| From: scott | 27/04/00
12:58:24 |
| Subject: Flat Universe?? | post id:
61565 |
| Did anyone read the story about
the theory that the universe is flat and not spherical? Any thoughts as to
how this could be considering that the Big Bang was supposed to spread
matter in all directions. | |
| From: Min-Zhao Lee | 27/04/00
13:06:52 |
| Subject: re: Flat Universe?? | post id:
61568 |
| I'm not too sure about what it
means, IMHO it seems to say that unlike the surface of the earth, which is
wrapped in 3 dimensions, the universe has three dimensions NOT wrapped in
a fourth dimension. | |
| From: David Brennan | 27/04/00
13:09:39 |
| Subject: re: Flat Universe?? | post id:
61570 |
| OK, when talking about a the
universe, the word "flat" doesn't mean what it does when you talk about a
flat table. Under current theories of the universe there are three
possible ultimate ends. 1. Universe doesn't contain enough matter to stop the expansion of the universe by gravitational attraction. This is called an "open" model. 2. Universe contains more than enough matter to stop the expansion of the universe, enough to reverse the expansion and cause the Big Crunch. This is called an "closed" model. 3. The universe has exactly enough matter to stop the expansion of the universe. This is called the flat model. I'm not really sure of the end result of a flat universal model. So flat here refers to the amount of matter in the universe. David | |
| From: Dan B. | 27/04/00
13:13:48 | ||
| Subject: re: Flat Universe?? | post id:
61573 | ||
|
Universe 'proven flat' http://news.bbc.co.uk/hi/english/sci/tech/newsid_727000/727073.stm  The Boomerang balloon inflating just before
launch A high-flying balloon that soared over Antarctica has
answered one of cosmology's greatest questions by revealing that the
fabric of the Universe is "flat".
To astronomers, flat means that the usual rules of geometry are observed - light not being bent by gravity travels in straight lines, not curves. But since Albert Einstein proposed that the Universe may be "curved", the debate has been open. Scientific opinion has moved towards a flat Universe and the latest data confirm this with greater certainty than ever before. Another result of the study is the prediction that the Universe will continue its steady expansion, which started at the Big Bang, and will not collapse into a "Big Crunch". "It's a tremendously exciting result - and one that will mean rewriting the text books on the history of the Universe," said one of the research team, Professor Peter Ade at Queen Mary College, University of London. Faint heat The new information is an exquisitely accurate map of the very faint afterglow of heat left behind by the Big Bang. This is called the Cosmic Microwave Background and is equivalent to the tiny warmth given off by something just a few degrees above absolute zero, -273 degC.
Tiny temperature variations in the CMB, just 0.1% at most, allow scientists to test different models of how the Universe began and expanded. The map paints a picture of the young Universe, just 300,000 years old - the cosmos is now over 12 billion years old. The chart was made by an international team led by Paulo de Bernardis of the University of Rome La Sapienza. He said: "It's really exciting to be able to see some of the fundamental structures of the Universe in their embryonic state. The achievement, he said, was distinguishing the CMB from other interference: "The light we have detected has travelled across the entire Universe and we are perfectly able to distinguish it from the light generated in our own galaxy." Sky high boomerang The project to map the CMB was called Boomerang (Balloon Observations of Millimetric Extragalactic Radiation and Geophysics).
It has taken since then to process the one billion measurements. The calculations alone would have taken six years to complete if run on a desktop computer. On the Cray T3E supercomputer at the Lawrence Berkeley National Laboratory, US, they took less than three weeks. The fundamental cosmic parameters derived from the work are accurate to within just a few percent. The research is published in the journal Nature and in an accompanying commentary, Wayne Hu, of the US School of Natural Sciences, New Jersey, said: "The Boomerang result supports a flat Universe. A perfectly flat Universe will keep on expanding forever, because there is not enough matter to make it recollapse in a 'Big Crunch'." The research backs the inflation theory of the Universe put forward in 1980, which suggests that the whole of the cosmos expanded from a single tiny point at the Big Bang. At that time, and for a short while after, space was curved because it
was confined in a small region. However, the Universe's expansion has been
so great that space has now been stretched to the point that it is
essentially flat.
