Does a finite universe make sense to you?

[epkid08]

Starting from any point in the universe, shine light in all directions; given infinite time has passed, will it have reached the edge of the universe?

It doesn't make sense to me to define the universe as finite, as there is no edge of the universe to cross.

You could imagine the universe shaped like a sphere, and traveling a constant distance in a straight path would eventually get you back to your original position, but still you would never reach the edge of the universe.

At the border of our universe lies a dimensionless quantity.

What are your thoughts?

 

[cristo]

If you model the universe as the surface of a sphere, then this is a finite universe but which has no boundary. Thus, it makes perfect sense to have a finite universe but which has no "edge."

At the border of our universe lies a dimensionless quantity.

I'm not sure what you mean here, could you expand?

 

[thenewmans]

Read How the Universe Got Its Spots by Janna Levin and then go read Ned Wright's Cosmology Tutorial website again. I swear to you that you will have a tough time believing the universe can be endless. It’s funny how that happens. Janna’s book is thin and easy. There’s no college math, no raisin bread and no balloons. Instead, it’s all the different possibilities and how to interpret the CMB and that kind of thing.

An endless universe has its issues. It needs an infinite mass at the time of the Big Bang. That means infinite galaxies and infinite worlds. So there must be one just like ours, in fact infinite worlds just like ours. Even so, I prefer an infinite universe too. But it’s nothing more than a preference.

 

[BoomBoom]

If you model the universe as the surface of a sphere, then this is a finite universe but which has no boundary. Thus, it makes perfect sense to have a finite universe but which has no "edge."

The problem with the "balloon" analogy is that, while it may make sense in 2 dimensions, we live in 3 dimensions... and there is no 3-D analogy, which is why it makes no sense.

A finite universe with no boundary/edge is difficult (if not impossible) to imagine or envision...which also makes it hard to believe.

This is one of those subjects that the cosmology community continually states as a "fact" when there is no way to verify it as such...nor will there ever be.

 

[NYSportsguy]

From what I am hearing the accepted theory by most modern theoretical physicists and cosmologists today is the fact that our universe is one of many in a so called "Cosmic Landscape". In other words, we can tell the that our present universe is constantly expanding everywhere all the time because of the cosmological constant and creation of dark energy.

However, the theory that is most strong today is that our universe (and all of it's physical laws) originated from another bigger expanding universe that we cannot see yet because of its enormity. This universe in turn, grew out of an even bigger universe that was expanding rapidly say 30 billion light years ago...etc. etc. So as we know it, there are several "megaverses" that were here and expanding before our universe is, and that will continue to develop more universes each with their own "Big Bang" that will grow and expand from our universe as we know it.

This is known as the "pocket universe" theory or a "universe born within another universe" type of theory.

 

[NYSportsguy]

Note: Each of those universes that preceded ours or will that should be created from within ours will have different physical laws and properties than our universe does (ie- different cosmological constants, different strengths for each of the four fundamental forces, perhaps more or less than four fundamental forces...etc.)

Basically every universe created from other universes will have variety. String theory accounts for all of this happening I heard.

 

[marcus]

From what I am hearing the accepted theory by most modern theoretical physicists and cosmologists today is the fact that our universe is one of many in a so called "Cosmic Landscape"...

Have to be more clear. There was a temporary union of two ideas----the string landscape (now out of fashion among string theorists) and the multiverse resulting from the eternal inflation scenario.

Your word "most" is probably inaccurate. String theorists are a minority of theoretical physicists. The landscape bunch was a minority within a minority.
This year's annual meeting (Strings 2008) has no landscape talks scheduled.
The landscape fad was mainly 2003-2007. At what was probably the height, in 2005, they had an informal poll at the annual meeting (Strings 2005) and rankandfile string theorists voted AGAINST landscape thinking by about 3 to 1. Steve Shenker, who was leading the panel+audience discussion and who posed the question was heard to say "holy shît" when he saw the hands raised in the auditorium. It surprised a number of prominent string leaders, who at that time were promoting landscape ideas.

