A number of years before the Internet was born,
I read an article in which the author claimed that,
at the site where the Big Bang happened,
a "naked singularity" should exist.

Like the Big Bang itself, which brought the Observed
Physical Universe into existence, a naked singularity
should also be able to violate the Energy Conservation
Law, and continuously spew stuff.

The implication is that the Big Bang might still
be happening! It's just happening farther away than
we can see. Let me see if I can explain my understanding
of the situation (should there happen to be something "to" it).

Cosmologists describe the expanding Universe in terms of
a balloon, something we all are familiar with. But their
simplification of the situation is "off" a Dimension. After all,
any small portion of the surface of a balloon resembles a
mostly-flat 2-Dimensional area, and our Universe is obviously
3-Dimensonal, at least.

Mathematicians know that the circle (a 2-D thing) and the
sphere (3-D) have a 4-Dimensional equivalent, which they
call a "hypersphere". Any portion of the surface of a
hypersphere is a 3-Dimensional volume, equivalent to what
I described above about a portion of the surface of an
ordinary sphere.

As we stand on the surface of the basically spherical Earth,
we see that there is a limit to our ability to view its surface,
known as "the horizon". Similarly, the Observable Universe
has a kind of "horizon", too, usually known as the "red shift
limit". It is not impossible that our entire 3-D Observable
Universe is just a tiny portion of the overall surface of a huge
huge 4-D hypersphere.

I'm aware that cosmologists have been looking for evidence
that Space has some "curvature", which would be strong
evidence in favor of a hyperspherical Universe, and that so
far, Space appears to be entirely "flat". Well, we know how
long it took humanity to find evidence that the surface of
the quite-larger-than-us Planet Earth was curved instead
of flat. The verdict is still "out", awaiting more evidence.

Imagine we could teleport instantly from the Earth to a distant
place, say 13 billion light-years away. We could look back
toward the Earth and see our Milky Way Galaxy to be very
strongly red-shifted, and possibly spewing a powerful jet
from its nucleus, like a quasar (because we would be seeing
it as it existed 13 billion years ago).

But suppose we turned around and looked farther away in
the direction we had just teleported? What would we see?
Even more galaxies, occupying an additional segment of the
surface of that huge huge 4-D hypersphere? To be determined!

Anyway, I've gotten distracted from the Big Banger.
It's location, whether still spewing or not, would obviously be
at the center of that 4-D hypersphere, and we have no way
of "looking" in that direction! Stuck in the 3-D surface we are,
unable to access the Dimension of "hypervolume".

However, just like we imagine Planet Earth to consist of various
layers, like "crust", "mantle", and "outer core", we can imagine
that 4-D hypersphere to be layered, too, like an onion. Each
layer could be a vast 3-D volume, such that any small portion of
it could be equivalent to our Observable Universe. We might not
actually be occupying the outermost layer!

Now the reason for writing this message is actually to ask a
Question. I just had to present the background information

So, IF the Big Banger is still Banging away, it logically follows that
the overall mass of that 4-D hypersphere has been growing for
a long long time. Might it eventually become massive enough
to stop the accelerating expansion of the Observable Universe,
and eventually lead to a Big Crunch???

Simon Bridge
Homework Helper
I read an article in which the author claimed that, at the site where the Big Bang happened, a "naked singularity" should exist.
The author was talking a load of rubbish - there is no site where the big bang happened: the big bang happened everywhere all at once.

So, IF the Big Banger is still Banging away, it logically follows that the overall mass of that 4-D hypersphere has been growing for a long long time. Might it eventually become massive enough to stop the accelerating expansion of the Observable Universe, and eventually lead to a Big Crunch?
Which would call for speculation .. which is against the rules of the forum.

What you are talking about sounds a bit like a steady-state Universe except with fast matter creation.
However, most of the description is too confused to work out.

It does sound like Hoyle"s steady state model where he tried to explain expansion through matter creation. However I can't be positive with whats provided either.

Part of what he was saying sounded more like Chaotic Inflation Theory, which is in some ways similar to Hoyle's Steady State Model. I can see how someone could view Inflation as 'Big Banger still banging away.' I can also see how some could call it speculation and then I wonder how we could discuss any theory no matter how many scientist think it does the best, but not complete, explanation. Sometimes it is hard to present facts without wanting to give conclusions. If you cling too tightly to only one theory or even to one understanding of a theory you become as the three blind men describing an elephant by what they feel. I will go drink my hemlock now, and I owe Asclepius a rooster.

