply undefined, it simply doesn't give you an answer because the equation screws up, as far as I know the answer to the our section of the universe might literaly be 42 (if you can remove the singularity by some mathematical gimmic, even tough I don't think that is going to be the case or else I would be confident that they would have done that already by now). It is also very likely to be what Andromedas has said, the model might just be incomplete.

 

[JustBusiness17]

A singularity is NOT an infinitely dense object, or infinitely small volume.

Couldn't it be both? Isn't 0 equal to 0? When you divide nothing by everything isn't it still nothing? I mean, in order to explore what nothing really means, wouldn't you have to look at it on an infinitely small scale? In other words, things are infinitely possible within nothing?

 

[Master_Ghost_Knight]

Couldn't it be both? Isn't 0 equal to 0? When you divide nothing by everything isn't it still nothing? I mean, in order to explore what nothing really means, wouldn't you have to look at it on an infinitely small scale? In other words, things are infinitely possible within nothing?

Not really.
Firstly a singularity is not a zero, a zero has a specific value and it's value is zero. A singulrity on the other hand doesn't.
I have given you an example of singularity. F(x)=1/x for x=0 is a singularity, the division by zero is simply not defined in mathematics. You can say, hey it is infinite, but then you would be wrong because if you aproach thefunction from the left it is tends to -inf if you aproach it from the right it tends to +inf.
If you take a sligtly different equation G(x)=1/x^2 the limit when x=0 tends twards +inf on both sides, but on the other hand if you have H(x)=1/-x^2 then the limit has x=0 on both sides is -inf. F(x), G(x) am H(x) are all 1/0 has x=0.
Let's take for instance another function F(x)=x/x, you can see that for x=0 you got something of the sort 0/0 which is also undefned and it is also a singularity, but this singularity has a particular proprety that the limit of F(x) as x=0 from both sides is equal to one and the residue of this function is also zero, in this particular function you can call that by continuity this singularity has a defined value and it is 1. If you had instead G(x)=5x/x then this singularity would be 5. if you had H(x)=x^2/x the limit for x=0 is 0 on the other hand I(x)=x/x^2 the limit has x=0 is undefined (inf on the right -inf on the left). And F(x), G(x), H(x) and I(x) are all 0/0 for x=0. Undefined just means undefined, thats it.

 

[TheBerserk]

This question fascinates me, as someone with no credentials to speak of at all.

The same people who seem to attack those who are attempting to understand the universe never seem to try and understand what they were before they were conceived.

If they think they were conceived for a reason, I suppose that is an idea, though wouldn't everyone have been conceived for a reason? If this is the case then shouldn't the squirrel dying during hibernation also have a reason etc etc.

If it all has reason, then what is the reason for a god caring whatsoever. If indeed there is a god I don't believe he cares, and I actually mean that in the most positive of ways. Yes I do believe that is positive.

I know nothing of philosophy and honestly know nothing about science other then what I see on vids and remembering textbooks from a crap highschool.

Infinity scares everyone I think. No one wants to die and be gone forever, but where were they before then? There's no answer really, unless you believe in reincarnation. (btw if there is a belief system that makes a modicum of sense on this it would have to be that) Though that would end up with the infinite as well,

Infinity is spooky shit, but so were werewolves, witches and vampires once. (I'm not equating reality vs superstition btw........just the fear)

Shit! I get spooked watching simulations showing Andromeda colliding with the Milky Way, and I know there's no chance it will happen in my lifetime. I get spooked seeing "the size of things in the universe video. I also got spooked on LSD and shrooms..........and when I was five years old "the creep show" scared the shit out of me.

Humanity, in so many ways, is still the scared child we all were once and still are. Though aren't we all glad we know Freddy, Dracula etc etc don't actually exist?

Generations from now, I think, children will think we were pussies for being scared of what were spooked of now.





I hope

 

[simonecuttlefish]

Its easy DUMMEH!

Once upons a times, teh big magics GOD thought, "I'm gunna makes me all this stuffs, so I cans intimidate and tortures them all into loving me for doings it - or I will kills thems all! Several times!" So he spent 6 days makings all the things and stuffs and was so good at it he was prefect and it was all good and lovelies! But some silly duffa put a tree with a talking snakes that had arms and legs in it and fruit that could make you know things like GOD if you ate it! And the only two people in the teh world DID eats it and fell down or somethings, and then we all got sick with diseases and had sex with our children and cousins and nieces and nephews to makes more peoples and lions started eating meat and the dinosaurs like T-REX started killing things rather than being a grass eating lovely friends!