Again, amongst cosmologists, only a small minority study inflation scenarios. It would be an exaggeration to say that the multiverse of eternal inflation is "accepted" by any but a small minority. The business of bubble universes or pocket universes is mainly speculation by a few. For ordinary working cosmologists, one universe with one inflation episode at the beginning is enough for them to investigate and be concerned with.

So when you look at the cosmology research papers being published in the professional journals you don't see very much about multiverse or eternal inflation---you see research into models of our universe.

========================

We shouldn't confuse landscape ideas with the fact that the standard model universe extendes beyond what is directly observable. The latter is normal. It is just part of the consensus picture of the universe that cosmologists work with. The observable portion is a small part of the whole thing. The whole can be finite spatial volume, or infinite----they are still working on determining which.

No reason to assume that physical laws and conditions are any different in the part we can't see from how they are here in the part we can see. No reason to speculate about a landscape just because the observable portion is not the whole thing.

Basically there was a buzz about cosmic landscape and it looks now as if it might be quieting down. One sign being that it seems to be less fashionable now with string theorists---as I said the schedule for the main annual conference Strings 2008 at the present has no landscape talks scheduled. If string people stop promoting it, probably the whole thing will get a flat tire. (just my guess)

 

[malawi_glenn]

BoomBoom: You just apply the same mathematics that you do on a 2D 'surface' which is finite, but yet without boundaries, to a 3D surface.

Just because we can't imagine things with our intuinition doesn't mean that it is true and can exist. The language of physics is math, not 'plain imagination' and similar.

 

[DaveC426913]

It doesn't make sense to me to define the universe as finite, as there is no edge of the universe to cross.
...
What are your thoughts?

My thoughts are: if we allowed our "common sense" to tell us how the universe worked, it would still be telling us that the Earth cannot be a sphere since the Australians would fall off into space.

 

[NYSportsguy]

Marcus -

First of all I apologize for my error in saying how the "eternal expanding universe" theorem was the popular belief amongst most theoretical physicists today. Thank you for clearing that up. However based on an article I read online the other week, it seems to be that the case for the "universe within a universe" is becoming more and more stronger. Check this link out:

http://space.newscientist.com/artic...in-space-is-1-billion-light-years-across.html

How can this not be proof that theoretical physics is headed towards a multi-universe view on things?

Big ups to Leaonard Susskind and Lisa Randall for opening me up to these ideas.

 

[BoomBoom]

Just because we can't imagine things with our intuinition doesn't mean that it is true and can exist. The language of physics is math, not 'plain imagination' and similar.

By the same token, I think one can put too much substance into the math itself without consideration as to what it actually means in the real physical universe.

I think that is why many ideas proposed by string theorists (multi-verses, parallel dimensions, etc.) seem so far off in "left-field" because they seem to ONLY see the math without any observation or logic to back it up.

The truth is that we will never be able to observe any of the universe that lies outside our observable threshold, so any postulations about the nature of it (any sort of outer edge boundary or lack of one) is nothing more than an assumption that cannot be verified.

 

[marcus]

Marcus -

First of all I apologize for my error in saying amongst most theoretical physicists today.
...
Big ups to Leaonard Susskind and Lisa Randall for opening me up to these ideas.

NYSport,
no need to apologize! I just meant to point out that there is a disconnect between the real research literature---stuff published and cited in peer-review professional journals, and what you get in New Scientist and in pop-sci mass market books.

Huge difference. Can't take NewSci seriously, if they give you the impression of a consensus amongst some professional group. Lot of ga-ga stuff in NewSci.

In the case of Susskind and Randall,
1. they are just 2 scientists out of many hundreds that sometimes do cosmology. not representative of community of working cosmologists (really in other specialties, string, braneworld models)

2. watch what they do, not what they say

3. both Susskind and Randall have authored popularization books. they naturally talk up the stuff they present in their books.
========================

Susskind wrote a pop-sci book called Cosmic Landscape. It came out in 2005 and he talked it up a lot on the media. It didn't sell well. Now three years later, he has just brought out A DIFFERENT popularization book that has nothing about multiverse or Landscape. It hits the market July 2008.

