Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Merccooper on 07/02/2015 16:53:58
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I'm sure this has been asked, but searching for the answer has proven difficult.
First part:
If the Big Bang theory is true, why can we not say the universe is spherical?
Second part:
Why, in relation to the Big Bang, is the universe depicted in a cone shape (as attached) and not some other shape?
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If the Big Bang theory is true, why can we not say the universe is spherical?
I think we can. See this article (http://edition.cnn.com/2004/TECH/space/05/24/universe.wide/) where cosmologist Neil Cornish claims that the universe is at least 156billion light years wide. See this bit:
"It can be thought of as a spherical diameter is the usual sense," Cornish added comfortingly. (You might have heard the universe is almost surely flat, not spherical. The flatness refers to its geometry being "normal," like what is taught in school; two parallel lines can never cross.)"
Why, in relation to the Big Bang, is the universe depicted in a cone shape (as attached) and not some other shape?
I don't know. I suppose they've dropped one dimension such that the physical shape of the universe is circular, then they're showing how it gets bigger over time from left to right.
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I'm sure this has been asked, but searching for the answer has proven difficult.
First part:
If the Big Bang theory is true, why can we not say the universe is spherical?
Second part:
Why, in relation to the Big Bang, is the universe depicted in a cone shape (as attached) and not some other shape?
[ Invalid Attachment ]
The reason these kinds of questions don't get answered is because it's apparent from the question that the person asking it won't understand the answer. The questions which thus follow become harder and harder to answer due to the lack of understanding of the physics.
For example: The universe can't be spherical because when the matter distribution is placed into Einstein's field equations the result yields various solutions, none of them being spherical. How could anybody, in words, explain why a certain solution to Einstein's field equation be as it is? Especially since it's well known as being the hardest equation to solve in all of the laws of classical physics!
If the mass density is too small then the universe will be closed meaning that a path leading off in one direction ends up coming back to where it started, regardless of the direction. If the mass density is too large then those paths go off into infinity and never come back. In that case the universe is infinite in size.
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For example: The universe can't be spherical because when the matter distribution is placed into Einstein's field equations the result yields various solutions, none of them being spherical.
Is it possible that confusion could arise because of a distinction between geometry and topology when talking about the shape of the Universe?
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Thanks for that input John.
PmbPhy, I'm sorry if I have wasted your time and bits of data by showing my lack of in-depth knowledge of Einstein's field equations asking that question. I thought this site's purpose was, in part to, "....help the general public to understand and engage with the worlds of science, technology and medicine". Am i wrong about that?
So, my question now is, if the universe can not be spherical, what is it?
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PmbPhy, I'm sorry if I have wasted your time....
I never suggested that you wasted my time. I was merely explaining the reason why questions like this don't get many answers.
and bits of data by showing my lack of in-depth knowledge of Einstein's field equations asking that question.
I understand. I'm assuming that you came here to learn that stuff.
I thought this site's purpose was, in part to, "....help the general public to understand and engage with the worlds of science, technology and medicine".
That's quite correct.
Am i wrong about that?
No. In fact I answered your question and explained why the answer would be difficult to understand.
So, my question now is, if the universe can not be spherical, what is it?
The best description of the universe that we have today is that it's flat, i.e. like a plane.
I'm sorry that you got a wrong impression from my response.
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The best description of the universe that we have today is that it's flat, i.e. like a plane.
With respect Pete, that's wrong. See this article (http://edition.cnn.com/2004/TECH/space/05/24/universe.wide/) where cosmologist Neil Cornish was saying he thought the universe was at least 156billion light years wide:
"It can be thought of as a spherical diameter is the usual sense," Cornish added comfortingly. (You might have heard the universe is almost surely flat, not spherical. The flatness refers to its geometry being "normal," like what is taught in school; two parallel lines can never cross.)"
A spherical universe is a "flat"universe if parallel light beams stay parallel and go straight. As for what happens if you try shining those light beams 78 billion light years from here, I don't know.
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Nah Pete, a perfectly good answer. And Mer :)
Don't get too prickly about it, sometimes the answers need a redefinition of the question.
That's just another way of getting it right.
