Questions about the Universe, Please help me here.

[Squidgey]

I'm not a particularly religious man. I believe in God but not to the extent alot of people do. It's because I can't understand nor grasp some of the higher concepts of Physics and am currently craving this knowledge. Basically, I don't get the Big Bang. All matter either didn't exist or it did but was so compressed as to be nothing (My facts are probably slightly out but it's never been fully explained to me before). Then it exploded to create the universe, which to current theories is still expanding, but what, I ask, is beyond the edge of our expanding universe? There's got to be something there, not Nothing. Heck, there's nothing in a vacuum, but then theories suggest that Super Strings are at the foundations of all space and they hold everything together. And if that's the case, what is then beyond the edge of the universe whence the Super Strings hold everything together?

So I seek a more thorough expansion of my knowledge. I was sent to this forum via invitation from Petrosjko and already know that I shall love this community and will attempt to contribute as much as I recieve, despite a limited knowledge in many things barring wargaming.

Anyways, thanks in advance for your replies to my first thread. Cheers,

Squidgey.

[Robert Walper]

There is no concept of "outside" of the universe, since the universe encompasses all of space/time.

Your question is much like those who propose the question "what was before the universe?". The question is meaningless, because time is a attribute of the universe and does not exist without the universe.

Imagine, if you would, a simple box. It has three dimensions: height, width and length. Now, let's effectively remove one of these dimensions, like height. Now the "box" has only width and length. Asking "what's above the box?" is a question with no meaning or answer because the concept no longer exists.

Hope that helps.

[Rogue 9]

If you remove height, the box becomes two-dimensional, a square. Things can indeed be above a square. What you're looking for is giving it infinite height, not taking height away.

[Robert Walper]

If you remove height, the box becomes two-dimensional, a square. Things can indeed be above a square. What you're looking for is giving it infinite height, not taking height away.

You're obviously not grasping what I said Rogue. I didn't say we're just removing the height of the box, I said we're removing the dimension of height altogether.

I'm using height, width and length for the sake of simplicity, rather than a 3D coordinate system. For example, you can program a virtual cube on a computer with three dimensions of X, Y and Z. Remove any one of the variables and that dimension no longer exists. The dimension does not become infinite, the return value of zero does not represent infinite. It simply no longer exists and inquiries about it's value are meaningless.

[Surlethe]

If you remove height, the box becomes two-dimensional, a square.

No, it becomes a two-dimensional subspace of R³. Walper is talking about removing the third coordinate, going from R³ to R². R² is not a subspace of R³.

[Surlethe]

As for your question about the Big Bang, squidguy, I'm going to use an analogy. Your flaw in understanding is the assumption only the matter was gathered up into a singularity before the Big Bang: essentially, a Euclidean view of space and time. This is not the case; but now, without further ado, the analogy:

Imagine a line, and on the line are a bunch of points equidistant from one another, like so:

...--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--...

Now, we're going to choose a point to be the center (0), and we're going to have every point move out to twice its distance from the center, so the second point goes out to the third spot; the third point goes out to the sixth spot; so on, so forth, resulting in this new line:

...----o----o----o----o----o----o----0----o----o----o----o----o--...

Note how the further away the point is, the further it moves. This is analogous to the further something is from us, the faster it is accelerating away from us.

Now note we don't have to choose a center; all we have to do is double the length of the line. When we do that, every point on the line sees every other point moving away from it at a speed proportional to distance.

[Robert Walper]

If you remove height, the box becomes two-dimensional, a square.

No, it becomes a two-dimensional subspace of R³. Walper is talking about removing the third coordinate, going from R³ to R². R² is not a subspace of R³.

Perhaps an even more simple way of putting it is thus:

Person A does not exist. How tall is person A?

The ability to formulate the question doesn't make it valid.

[Squidgey]

As for your question about the Big Bang, squidguy, I'm going to use an analogy. Your flaw in understanding is the assumption only the matter was gathered up into a singularity before the Big Bang: essentially, a Euclidean view of space and time. This is not the case; but now, without further ado, the analogy:

Imagine a line, and on the line are a bunch of points equidistant from one another, like so:

...--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--...