Are yous dum or sumthings?

 

[Deleted member 619]

Infinity scares everyone I think. No one wants to die and be gone forever,

A bit of a sweeping generalisation you have there. Firstly, infinity, in physics, simply means 'a really big number', and doesn't actually correlate to a specific value. Secondly, not everybody likes the idea of eternal life. For me, the idea is pretty horrible. That's not to say that I look forward to death, but I certainly don't want eternity. A reasonably long, vigorous life is plenty for me. In fact, it's the finitude of life that makes it interesting.

unless you believe in reincarnation. (btw if there is a belief system that makes a modicum of sense on this it would have to be that)

Not really. There's nothing that makes sense in any conception of reincarnation or, at least, not to anybody who understands what the self really is.

 

[simonecuttlefish]

@ Chattiestspike2
I assume this is the video you mentioned. Totally out of my reach but interesting none the less.

'A Universe From Nothing' by Lawrence Krauss, AAI 2009

 

[TheMaw]

The Lawrence Krauss video is incredibly interesting, plus his, "The Stars died for you" really is rather poetic. It's just a shame he was only given an hour since there was many other interesting points he wanted to make but couldn't.

And thanks AndromedaWake and Master Ghost Knight for those enlightening answers. I have to wonder though, why do scientists say "Nothing" when they actually do mean something when talking about Cosmogony and Cosmology to the public?

 

[AndromedasWake]

The Lawrence Krauss video is incredibly interesting, plus his, "The Stars died for you" really is rather poetic. It's just a shame he was only given an hour since there was many other interesting points he wanted to make but couldn't.

And thanks AndromedaWake and Master Ghost Knight for those enlightening answers. I have to wonder though, why do scientists say "Nothing" when they actually do mean something when talking about Cosmogony and Cosmology to the public?

It's probably mostly to make the subject mysterious, and because when people think of something, they think of matter. When Krauss called his talk 'A Universe from Nothing' he was appealing to the physicist's version of nothing, in which quantum preconditions must still exist. In a crude way, the laws of physics must transcend the physical Universe, and if those laws can be said to be derived from a material substance, that substance must exist 'before' the Universe.

For example, the Heisenberg Uncertainty Principle predicts that vacuum fluctuations will occur, because it requires that for very short times a region of space be allowed to possess much more energy than its surroundings. Energy bubbles around all over the place, giving rise to pairs or particles. Suppose the initial energy state of a region of space is zero, but briefly it borrows energy from the HUP and triggers and inflation event (which the eventual inhabitants look back at and think of as a big bang). The initial state is absent of matter and radiation, but is it nothing? Most people kinda think so, or will believe it is if you tell them. What about the HUP though? Where did that come from? What is the substance of physical law? Rather than try to explain whether nothing is something or not, I prefer to tell people "This is the Big Bang, anything beyond this is highly speculative". I'm a professional science communicator, so I have to be responsible, whereas Krauss is an astrophysicist and can do what he wants!

Also, don't forget that he's addressing an atheist audience in that talk, and perhaps that's what the majority of atheists want to hear. Although he talks about valid hypotheses, they aren't by any means consensus in the same way the Big Bang and expanding universe scenario are.

In cosmogony, the level of abstraction used by scientists to discuss their theories is often so great that their peers can't really get to grips with it. Some suggest that what we have is already a grand theory (say, General Relativity) with ultimate predictive power, and we just haven't found the right solution yet. Others (including me) maintain that current physics will have to be extended, or a major paradigm shift will occur before we can build valid models of cosmogony.

 

[TheMaw]

Ah I see. Thanks again.

 

[borrofburi]

A singularity is NOT an infinitely dense object, or infinitely small volume.

Couldn't it be both? Isn't 0 equal to 0? When you divide nothing by everything isn't it still nothing? I mean, in order to explore what nothing really means, wouldn't you have to look at it on an infinitely small scale? In other words, things are infinitely possible within nothing?

Yes but a singularity has volume and density, probably. The thing with singularities is that our normal models break down; in junior high they taught us (err me) that gravity had overcome the electromagnetic force and all that matter compressed into a point, but we don't actually have any reason to think that is precisely what happens (and indeed, I think we have reason to think that is *not* what happens).

It's probably mostly to make the subject mysterious, and because when people think of something, they think of matter. When Krauss called his talk 'A Universe from Nothing' he was appealing to the physicist's version of nothing, in which quantum preconditions must still exist. In a crude way, the laws of physics must transcend the physical Universe, and if those laws can be said to be derived from a material substance, that substance must exist 'before' the Universe.