When they had that informal show of hands at Strings 05 in Toronto it was a room full of about 400-some string theorists. They voted over 3 to 1 against Susskind's pet idea of the anthropic string theory Landscape. Of course science is not a democracy and Susskind has support money and visibility and tenure at Stanford. He is prominent and carries a lot of weight. But you can't say he represents a majority or a consensus.

Science in the media is to some extent personality-driven. It is different from actual science.

Neither Susskind nor Randall got invited to give talks at the main annual string meeting, Strings 2008.

whereas they were very big in past years. Indeed in 2005, in Toronto, Susskind gave one of the two public lectures in the big auditorium. The other big talk was given by Robbert Dijkgraaf. Multiverse and Landscape were very big that year.

Now there is a quiet unpublicized reaction against that stuff. Coupled with a cutback in faculty jobs for string theorists in the US.

Basically Susskind, a smart guy, is changing his message and how he presents himself. He recently said he doesn't like to be labeled as a string theorist. He has other research interests, other directions, he points out. And he has stopped promoting the Landscape so vociferously as he was back in 2003-2005. His new book is about something else. He is presenting a new face.

Maybe in 2009 he will be invited to give a talk at Strings 09----and if so it will probably not be about Multiverses or the landscape of possible string theories. We'll see. Nobody can predict the future course of fundamental physics research. We can bet, though. Would you like to bet? No money, just go on record with a prediction.

 

[marcus]

...
It doesn't make sense to me to define the universe as finite, as there is no edge of the universe to cross.

By finite, I mean finite spatial volume. At this moment in cmb rest frame time. Is that what you mean by finite? I wouldn't expect a spatially finite universe to have an edge.

You could imagine the universe shaped like a sphere, and traveling a constant distance in a straight path would eventually get you back to your original position, but still you would never reach the edge of the universe.

Yes! That is a good way to imagine a finite spatial volume. The 3D analog of the 2D surface of a sphere.

If you can imagine a 3D sphere analog, which a lot of people can (but some people here claim they can't), then why do you say it wouldn't be finite? It pretty clearly has a definite finite volume. I can give you a formula to calculate it if you want, using the radius of curvature.

One estimate, based on latest WMAP data, of the radius of curvature of the universe is 130 billion LY. It could also be infinite. We don't know. But if it happens to be 130 billion LY then the current spatial circumference would be about 800 billion LY. and we can also say what the current volume would be, in cubic LY. Maybe I will do the calculation.
...
=============
Yeah. here goes
we have to plug 130 billion LY into this
2\pi^2R^3

and pi-square is about 10, so
2\pi^2
is about 20

Now we have to cube R. The cube of 1.3 is 2.2, so if R is 130 billion LY then
R^3 is 2.2 E33 cubic LY

All that remains is to multiply that by 20.

4.4 E34 cubic LY.

This is the spatial volume of the universe at this moment in cmb restframe time---estimate based on the 130 billion LY estimate of the radius of curvature.

We have estimates of the average mass density at the present moment (same standard idea of present moment)---grams per unit volume--- or equivalently converting mass to energy we have estimates of the energy density---joules per unit volume---
so we can take that estimated volume if we want and easily derive an estimate of the total mass or the total energy equivalent (of the matter in the universe.)

Note that this is not an estimate for the observable portion. this is for the whole thing.

The key is having an estimate for the radius of curvature. the data so far does not rule out either the finite radius of curvature, or the infinite case. we can make "best guess" estimates but we don't know, so have to keep open to either case.

Anyway finite is certainly not unimaginable. It is very straightforward imaginable, and I have given you a sample possible volume.

 

[Harut82]

From what I am hearing the accepted theory by most modern theoretical physicists and cosmologists today is the fact that our universe is one of many in a so called "Cosmic Landscape". In other words, we can tell the that our present universe is constantly expanding everywhere all the time because of the cosmological constant and creation of dark energy.

