Thread: Confusing Space Theory

Hello! I am here to pose a question. We all know that space is infinite and constantly expanding, right? But what if we could reach the area where space has not yet reached. An area with no matter, nothing. I believe that since there is no matter, there can be no matter, so if you got there, you would automatically decay because there can not be matter where there is not matter. Right?

Here is another theory of mine. What happens if we surpass light speed? It is known that we can not surpass light speed. But what if, in some unimaginable way to the human mind in our species current state, we could? I believe that th e matter that is travelling at or above light speed would begin to "fall apart." The electrons would break off of the nuclei orbit, and it would be kind of like a nuclear fusion chain reaction. Technically, the atoms would be plasma now. Also, the heat generated from travelling that fast would be enormous! Also, you would probably travel through time as Einstein theorized. One more thing. If you were travelling at light speed, could you see the light move?

This has been Theory time, brought to you by Riddell! Have a nice night, folks!

Originally Posted by Riddell

Hello! I am here to pose a question. We all know that space is infinite and constantly expanding, right? But what if we could reach the area where space has not yet reached. An area with no matter, nothing. I believe that since there is no matter, there can be no matter, so if you got there, you would automatically decay because there can not be matter where there is not matter. Right?

We don't know that space is infinite. It might or might not be so.

The vacuum is not quite empty. But the vacuum of space is reachsable by rocket, and there is no uinusual decay.

So far as is known, space is uniform on the largest scales, so there is no "edge" and nowhere where the distribution of matter just stops.

Originally Posted by Riddell

Here is another theory of mine. What happens if we surpass light speed? It is known that we can not surpass light speed. But what if, in some unimaginable way to the human mind in our species current state, we could? I believe that th e matter that is travelling at or above light speed would begin to "fall apart." The electrons would break off of the nuclei orbit, and it would be kind of like a nuclear fusion chain reaction. Technically, the atoms would be plasma now. Also, the heat generated from travelling that fast would be enormous! Also, you would probably travel through time as Einstein theorized. One more thing. If you were travelling at light speed, could you see the light move?

This has been Theory time, brought to you by Riddell! Have a nice night, folks!

This would be a gross violation of relativity, and special relativity is an important part of our best theories of elementary particles -- quantum field theories.

Thanks for giving me the extra info! It is noted.

Originally Posted by DrRocket

Originally Posted by Riddell

Hello! I am here to pose a question. We all know that space is infinite not matter.

We don't know that space is infinite. It might or might not be so.

At the risk of revealing my ignorance about infinity I want to ask how it is possible for space to be infinite, in extent, given that matter, time and space were created in the Big Bang a finite time ago.

That's pretty much along the same line of questioning as "what caused the big bang." The big bang didn't happen at one particular point in space. It was space, all of it. Whether it banged and created a finite or infinite space is unknown since we can't see infinitely far away.

For things to be uniform at the largest scale, either the universe would have to be empty, or it'd have to be closed (looping around for example), or something even stranger. Currently, no one knows.

Originally Posted by MagiMaster

For things to be uniform at the largest scale, either the universe would have to be empty, or it'd have to be closed (looping around for example), or something even stranger. Currently, no one knows.

Empty? Can we say it is uniform if it is empty? How can we know? :wink:

Originally Posted by MagiMaster

For things to be uniform at the largest scale, either the universe would have to be empty, or it'd have to be closed (looping around for example), or something even stranger. Currently, no one knows.

no. It could quite easily be open. It is quite obviously not empty.

Originally Posted by Halliday

Originally Posted by DrRocket

Originally Posted by Riddell

Hello! I am here to pose a question. We all know that space is infinite not matter.

We don't know that space is infinite. It might or might not be so.

At the risk of revealing my ignorance about infinity I want to ask how it is possible for space to be infinite, in extent, given that matter, time and space were created in the Big Bang a finite time ago.

, is a map that takes to a point for and simply scales for

This is not quite what happened in the big bang, but it gets the general idea across.

I have no idea why I wrote "empty" when what was going through my head was "infinite." :P

Originally Posted by MagiMaster

That's pretty much along the same line of questioning as "what caused the big bang." The big bang didn't happen at one particular point in space. It was space, all of it. Whether it banged and created a finite or infinite space is unknown since we can't see infinitely far away.

I don't think it is the same line of questioning because I don't see how it is thought that the event, which formed space, is equally likely have created finite or infinite space. Infinite space sounds more like magic than science.
If there is no scientific evidence to believe space is infinite the surely one should assume it is finite.

Originally Posted by DrRocket

[, is a map that takes to a point for and simply scales for

This is not quite what happened in the big bang, but it gets the general idea across.