And as such we necessarily can not possibly get evidence of what came "before". The concept of "before" is simply meaningless.

 

[Deleted member 619]

Yes but a singularity has volume and density, probably.

Hmmm. I must take exception to that. The classical view of a singularity (which has not been established, it must be said) has not volume, being essentially a superdense, supermassive point. It certainly has density, which is, to all intents and purposes, infinite.

All of this with reference to the fact that infinity is not actually a quantitative number, but just means 'really, really huge. No, bigger than that. I mean, you might think it's long way to the chemist's, yada, yada...'

The thing with singularities is that our normal models break down

And that's the real point. It may be that the classical view of a singularity is true (it hasn't yet been falsified), but what it really means is that our models render infinities, or numbers beyond our ability to comprehend. If we can't comprehend the numbers, we can't model them. This is precisely the definition of infinity used in physics. Indeed, this is the big barrier to any evidence of string theory, although the unification under the rubric of M-Theory has yielded some promising lines of enquiry.

in junior high they taught us (err me) that gravity had overcome the electromagnetic force and all that matter compressed into a point, but we don't actually have any reason to think that is precisely what happens (and indeed, I think we have reason to think that is *not* what happens).

One of the problems here is that what is taught at various levels is ever more sophisticated models or, as Terry Pratchett labelled them 'lies-to-children'. He wasn't being pejorative when he called it that, he was simply pointing out that what we teach at various levels of education is not the truth, but ever-closer models of the truth, built to garner easier understanding when you reach the next level. In this instance, the separation of the forces (gravity hasn't been properly included in this as yet) was not actually a separation, but a separation of values. The forces didn't actually emerge from a single force, but their values began to separate. In other words, the forces were always separate forces, but had the same or similar values, and when the density and temperature had cooled sufficiently, the values of the forces began to diverge, so that they could actually be distinguished.

And as such we necessarily can not possibly get evidence of what came "before". The concept of "before" is simply meaningless.

That sounds a good deal like a categorical statement, in my opinion. At least one of the models currently on the table for cosmic instantiation is, in principle, testable. if experiments yield the predicted results, we may be a good deal closer to determining what came before. It is not remotely clear that time began at the big bang, and until that is categorically determined, it's impossible to say what we can learn about what went before. If time did exist before the big bang, and there aren't many cosmologists left who really think that it did, then the concept of 'before' is anything but meaningless. I'll leave you with some words from the father of inflationary theory:

So far, it's been made to sound, I think for the purposes of simplifying things, that until the cyclic model, all scientists had believed that the big bang was the origin of time itself. That idea is certainly part of the classic theory of the big bang, but it's an idea which I think most cosmologists have not taken seriously in quite a while. That is, the idea that there's something that happened before what we call the big bang has been around for quite a number of years... In what I would regard as the conventional version of the inflationary theory, the Big Bang was also not in that theory the origin of everything but rather one had a very long period of this exponential expansion of the universe, which is what inflation means, and, at different points, different pieces of this inflating universe had stopped inflating and become what I sometimes call pocket universes.

He goes on to say:

What we call the Big Bang was almost certainly not the actual origin of time in either of the theories that we're talking about. "¦ The main difference I think [between the inflationary theory and Neil and Paul's theory] is the answer to the question of what is it that made the universe large and smooth everything out. "¦ The inflationary version of cosmology is not cyclic. "¦ It goes on literally forever with new universes being created in other places. The inflationary prediction is that our region of the universe would become ultimately empty and void but meanwhile other universes would sprout out in other places in this multiverse.

 

[Master_Ghost_Knight]

I am a bit disapointed whit the way this turned out, I have writen a somewhat tricky text to try and show you what an actual singularity means while stil be acessible (even tough I have screwed up a bit on the acessible part). I have given several examples of singularities, stressed that a singularity is not a physical entity but exclusively mathematical one. Then you grabed all that, throw it in the bin and claimed exactly what I have said not to.
The equations don't break down because of the singularity, the singularty is the equations screwing up in a specific maner.
What the hell is classical singularity? And how can it be shown to be true when the answer is NAN?

And I am partialy guilty in this since this is an engineering aproximation, since when is infinity equal to a very large number? Yeah, in some situation when we mean infinity it is just a careless way to adress a rough estimate of a unpratically large number (i.e. for all aplications it might as well be infinite and simplify the analisis), but apart from those situation infinity does literaly mean infinity.

If at least I can clean up this missconceptions I will become quite happy.