Now, we're going to choose a point to be the center (0), and we're going to have every point move out to twice its distance from the center, so the second point goes out to the third spot; the third point goes out to the sixth spot; so on, so forth, resulting in this new line:

...----o----o----o----o----o----o----0----o----o----o----o----o--...

Note how the further away the point is, the further it moves. This is analogous to the further something is from us, the faster it is accelerating away from us.

Now note we don't have to choose a center; all we have to do is double the length of the line. When we do that, every point on the line sees every other point moving away from it at a speed proportional to distance.

So basically, what you're saying is everything in space and time, no matter what form it took, was compressed into a singularity prior to the Big Bang. However, once the Big Bang occurred, all the stuff (of want for a better word) within the singularity just suddenly expanded at a constant rate outwards. Am I grasping that much at least? And if that is true, because this line of 'stuff' is equally proportional in both size and distance as an infinite quantity, and coupled with what Robert Walper said about Time being relative only within the universe itself, then the universe is currently of an infinite size within Its' frame of reference. So the Big Bang, and in particular, the Singularity before the Big Bang had in itself, a size of infinite proportions within Its' own reference point. But, as soon as The Big Bang occurred, the reference point changed to encompass a much larger area. But if that's true, then could it be possible that within this reference frame, we are just another Big Bang waiting to occur? It's an intriguing thought, is this what you guys were trying to convey to me?

Oh, and although Squidguy sounds rather cool, my actual username is Squidgey, no offense taken though. Just pointing it out.

[Surlethe]

So basically, what you're saying is everything in space and time, no matter what form it took, was compressed into a singularity prior to the Big Bang.

Not quite: rather, space and time were compressed into a singularity, not just everything in space and time. Spacetime itself was a singularity.

However, once the Big Bang occurred, all the stuff (of want for a better word) within the singularity just suddenly expanded at a constant rate outwards.

Not necessarily a constant rate, but that's the general idea.

Am I grasping that much at least? And if that is true, because this line of 'stuff' is equally proportional in both size and distance as an infinite quantity, and coupled with what Robert Walper said about Time being relative only within the universe itself, then the universe is currently of an infinite size within Its' frame of reference.

No, the universe isn't infinite in size. Think of the universe like the surface of a hypersphere: it's not infinite in size, but if you keep going, you'll never stop.

So the Big Bang, and in particular, the Singularity before the Big Bang had in itself, a size of infinite proportions within Its' own reference point. But, as soon as The Big Bang occurred, the reference point changed to encompass a much larger area. But if that's true, then could it be possible that within this reference frame, we are just another Big Bang waiting to occur? It's an intriguing thought, is this what you guys were trying to convey to me?

Nope; we're just trying to convey at one point the entire universe was much smaller than it is now.

Oh, and although Squidguy sounds rather cool, my actual username is Squidgey, no offense taken though. Just pointing it out.

My bad, Squidgey. Sorry.

[Squidgey]

Squidgey wrote:
So basically, what you're saying is everything in space and time, no matter what form it took, was compressed into a singularity prior to the Big Bang.


Not quite: rather, space and time were compressed into a singularity, not just everything in space and time. Spacetime itself was a singularity.

Okay, that's cool, I can grasp that.

Quote:
However, once the Big Bang occurred, all the stuff (of want for a better word) within the singularity just suddenly expanded at a constant rate outwards.


Not necessarily a constant rate, but that's the general idea.

Cool.

Quote:
Am I grasping that much at least? And if that is true, because this line of 'stuff' is equally proportional in both size and distance as an infinite quantity, and coupled with what Robert Walper said about Time being relative only within the universe itself, then the universe is currently of an infinite size within Its' frame of reference.


No, the universe isn't infinite in size. Think of the universe like the surface of a hypersphere: it's not infinite in size, but if you keep going, you'll never stop.