It certainly does appear to get the general idea across altho' I am equally sure it is not exactly what happened.
I have to add I am far from certain I get the general idea.

Originally Posted by Halliday

If there is no scientific evidence to believe space is infinite the surely one should assume it is finite.

If the universe can be considered to be globally homogeneous and isotropic then the question of whether it is open or closed comes down to curvature. It will be open (infinite) if the curvature is negative or zero. It will be closed (finite) if the curvature is positive.

Observational evidence is that the curvature is very close to zero, but could be slightly positive or slightly negative.

Global isotropy rules out things like a flat torus, and that to me is a bit hard to justify.

To rule out anything because you no evidence to support it, when you equally have no evidence to support the opposite, is most unscientific. Absence of evidence is not evidence of absence.

Whether the universe is finite or infinite is unknown. What is known is that it is really big.

NASA purposely picked a seemingly dark portion of the night sky—no larger than a grain of sand, and pointed a telescope at it, collecting light for about 11 days. Something like 10,000 galaxies appeared.

Originally Posted by Halliday

Originally Posted by MagiMaster

That's pretty much along the same line of questioning as "what caused the big bang." The big bang didn't happen at one particular point in space. It was space, all of it. Whether it banged and created a finite or infinite space is unknown since we can't see infinitely far away.

I don't think it is the same line of questioning because I don't see how it is thought that the event, which formed space, is equally likely have created finite or infinite space. Infinite space sounds more like magic than science.
If there is no scientific evidence to believe space is infinite the surely one should assume it is finite.

The reason you see it this way is because you're still imagining the big bang as a conventional explosion, radiating out from a point. If it were actually like that, then I'd agree, the universe should be finite, but it's not. When the big bang happened, all of space suddenly came in to existence. It was just highly compressed at the time. Compressing an infinite volume still gives you an infinite volume, just a denser, hotter one.

Basically, the big bang happened everywhere all at once. Whether that everywhere was some finite, closed volume, that then expanded, or an infinite, open one, that became less dense, is unknown.

I did not expect my topic to be so contraversial. It was just a thought in my head. Now I have all kinds of info about what I wrote. And we do'nt know that space is empty. It could be infinite by constantly expanding forever. Even though it was created a finite amount of time ago. We will never know for sure if it's infinite. Welll, at least not with our technology. Or, any.

Originally Posted by DrRocket

To rule out anything because you no evidence to support it, when you equally have no evidence to support the opposite, is most unscientific. Absence of evidence is not evidence of absence.

Whether the universe is finite or infinite is unknown. What is known is that it is really big.

I accept there are individuals, on this forum, who know a lot more about maths and physics than myself. It is likely then that my lack of technical knowledge means my understanding of concepts, such as infinity, is naive and limited.
I see the number system as infinite because it is never-ending, but numbers are abstract concepts created by the human mind. They do not exist in the physical universe. Altho' I do not regard infinity as a number I do see it as a product of the human mind/imagination and that raises the question as to whether it can really exist.
Numbers may go on forever but when these numbers correspond to things, in the real universe, they lead to finite results. Estimates about the number of sub atomic particles, in the cosmos, give very large numbers but these numbers are not infinite. Everything around us appears to be finite. Perhaps the universe, having been formed in the BB will exist forever, in some form, and become unimaginably large-but infinite in extent?
I also understand that sometimes well established scientific theories give answers that lead to infinities. Even in these cases it is not claimed that the infinities actually exist. The answers are usually taken to mean the theory has flaws in certain extreme circumstances.
Putting it crudely I don't believe that the odds on a finite/infinite universe are even odds.
Probably this post should not be in the physics sub forum. I'm neither a physicist nor a philosopher and I am not putting forward a new hypothesis. Maybe there should another sub forum with a slightly higher status than Pseudoscience or Trash.

Originally Posted by Halliday

Putting it crudely I don't believe that the odds on a finite/infinite universe are even odds.

What you believe is irrelevant.

The question as to whether the universe is open (infinite in extent) or closed (finite in extent) is an unsolved problem. Your belief changes nothing.

http://www.astronomy.ohio-state.edu/...9/notes40.html

http://en.wikipedia.org/wiki/Shape_of_the_Universe

Belief without foundation is superstition.

Oh, it might or might not be so.

Originally Posted by Halliday

Maybe there should another sub forum with a slightly higher status than Pseudoscience or Trash.

New Hypotheses and Ideas already exists.

Originally Posted by Ophiolite

Originally Posted by Halliday

Maybe there should another sub forum with a slightly higher status than Pseudoscience or Trash.

New Hypotheses and Ideas already exists.