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Simon Bridge
Homework Helper
@Ogr8bearded1:
That is an understandable position and I remember arguing something similar when I first showed up.
However, this is a forum with rules ... at first it seems quite restrictive: as you point out, how can we discuss anything? However - there are other forums with different rules, people are free to visit those forums and discuss whatever "what if"'s they like.

A quick look at the rules tells us the reasonable limits to the kinds of discussions that are desired here.

Generally, discussion topics should be traceable to standard textbooks or to peer-reviewed scientific literature.

The statement "what if the big banger were still banging" fits neatly into "Personal theories or speculations that go beyond or counter to generally-accepted science" ... but if we squint a bit it is possible to see some aspects of post #1 which may be made to fit into: "Challenges to mainstream theories (relativity, the Big Bang, etc.) that do not go too far beyond current professional discussion" (see the rules under "discussion guidelines").

Therefore - we need clarification from OP to figure it out.
No need for hemlock ;)

Fredrik
Staff Emeritus
Gold Member
at the site where the Big Bang happened,
As Simon Bridge said, there's no such site.

Like the Big Bang itself, which brought the Observed
Physical Universe into existence, a naked singularity
should also be able to violate the Energy Conservation
Law, and continuously spew stuff.
This violates the forum rules against speculation.

The implication is that the Big Bang might still
be happening!
A naked singularity that spews forth matter is something very different from the big bang.

Mathematicians know that the circle (a 2-D thing) and the
sphere (3-D)
A circle is a 1-D thing, and a sphere is a 2-D thing. (What's inside the sphere is called a "ball". The "sphere" is just the surface). The spheres that represent space at different times in some solutions of Einstein's equation are however 3-dimensional, and can therefore be called 3-spheres.

Anyway, I've gotten distracted from the Big Banger.
It's location, whether still spewing or not, would obviously be
at the center of that 4-D hypersphere,
This is false. If it had a location at all, it would be on the 3-sphere. That's what it means to have a location.

So, IF the Big Banger is still Banging away, it logically follows that
the overall mass of that 4-D hypersphere has been growing for
a long long time.
It would also follow that space isn't a 3-sphere. The solutions that describe space at different times as 3-spheres with different radii, are found when we assume that space is homogeneous and isotropic. A naked singularity that spews forth matter would certainly violate that assumption, and probably general relativity too.

Might it eventually become massive enough
to stop the accelerating expansion of the Observable Universe,
and eventually lead to a Big Crunch???
This is the sort of speculation we don't do at Physics Forums.

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SteamKing
Staff Emeritus
Homework Helper
There once was a Big Bopper, there is now a Big Dipper, but I don't know nothin about a Big Banger.

phinds
Gold Member
There once was a Big Bopper, there is now a Big Dipper, but I don't know nothin about a Big Banger.

Gee, I thought "Big Banger" was one of the more coherent parts of the OP's post

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lol that was the one term i sort of liked, rolled off the tongue

Simon Bridge
Homework Helper
@VernonNemitz: any of this any use?

OP has been active since this thread was started...
I was wondering if a big banger could be a kind of sausage... hmmm... sausage...

phinds
Gold Member
OP has been active since this thread was started...

I think you mean he has NOT been active since ...

Simon Bridge
Homework Helper
I think you mean he has NOT been active since ...

I may have misunderstood or misread:
OP's profile says last activity was 6am-ish today (my time?), it's 1pm-ish now, and post#1 was "19 hours ago" which would be late yesterday evening... sooo... OP's been here since making the post?

phinds
Gold Member
I may have misunderstood or misread:
OP's profile says last activity was 6am-ish today (my time?), it's 1pm-ish now, and post#1 was "19 hours ago" which would be late yesterday evening... sooo... OP's been here since making the post?

Well, we don't seem to be reading the same info. According to what I see he made a post 2 weeks ago and nothing else since starting this thread which on my browser shows as 1:38am today.

EDIT: ok, doing time conversion we are seeing the same thing, you just misinterpreted it.

What I explained about a hypersphere was my personal understanding of
what I've read about the expansion of the universe. That is, if a 3D balloon
expands, its surface stretches; if a 4D hypersphere expands, its surface
stretches. And since the surface of a hypersphere really is a volume of "curved
space", just like the surface of a sphere is a curved 2D area, then for an expanding
hypersphere, its curved-space surface expands in all of the regular 3 Dimensions.
Uniformly!