However, the theory that is most strong today is that our universe (and all of it's physical laws) originated from another bigger expanding universe that we cannot see yet because of its enormity. This universe in turn, grew out of an even bigger universe that was expanding rapidly say 30 billion light years ago...etc. etc. So as we know it, there are several "megaverses" that were here and expanding before our universe is, and that will continue to develop more universes each with their own "Big Bang" that will grow and expand from our universe as we know it.

This is known as the "pocket universe" theory or a "universe born within another universe" type of theory.

A light year is not a measurement of time!

 

[MeJennifer]

It seems that me that it is not impossible for a finite universe to have an infinite volume. Curved spacetime can play tricky things on spatial volumes. For instance, consider the spatial volume of a black hole.

 

[Harut82]

It seems that me that it is not impossible for a finite universe to have an infinite volume. Curved spacetime can play tricky things on spatial volumes. For instance, consider the spatial volume of a black hole.

I never thought about that. A 1 dimensional line can be infinite if we curve it into a circle, something two dimensional. Same way the universe can be infinite in the curved spacetime in higher dimension.

 

[turbo]

My intuition and preference is for a universe that is both spatially and temporally infinite. If you will mine Edwin Hubble's writings, you'll find that he felt the same way. He knew that his redshift-distance relationship was being popularly interpreted as if the universe was undergoing expansion, but he resisted this explanation even to his death, choosing to contemplate an infinite (both S&T) steady-state universe in which light was redshifted in its trip from distant galaxies to us. He was a good friend and collaborator of Zwickey, whose tired-light hypothesis gave support to Hubble's intuition that redshift was not a function of a Doppler-like universal expansion.

Can light lose energy to the space through which it propagates? It sounds very foreign to many of us, but there are believers. The MAGIC consortium published a result that purports to show that ultra-high-frequency gamma-rays are slowed compared to gamma rays of more modest energies. Fotini Markopoulo of the Perimeter Institute had predicted such a frequency-energy related delay years back and had proposed that such a delay might bee seen in the GLAST observations. We will see. Such a result would bring the vacuum back into play as a player in the propagation of EM and usher in a re-emergence of ether-theory.

 

[MeJennifer]

My intuition and preference is for a universe that is both spatially and temporally infinite.

In GR one implies the other.

 

[turbo]

In GR one implies the other.

One might think so, until you get to the point at which parameters are adjusted to accommodate open or closed universal curvatures in order to make observations fit with theories of various cosmologists. I have problems getting really comfortable with this.

 

[epkid08]

If you model the universe as the surface of a sphere, then this is a finite universe but which has no boundary. Thus, it makes perfect sense to have a finite universe but which has no "edge."

A sphere with a normal quantity radius has a boundary which can be reached. If the universe's boundary cannot be reached, doesn't this call for a non-normal quantity radius?

 

[NYSportsguy]

Marcus -

Well that link I put in my last response. What do you account that for missing space region for...I am just curious.

And by the way, Susskind's new book argues about what happens when light or any matter reaches a black hole. Him and Stephen Hawking disagreed about this and the disagreement went on for about 25 years or so.

It has nothing to do with the "Cosmic Landscape" or our origin or shape of the universe. It's a totally different idea and topic in of itself. The reason Susskind wasn't so high on String Theory was because he said it wasn't elegant enough...it was more like a "Rube Goldberg's machine" than it was an explanation for why things occur in nature. Not to put down String theorists, but so far Susskind seems correct.

He doesn't mention that String Theory won't eventually be right...just for now its becoming to messy and complicated.

 

[malawi_glenn]

epkid08: You understand wrong here, the SURFACE of the sphere has no boundary, but is still finite.

 

[marcus]

Marcus -

Well that link I put in my last response. What do you account that for missing space region for...I am just curious.
...

It is an interesting topic! Your link was to an August 2007 NewSci article

http://space.newscientist.com/artic...in-space-is-1-billion-light-years-across.html

Keep in mind that NewSci style tends to be misleading and sensationalist---there is no "missing space" in any simple sense. The region in question is known to contain many galaxies. We can see them. But some scientists think that it contains significantly fewer than average.

There are many hot spots and cold spots in the CMB and one cold spot happens to be especially big. So there are various proposed explanations for the Big Cold Spot.

