View Full Version : How do we know space is not infinite?
How do we know space is not infinite? How can we be sure that the objects we see moving through space aren't just moving away from each other through space, rather than 'expanding space' as they change positions in outer space?
How do we know space is not infinite? How can we be sure that the objects we see moving through space aren't just moving away from each other through space, rather than 'expanding space' as they change positions in outer space?
You have a fundamental misconception here if you think "moving away IN space" and "moving away due to space expanding" cannot be happening at the same time.
We do NOT know for sure that space is or is not infinite but we DO know that space is expanding. If I understand it correctly, all galaxies are moving IN space in random directions but their motion relative to each other (small) is totally dominated (NOW) by their apparent motion (LARGE) due to the expansion of space.
EDIT: if galaxies were NOT moving IN space in random directions, and in particular if they were all moving away from US (or from ANY single point) IN space, this would imply a point-position for the big bang and I don't think you'll find any support in science for that point of view.
FURTHER EDIT: Just in case you don't get another point, expanding space and infinite space are NOT in any way contradictory terms.
chrisbaird
Sep9-11, 12:19 PM
The observable universe is finite. The big bang happened about 14 billion years ago, so light from points in space that are 14 billion-light years away (actually 46 because of expansion) are just now reaching us and showing us the big bang. If we try to see farther than 46 billion light years away, we can't, because there is a wall of light caused by the big bang we are trying to see passed.
The unobservable universe may be infinite, but we can't know because we can't see it. But even if we could, how can you prove something like "infinite". It would take an infinite amount of time to measure something infinitely large.
The observable universe is finite. The big bang happened about 14 billion years ago, so light from points in space that are 14 billion-light years away (actually 93 because of expansion) are just now reaching us and showing us the big bang. If we try to see farther than 93 billion light years away, we can't, because there is a wall of light caused by the big bang we are trying to see passed.
.
Zeffur, the "wall of light" mentioned here is best understood if you look up "surface of last scattering"
soulcoma
Sep9-11, 03:33 PM
Just to be a bit more concise...yes, the Observable Universe is always finite, but also increasing every year.
At present the Comoving Distance ([http://en.wikipedia.org/wiki/Comoving_distance]) has a radius of about 47 billion light years, while the diameter is, of course, doubled to around 93 billion light years. We can't actually see objects 93 billion light years away in one direction.
How do we know space is not infinite?
Cosmic microwave background radiation?
Cosmic microwave background radiation?
The CMB tells us absolutly nothing about whether the universe is infinite or not. What is it that makes you think it does?
Rishavutkarsh
Sep10-11, 01:18 AM
The CMB tells us absolutly nothing about whether the universe is infinite or not. What is it that makes you think it does?
but does infinite expand? i mean it's already infinite and it's getting bigger infinite?
Chronos
Sep10-11, 01:50 AM
Infinite is unbounded, so I fail to see your point.
jackmell
Sep10-11, 03:55 AM
How do we know space is not infinite?
I suspect it will turn out to be more like a paradigm shift. Doesn't that make more sense rather than the two options of finite or infinite especially when you consider how our views of the Universe have changed in history? Our understanding of Nature I'm optimistic will continue to improve, perhaps we'll replace General Relativity with something more broad, new discoveries will be made, and our views of the Universe will change once again. It may not be just more of the same like 2000 years ago when one considered walking along the "flat" earth. The spherical earth was a paradigm shift and resolved the paradox of "falling" off. Perhaps will will reach another in the future which may resolve our puzzle about the "size" of the Universe. That to me makes more sense than wondering if it's finite or infinite.
yenchin
Sep10-11, 05:14 AM
but does infinite expand? i mean it's already infinite and it's getting bigger infinite?