I said a few things but I was not putting forward a new hypothesis.
Naturally I do not want my posts to be seen as worthy of the Pseudoscience or Trash sections. As I see it New Hypotheses is pretty much on a par with these aforementioned sub forums.
Anyway, Ophiolite, I read many of your posts- after all, us Scottish boys gotta stick together!

If the universe is infinite and accelerating into an endless universe, how would matter return to create a new singularity in the recycling universe theory?

Shouldn't there be an expanding void of open space where the Big Bang occurred, with matter expanding into infinite space in an outward accelerating sphere pattern?

One last very small question, if space were finite what might we find when we come to end of it?

Originally Posted by Lost(in)thought

If the universe is infinite and accelerating into an endless universe, how would matter return to create a new singularity in the recycling universe theory?

This makes no sense.

Originally Posted by Lost(in)thought

Shouldn't there be an expanding void of open space where the Big Bang occurred, with matter expanding into infinite space in an outward accelerating sphere pattern?

No

Originally Posted by Lost(in)thought

One last very small question, if space were finite what might we find when we come to end of it?

No matter whether the universe is finite or infinite, it does not have an edge.

Lost(in)thought wrote:
If the universe is infinite and accelerating into an endless universe, how would matter return to create a new singularity in the recycling universe theory?


DrRocket wrote:
This makes no sense.

I was describing the Big Crunch Theory, any thoughts about the Big Crunch?

Lost(in)thought wrote:
Shouldn't there be an expanding void of open space where the Big Bang occurred, with matter expanding into infinite space in an outward accelerating sphere pattern?


DrRocket wrote:
No

Is there a known center of the universe and if so would not the matter at the center of the universe be stationary, that is not expanding into space?

Lost(in)thought wrote:
One last very small question, if space were finite what might we find when we come to end of it?

DrRocket wrote:
No matter whether the universe is finite or infinite, it does not have an edge.

So as the outer most matter in the universe travels outward does space expand with the matter?

Originally Posted by Lost(in)thought

Lost(in)thought wrote:
If the universe is infinite and accelerating into an endless universe, how would matter return to create a new singularity in the recycling universe theory?


DrRocket wrote:
This makes no sense.

I was describing the Big Crunch Theory, any thoughts about the Big Crunch?

No, you were not.

In any case with the data suggesting that the expansion of the universe is acceleerating, the big crunch is pretty much dead -- unless future revelations regarding "dark energy" somehow reverse the expansion (which is not likely).

Originally Posted by Lost(in)thought

Lost(in)thought wrote:
Shouldn't there be an expanding void of open space where the Big Bang occurred, with matter expanding into infinite space in an outward accelerating sphere pattern?


DrRocket wrote:
No

Is there a known center of the universe and if so would not the matter at the center of the universe be stationary, that is not expanding into space

There is no center of the universe. Matter is not expanding into space. Space itself is expanding.

Originally Posted by Lost(in)thought

Lost(in)thought wrote:
One last very small question, if space were finite what might we find when we come to end of it?

DrRocket wrote:
No matter whether the universe is finite or infinite, it does not have an edge.

So as the outer most matter in the universe travels outward does space expand with the matter?

There is no outermost matter in the universe. Space is expanding and matter just goes along with that expansion. There is no "outer" either.

You have a lot of fundamental misconceptions. I recommend that you read a book by one of the real experts. Two that might be good for you are A Brief History of Time" by Stephen Hawking and The Road to Reality, A Complete Guide to the Laws of the Universe" by Roger Penrose.

DrRocket

I'm just trying to rap my mind around these unproven concepts, the problem is, is that I'm trying to rap my mind around unproven concepts.

In the Big Bang theory my main problem is where did all of the matter and energy that comprised the Big Bang singularity come from. I have heard the numerous explanations of different possible causes of its existence. I don’t think that space, energy and matter seen or unseen are eternal and have always existed in one form or another without a beginning. In my mind there had to be a state of nothingness.

But we did come from nothing and I just can’t rap my mind around how.

Thank you for the book recommendations, I value your vast experience and diligence in this field and on this forum.

The Brief History of Time" by Stephen Hawking, was written in 1988 is there anything more current? 23 years is a long time in this field.

Originally Posted by Lost(in)thought

The Brief History of Time" by Stephen Hawking, was written in 1988 is there anything more current? 23 years is a long time in this field.

There is lots of recent speculative junk, including a new book with Hawking's name on it, but the basics of A Brief History of Time are still valid. The biggest change since it was written is the discovery that the expansion of space is accelerating, and with it the lack of viability of the "big crunch". The book is far more solid than some recent writings that are indeed "unproven" and in many cases unprovable.