| |||
| From: Chris (Avatar) | 27/04/00
13:54:48 |
| Subject: re: Flat Universe?? | post id:
61594 |
When talking about the "flatness" of the universe, cosmologers don't mean flatness in the way we'd understand from everyday common experience. When cosmologers describe our universe they do so with a mathematical relationship(s) which relate a number of cosmological constants into a model. The values of the different constants (including the Hubble constant, the deceleration parameter, the cosmological constant, etc) help define the type of space in the model. When we talk of flatness, the parameter we're dealing with is a ratio called Omega (W). Omega is the ratio of the density of the large scale universe, r, to the critical density, rcrit: W = r / rcrit rcrit is the density required for the universe to stop expansion and eventually collapse back onto itself. In the Einstein-De Sitter model, rcrit = 3H2 / 8pG (where G is the gravitational constant and H Hubble constant) Omega can have a range of values which describes the type of geometry of the universe. In the case where r = rcrit, that is W = 1, the geometry of space-time is called Euclidean, which corresponds to flat space-time. In such a universe the sum of the angles of a triangle of infinite size is always exactly 180o. Values of W which are less than 1 or greater than 1 describe curved space-times.  This graph shows values for Omega graphed against the universe scale factor a(t) and time (with Ho = 65km/s/Mpc). The green graph shows Omega equal to 0 indicating a negatively curved or hyperbolic space-time. The black line shows omega equal to 1 which is a flat euclidean space-time. The red line shows omega=2 which is a positively curved or hyperspherical space-time. This second picture matches each omega ratio to its space-time:  It is important to remember that our universe has three spatial dimensions, whilst the diagram above only shows 2D representations. The way to tell the difference between one curvature and another is to take what we call a "hyperslice" of the universe's geometry, basically just cut out a 2D strip, and see the way it curves. An example of a way of doing this is to measure the angles of a triangle. In a flat space they will total exactly 180o. In a positively curved geometry the angles will total more than 180o and in a negatively curved universe they will total less than 180o. A measurement of the angles in a very large triangle should tell us what curvature our universe has, and Gauss actually tried this experiment when playing with non-Euclidean geometry (he claimed to have invented it). As a result, he found the sum of his triangle angles to be 180o, presumably indicating flatness. The reason he got this result is because his triangle was not very big, and because the universe is at least very close to flat - ie W is very close to 1. In fact it is so close to 1 that we can't tell for sure whether the universe is positively (closed) or negatively (open) curved. This graph shows values for Omega graphed against the universe scale factor a(t) and time (with Ho = 65km/s/Mpc). The green graph shows Omega equal to 0 indicating a negatively curved or hyperbolic space-time. The black line shows omega equal to 1 which is a flat euclidean space-time. The red line shows omega=2 which is a positively curved or hyperspherical space-time. This second picture matches each omega ratio to its space-time: Hope this helps! Chris | |
| From: scott | 27/04/00
14:11:55 |
| Subject: re: Flat Universe?? | post id:
61602 |
| Let me see if I've got this
correct (sorry I only did 3U Physics at high school). The term flat is not
related to flatness but the amount o matter, And the universe does
actually expand in all directions, to an either specified or unspecified
maximum depending on which theory you use. | |
| From: James Richmond (Avatar) | 27/04/00
14:32:06 |
| Subject: re: Flat Universe?? | post id:
61608 |
| The consequences of different
curvatures for the universe are as follows: 1. If the universe is closed (omega > 1, positive curvature), then the universe will eventually recollapse to a "big crunch". 2. If the universe is open (omega < 1, negative curvature), the universe will expand forever, at an ever-increasing rate. 3. If the universe is flat (omega = 1, no curvature), the universe will also expand forever, but at an ever-decreasing rate. JR | |
| From: Chris (Avatar) | 27/04/00
15:17:03 |
| Subject: re: Flat Universe?? | post id:
61645 |
Scott That's a pretty concise summary! :o) You've got the essentials right. The universe is still expanding in 3D, the curvature is related to the mass-energy in the universe. Flatness does mean flatness, it just means flatness in 3D (4D) rather than our usual 2D notion. Chris | |
| From: Robert | 27/04/00
20:09:18 |