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And John :)
No such thing as your spherical universe, unless you refer to the 'light sphere' we observe from here? Assuming there was though, one now will have to explain why there is no 'edge'.
However one try to do that, it's not simple. Physics always go for the simplest definition possible.
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Lookiong at his definition, I would call it 'pop science', good enough for CNN and Fox possibly?
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As for number one Mer.
"If the Big Bang theory is true, why can we not say the universe is spherical?"
That one is best explained by thinking two dimensionally about it. Using the surface of a inflatable balloon. the beginning is 'no balloon' but as soon as you find your surface the 'inflation' starts 'everywhere on it'. The balloon, looked on that way, also becomes a representation of a later expansion. If there is no defined 'origin', how can you get to your 'balloon', you may ask? :) Well, you can't, but it's the definition that fits best, just the same.
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There is a alternative way though, to think about it, naively. Imagine it as a mathematical space, not a geometrical nota bene. In that 'space' you find 'points' that's 'disconnected', as defined from us. When they start to 'connect' you will get your inflation, and expansion, and 'space' as in 'universe', assuming it to happen 'simultaneously'. To make it happen you need one more thing, a local arrow, that also are a local constant, namely 'c'. They all need that one, equivalently. And it needs its equivalence, to create those 'repeatable experiments' we define physics from.
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Hi Merccooper, welcome.
I have to say that Pete can come across as a bit curmudgeonly at times, but tap into the patience – it’s there. Don’t be put off posting questions. I’ve sampled a few science discussion forums and this is the best I have found.
As is well known in this forum, I am not a scientist, and am inclined to try the patience of experts by persistently working at problems until I feel at least reasonably happy that either I have grasped the solution, or that I never will. (The latter is rare, but that’s just conceit.)
Like so many things in science, talking about the shape of the Universe is not intuitively straightforward. Cosmologists tend to link the shape to the density/critical density ratio. In order for a cosmologist to accept that the Universe was spherical, it would have to be established that the density was greater than the critical density. That seems to be the scientific definition of a spherical universe; it’s certainly the image that goes with the “open/closed/flat universe scenario.
By the same token, a flat universe is depicted as a flat rectangular shape. I doubt that we are expected to believe that the physical universe has right-angled corners, so defined shape may not always be the same as actual shape. We also have to remember that these images are analogies. Sometimes we non-scientists have to put our intuitive thoughts on the back burner and just try to understand what the experts are saying.
Don’t get rid of those intuitive thoughts completely, though; they might come into fashion (again) one day. [:)]
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I think it's important to point out that "the shape of the universe" can be very misleading. If you take a look at the Wikipedia article (http://en.wikipedia.org/wiki/Shape_of_the_universe#Two_aspects_of_shape) of that name, you can see this picture:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2F9%2F98%2FEnd_of_universe.jpg%2F275px-End_of_universe.jpg&hash=e58915cc7aca4cd2e91f3ab42b39ef1b)
However it isn't depicting the shape of the universe at all. It's depicting the geometry via "two-dimensional surfaces". The "flat" universe is the third of the shapes above, but don't think the universe is shaped like a flat board. It isn't two-dimensional, it's three-dimensional. And note that the simplest three-dimensional shape you can come up with is spherical.
Like so many things in science, talking about the shape of the Universe is not intuitively straightforward.
I think it is. To be honest, I don't know why anybody ever entertains the first two options above. On the large scale space is homogeneous and isotropic. And if space is like this, light moving through it doesn't curve. Einstein said as much in his Leyden Address, but he didn't apply this to cosmology. When it comes to cosmology it was as if he totally lost his usual confidence in his own theory. IMHO it's rather strange, and maybe it's related to the fact that he didn't achieve much after about 1920. One guy I was talking to said it was as if he'd had a stroke or a breakdown or something.
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Thank you for your encouragement Bill. I enjoy thinking about and reading about various aspects of science. The universe and gravity have always kept my attention. Then, by chance, I read some articles about quantum physics and was amazed about Heisenberg’s uncertainty principle and other aspects of quantum physics. I know I will never have the mathematical smarts to even come close to understanding these things from that aspect, but was hoping to talk about them in more basic terms. My wife and kids roll their eyes when I want to talk about these subjects, which is why I turned to the naked scientists.