Infinitely large can expand to still be...well...infinitely large. For example, the set of all natural number has the same "size" as the set of all even natural numbers. Check out the idea of cardinality of infinite set.
yenchin
Sep10-11, 05:15 AM
I suspect it will turn out to be more like a paradigm shift. Doesn't that make more sense rather than the two options of finite or infinite especially when you consider how our views of the Universe have changed in history? Our understanding of Nature I'm optimistic will continue to improve, perhaps we'll replace General Relativity with something more broad, new discoveries will be made, and our views of the Universe will change once again. It may not be just more of the same like 2000 years ago when one considered walking along the "flat" earth. The spherical earth was a paradigm shift and resolved the paradox of "falling" off. Perhaps will will reach another in the future which may resolve our puzzle about the "size" of the Universe. That to me makes more sense than wondering if it's finite or infinite.
It is possible that the universe is finite but with non-trivial topology.
... it's already infinite and it's getting bigger infinite?
exactly
Oldfart
Sep10-11, 11:59 AM
exactly
Bigger infinite?? Wouldn't that imply a bounded space?
yenchin
Sep10-11, 12:04 PM
Bigger infinite?? Wouldn't that imply a bounded space?
Why would it imply a bounded space? Forget about the universe for now and read about Hilbert's Hotel (http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel).
Oldfart
Sep10-11, 03:33 PM
Why would it imply a bounded space?
Well, it just seemed to me that if space was already infinite, it would be meaningless to consider that it was becoming infiniter. Anyway, thanks -- I read about Hilbert's Hotel, no joy. I evidently have a personel conceptual problem with infinity, possibly stemming from incorrectly thinking that if something increases, it increases from a defined point in space and time. and the amount of increase would be measured from that point.
Well, it just seemed to me that if space was already infinite, it would be meaningless to consider that it was becoming infiniter. Anyway, thanks -- I read about Hilbert's Hotel, no joy. I evidently have a personel conceptual problem with infinity, possibly stemming from incorrectly thinking that if something increases, it increases from a defined point in space and time. and the amount of increase would be measured from that point.
Yes, that is DEFINITELY a misconception when it comes to infinities. Do you have a problem with the following algebraic statement?
infinity + 1 = infinity
The thing represented by the word "infinity" is EXACTLY the same on both sides of the equation. If you can't get your head around this, then you will not get any further with the concept of infinity. This, by the way, is just an algebraic version of Hilbert's Hotel.
Oldfart
Sep10-11, 05:15 PM
Yes, that is DEFINITELY a misconception when it comes to infinities. Do you have a problem with the following algebraic statement?
infinity + 1 = infinity
The thing represented by the word "infinity" is EXACTLY the same on both sides of the equation. If you can't get your head around this, then you will not get any further with the concept of infinity. This, by the way, is just an algebraic version of Hilbert's Hotel.
Oh, I can get my head around that equation OK. The hard part is ascribing meaning to it. Like, what's the point? Can infinity be increased? Or is infinity plus 1 senseless?
My problem, not yours.,,
The CMB tells us absolutly nothing about whether the universe is infinite or not. What is it that makes you think it does?
CMB radiation is almost homogeneous, but it has small differences. If you build models were space can be infinite or can be compact, it turns out that compact space models can explain those small differences better that infinite space models.
CMB radiation is almost homogeneous, but it has small differences. If you build models were space can be infinite or can be compact, it turns out that compact space models can explain those small differences better that infinite space models.
How "compact" are we talking about here? I'm assuming that you are not implying small here, just not infinite.
Billions of light years across, but it’s not static. Space seems to be expanding, and that expansion seems to be accelerating.
Billions of light years across, but it’s not static. Space seems to be expanding, and that expansion seems to be accelerating.
"Billions" could be smaller than the diameter of the observable universe. I assume you DON'T mean that, but I now assume that you ARE talking about VERY small --- that is, not much bigger than the observable universe. I certainly can't argue persuasively that this is impossible, but I believe the consensus is that it is MUCH bigger than that at the very least.
It depends on whether or not we can identify ghost images. If space is compact, then light from a distant galaxy can travel in two directions, towards us or it can circumnavigate the universe and appear somewhere else as a ghost image.