Okay, now this I can't really grasp because I can' see it clearly. I can accept the concept that the universe is not infinite in size, but that we can't actually get to the end of it (Oh and what's a Hypersphere?). But now, theoretically, if we could get to the end of it, it doesn't matter how, just that we could get to the end of it because it's not impossible if the universe is of non-infinite size, then what theories etc are there for what exists OUTSIDE of the universe, if any at all, or does our current understanding prevent any plausible or accurate theorems to occur?

Quote:
So the Big Bang, and in particular, the Singularity before the Big Bang had in itself, a size of infinite proportions within Its' own reference point. But, as soon as The Big Bang occurred, the reference point changed to encompass a much larger area. But if that's true, then could it be possible that within this reference frame, we are just another Big Bang waiting to occur? It's an intriguing thought, is this what you guys were trying to convey to me?


Nope; we're just trying to convey at one point the entire universe was much smaller than it is now.

Okay, I can grasp that, especially as by current understanding the universe is not infinite of size but is ever expanding...

Quote:
Oh, and although Squidguy sounds rather cool, my actual username is Squidgey, no offense taken though. Just pointing it out.


My bad, Squidgey. Sorry.

No worries at all mate. Thanks for the clarrifications. It's made my week much more interesting! :cheers

Squidgey.

[Surlethe]

Okay, now this I can't really grasp because I can' see it clearly. I can accept the concept that the universe is not infinite in size, but that we can't actually get to the end of it (Oh and what's a Hypersphere?).

A four-dimensional sphere.

But now, theoretically, if we could get to the end of it, it doesn't matter how, just that we could get to the end of it because it's not impossible if the universe is of non-infinite size, then what theories etc are there for what exists OUTSIDE of the universe, if any at all, or does our current understanding prevent any plausible or accurate theorems to occur?

Nothing exists outside of the universe, because the universe, by definition, includes everything which exists.

Thanks for the clarrifications. It's made my week much more interesting!

My pleasure.

[Squidgey]

Squidgey wrote:
Okay, now this I can't really grasp because I can' see it clearly. I can accept the concept that the universe is not infinite in size, but that we can't actually get to the end of it (Oh and what's a Hypersphere?).


A four-dimensional sphere.

So, a Sphere with Time? ie, length, breadth (width), height and time?

Quote:
But now, theoretically, if we could get to the end of it, it doesn't matter how, just that we could get to the end of it because it's not impossible if the universe is of non-infinite size, then what theories etc are there for what exists OUTSIDE of the universe, if any at all, or does our current understanding prevent any plausible or accurate theorems to occur?


Nothing exists outside of the universe, because the universe, by definition, includes everything which exists.

By definition.

It's Mind-Boggling! :nukeem:

Now, if we take the By Definition apart, do my previous queries about theories etc of what exists outside the universe exist or not because of the fact that as we know it, the universe, despite being of a non-infinite size encompasses ALL things that exist?

Quote:
Thanks for the clarrifications. It's made my week much more interesting!


My pleasure.

Good to hear. I've actually quite enjoyed it as it's been quite fascinating to again after a two year period of gradual intellectual stagnation on my part, finally be able to much more shall we say be stimulated as I once had been.

Cheers mate.

Squidgey.

[Kuroneko]

... Am I grasping that much at least? And if that is true, because this line of 'stuff' is equally proportional in both size and distance as an infinite quantity, and coupled with what Robert Walper said about Time being relative only within the universe itself, then the universe is currently of an infinite size within Its' frame of reference.

Not necessarily so. It is possible for it to curve on itself. Repeat Surlethe's diagram for a circle of o's instead of a line, expanding the same way. However, you're right in that if Surlethe's diagram is literally representative of the universe, then the universe is infinite.

So the Big Bang, and in particular, the Singularity before the Big Bang had in itself, a size of infinite proportions within Its' own reference point.