Anyhow, that aside, I apologize to Pete that I have taken is input out of context.
Now, that aside, I’ve read about the balloon analogy before but will hold my questions until I put more thought into it. I also found an article about Einstein’s Equations that suggests to explain his equations in “plain English”. I say this with a smile as even this has why too much math for me! But, I’m going to try and absorb some of it. Here is the article: http://math.ucr.edu/home/baez/einstein/
At the risk of asking a poor question, to what extent has it be proven that light beams traveling through space do not 'ever' curve? I assume 'ever curve' implies without the influences of gravity from massive objects. (I just read John's post so have not yet had the chance to "research" it, so if it isn't a valid question, feel free to ignore).
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I second to Bill. This is the best science forum I found.
My thought, the space/universe we can detected today, maybe just a sand on the beach.
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Merc: I think most cosmologists are happy that space is "flat" such that light doesn't curve. WMAP demonstrated this, see for example this article (http://map.gsfc.nasa.gov/universe/uni_shape.html). It gives the illustration as above, and says this:
"The WMAP spacecraft can measure the basic parameters of the Big Bang theory including the geometry of the universe. If the universe were flat, the brightest microwave background fluctuations (or "spots") would be about one degree across. If the universe were open, the spots would be less than one degree across. If the universe were closed, the brightest spots would be greater than one degree across. Recent measurements (c. 2001) by a number of ground-based and balloon-based experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know (as of 2013) that the universe is flat with only a 0.4% margin of error."
All that is fairly reasonable, and is backed up by the Planck mission. However the next bit of the WMAP article isn't reasonable:
"This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe."
This is a non-sequitur. A flat universe does not suggest that the universe is infinite in extent. We cannot truly conclude is that the universe is much larger than the volume we can directly observe. If anybody says we can, ask them to explain this conclusion. They will not be able to.
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A flat universe does not suggest that the universe is infinite in extent.
It risk of seeming like a stuck record, I would think it quite reasonable to consider that a flat universe would be unbounded, but not necessarily infinite. Is that too nice a distinction?
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I'm with you too there John. Myself I think of it as undefinable, meaning that whatever size we would like to put to it will be found wrong. It's 'dynamically existing' in my thoughts, using 'c'. But the 'light sphere' existing will be there wherever I go, defining a envelope of time.
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It risk of seeming like a stuck record, I would think it quite reasonable to consider that a flat universe would be unbounded, but not necessarily infinite. Is that too nice a distinction?
IMHO it's perfectly reasonable to consider anything. That's kind of my point, the "infinite universe" non-sequitur arises because people are asserting things without considering the alternatives.
I'm with you too there John. Myself I think of it as undefinable, meaning that whatever size we would like to put to it will be found wrong. It's 'dynamically existing' in my thoughts, using 'c'. But the 'light sphere' existing will be there wherever I go, defining a envelope of time.
And if we could take a snapshot of the universe as it exists now? What shape is it? Since it's space expanding, how can it be expanding into anything? What would you see if you were 76 billion light years away from here? A black half to the sky? One half of the sky looking like a mirror image of the other? None of the above? It's interesting stuff, far more interesting than the "infinite universe" non-answer that just doesn't square with big-bang cosmology.
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The pictures from the Hubble telescope show composite objects in any selected direction, which would seem to indicate a 3D volume for the universe. In addition to the CMB analysis, if space is not approx. flat or euclidean, we would not have the those detailed photos. The resolution would deteriorate over many lightyears.
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If spacetime is not flat due to gravity and space is flat then it is not spacetime that is being affected. Space is part of spacetime, it can't exist without both space and time. For time we have experimental evidence that it isn't 'flat' although flat is not a good term for time. We do not have evidence of space contraction. Length contraction is more an effect on mass. If we measure 1 metre what are we actually measuring? We usually measure objects. You wouldn't normally show someone a metre of empty space. Some of the concepts have to be thought of as conveniences that are used because they work out in the equations. We never properly describe a phenomena in all its aspects as that is far too complex an exercise.
