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?
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." I'm not sure what you mean here, could you expand?
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.
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.
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.
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.
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 cant 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)
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.
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.
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.
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.
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.
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. 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 [tex]2\pi^2R^3[/tex] and pi-square is about 10, so [tex]2\pi^2[/tex] 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 [tex]R^3[/tex] 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.
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.
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.
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.
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?