| Subject: re: Flat Universe?? | post id:
61943 |
| Some questions: 1) This is the same kind of curvature produced by masses on small (like 10 ly) scales to give gravity, right? 2) Are metrics easy to explain (either mathematically and/or semantically)? Please no tensors, field equations or those wierd partial derivative things - I am still trying to understand the supernovae problem. Thanks. | |
| From: B.C. | 27/04/00
22:04:40 |
| Subject: re: Flat Universe?? | post id:
62006 |
| If this "flat universe theory is
correct,how does it fit in with Alan Guths inflationary model,re the
theory that the incredible density of mass just before the big bang gave
rise to a condition called a "false vacuum " .which in turn made gravity
repulsive, and put the kick in the big
bang? | |
| From: Robert | 27/04/00
22:10:29 |
| Subject: re: Flat Universe?? | post id:
62012 |
| BC, Re: The supernovae I think I've got it - the further away one will be observed to take longer because of SR. It seems that GR has no effects on the time taken since for every second a photon travels one light-second no matter what the state of the space-time manifold is. Although, the question remains does the distant supernova really have velocity to give it the SR solution - after all, doppler shift isn't used to explain redshift of distant galxies/quasars, but the stretching of wavelength due to changes in the space-time manifold. Damn. | |
| From: Chris (Avatar) | 28/04/00
10:25:06 |
| Subject: re: Flat Universe?? | post id:
62129 |
Hi Robert 1) This is the same kind of curvature produced by masses on small (like 10 ly) scales to give gravity, right? Similar, but not the same. If you look closely at the Omega factor described above, you'll see that it relies on more than mass-energy density, which is responsible for smaller scale gravitational curvature. The rcrit value is dependant on (at least one) cosmological scale factor, which removes the curvature from intra-galactic scales. 2) Are metrics easy to explain (either mathematically and/or semantically)? Please no tensors, field equations or those wierd partial derivative things - I am still trying to understand the supernovae problem. Yes. A metric is basically a distance function. The metric function f(x,y) computes distances between neighbouring points in the set (x,y). A metric has the following properties: * it is always non-negative (being a distance function) * it obeys the triangle inequality: the distance from A to B + from B to C is always greater than or equal to the distance from A to C - f(x,y) + f(y,z) ³ f(x,z) * it is symmetric: the distance from A to B = distance from B to A - f(x,y) = f(y,x) A metric tensor is a tensor which has the above properties of a metric (and is hence a distance function). A tensor is an m dimensional object in any m-space. The rank of a tensor determines its indices and components in m-space. A zero-rank tensor is simply a scalar (eg temperature) and a first rank tensor is a vector (eg velocity). Second rank tensors resemble matrices. Hope this helps! Chris | |
| From: James Richmond (Avatar) | 28/04/00
10:57:53 |
| Subject: re: Flat Universe?? | post id:
62149 |
| If this
"flat universe theory is correct,how does it fit in with Alan Guths
inflationary model? It fits very well. One of the predictions of the inflationary model is that the resulting universe should be flat. The inflationary model postulates a period of extremely rapid expansion immediately following the big bang. The "antigravity" force leading to this expansion then switched off, leaving normal gravity to do its thing. The inflationary model was motivated by a desire to solve a couple of apparent problems in the big bang model, known as the horizon problem and the flatness problem. The second of these refers to the observations that the universe is flat, or very close to it. Inflation explains why we would expect this to be the case, when otherwise it would seem quite an extraordinary coincidence. JR | |
| From: Robert | 28/04/00
15:22:46 |
| Subject: re: Flat Universe?? | post id:
62288 |
| Thanks Chris :-) I would still love it though, if you (or anyone else for that matter) could provide a solution to your own problem here: Perhaps an interesting question to ask would be to take two supernovae of suns of equal mass. One in a neighbouring galaxy, and one in a galaxy at a significant redshift (and hence in an earlier universe). We measure the time taken for each supernova to occur to some significant phase. Now lets consider what we might see. The time taken for the supernovae, were they near each other, would be equal (in this idealised example). Would you expect that the more distant supernova would appear to happen in a shorter time as measured in an observation station on earth? A longer time? What would either case say about the time coordinate system? Would it matter that the image of the more distant SN has had to travel the intervening space-time to reach us? | |