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Length contraction is more an effect on mass. If we measure 1 metre what are we actually measuring? We usually measure objects. You wouldn't normally show someone a metre of empty space.
That's an interesting point. Jeffrey. If we consider an object that is 1m long, it occupies 1m of space. if the object is subjected to length contraction, does the space it occupies contract as well? It would seem logical to assume it would, but how could we tell, one way or the other?
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If spacetime is not flat due to gravity and space is flat then it is not spacetime that is being affected. Space is part of spacetime
I'm afraid it isn't. Space is space. Spacetime is a mathematical abstraction in which there is no motion. You can draw worldlines in it to depict motion through space over time, but it models an "all times at once" block universe. So it's static. So you cannot move through it. You move through space, and when you change your state of motion, your measurements of distance and time change. And how did you make these measurements? Using light, moving through space.
That's an interesting point. Jeffrey. If we consider an object that is 1m long, it occupies 1m of space. If the object is subjected to length contraction, does the space it occupies contract as well?
No, because the object is moving through space. Besides, length contraction is a can of worms. If you accelerate such that you see everything length-contracted to half its former length, what do you think changed? Everything? Or you?
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If spacetime is not flat due to gravity and space is flat then it is not spacetime that is being affected. Space is part of spacetime
I'm afraid it isn't. Space is space. Spacetime is a mathematical abstraction in which there is no motion. You can draw worldlines in it to depict motion through space over time, but it models an "all times at once" block universe. So it's static. So you cannot move through it. You move through space, and when you change your state of motion, your measurements of distance and time change. And how did you make these measurements? Using light, moving through space.
Why would you make measurements using light? You can use the speed of light as a reference point but this tells you nothing about the spacetime in your own frame of reference. It looks like any other frame you have passed through. Light speed is a very bad indicator. The shifting of the wavelength of light can tell you what the state of a remote frame may be but that is inferred from the assumed behavior of light.
That's an interesting point. Jeffrey. If we consider an object that is 1m long, it occupies 1m of space. If the object is subjected to length contraction, does the space it occupies contract as well?
No, because the object is moving through space. Besides, length contraction is a can of worms. If you accelerate such that you see everything length-contracted to half its former length, what do you think changed? Everything? Or you?
Define space. In the vacuum there is an energy present so can that be described as space. Like time, space is a concept we have developed to aid us in understanding the physical world. When we talk about empty space what do we mean? A void? If space is empty of everything then that is what it must be considered to be. As for a static spacetime, that can't be true when considering massive bodies moving through the coordinates of the system. The nature of the spacetime events change the nature of the spacetime.
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Why would you make measurements using light?
Because it's "the most fundamental" way of doing it, and it's what you do in practice. The most accurate clocks are optical clocks, and you measure distance using radar. The electromagnetic waves pinging back and forth are light in the wider sense.
You can use the speed of light as a reference point but this tells you nothing about the spacetime in your own frame of reference. It looks like any other frame you have passed through. Light speed is a very bad indicator. The shifting of the wavelength of light can tell you what the state of a remote frame may be but that is inferred from the assumed behavior of light.
Your own frame of reference is little more than your state of motion. A reference frame is not something that exists in its own right.
Define space. In the vacuum there is an energy present so can that be described as space.
Yes, in some respects energy and space seem to be the same thing. But it's difficult to define them. Light is essentially E=hf waves in space, and we can make matter out of light. So you could say matter is made of waves in space. But what do you say space is? It isn't made out of matter or waves. Instead those things are made of it.
Like time, space is a concept we have developed to aid us in understanding the physical world. When we talk about empty space what do we mean? A void? If space is empty of everything then that is what it must be considered to be.
No, it isn't a void. It's a something. Read Einstein's Leyden Address (http://www-history.mcs.st-and.ac.uk/Extras/Einstein_ether.html) where he describes space as a thing that can have a state: "This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that "empty space" in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gmn), has, I think, finally disposed of the view that space is physically empty."
As for a static spacetime, that can't be true when considering massive bodies moving through the coordinates of the system. The nature of the spacetime events change the nature of the spacetime.