There is no 'before' the big bang. The singularity isn't even physically real in the normal sense of the term. Intuitively, a singularity is a 'hole' in spacetime--a lack of spacetime rather than any sort of physical state at that location. The big bang singularity is special in that it is global, unlike black hole singularities.

The worldline of an object is the sum total of its history. It makes a certain (possibly complicated) curve in spacetime. From this perspective, worldlines are unchanging because time is just another dimension in spacetime--if will be at some place X an hour from now, (X,now+1hr) is part of its worldline. (General relativity is completely deterministic in this sense.) Now, since the wordline is one-dimensional, we can parametrize it monotonically by some variable λ (a good choice would be the proper time of the particle--the time it perceives--but the parameter is completely arbitrary doesn't have to have any such meaning). When a physicist says that there was a Big Bang singularity, what he or she really means is that no wordline can be extended infinitely far into the past.

If that's too detailed, perhaps a much looser analogy might help. Take out a sheet of paper; it should have corners and edges. Let it represent the spacetime manifold. If the universe if finite, the big bang singularity is like a corner. If it is infinite, it is like an edge. Either way, there is nothing beyond it any more there is paper past its edge.

But, as soon as The Big Bang occurred, the reference point changed to encompass a much larger area. But if that's true, then could it be possible that within this reference frame, we are just another Big Bang waiting to occur? It's an intriguing thought, is this what you guys were trying to convey to me?

For that to be the case, we need to have a singularity somewhere. Interestingly, there is a 'baby universes' idea in that black hole singularities are big bang singularity for 'child' universes.

No, the universe isn't infinite in size. Think of the universe like the surface of a hypersphere: it's not infinite in size, but if you keep going, you'll never stop.

Maybe. Maybe not. By all available evidence, the early universe was highly isotropic, so we may assume complete spherical symmetry and uniform matter density as a good approximation, at least on the large scale. Let's assume that the universe is in fact infinite and run it backwards in time. From the point of view of any given particle, it is surrounded by uniform shells of matter; hence, it will gravitationally attract them, increasing the matter density in its vicinity. Since this is true from any vantage point, the matter density stays uniform and increases everywhere, reaching an infinite density in a finite amount of time [1]. Singularity--everywhere at once (note that at any particular time, the universe alaways still infinite). Therefore, there is nothing contradictory about having a big bang for an infinite universe.

[1] According to Birkhoff's theorem, the Schwarzschild metric is the unique solution for spherical symmetry. Freefall in the Schwarzschild metric is Newtonian in proper time, so this is essentially the same as the analogous Newtonian situation, which is easy to analyze.

[Surlethe]

Now, if we take the By Definition apart, do my previous queries about theories etc of what exists outside the universe exist or not because of the fact that as we know it, the universe, despite being of a non-infinite size encompasses ALL things that exist?

I don't quite understand what you're asking.

So, a Sphere with Time? ie, length, breadth (width), height and time?

Erm, no. I was thinking about the universe as a three dimensional surface in a four dimensional space, not considering time as a spatial dimension. This is the analogue to the surface of a sphere embedded in three dimensional space.

[Surlethe]

No, the universe isn't infinite in size. Think of the universe like the surface of a hypersphere: it's not infinite in size, but if you keep going, you'll never stop.

Maybe. Maybe not. By all available evidence, the early universe was highly isotropic, so we may assume complete spherical symmetry and uniform matter density as a good approximation, at least on the large scale. Let's assume that the universe is in fact infinite and run it backwards in time. From the point of view of any given particle, it is surrounded by uniform shells of matter; hence, it will gravitationally attract them, increasing the matter density in its vicinity. Since this is true from any vantage point, the matter density stays uniform and increases everywhere, reaching an infinite density in a finite amount of time [1]. Singularity--everywhere at once (note that at any particular time, the universe alaways still infinite). Therefore, there is nothing contradictory about having a big bang for an infinite universe.

[1] According to Birkhoff's theorem, the Schwarzschild metric is the unique solution for spherical symmetry. Freefall in the Schwarzschild metric is Newtonian in proper time, so this is essentially the same as the analogous Newtonian situation, which is easy to analyze.