One explanation involves postulating a large "void" region. A region that is not entirely empty of galaxies but which has significantly less than average. Light can be heated as it passes thru a cluster of galaxies and the idea is fewer clusters would mean less heating.

There are other proposed explanations. Some astronomers challenge the "void" explanation and offer other explanations for the Cold Spot. Including that it is just a random fluctuation in the CMB. Some random fluctuation is to be expected, and is observed elsewhere in the sky.======================

I don't take a personal stand on most issues like this. I do try to watch how professional opinion is going, and spot trends. I haven't seen any signs of a consensus building up about this. Maybe someone else has, and will comment.

AFAIK if there indeed is a large void---a region with fewer galaxies than average---it wouldn't be the only one. It would just be an unusually large one. The distribution of clusters of galaxies is WISPY. Comparatively thick some places and thin other places----like cobweb.

There is a bunch of models for how this kind of pattern forms called "structure formation". It is getting to be better understood. It is part of ordinary mainstream theory of our universe-----not part of "multi" speculations.

 

[epkid08]

epkid08: You understand wrong here, the SURFACE of the sphere has no boundary, but is still finite.

I guess you misunderstood me. Take a basketball for example; Let's call it a sphere. It would be possible for a particle to travel from the center of the ball to the very edge of the ball, but also, it could travel out of the ball. So we can say that because the particle was able to pass the edge of the ball, it then has a normal sized radius. When you say we can't pass the edge of our universe, you have to assume that the radius, or the length from any point to the 'edge' is infinite.

Of course this is if, and only if, we cannot physically pass the edge of the universe. What would lie outside the edge anyways?

 

[yuiop]

I guess you misunderstood me. Take a basketball for example; Let's call it a sphere. It would be possible for a particle to travel from the center of the ball to the very edge of the ball, but also, it could travel out of the ball. So we can say that because the particle was able to pass the edge of the ball, it then has a normal sized radius. When you say we can't pass the edge of our universe, you have to assume that the radius, or the length from any point to the 'edge' is infinite.

Of course this is if, and only if, we cannot physically pass the edge of the universe. What would lie outside the edge anyways?

If the basketball was expanding at the speed of light (or greater depending on th emodel you prefer) then you would have great difficulty getting from the centre of the ball to the surface of the ball. To get from the centre to the surface you would also have to be sure you were traveling in a straight line to avoid moving in large circles and it turns out that is not as easy as it seams. If you shone a laser beam outwards and followed that, how could you be sure that the beam is not curved by the mass of the universe? If you actually got to the edge of the universe it would be very hard to tell that you were actually there because of gravitational and possibly relativistic abberation that makes light appear to be coming towards you from regions where there are no galaxies, so you would not actually see a void beyond the edge of the universe.

 

[cristo]

I guess you misunderstood me. Take a basketball for example; Let's call it a sphere. It would be possible for a particle to travel from the center of the ball to the very edge of the ball, but also, it could travel out of the ball.

But this isn't the model that I proposed back in post #2. I spoke about the surface of such a basketball. This, as malawi says, does not have a boundary.

 

[LowlyPion]

But this isn't the model that I proposed back in post #2. I spoke about the surface of such a basketball. This, as malawi says, does not have a boundary.

Perhaps you can expand my understanding of how an inflating balloon surface universe would work in our experience of it? I can see that there is some satisfaction in noting that things would be receding as the balloon inflates as is even our childhood experience of such things. That galaxies would hang more together by their gravity but recede from each other with this inflation.

But where my limited imagination founders is in seeing the balloon as more than just a surface. How is the "innerness" and the "outerness" of our experience of being on such a surface hidden from our ability to detect it such that we perceive 3 spatial dimensions that look uniform in all direction?

That we have no way to feel the effects of whatever outward means by which the whole surface is inflating? Shouldn't there be some form of gradient in the direction of outward expansion that corresponds to the expansion that would be experienced on this surface? Or is it an expansion with no outwardness to it?

Thanks in advance.