Nobody has any idea what happened at the actual moment of the big bang, though there is lots of speculation.

The big bang scenario is not "unproven". There is a mountain of empirical data, consistent with general relativity that supports it. What is speculative is the first 10^-33 seconds or so, and what will happen in the far far distant future..


The Penrose book is more recent, and more demanding of the reader.

Read the Hawking book. It will help to dispel some serious misconceptions.

No, don't read the Hawking book.

Don't listen to Farsight.
(See how helpful that was?)

DrRocket,

I'm halfway through A Brief History of Time, having trouble understanding GR.

Lets say we have two non-mechanical clocks that are unaffected by their surrounding environments (motion, radiation, temperature and gravity) I place one clock on the south pole and take the second clock on a ten year trip to Proxima Centauri at near light speed. If the clock from the ship reads 10 years exactly when we land back at the South Pole and compare the two clocks, what will the South Pole clock read?

Originally Posted by Lost(in)thought

DrRocket,

I'm halfway through A Brief History of Time, having trouble understanding GR.

Lets say we have two non-mechanical clocks that are unaffected by their surrounding environments (motion, radiation, temperature and gravity) I place one clock on the south pole and take the second clock on a ten year trip to Proxima Centauri at near light speed. If the clock from the ship reads 10 years exactly when we land back at the South Pole and compare the two clocks, what will the South Pole clock read?

I can not answer precisely because it depends on the details of the trip to Proxima Centari. But, since the clock at the South Pole is in free fall (The orbit of the Earth about the Sun), it will show a greater time interval than any clock that is initially synchronized with it, that takes a trip, and then returns to the South Pole for a comparison. It is a general principle of GR that the length (proper time) of the world line of an object in free fall is longer than any other world line with the same starting point and end point. The world line of an object in free fall is a spacetime geodesic. The world line of an accelerated object is not.

Note that because the metric of spacetime is Lorentzian, not Riemannian, that geodesics maximize length rather than minimize length.

Don't feel badly, many people have trouble understanding GR. It is a non-intuitive theory and the mathematics is relatively difficult. Because of the mathematics involved the clearest texts on GR tend to also be the most demanding. Wolfgang Rindler's Relativity: Special. General and Cosmological is less demanding than most and is still accurate and fairly clear. But it does use some mathematics and is not a popularization.

I started reading a book by Heinz Pagels called Perfect Symmetry ( a popularization ). Has anyone read it, it is fairly old, about 20-25 yrs, and what do you think of the ideas expressed in it ??

Originally Posted by MigL

I started reading a book by Heinz Pagels called Perfect Symmetry ( a popularization ). Has anyone read it, it is fairly old, about 20-25 yrs, and what do you think of the ideas expressed in it ??

I had not heard of it, so I found a summary/review.

I can find the book for about $4, hardback, including shipping. I will pass.

From its overview… FIRST-PERSON SCIENCE, by contrast, cannot strive to be meaningful for all people, as does third-person science. It is "the personal thoughts of an individual interpreting and responding to the reality of the world discovered by [third-person] science."

He is speaking of what I call the second “story”, one which cannot be relied on as the final narrative of All, via felt sensations, or whatever states of being are at that level, for one must, at least, be informed by science of the states of the first floor beneath, in order not to be limited and thus go beyond to learn of the larger realm.

Originally Posted by DrRocket

Originally Posted by Halliday

If there is no scientific evidence to believe space is infinite the surely one should assume it is finite.

If the universe can be considered to be globally homogeneous and isotropic then the question of whether it is open or closed comes down to curvature. It will be open (infinite) if the curvature is negative or zero. It will be closed (finite) if the curvature is positive.

Observational evidence is that the curvature is very close to zero, but could be slightly positive or slightly negative.

Global isotropy rules out things like a flat torus, and that to me is a bit hard to justify.

To rule out anything because you no evidence to support it, when you equally have no evidence to support the opposite, is most unscientific. Absence of evidence is not evidence of absence.

Whether the universe is finite or infinite is unknown. What is known is that it is really big.

At the risk of becoming an "infinity" bore I feel you give equal weight to the hypotheses as to whether the universe is infinite, in extent, or not.
I accept your statement "whether the universe is finite or infinite is unknown" but how can it be scientific to give equal billing to those two ideas when there do not appear to be any actual infinities in nature.

Originally Posted by Halliday

I accept your statement "whether the universe is finite or infinite is unknown" but how can it be scientific to give equal billing to those two ideas when there do not appear to be any actual infinities in nature.

Because the use of "finite" and "infinite" in this context is historical and not really accurate, and because there are infinities in nature.