That's because multidimensional geometry is very consistent about certain things.
I will therefore disagree strongly with Fredrik. A circle is a 2D thing, period.
You can call it a "curved line", but while the line is a 1D thing, you cannot
curve it without invoking the 2nd Dimension
. Likewise, a sphere is a 3D thing.
Its surface is a curved area (and normally an area is a 2D thing), but you cannot
get that curvature into that area without invoking the 3rd Dimension. And so,
if the Space of the Universe is curved, however slightly, it will most logically
involve the 4th geometric Dimension. Very simple!

Here is how those shapes are related. Start with a straight line segment (1D), and
select its center point. Rotate the line around the point to generate a 2D circle
(not just the edge, but the area as well). With the original line bisecting that circle,
we can now imagine rotating the circle around the line to generate a 3D sphere.
The next stage is perfectly logical, but mind-bendingly difficult to imagine: With
the circle bisecting the sphere, imagine rotating the sphere "around" that circle to
generate a 4D hypersphere.... Despite the difficulty of imagining that, it remains
very true that multidimensional geometry is extremely consistent about certain
things!

Anyway, if a hypersphere is large enough, it could quite logically be difficult
to detect the curvature of its surface. I did note in the original post that
so far we haven't been able to detect any large-scale curvature, in the Observable
Universe.

It is therefore quite possible that my understanding of the situation has been
faulty for a long time. I am fully aware that the phrase "curved space",
especially when talking about gravitational fields, might be nothing more than
an analogy, while the real-thing-going-on is something else altogether.
And the expansion of the Universe doesn't have to be associated with a
hypersphere.

There is still a Question, though. Please recall that teleportation thought-
experiment in the original post. What is the most logical thing that might
be seen, looking further away from the Milky Way, if one was doing the
looking after being teleported 13 billion light-years from here? I'm almost
certain that I've read articles that basically say, "if you keep going in
that direction (or any other direction) far enough, you will end up back
at the Milky Way" ---and that, folks, can very accurately be
called "circumnavigating the surface of a hypersphere!" Which is why
cosmologists have been looking for some large-scale curvature of Space!

Simon Bridge
Homework Helper
What I explained about a hypersphere was my personal understanding of
Fair enough - you realize you are not the first to consider the multidimensional topology of the Universe? So many people have thought about this that a standard language has been developed to help people talk about it.

You should think of Fredrik's descriptions as providing you with that common language - which will help you communicate your ideas to others. What you have been calling a "sphere" is known to mathematicians and physicists as a "ball".

http://en.wikipedia.org/wiki/Ball_(mathematics [Broken])

Hence - the surface of a 3-ball is a sphere.
Spheres are 2D - viewed from the inside.

The surface of a 2-ball is a circle - 1D from the inside.

Since there is no "outside" to the Universe, it is the view from the inside that counts.

Two straight lines intersecting a third at the same angle will be parallel.
The curvature of the Universe would be manifest if the two lines would ever intersect each other.
That sort of thing has other consequences that should be detectable - that's what all the "large scale curvature" is about.

Per your question - an observer at, say, the limit of the observable Universe from us would see much the same Universe as us. The Universe is very very big and expanding, so it won't be possible to travel far enough to end up approaching your starting place.

The field that covers what you are talking about is "topology". It's a big topic, see:
http://scientopia.org/blogs/goodmath/2010/08/19/an-introduction-to-topology/
http://www-history.mcs.st-andrews.ac.uk/Extras/Kuratowski_Topology.html
http://en.wikipedia.org/wiki/Spacetime_topology

Texts on general relativity should give you a crash course.

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phinds
Gold Member
Since there is no "outside" to the Universe, it is the view from the inside that counts.

I think the way you use the term "inside" throughout your post, regarding various shapes, is unfortunately subject to easy misunderstanding and could generate argument.

EDIT: for example, if I am "inside" a circle sitting at the center point of the circle, I can't see the points on the circle without looking in 2D directions.

Wouldn't "on the surface" be a better way of saying what you're saying?

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phinds
Gold Member
I'm almost
certain that I've read articles that basically say, "if you keep going in
that direction (or any other direction) far enough, you will end up back
at the Milky Way" ---and that, folks, can very accurately be
called "circumnavigating the surface of a hypersphere!" Which is why
cosmologists have been looking for some large-scale curvature of Space!