It's true Jeffrey. Pay attention to Einstein's use of the words space and spacetime. He didn't confuse the two, but some people do. They forget that spacetime is not something you can move through. Have a google on no motion in spacetime (https://www.google.co.uk/?gws_rd=ssl#q=%22no+motion+in+spacetime%22+). I'm afraid some of the links are where I say it, but plenty are where somebody else is saying it.
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"And if we could take a snapshot of the universe as it exists now? What shape is it? Since it's space expanding, how can it be expanding into anything? What would you see if you were 76 billion light years away from here? A black half to the sky? One half of the sky looking like a mirror image of the other? None of the above?
It's interesting stuff, far more interesting than the "infinite universe" non-answer that just doesn't square with big-bang cosmology. "
I've been wondering about how to define it too John. For me the best way I've found is through assuming that it is 'information & communication' that defines it. That one fit observer dependencies as well as the idea of a commonly agreeable upon universe existing. If you 'back track' that type of logic, asking yourself what such a universe would need to start a communication, then it's those 'points', junctions, whatever, that need to be existent. Furthermore you need something 'doing' the communication. And of course, a arrow if we want a logic similar to the one we meet. The arrow is weird in that it is locally unchanging for you, being a 'constant' for you, but when looking at a 'common universe' creating those time dilations. If you 'back track' that one you will find that the arrow is a local definition, and that what we call 'repeatable experiment' also are strictly local definitions, although presumed applicable over a whole universe. The same should then go for all constants.
In essence, the way I see it this universe is created and defined locally. If it is, then a inflation which starts 'in all points' becomes a natural.
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As for how it can 'expand', that's more a question of our presumptions to me. We can't avoid them as this is how we find it to be from a inside, a solution diluting in another for example. But if we assume that you need 'points' and this communication, then information is all. Tweak the information and the universe 'expands' for me. And the thing one might wonder there is if this needs some 'background', on where it can do it, myself I don't think so. The junctions define a universe geometrically and topologically, no 'back ground' needed. We're inside it, and we measure from a inside too. That doesn't state that there must be a 'outside' or 'back ground' on where a universe 'takes place'.
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It's a symmetry break to me. And the arrow is what defines 'c', locally, always locally. The universe defined this way is constricted by constants and rules, emergences and 'properties'. There is no 'box' in where it is 'fitted', and the best way to define a size is to call in indefinable. And the 'light sphere' you see around you tells you when this symmetry break happened, as measured through constants (local clock or 'time'), and that one you will find everywhere you go. You have something else though, that's really interesting to me, much more interesting than defining a 'size to a universe'.
You have scales, as in QM :)
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And the closest you get to a 'container model', in my thoughts, are conservation laws. But those are rules too. And if you look at time in itself there are two ways. One is time as a essence more or less, as a 'property'. Then it should be a 'smooth phenomena'. Or you define it by Planck scale, making it into 'bits', impossible for us to separate other than by theory. The last makes the arrow I have into a macroscopic 'emergence' using scaling (see why I'm so interested in it?). But, nota bene, also a local constant, shared equivalently in all 'points'. I guess one can call that a 'property' too, depending on taste. Actually the last definitions won't matter for us, as we can't separate them measuring. You consist of 'time', as do I. No way we can measure in between those 'bits', if they exist.
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There's another thing with defining time my way. If you think of this universe as a 'field', then translate that into 'points' in a mathematical space, using 'c' as a constant local speed, information carrier, and clock, equivalently, you find two directions. One is the macroscopic arrow, the other represented of this field. In the field I don't want light to propagate, I want it as a 'beat' following rules, a 'flickering universe' following Mach principle so that when a event unfolds it is a representation of the whole 'field', well in essence although one can argue that one. So the fields 'beat' has one direction, the macroscopic arrow though, as described by us, have another.
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But both obeys 'c', which is why I find Planck scale so appropriate for defining a smallest 'bit/quanta' of 'time'. Whatever exist past that one, if that is correct, has nothing to do with the arrow we define though. Even though it may be what results in it. And the way this field should exist, avoiding ideas of ftl :) although you do have entanglements, is in a equilibrium. A event is a change of that equilibrium into a new unique configuration, or pattern. Well, as a suggestion:)
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And then, just add 'free will' and non linearities, as well as those patterns and constants expressed in chaos mathematics. Then you are where we live.