| From: David Brennan | 28/04/00
15:30:16 |
| Subject: re: Flat Universe?? | post id:
62293 |
| I can't think of a reason why the
more distant SN would appaer to take longer. Certainly the light from it
would arrive after the light from the closer SN (if the SN's occured
simultaneously WRT the Earthbound observer, note that simultaneous is a
fuzzy concept in this situation for reasons outlined in General
Relativity). The intervening space might contain matter that might affect
the light from the distant SN more than the nearer SN, but thats about all
I could see happening. David | |
| From: Robert | 28/04/00
15:36:45 |
| Subject: re: Flat Universe?? | post id:
62297 |
| There are two factors at play
here, though: 1) The 'velocity' of the distant SN ( => SR time dilation?) 2) The change in the space-time manifold over time (?) | |
| From: David Brennan | 28/04/00
15:45:32 |
| Subject: re: Flat Universe?? | post id:
62300 |
| Ahh, I see your point. Hmm, bares
more consideration. So a more distant SN is moving at greater speed away
from us. But surely the apparent duration of the SN depends on the length
of time light from the event is emitted. So if both SN's take say one
second to occur at local reckoning ie. WRT am observer at the location of
the SN, then one second of light will arrive at the destination (Earth)
after the required travel time,
surely? David | |
| From: Robert | 28/04/00
15:56:47 |
| Subject: re: Flat Universe?? | post id:
62309 |
| So if both
SN's take say one second to occur at local reckoning ie. WRT am observer
at the location of the SN, then one second of light will arrive at the
destination (Earth) after the required travel time,
surely? Right, so if they are observed to initially undergo SN at the same (Earth) time, then the distant SN must have occured some longer time ago as well as some farther distance away. Where to from there? | |
| From: Chris (Avatar) | 28/04/00
16:20:55 |
| Subject: re: Flat Universe?? | post id:
62321 |
Hi Robert Re the supernova, the reason I haven't got back to you on this is because I've realised the thought experiment is ill-conceived for what I was trying to explore - and I haven't come up with a suitable replacement! What I was after was an exploration of identical fixed time intervals separated in space-time to see whether we could expose universal expansion in time. Unfortunately the supernova has problems in scale, which can be seen by the focus of the analyses on relativistic time dilation and timing of light curves. Universal expansion is on a scale away from relativistic effects - time dilation and doppler effects of SR and GR won't figure in the answer. That doesn't mean your answers are wrong - it is the problem as posed which is incorrect. But an interesting discussion is developing from it nonetheless! Cheers Chris | |
| From: David Jones | 18/05/00
10:44:11 |
| Subject: re: Flat Universe?? | post id:
71114 |
| Chris, back to your initial
question at this post (ie if the universe is flat, how come it spreads out
un all directions): this is an unanswered problem (even after considering
the esoteric mathematical "representations" of the universe set out by the
people who are trying to solve it at this post). The problem is that the
universe can be seen as a geographical entity (which is understandable),
in which its mass creates a state of curved geometry (what is sometimes
referred to as curved space-time) with the extent of overall curvature
(for the universe taken as a whole; as a totality of mass) depending on
the extent to which it has been spread out by its state of expansion
(originating in what is termed the "big bang"). We don't know what caused
the "big bang" despite references to various theories including the theory
of "inflation", however, we are able to estimate in various ways the rate
of expansion from actual evidence of the "real" -not theoretical-
expansion of galaxies spreading out in all directions away from eachother
and from evidence of distortions (including of curvature) in our
observations of the distribution of the mass of the universe (which,
importantly, but not directly relevantly to your question, includes a
permanent faint haze of electromagnetic radiation more or less evenly
distributed throughout the universe). The measurements reveal that the
universe as a whole shows no curvature between its distant galaxies
accross the haze of radiation, and, therefore, it is as if there are flat
straight lines drawn accross the universe in all directions from each bit
of mass to each other bit of mass along which they are expanding from