There are an infinite number of points between the 0 and 1-inch marks in your ruler.

The distinction between a "finite" universe and an "infinite" universe is topological. A finite universe is a compact manifold. An infinite universe is a non-compact manifold. That is the proper mathematical terminology.

In the face of uncertainty it would be unscientific to not give equal billing to the various possible cases.

You have to be very careful with the terms "finite" and "infinite". They are much abused, particularly in physics.

Wether finite or infinite, everyone does agree that the universe is unbounded, ie there is no edge or end and a resultant 'outside'. Examples in 2 dimensions would be an infinitely long line, infinite and unbounded and a circular line segment, obviously finite but you still canont get to a boundary by following the line. In 3 dimensions the analogues are a sphere and an infinite plane. Someone else can try to explane the 4 dimensional analogue.

So no-one has actually read Perfect Symmetry by Pagels ? Pity !
I found it quite interesting and informative and contained one of the best explanations of Guth's inflation, the problems it solved inherent in the earlier model such as isotropy, flatness lack of monopoles and antimatter, and the false vacuum and symmetry breaking (excellent explanation) that led to it.
I found it much more informative, although a litle speculative, for the layperson, than A Brief History of Time.

Go on Doc., for $4 you can't go wrong, give it a spin.

Originally Posted by MigL

Someone else can try to explane the 4 dimensional analogue.

3D space would be the infinite "surface" of a finite 4D hypercube.

Originally Posted by MigL

So no-one has actually read Perfect Symmetry by Pagels ? Pity !
I found it quite interesting and informative and contained one of the best explanations of Guth's inflation, the problems it solved inherent in the earlier model such as isotropy, flatness lack of monopoles and antimatter, and the false vacuum and symmetry breaking (excellent explanation) that led to it.
I found it much more informative, although a litle speculative, for the layperson, than A Brief History of Time.

Go on Doc., for $4 you can't go wrong, give it a spin.

I have seen enough bad popularizations that I tend to read only those by first-rank researchers. Pagels is a real physicist, but not on the A-team. My bookshelves are already overflowing.

My criteria is not foolroof. There are some good books by other than the superstars. There are some stinkers by the big boys -- Hawking's recent The Grand Design is awful ( inaccurate and wildly speculative).

Alan Guth wrote a good book on inflation, The Inflationary Universe. There is also a discussion in Steven Weinberg's Cosmology (this one is not a popularization).[/i]

Originally Posted by questor

Originally Posted by MigL

Someone else can try to explane the 4 dimensional analogue.

3D space would be the infinite "surface" of a finite 4D hypercube.

wrong

The surface of a 4D hypercube is the 3-sphere, which is compact. ANY closed subset of a compact space is compact.

As usual, you have no idea what you are talking about.

Originally Posted by MigL

Whether finite or infinite, everyone does agree that the universe is unbounded, ie there is no edge or end and a resultant 'outside'.

I don't agree that the universe is unbounded. The universe is said to be "flat", and like Halliday said, there are no infinities in nature. An infinite number of points between the 0 and 1-inch marks in your ruler doesn't count. That's an inch, not infinity. People tend to think of the universe as a hypersphere because they can't conceive of space having a boundary. But there is a way to think about it, something like this:

Set aside the expansion of the universe, and think of space as something like a sphere of water. Ripples within that sphere of water cannot pass beyond that surface. In similar vein waves in space cannot pass beyond the space that is the universe. Now think pair production: an electron is "made from light", and light is a wave in space. You're made out of electrons. And other things too, but the same principle applies. So in simple terms, you're made out of waves in space. Hence you can't jump out through the boundary as if you're a fish jumping out of the sphere of water. Don't forget, this is the edge of space we're talking about here. There is no space beyond it, so there is no beyond it.

Originally Posted by Farsight

Originally Posted by MigL

Whether finite or infinite, everyone does agree that the universe is unbounded, ie there is no edge or end and a resultant 'outside'.

I don't agree that the universe is unbounded. The universe is said to be "flat", and like Halliday said, there are no infinities in nature. An infinite number of points between the 0 and 1-inch marks in your ruler doesn't count. That's an inch, not infinity.

How is that an argument? Infinity is not a distance.

Originally Posted by Farsight

Originally Posted by MigL

Whether finite or infinite, everyone does agree that the universe is unbounded, ie there is no edge or end and a resultant 'outside'.