 

[BoomBoom]

I guess you misunderstood me. Take a basketball for example; Let's call it a sphere. It would be possible for a particle to travel from the center of the ball to the very edge of the ball, but also, it could travel out of the ball.

You misunderstood the analogy. This is strictly a 2-dimensional analogy...there is no inside or outside of the ball since there is no 3rd dimension.


You will not hear of a 3-D analogy because there is none.

 

[LowlyPion]

You misunderstood the analogy. This is strictly a 2-dimensional analogy...there is no inside or outside of the ball since there is no 3rd dimension.

You will not hear of a 3-D analogy because there is none.

Your comment wasn't directed to me, but I appreciate that it addresses the deficiency of my understanding in my previous questions. But that said why is it that this basketball/balloon analogy keeps getting forwarded (I've seen it a number of times employed elsewhere) as some aide to understanding the expanding nature of the universe when it carries about as much relevance to our 3D world as there is to our understanding the laws of physics from Flatland?

Maybe an infinitely expandable marshmallow dropped into a vacuum?

 

[turbo]

Your comment wasn't directed to me, but I appreciate that it addresses the deficiency of my understanding in my previous questions. But that said why is it that this basketball/balloon analogy keeps getting forwarded (I've seen it a number of times employed elsewhere) as some aide to understanding the expanding nature of the universe when it carries about as much relevance to our 3D world as there is to our understanding the laws of physics from Flatland?

Maybe an infinitely expandable marshmallow dropped into a vacuum?

The analogy (which is poor and hard to visualize for 3-dimensional critters like us) usually describes 2-D space as the outer surface of a balloon that can expand such that distances between dots of material glued to the balloon can increase without themselves expanding, AND the surface of the balloon is finite, yet unbounded. If you are an ant, you can travel from one dot to another on the surface of the balloon without every reaching an "edge". We do not have the mental horsepower to translate this 2-D analogy to a 3-D universe, and that is the source of a lot of questions and confusion about the analogy.

 

[epkid08]

If the basketball was expanding at the speed of light (or greater depending on th emodel you prefer) then you would have great difficulty getting from the centre of the ball to the surface of the ball. To get from the centre to the surface you would also have to be sure you were traveling in a straight line to avoid moving in large circles and it turns out that is not as easy as it seams. If you shone a laser beam outwards and followed that, how could you be sure that the beam is not curved by the mass of the universe? If you actually got to the edge of the universe it would be very hard to tell that you were actually there because of gravitational and possibly relativistic abberation that makes light appear to be coming towards you from regions where there are no galaxies, so you would not actually see a void beyond the edge of the universe.

If the universe had an edge, what would lie beyond that edge? There either has to be an explanation of what is beyond the edge, or an explanation of why we cannot physically cross it.

 

[LowlyPion]

We do not have the mental horsepower to translate this 2-D analogy to a 3-D universe, and that is the source of a lot of questions and confusion about the analogy.

No possibility that it's not a matter of our mental horsepower, but a fundamental flaw of the analogy to attempt to use 2 space constructs in 3 land?

If the analogy fails to satisfy our actual experience, then I have to question its utility.

Thanks for the explanation.

 

[cristo]

No possibility that it's not a matter of our mental horsepower, but a fundamental flaw of the analogy to attempt to use 2 space constructs in 3 land?

If the analogy fails to satisfy our actual experience, then I have to question its utility.

Thanks for the explanation.

This is only an analogy. The reason that cosmologists use such an analogy is so that people can imagine the scenario, and thus paint a picture in their head. Of course, we all know that this has a dimension missing, and that the equivalent "real" model would be the three dimensional surface of a higher dimensional sphere (i.e. S^3, in maths terms).

Note that we are not attempting to use a 2D analogy in "3 land", as you say in your post, but are rather reducing the higher dimensional topology into one that can be pictured by throwing away a dimension.

 

[turbo]

Note that we are not attempting to use a 2D analogy in "3 land", as you say in your post, but are rather reducing the higher dimensional topology into one that can be pictured by throwing away a dimension.

Exactly! And throwing away a dimension is something that is either misunderstood or poorly explained (or both). The person hearing the analogy misses that and imagines that there are three degrees of freedom (not just two) because a balloon is a 3-D object.