eachother. But here is the problem. It is not actually a flat straight
line; the result is "described" in a mathematical "representation" as a
flat sheet rather than as lines, thus turniing three dimensional "real"
expansion in all directions into (cont) | |
| From: David Jones | 18/05/00
10:58:52 |
| Subject: re: Flat Universe?? | post id:
71121 |
| (cont) a two dimensional
representation that is flat rather than curved like the two-D surface of a
spher or the two-D surface of a saddle (which are alternative
"representations" of three-D space -plus time- which would have been
supported by different findings about the evidence of curvature from the
actual observations). Now, with apologies for the long-winded explanation,
and without going into the actual rate or extent of expansion necessary to
support the recent "BOOMERANG" finding, or the rate necessary to support
either of the two alternative theories, the key issue is whether it is
"appropriate" or "valid" to use two-D representations (encompassing both
space and time, given that the flat sheet is moving through space and
time) for a "real world of three-Ds plus time. I think not, but will
elaborate further at a future date. | |
| From: Chris (Avatar) | 18/05/00
11:12:36 |
| Subject: re: Flat Universe?? | post id:
71131 |
...and this is ultimately the problem with analogies. Analogies including the stretched rubber mat, the inflating balloon, etc are useful tools for aiding in general understanding of difficult concepts - particularly in that visualisations will help those without mathematical training (and even some of those with it!). However it is dangerous to use the analogies to lead or inspire further insight into what is really happening. The universe does not behave like an expanding balloon, or a stretchable mat - these concepts only illustrate uniform recession or distortion of a surface (respectively). They do not represent the universe. This is the most common mistake made by the "crackpot theory" brigade. Their appeals to "common sense" and their stretched analogies are not science and are ultimately limited and shortsighted. Like it or lump it, the universe looks most like the most complete descriptions of it and at present the most accurate complete descriptions are mathematical. Chris | |
| From: david jones | 19/05/00
10:28:45 |
| Subject: re: Flat Universe?? | post id:
71707 |
| I suppose, then, that you would
call just about every popular (and well-credentialled) writer on cosmology
a "crackpot", because, if you review the literature, just about every one
of them uses the flat or curved stretched two-D plus time rubber sheet as
a "representation" or "analogy" for the motion of galaxies (and mass
generally) without explaining how it can be transformed into "real"
three-D plus time. Can you explain the transformation? (ie simply, as
might an expert in command of his subject, rather than someone sheltering
behind the excuse that it is too mathematically technical to be understood
in "commonsense" terms). If it doesn't make sense, it doesn't conform to
reason: and the simpler (more common) the better. And, by the way, a
"representation" or "analogy" is not a "description". A description is
more "direct"; the others rely on interpretation (ie mathematical tools
for interpretation) to conform with the real world of observation (ie
three-D space plus time). Good luck. | |
| From: Chris (Avatar) | 19/05/00
11:30:03 |
| Subject: re: Flat Universe?? | post id:
71726 |
Whoah there big fella! Settle down a bit! :o) If you re-read my previous post you'll see that I said analogies are useful illustrations or visualisation tools, but are ultimately limited in further developing ideas. A popular science author will use analogies to help illustrate difficult concepts to the uninitiated, a crackpot theorist will use an analogy as the basis for a theory. Fundamental distinction. My point is that it is important to keep in mind that analogies are only aids in understanding, they are not understanding itself. As for providing an extension of 2D analogies for space-time into a 4D analogy, that kind of defeats the whole point, doesn't it? I mean the whole point of an analogy in this context is to take something we can't visualise and provide a visual substitution based on everyday experience. If we could visualise 4-space, then why bother with the analogy? Why not just describe it as it is? hmmm? :o) In the end, our descriptions of 4-space are mathematical. When the holes or shortcomings in the analogies surface and you need to go further then you need to start looking at the math. I think helping people understand the math is the real challenge, don't you? Helps distinguish between "hiding behind it" and "hiding from it", don't you think? Chris | |
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