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However the next bit of the WMAP article isn't reasonable:
"This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe."
This is a non-sequitur. A flat universe does not suggest that the universe is infinite in extent.
Actually, yes it does, as long as one accepts general relativity and that the universe is as (roughly) homogeneous and isotropic as it appears to be to us. It might be hard for one to accept, but a good cosmology textbook can probably walk one through the steps in this essentially mathematical proof.
We cannot truly conclude is that the universe is much larger than the volume we can directly observe. If anybody says we can, ask them to explain this conclusion. They will not be able to.
It might be the case that nobody can explain this to a particular person, but this thing is explained every semester in hundreds of classes across the planet.
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This is a non-sequitur. A flat universe does not suggest that the universe is infinite in extent.
John, are you making a distinction between infinite and boundless?
My feeling is that much confusion could be avoided if those terms were kept apart.
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This is a non-sequitur. A flat universe does not suggest that the universe is infinite in extent.
Of, for cripes sake. Of course it does. EVERY relativist and cosmologist knows this as a FACT.
See? Yet another error that I told you that you keep making all the time.
We cannot truly conclude ....
So what? This is physics, dude. In physics nobody can "truly" conclude anything!!! Sheesh! Read something on the philosophy of physics for once.
Read http://home.comcast.net/~peter.m.brown/ref/philosophy_physics.pdf
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John, are you making a distinction between infinite and boundless?
Yes. An infinite universe is one that goes on forever. A boundless universe might be finite, wherein you never reach any kind of edge, and instead you end up coming round full circle.
Of, for cripes sake. Of course it does. EVERY relativist and cosmologist knows this as a FACT.
No they don't. Because it isn't a fact. It's a non-sequitur. A myth.
Actually, yes it does, as long as one accepts general relativity and that the universe is as (roughly) homogeneous and isotropic as it appears to be to us. It might be hard for one to accept, but a good cosmology textbook can probably walk one through the steps in this essentially mathematical proof.
I accept general relativity, but I do not accept that the universe is homogeneous and isotropic. That's an assumption, that's all. For all we know, some guy fifty billion light years away might be looking up at the night sky, and one half is totally black.
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No they don't. Because it isn't a fact. It's a non-sequitur. A myth.
Nonsense. You have a server problem here. You seem to be of the opinion that all you have to do is make a claim and everyone will accept it just because you claimed it was true. That's nonsense and you know it. Therefore instead of claiming that the entire physics community is wrong why not at least attempt to justify this ridiculous claim of yours? Or remain the fool.
In the mean time I'll prove that it is.
Postulate: The universe is spatially flat (everywhere).
Theorem: A spatially flat universe is spatially infinite.
Proof: Since spatial geodesics are straight lines it follows that any straight line going off in one direction and never terminates. This holds for all spatial geodesics. This implies that since all these geodesics go off into infinity the space must be infinite. Otherwise the line would simply stop in space which is physically absurd. Therefore a spatially flat universe is infinite.
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LOL! That's no proof! Look again at this:
Otherwise the line would simply stop in space which is physically absurd.
Now imagine that a wave in space can be likened to wave inside a water droplet. It travels in a straight line. When it encounters the edge of the droplet it undergoes total internal reflection. That isn't absurd. Nor is the "hall of mirrors" mentioned in this article (http://www.cnn.com/2004/TECH/space/05/24/universe.wide/) featuring cosmologist Neil Cornish. What's absurd is proposing a spatially flat infinite universe that was a singularity 13.8 billion years ago.
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LOL! That's no proof! Look again at this:
Otherwise the line would simply stop in space which is physically absurd.
Now imagine that a wave in space can be likened to wave inside a water droplet. It travels in a straight line. When it encounters the edge of the droplet it undergoes total internal reflection. That isn't absurd. Nor is the "hall of mirrors" mentioned in this article (http://www.cnn.com/2004/TECH/space/05/24/universe.wide/) featuring cosmologist Neil Cornish. What's absurd is proposing a spatially flat infinite universe that was a singularity 13.8 billion years ago.
That article describes a curved space, not a flat one, and not one with reflection.