I don't agree that the universe is unbounded. The universe is said to be "flat", and like Halliday said, there are no infinities in nature. An infinite number of points between the 0 and 1-inch marks in your ruler doesn't count. That's an inch, not infinity. People tend to think of the universe as a hypersphere because they can't conceive of space having a boundary. But there is a way to think about it, something like this:

Set aside the expansion of the universe, and think of space as something like a sphere of water. Ripples within that sphere of water cannot pass beyond that surface. In similar vein waves in space cannot pass beyond the space that is the universe. Now think pair production: an electron is "made from light", and light is a wave in space. You're made out of electrons. And other things too, but the same principle applies. So in simple terms, you're made out of waves in space. Hence you can't jump out through the boundary as if you're a fish jumping out of the sphere of water. Don't forget, this is the edge of space we're talking about here. There is no space beyond it, so there is no beyond it.

The universe is treated as an intrinsic manifold, not an embedded manifold. It is not contained in anything. That makes it very different from sphere of water. Your analogy does not work.

To say that space (a spacelike hypersurface in spacetime) has a boundary is to say that there is a part of space that is two-dimensional, without boundary. That is not physically plausible. There is not one shread of evidence to support such a notion.

In such a region, were it to exist, the very laws of physics would be different. Huygens principle applies only with one time dimension and an odd number of spatial dimensions.

On what do you base your disagreement with mainstream cosmologists that the universe is a manifold without boundary ?

Originally Posted by DrRocket

The universe is treated as an intrinsic manifold, not an embedded manifold. It is not contained in anything. That makes it very different from sphere of water. Your analogy does not work.

It works well enough. The water is analogous to space. No water, no space.

Originally Posted by DrRocket

To say that space (a spacelike hypersurface in spacetime) has a boundary is to say that there is a part of space that is two-dimensional, without boundary. That is not physically plausible. There is not one shred of evidence to support such a notion.

No it doesn't. Space is space. It sustains waves and fields, and has the properties of vacuum permittivity and permeability. It's three dimensional, the universe is flat, and if it isn't infinite, it has a boundary. Describing space as "a spacelike hypersurface in spacetime" is favouring a mathematical "space" over the real thing.

Originally Posted by DrRocket

In such a region, were it to exist, the very laws of physics would be different. Huygens principle applies only with one time dimension and an odd number of spatial dimensions.

Spare me straw man, Doc. Huygens principle doesn't stand in the way of internal reflection.

Originally Posted by DrRocket

On what do you base your disagreement with mainstream cosmologists that the universe is a manifold without boundary?

A lack of supporting scientific evidence, coupled with scientific evidence of a flat universe that began 13.7 billion years ago.

(Someone correct my terminology if I get it wrong.) Consider a flat torus. It's a two-dimensional manifold that has no curvature, yet is not infinite. Compare that to a disc. That's a two-dimension manifold with zero curvature, but has a one-dimensional boundary.

I'm not saying space is a 3 (or 4) dimensional flat torus (Dr. Rocket mentioned there's evidence that it isn't), but there are other geometries that result in the same general thing: flat, without boundary, but not infinite. That there are also flat, unbounded, infinite geometries, and that we have no evidence to support one over the other, means that we shouldn't rule either out yet.

And yeah, if you have a 3D manifold with a boundary, that boundary necessarily has fewer than 3 dimensions.

Originally Posted by MagiMaster

.... if you have a 3D manifold with a boundary, that boundary necessarily has fewer than 3 dimensions.

In fact the boundary must be a 2-manifold without boundary.

Originally Posted by Farsight

Originally Posted by DrRocket

The universe is treated as an intrinsic manifold, not an embedded manifold. It is not contained in anything. That makes it very different from sphere of water. Your analogy does not work.

It works well enough. The water is analogous to space. No water, no space.

Originally Posted by DrRocket

To say that space (a spacelike hypersurface in spacetime) has a boundary is to say that there is a part of space that is two-dimensional, without boundary. That is not physically plausible. There is not one shred of evidence to support such a notion.

No it doesn't. Space is space. It sustains waves and fields, and has the properties of vacuum permittivity and permeability. It's three dimensional, the universe is flat, and if it isn't infinite, it has a boundary. Describing space as "a spacelike hypersurface in spacetime" is favouring a mathematical "space" over the real thing.

Originally Posted by DrRocket

In such a region, were it to exist, the very laws of physics would be different. Huygens principle applies only with one time dimension and an odd number of spatial dimensions.

Spare me straw man, Doc. Huygens principle doesn't stand in the way of internal reflection.

Originally Posted by DrRocket

On what do you base your disagreement with mainstream cosmologists that the universe is a manifold without boundary?

A lack of supporting scientific evidence, coupled with scientific evidence of a flat universe that began 13.7 billion years ago.

You don't know what in the hell you are talking about.

This is completely wrong, as we have come to expect from internet cranks.