 

[Chattiestspike2]

Couldn't it be both? Isn't 0 equal to 0? When you divide nothing by everything isn't it still nothing? I mean, in order to explore what nothing really means, wouldn't you have to look at it on an infinitely small scale? In other words, things are infinitely possible within nothing?

Not really.
Firstly a singularity is not a zero, a zero has a specific value and it's value is zero. A singulrity on the other hand doesn't.
I have given you an example of singularity. F(x)=1/x for x=0 is a singularity, the division by zero is simply not defined in mathematics. You can say, hey it is infinite, but then you would be wrong because if you aproach thefunction from the left it is tends to -inf if you aproach it from the right it tends to +inf.
If you take a sligtly different equation G(x)=1/x^2 the limit when x=0 tends twards +inf on both sides, but on the other hand if you have H(x)=1/-x^2 then the limit has x=0 on both sides is -inf. F(x), G(x) am H(x) are all 1/0 has x=0.
Let's take for instance another function F(x)=x/x, you can see that for x=0 you got something of the sort 0/0 which is also undefned and it is also a singularity, but this singularity has a particular proprety that the limit of F(x) as x=0 from both sides is equal to one and the residue of this function is also zero, in this particular function you can call that by continuity this singularity has a defined value and it is 1. If you had instead G(x)=5x/x then this singularity would be 5. if you had H(x)=x^2/x the limit for x=0 is 0 on the other hand I(x)=x/x^2 the limit has x=0 is undefined (inf on the right -inf on the left). And F(x), G(x), H(x) and I(x) are all 0/0 for x=0. Undefined just means undefined, thats it.

You know, this actually makes a lot of sense to me righ now. It does approach a bit of an asymptote but never reaches 0. Just to be clear, in the singularity example of F(x)=1/x is x all the matter and energy in the universe? Or is that 1? And is the other one the volume? If you could clarify that for me, if I am even on the right track, that would be great. Thanks. That does help.

 

[Master_Ghost_Knight]

Are you being sarcastic? Yeah I know I messed a bit on making things clear but let me try to clarify and sort of redeem this mess.

You know, this actually makes a lot of sense to me righ now. It does approach a bit of an asymptote but never reaches 0.

Ok, If you are thinking F(x)=0 then you have missed the sigularity all togheter, you got it all backwards, F(x)=0 is not a singularity it is a zero, and it this case it is a zero in infinity (special kind of zero different from a regular zero). F(x)=1/x for x=0 (i.e. F(0)=1/0) is a singularity of the function F(x) because in this case the division by zero is not defined in mathematics. To put it in a laymans terms (not exactly correct but close enough) a singularity is a point where the function has no value (i.e. the singularity is of sorts a point of the domain for which the function can not atribute a corresponding value in the counterdomain).

Just to be clear, in the singularity example of F(x)=1/x is x all the matter and energy in the universe? Or is that 1? And is the other one the volume? If you could clarify that for me, if I am even on the right track, that would be great. Thanks. That does help.

It's neither, it was a generic mathematical example without any strings atatched to anything real what so ever, I taught this would help slay the monster that a singularity is a physical thing (which isn't). Let me give you another example of a singularity of equivalent sorts that might be easier for you to grasp.

Take for instance the Newtonian Function of gravitical field of a particle in polar coordinates.
(damn it, now I am going to explain what is a polar coordinate, this is why mathematics is fundamentaly important n physics)
Polar coordinates, instead of trying to measure the position of things in relation to the cartesian X Y Z, we just measure it in terms of distance, angle of elevation and angle of rotation (simple?).

The intensity of aceleration caused by the particle is:
F(r)=-GM/r^2 (r is the radius, M is the mass of the particle, G the gravitical constant, I hope everyone has seen this before).

Now you can ask what is the intensity of the aceleration on a point at a distance 4m from a particle with 3kg of mass?
Well you first set out the constants M=4kg; G=6.674*10^-11 m^2/(Kg*s^2), then you would get:
F(r)=-2.6696*10^-10 (m^3/s^2) /r^2 (which is your genericl field for this particle in function of the radius)
then you replace r by 4m and you get the result of:
F(4m)=-1.6685*10^-11 m/s^2.
With me so far? And you can do this for any other points and get a result, except you can't do it for the point where r=0 because division by zero isn't defined, this point r=0 is a singularity in the this equation. (it is actualy 2 pole type singularities because of the r^2 but that is another detail).

If you asked me what type of singularity did they arrive or what the equation was supoused to describe for the pertrained singularity problem of the bigbang, then I would have to tell you I don't have a clue (AndromedasWake would have to tell you that), I just know what singularities are because their analisys are usefull in many engineering aspects.