 

[LowlyPion]

Of course, we all know that this has a dimension missing, ...

Ok I get that and it's helpful to know that it's a simple minded analogy and all, but if I might ask then what is this missing dimension?

 

[sketchtrack]

This is only an analogy. The reason that cosmologists use such an analogy is so that people can imagine the scenario, and thus paint a picture in their head. Of course, we all know that this has a dimension missing, and that the equivalent "real" model would be the three dimensional surface of a higher dimensional sphere (i.e. S^3, in maths terms).

Note that we are not attempting to use a 2D analogy in "3 land", as you say in your post, but are rather reducing the higher dimensional topology into one that can be pictured by throwing away a dimension.

Isn't a sphere a 3d object anyways?

Why should we picture in our heads something that isn't relevant to physics?

 

[cristo]

Ok I get that and it's helpful to know that it's a simple minded analogy and all, but if I might ask then what is this missing dimension?

I'm not sure I get your question: when transforming from the model to the 2D analogy, we discard one spatial dimension.

Isn't a sphere a 3d object anyways?

Technically, no; a 2-sphere is the two dimensional surface of the three dimensional object.

Why should we picture in our heads something that isn't relevant to physics?

What do you mean why should you? I'm simply saying that, if you wish to picture how such a closed universe could look, then you can use the analogy of the surface of an inflating balloon, by considering only two spatial dimensions. If not, and you are comfortable dealing with the model of the 3-sphere, then that is fine.

 

[sketchtrack]

Yeah, but the universe isn't a surface of a sphere, and that is pretty easy to prove, so what is the point? You could say if the universe is a strait line that never ends, then it would look like that, but it isn't.

 

[LowlyPion]

... when transforming from the model to the 2D analogy, we discard one spatial dimension.

OK. I think I got that a space dimension was discarded. I guess my question is what is the 4th dimension of this presumed 4 space on which the 3-space is mapped so as to be able to represent it as the "surface" of a giant inflating balloon?

 

[MeJennifer]

OK. I think I got that a space dimension was discarded. I guess my question is what is the 4th dimension of this presumed 4 space on which the 3-space is mapped so as to be able to represent it as the "surface" of a giant inflating balloon?

Actually you should think of a 4 dimensional space being mapped onto a closed surface.

GR deals with curved 4 dimensional spacetimes.

 

[LowlyPion]

Actually you should think of a 4 dimensional space being mapped onto a closed surface.

GR deals with curved 4 dimensional spacetimes.

Not to be tedious about this but when the analogy is employed of using the expanding balloon and a space dimension is dropped out for this purpose, then what you are saying should be visualized is a 2-space that is mapped on the surface of this balloon and the third dimension is "time". Implying solely in the case of the analogy that the balloon is visualized which captures a single instant, as a spherical surface with radius representing the age of the universe from the big bang? That a picture of all time from the big bang by extension would be a layered solid onion of all the accumulated instants piled one upon another?

 

[NYSportsguy]

No possibility that it's not a matter of our mental horsepower, but a fundamental flaw of the analogy to attempt to use 2 space constructs in 3 land?

If the analogy fails to satisfy our actual experience, then I have to question its utility.

Thanks for the explanation.

Okay simply put, the analogy is similar to the reason why Columbus was able to travel across the globe by sea in 1492 and circumnavigate his way back to wherever it was he sailed from. He saw an "edge" however wasn't able to go over that "Edge" becasue there was more land and sea there. It revolves around forever becasue the surface on which he traveled on (our Earth) is in sphere form. HOwever we do knownthere is an "edge" between our upper atmospshere and space. This is similar to the "edge" we see between "space" and whatever lays on the other side.

For us, so far, it is humanly impossible to detect this "outer boundary". It may not exist for all we know. The laws of physics might prevent us from ever getting that far.

Nobody knows.

 

[yuiop]

If the universe had an edge, what would lie beyond that edge? There either has to be an explanation of what is beyond the edge, or an explanation of why we cannot physically cross it.