You are a menace to neophytes who might be taken by your nonsensical distortions of science.

Go bread any of the classic references provided to you in other threads.

I think an issue that might have led to some confusion is the assumption that a "finite" space must have a boundary. This is not necessarily true.

For example, a 1-dimensional circle is finite, but it has no boundary. If you were a dot moving around on the circle, you'd never run into any barriers. It could be that our 3-dimensional universe is analogous to this (to be precise, it could be that the "space-like foliations" of our universe are like this).

But maybe the universe is finite AND has a boundary. That would be really weird, and it would violate a lot of assumptions in cosmology, but that doesn't make it impossible. Cosmologists tend to assume that the universe looks roughly the same in all places and in all directions. The existence of a boundary would certainly violate this. But hey, who knows? I wouldn't bet serious money on it though.

Originally Posted by salsaonline

But maybe the universe is finite AND has a boundary. That would be really weird, and it would violate a lot of assumptions in cosmology, but that doesn't make it impossible. Cosmologists tend to assume that the universe looks roughly the same in all places and in all directions. The existence of a boundary would certainly violate this. But hey, who knows? I wouldn't bet serious money on it though.

It would be really weird. Physics on the boundary would be very different. Huygens principle would not hold. Random walks would be recurrent. etc.

I would not bet serious money either.

Even without the cosmological assumption of homogeneity and isotropy, the assumption that spacetime is without boundary is pretty fundamental to GR.

I think I could fairly easily forgo the technical condition of isotropy, which apparently excludes the flat torus. Homogeneity on the large scale would be harder to give up. But a boundary would really be strange.

Well now you got me thinking about finite versus infinite universes.
If the universe were infinite how exactly would conservation laws, say of mass/energy, work ?? If the universe is infinite it would necessarily contain an infinite amount of mass/energy and infinity minus any arbitrarily large number is still infinite. So it seems to me conservation laws no longer make sense in an infinite universe.
Or would it make more sense to speak of causally connected domains having valid conservation laws. Then again, energy could move across domain boundaries and screw up the conservation laws for that domain. Or am I missing something here.

As for finite universes, A simply connected three-sphere where every point on the surface is connected to the surface of another sphere is I believe, the one most favoured, since there are no boundaries and no irreducible loops.
Now I don't know much topology so feel free to correct my wrong assumptions and mistakes DrR, but wasn't this Poicaire's conjecture which was recently proven by some Russian (?) mathematitian a few years ago ??

Originally Posted by MigL

Well now you got me thinking about finite versus infinite universes.
If the universe were infinite how exactly would conservation laws, say of mass/energy, work ?? If the universe is infinite it would necessarily contain an infinite amount of mass/energy and infinity minus any arbitrarily large number is still infinite. So it seems to me conservation laws no longer make sense in an infinite universe.
Or would it make more sense to speak of causally connected domains having valid conservation laws. Then again, energy could move across domain boundaries and screw up the conservation laws for that domain. Or am I missing something here.

As for finite universes, A simply connected three-sphere where every point on the surface is connected to the surface of another sphere is I believe, the one most favoured, since there are no boundaries and no irreducible loops.
Now I don't know much topology so feel free to correct my wrong assumptions and mistakes DrR, but wasn't this Poicaire's conjecture which was recently proven by some Russian (?) mathematitian a few years ago ??

Conservation of energy is really a local law. So the issue of finiteness or infiniteness of the universe is not an issue in that regard.

On the other hand it turns out that conservation of energy, and even the basic idea of energy, is difficult to handle in genetral relativity. I don't understand all of the nuances, but you might take a look here

http://www.phys.ncku.edu.tw/mirrors/...energy_gr.html

Originally Posted by DrRocket

Conservation of energy is really a local law. So the issue of finiteness or infiniteness of the universe is not an issue in that regard.

On the other hand it turns out that conservation of energy, and even the basic idea of energy, is difficult to handle in genetral relativity. I don't understand all of the nuances, but you might take a look here

http://www.phys.ncku.edu.tw/mirrors/...energy_gr.html

As I understand it, the present size of our observable universe (the comoving distance) is a sphere that extends about 46 billion light years radially from our point in space. There is also a "future visibility limit" (the maximum observable univerve that we would ever be able to see at some distant time in the future) that will have an estimated comoving distance of ~62 billion light years (at the distant future time of observation).
(ref. http://en.wikipedia.org/wiki/Observable_universe )

My question is: Can anything (mass or energy) outside our present or future observable universe have an effect on our observable universe?

Another way of asking the same question is: Would such things as the observed flatness of the universe or the accelerated expansion of the universe be different in a finite universe than they would be in a universe that is infinite?