I'm sure you have read such articles but that being one hypothesis (the "pac man universe") does NOT make it fact. It MAY be a valid hypothesis but stating it as a fact is personal speculation.

Simon Bridge
Homework Helper
I think the way you use the term "inside" throughout your post, regarding various shapes, is unfortunately subject to easy misunderstanding and could generate argument.
Yeah - it's far from mathematically rigorous and I am hoping the context will carry it forward. If not then I can deal with it when it comes up.

You can follow what I am trying to do there?
If you can come up with a better way, do tell.

you cannot curve it without invoking the 2nd Dimension.

That is not correct. There is the concept of intrinsic curvature, which does not require the manifold to be embedded in a higher dimensional space. This is well defined in a mathematically rigorous way.
So yes, you can indeed "curve" it without invoking a 2nd dimension.

Fredrik
Staff Emeritus
Gold Member
A circle is a 2D thing, period.
You can call it a "curved line", but while the line is a 1D thing, you cannot
curve it without invoking the 2nd Dimension
. Likewise, a sphere is a 3D thing.
Its surface is a curved area (and normally an area is a 2D thing), but you cannot
get that curvature into that area without invoking the 3rd Dimension. And so,
if the Space of the Universe is curved, however slightly, it will most logically
involve the 4th geometric Dimension.
The dimension of a manifold is how many real numbers a coordinate system assigns to each point in its domain. For a circle, this is 1. For a sphere, it's 2. This is not an opinion, it's how these things are defined in mathematics. The definitions also ensure that curved manifolds don't have to be subsets of higher-dimensional Euclidean spaces. There are however theorems that say that there's always another manifold, that is a subset of a higher-dimensional Euclidean space, and is still equivalent for all practical purposes to the one we're interested in. But the point is that we don't need a higher-dimensional space to define curvature.

Anyway, if a hypersphere is large enough, it could quite logically be difficult
to detect the curvature of its surface. I did note in the original post that
so far we haven't been able to detect any large-scale curvature, in the Observable
Universe.

It is therefore quite possible that my understanding of the situation has been
faulty for a long time.
This part of your understanding is good enough. But 3-spheres (what you call 4-D hyperspheres) is only of three possibilities that's consistent with the assumption that the space is homogeneous and isotropic. It's the "positive curvature" option, but there's also a "flat" option, and a "negative curvature" option.

I'm almost
certain that I've read articles that basically say, "if you keep going in
that direction (or any other direction) far enough, you will end up back
at the Milky Way" ---and that, folks, can very accurately be
called "circumnavigating the surface of a hypersphere!" Which is why
cosmologists have been looking for some large-scale curvature of Space!
If the curvature is positive, then you might be able to travel along the surface of the (expanding or shrinking) 3-sphere until you come back to the same point from the other direction. I don't know if this is possible though. I know that in the simplest solutions (which end with a big crunch), you don't have time to go all the way before the crunch. And I expect that in solutions with accelerating expansion, you won't be able to do it in a finite time.

The other possibility is that the universe has a non-trivial topology, like e.g. the universe in the classic video game Asteroids. Then you might be able to "come back from the other direction" in a finite time, even space is flat or has negative curvature. That may be what you have read about. (I know that I've seen a sciam article about it). There is however no evidence supporting this idea.

WannabeNewton
A regular curve has no intrinsic curvature in the Gaussian sense. It only has extrinsic curvature i.e. normal curvature when embedded in a higher dimensional space. However it is certainly true that regular surfaces have intrinsic curvature as well as extrinsic curvature (e.g. mean curvature) due to their embedding in ##\mathbb{R}^{3}##.

I can agree that if one is "inside/part-of the line" that constitutes the edge of a circle, then one only experiences one Dimension. And if one is "inside/part-of the surface-area" of a sphere, then one only experiences two Dimensions. (As phind pointed out, Fredrick and Simon Bridge were not being precise enough to avoid confusion.) Meanwhile, just because we happen to be inside/part-of (and experiencing) a three-Dimensional Space, that does not automatically mean that our Space qualifies as the surface of a hyperball. We need more data before such a conclusion can be made.