So, the density will accrue asymptotically?

How can the universe be infinite spatially and yet possess infinite matter density?

[Kuroneko]

So, the density will accrue asymptotically?

Of course. Start with a homegenous matter distribution, assume that gravitational force dominates over large distances, pick an arbitrary origin, and treat the rest of the universe as layers of spheres which will gravitationally contract toward the origin, increasing the matter density asymptotically. The calculuation is easy enough--you can assume Newtonian gravity because Birkhoff's theorem guarantees it. The scenario holds no matter which point is labelled as the origin, so matter density diverges in finite time everywhere in the universe.

How can the universe be infinite spatially and yet possess infinite matter density?

It doesn't. But the universe in the above scenario reaches infinite matter density, and hence singularity, in a finite amount of time. A big bang would be just the time-reversal of that situation.

[Surlethe]

So, the density will accrue asymptotically?

Of course. Start with a homegenous matter distribution, assume that gravitational force dominates over large distances, pick an arbitrary origin, and treat the rest of the universe as layers of spheres which will gravitationally contract toward the origin, increasing the matter density asymptotically. The calculuation is easy enough--you can assume Newtonian gravity because Birkhoff's theorem guarantees it. The scenario holds no matter which point is labelled as the origin, so matter density diverges in finite time everywhere in the universe.

*starts to work on the math*

How can the universe be infinite spatially and yet possess infinite matter density?

It doesn't. But the universe in the above scenario reaches infinite matter density, and hence singularity, in a finite amount of time. A big bang would be just the time-reversal of that situation.

That's what I meant: the universe in that scenario is infinite spatially, and contracts asymptotically toward infinite density; how can it be both infinite spatially and tend to singularity?

[Kuroneko]

That's what I meant: the universe in that scenario is infinite spatially, and contracts asymptotically toward infinite density; how can it be both infinite spatially and tend to singularity?

I'm not quite certain what it is that you're asking. If the matter distribution is homogenous and the universe is spatially infinite, then it has an infinite amount of matter already, so it's not as if there is more produced. If that's not what you perceive to be the problem, perhaps you are under the impression that singularities must be pointlike. If so, get rid of that notion--a rotating black hole a ring singularity in its equatorial plane, for example, although it is debatable as to how physical the Kerr solution really is. If your concern is neither of these, please clarify.

[Surlethe]

That's what I meant: the universe in that scenario is infinite spatially, and contracts asymptotically toward infinite density; how can it be both infinite spatially and tend to singularity?

I'm not quite certain what it is that you're asking. If the matter distribution is homogenous and the universe is spatially infinite, then it has an infinite amount of matter already, so it's not as if there is more produced. If that's not what you perceive to be the problem, perhaps you are under the impression that singularities must be pointlike. If so, get rid of that notion--a rotating black hole a ring singularity in its equatorial plane, for example, although it is debatable as to how physical the Kerr solution really is. If your concern is neither of these, please clarify.

*gets rid of the notion*

Okay. I was under the impression singularities must be pointlike. Is this example analogous to a singularity not at a point? f(x) = x^(1/2) has a singularity on (-\inf,0].

[Kuroneko]

Okay. I was under the impression singularities must be pointlike. Is this example analogous to a singularity not at a point? f(x) = x^(1/2) has a singularity on (-\inf,0].

On (-\inf,0), surely. It's somewhat analogous, yes, but perhaps with some caveats. Although I suppose that to preserve mathematical accuracy, one should say that there are infinitely many singularities that happen to form a continuous semi-infinite region of the real line. In any case, whether one calls it one singularity or infinitely many of them, the point stands. In the context of GTR, physicists prefer to call it one singularity, which also makes more sense there, especially in the case of the big bang--if the singularity is "everywhere", there is no "anywhere", and hence no meaningful way to count them, unlike in the f(x) = x^(1/2) example on the reals.