The reason I ask this is that I'm thinking of the edge of our observable universe as a sort of cosmological event horizon. If I equate this with the event horizon of a black hole then I would wonder if the density and distribution of energy and matter in the space outside the event horizon of a black hole has any effect on the properties of space inside a black hole. The only effects of which I'm aware are that matter and energy crossing an event horizon will expand the event horizon and very probably add angular momentum. In terms of cosmology, I don't think our observable universe is thought to possess any overall net angular momentum - but I could be wrong about that.

Chris

Originally Posted by CSMYTH3025

My question is: Can anything (mass or energy) outside our present or future observable universe have an effect on our observable universe?

That all depends on how we define our observable universe, and about when you are asking the question, but in simple terms, no. If we see a distant object, and see the effects a more distant object is having upon it, then we can also see the more distant object, so both are inside our observable universe.

As we look out into the universe we are seeing what is known in cosmology as our past light-cone. Light is reaching us from all directions, all at the same time, but it was all emitted at different times throughout the history of the universe. At any given time, we see a different slice of the whole history of the universe, played out across an increasing distance as the history progresses.

As we trace our light-cone backwards in time, we see it slice through the history (or worldline) of different objects at different times, and the most distant time we can see is where our light-cone intersects the universal wide event of the release of the CMBR (our particle horizon).

The particle horizon usually defines the edge of our observable universe, and if a CMB photon had passed through a series of galaxies in order to reach us, all those galaxies could be causally connected as their influence would also travel at the speed of light. So if we can see the effect of a more distant event on an object, we should also be able to see the origin of that more distant event.

Our past light-cone is an event horizon in itself - it is today's cosmological event horizon. But you also mentioned the future of our observable universe. If there has been an event outside of our light-cone, it has not, from our vantage point, had any effect on any of the objects on our light-cone, as that event is in the future of an object on our light-cone.

Our past light cone as time tends towards infinity is our ultimate cosmological event horizon, and due to the acceleration of the expansion (based on the most popular projections) we will then be able to see events that are happening today, 16 billion light-years away, and events that happened in the past, all the way back to the CMBR, which would have been released from a co-moving radial distance of around 62 billion years, as you have said.

Then again, it all depends on how you define observable universe. Right now, a galaxy 1 billion light-years away, has an observable universe that reaches further in that direction than our observable universe does. Presumably, there are influences that will reach that galaxy, that will never reach us.

Originally Posted by CSMYTH3025

Originally Posted by DrRocket

Conservation of energy is really a local law. So the issue of finiteness or infiniteness of the universe is not an issue in that regard.

On the other hand it turns out that conservation of energy, and even the basic idea of energy, is difficult to handle in genetral relativity. I don't understand all of the nuances, but you might take a look here

http://www.phys.ncku.edu.tw/mirrors/...energy_gr.html

As I understand it, the present size of our observable universe (the comoving distance) is a sphere that extends about 46 billion light years radially from our point in space. There is also a "future visibility limit" (the maximum observable univerve that we would ever be able to see at some distant time in the future) that will have an estimated comoving distance of ~62 billion light years (at the distant future time of observation).
(ref. http://en.wikipedia.org/wiki/Observable_universe )

My question is: Can anything (mass or energy) outside our present or future observable universe have an effect on our observable universe?

No.

See post by Speedfreak

Originally Posted by CSMYTH3025

Another way of asking the same question is: Would such things as the observed flatness of the universe or the accelerated expansion of the universe be different in a finite universe than they would be in a universe that is infinite?

Not really. Though perhaps the amount of "dark energy" might affect the curvature of space and therefore the topology, but that connection is less direct and more conjectural than what I infer to be your question.

Originally Posted by CSMYTH3025

[The reason I ask this is that I'm thinking of the edge of our observable universe as a sort of cosmological event horizon. If I equate this with the event horizon of a black hole then I would wonder if the density and distribution of energy and matter in the space outside the event horizon of a black hole has any effect on the properties of space inside a black hole. The only effects of which I'm aware are that matter and energy crossing an event horizon will expand the event horizon and very probably add angular momentum. In terms of cosmology, I don't think our observable universe is thought to possess any overall net angular momentum - but I could be wrong about that.

There is a sort of cosmological event horizon, called the "Hubble Sphere". The Hubble Sphere however is not invariant, and depends on the location of the observer. That is a big difference between the Hubble Sphere and the event horizon of a black hole.

If you want to study black holes you are going to have to get into a detailed study of the theory. I am not an expert. Two references on the subject are The Mathematical Theory of Black Holes by Chandrasekhar and Gravitation by Misner, Thorne, and Wheeler.