And logical conclusions will be exactly as accurate as the data upon which the logic is based. IF the Universe can be circumnavigated, after leaving the Milky Way in any 3D direction, then the simplest geometric description involves the surface of a hyperball. IF our Observable Universe is part of the surface (or any other of an infinite number of 4D layers/shells) of an expanding hyperball, then it does indeed logically follow that the location of the Big Bang was the center of that hyperball.

Note that when Fredrik wrote: "This is false. If it had a location at all, it would be on the 3-sphere. That's what it means to have a location." --he is as much stating a description of a hypothesis as I was. Because we don't yet know for certain what the large-scale geometry of Space really is. I am quite certain, though, that if we find ourselves needing to invoke a 4th geometric Dimension to describe some things, then the definition of "location" will have to be expanded to include that extra Dimension, when appropriate. Which means that the site of the Big Bang cannot yet be excluded from being associated with the center of an expanding hyperball.

I started this Message Thread because I had been wondering for years about what other cosmologists had thought about the claim I had read, that a naked singularity should exist at the site of the Big Bang. From the replies here, it seems that the notion didn't go over too well, but I do wonder. Like I previously indicated, IF our physical existence is part of an expanding hyperball, then our inability to access a 4th geometric Dimension obviously prevents us from examining the site of the Big Bang, whether a naked singularity is there or not.

phinds
Gold Member
the site of the Big Bang, whether a naked singularity is there or not.

The problem with positing a "site" of the singularity is that it violates the Cosmological Principle which is based on several observations (the CMB, etc.)

You really need to get away from this belief that the big bang happened at a point.

The problem with positing a "site" of the singularity is that it violates the Cosmological Principle which is based on several observations (the CMB, etc.)

You really need to get away from this belief that the big bang happened at a point.

To add to this expansion from a point indicates a preferred direction and location. We do Not observe this as occuring. What we do observe is a homogeneous and isotropic expansion. (no preferred location or direction). Meaning that its uniform thoughout the cosmos. (except where gravity overpowers it in gravitationally bound regions).
The differences between the two are easily measured and calculated. look at phinds signature at his balloon analogy.
My signature has further tools such as the cosmocalculator and lightcone calculator. As well as numerous articles with regards to expansion. I would recommend reading predujice against a constant in particular. As well as "What we have learned from Observational cosmology" . the redshift and expansion article will
also help. See second signature

A naked singularity would have an expansion flow from a central point. This is not observed. The singularity in BB is simply a time slice where are math no longer makes sense Ie leads to infinities.
It is of unknown size and origin.

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Fredrik
Staff Emeritus
Gold Member
IF our Observable Universe is part of the surface (or any other of an infinite number of 4D layers/shells) of an expanding hyperball, then it does indeed logically follow that the location of the Big Bang was the center of that hyperball.
General relativity doesn't actually define a point at the center. In this class of solutions, spacetime is sliced into 3-spheres labeled by a parameter t that we choose to think of as a time coordinate. The problem for your idea is that all events in spacetime are on a 3-sphere labeled by a positive value of t. So the big bang isn't an event in spacetime. In particular, it's not the point at the center.

Note that when Fredrik wrote: "This is false. If it had a location at all, it would be on the 3-sphere. That's what it means to have a location." --he is as much stating a description of a hypothesis as I was. Because we don't yet know for certain what the large-scale geometry of Space really is.
You were only talking about the positive curvature homogeneous and isotropic solutions, so I assumed that you wanted to know what they say.

You kept talking about the present ("might still be happening", "still spewing", "still Banging away") when you were talking about the big bang(er) and its location. That made it impossible to think that you were talking about a location in spacetime, i.e. an event. You made it seem very clear that you were talking about a location in space, in the present. This would be a point on a t=13.7 Gyear 3-sphere, not a point at the center.

I am quite certain, though, that if we find ourselves needing to invoke a 4th geometric Dimension to describe some things, then the definition of "location" will have to be expanded to include that extra Dimension, when appropriate. Which means that the site of the Big Bang cannot yet be excluded from being associated with the center of an expanding hyperball.
I can't make sense of what you're saying. What do you mean by "if we find ourselves needing to invoke a 4th geometric Dimension"? You seem to be aware that we're already using a 4-dimensional spacetime in general relativity. So do you mean a 4th spatial dimension? In that case, I guess I need to remind you of the forum rules about speculative personal theories.

...the site of the Big Bang, whether a naked singularity is there or not.
"The site"... "is there". You keep using language that very strongly suggest that you're talking about a position in space, in the present.