Beyond the edge is nothing, an infinite amount of nothing.

To explain why we can not cross it we first have to define what would be classified as the edge of the universe. Do we consider where the universe runs out of stars and galaxies as the edge or is the edge the surface created by the expanding ball of light from the big bang? To cross that boundary you would have to exceed the speed of light. The expanding surface of light and gravity leads the ways in virginal space preparing the way for matter that follows. Of course there is no way to be sure that are not other island universes out there O:

Can we detect anything about the what is beyond our visible universe? I believe the answer is yes. If the universe is larger than our visible horizon yet finite and if we are not exactly at the centre of that larger universe then we should detect some small anisotopy between two hemispheres of the CMB after the small anisotropy of the CMB redshift due to our peculiar motion has been allowed for.

Very accurate measurements of supernova, CMB and cluster data will eventually get all the data to agree with each other and give us an anser to whether the universe if infinite or not. The current best guess is that the universe is finite but not the infinite case is not elliminated by the current error bars.

For what it worth, Einstein felt quite strongly that an infinite universe is not compatible with General Relativity.

 

[yuiop]

Why do we need to drop a dimension to find an analogy? For example a solid cannon ball is a 4D object. It has 3 spatial dimension and one of time. So the challenge is explain why creatures living inside the cannon ball can not leave it and why the cannonball has no edge.

 

[LowlyPion]

The current best guess is that the universe is finite but not the infinite case is not elliminated by the current error bars.

For what it worth, Einstein felt quite strongly that an infinite universe is not compatible with General Relativity.

Since I have no theory in the hunt, for my money I'll take infinite.

If it's finite what's the count?

Before anyone may want to win such a bet though, keep in mind I will demand a recount.

 

[epkid08]

Beyond the edge is nothing, an infinite amount of nothing.

To explain why we can not cross it we first have to define what would be classified as the edge of the universe.

Any finite amount of matter has an edge. If there is no physical edge to cross, the matter cannot be finite, but infinite. (if you have an example to prove this statement wrong, say it)

Even if a finite amount of matter was expanding at a constant acceleration,a<\infty, a particle traveling at a=a_{m}+1 given infinity time would reach an edge of the matter.

Edit: The only explanation I can come up with that goes against what I said, is as you approach the edge of the universe, some undiscovered force, that is applied to you towards the center of the universe, is approaching infinity. Why else would it be impossible to reach the edge of a finite universe?

 

[yuiop]

Since I have no theory in the hunt, for my money I'll take infinite.

If it's finite what's the count?

Before anyone may want to win such a bet though, keep in mind I will demand a recount.

By count, do you mean count the number of galaxies for example? Are there an infinite number of galaxies in the universe? You do realize how big infinite is? Think of the biggest number you can possibly think of, square it, add it to iteself, cube it, multiply by 10^999999999999999999999999, double it again, and one, cube it again and so on and you still haven't got to an infinite number and you could continue cubing it every second for the next 14 billion years you still would not have an infinite number. Are there really an infinite number of galaxies in the universe? Now if you are saying there is an infinite amount of nothing beyond the matter universe I wouldn't exclude that as a possibility.

 

[BoomBoom]

... then what you are saying should be visualized is a 2-space that is mapped on the surface of this balloon and the third dimension is "time".

I believe the "3rd dimension" as you refer to it as is actually the physical curvature of the 2-D surface...not time.

In the real 3-D universe this ( http://en.wikipedia.org/wiki/3-sphere" ) is what they refer to as a 3 sphere. Its application seems to me to be purely mathematical...which is why there is no analogy to describe it.

 

[LowlyPion]

By count, do you mean ...

Just to keep it simple for you make it the number of quarks ... oh and say any photons now in transit.

You needn't count the virtual particles. That might be too tedious.

 

[yuiop]

Just to keep it simple for you make it the number of quarks ... oh and say any photons now in transit.

You needn't count the virtual particles. That might be too tedious.

I would say a rough estimate is that all the quarks in the universe, plus all the photons in transit, plus all the photons that have ever been emitted since the big bang is a big number, but less than infinite ;)