It depends on whether or not we can identify ghost images. If space is compact, then light from a distant galaxy can travel in two directions, towards us or it can circumnavigate the universe and appear somewhere else as a ghost image.
I completely understand this concept, but would be astounded if it ever turned out to be the case. I DO believe it possible that the universe has the topology that you suggest but even if it does, the thought that it could be small enough that the light would actually reach us from both directions just strikes me as so unlikely as to be silly.
It’s not small. Light from ghosts can take billions of years to reach us
Chronos
Sep12-11, 01:22 AM
The observable universe is finite. Given that is the only part observationally accessible, the rest is scientifically irrelevant until an observationally detectable effect on the observable part is confirmed.
It’s not small. Light from ghosts can take billions of years to reach us
since the current diameter of the observable universe is pushing 100 billion light years, I consider "billions" to be QUITE small.
...but does infinite expand?
Like oldfart, I too had a misconception about infinity....turns out there are dozens of different infinity concepts discussed and easily accessible in Wikipedia...
One is enough to occupy my brain for the time being.
The observable universe is finite. Given that is the only part observationally accessible, the rest is scientifically irrelevant until an observationally detectable effect on the observable part is confirmed.
Chronos, I have seen you make this exact point numerous times, including one in a thread when I first joined many months ago. I was quite taken aback at the time because it seemed then, as it seems now, that you wish to shut down all discussion of the possibilities of what might exist outside the observable universe.
I have been very encouraged since then to see that your point of view is decidedly in the minority and I now find your point of view tiresome.
I do not mean that I think there is anything wrong with the technical accuracy of your point of view, but it strikes me as identical to a hypothetical critic of Columbus wanting to sail around the world because after all, our current experience says hey Chris, there's nothing out there.
I DO understand that this is a very flawed analogy since the earth is observable and outside the observable universe is not, but my fundamental point is that it seems to me that you want to shut down discussion and have us hunker down in ignorance.
Since it seems to bother you that most of the rest of us have an interest in discussing the existance of things outside the OU, why don't you just ignore these threads, write us all off as willfully ignorant, and go about your merry way?
Calimero
Sep12-11, 08:30 AM
The observable universe is finite. Given that is the only part observationally accessible, the rest is scientifically irrelevant until an observationally detectable effect on the observable part is confirmed.
Completely true. No use debating things that cannot be verified in any way, and infiniteness is inherently such thing.
chrisbaird
Sep12-11, 10:41 AM
Yes, that is DEFINITELY a misconception when it comes to infinities. Do you have a problem with the following algebraic statement?
infinity + 1 = infinity
The thing represented by the word "infinity" is EXACTLY the same on both sides of the equation. If you can't get your head around this, then you will not get any further with the concept of infinity. This, by the way, is just an algebraic version of Hilbert's Hotel.
You don't have to think about infinity as some eternally inaccesible twilight zone. You can get a very good feel for what infinity means by going large compared to the system, but still small numerically. For instance, x + 1 = x becomes very close to true when x = 1 million.
Oldfart
Sep12-11, 01:23 PM
Like oldfart, I too had a misconception about infinity....
Whoa there! What's this "we" stuff, white man? (Tonto to the Lone Ranger, as they find themselves surrounded by hostile indians.)
I actually don't admit to having a misconception, at least relative to the real world/universe, but am fine with infinity being an useful mathematical concept.
zeffur7
Sep12-11, 02:42 PM
You have a fundamental misconception here if you think "moving away IN space" and "moving away due to space expanding" cannot be happening at the same time.
I did not think I made such an assertion.
...we DO know that space is expanding. If I understand it correctly, all galaxies are moving IN space in random directions but their motion relative to each other (small) is totally dominated (NOW) by their apparent motion (LARGE) due to the expansion of space.
Visible objects in solar systems obviously have orbits and the contents of galaxies appear to be accelerating away from each other, but how can we be certain that the explanation for those galaxies moving away from each other is caused by space expanding? Consider the conjecture that the big bang was a singularity that began to expand at some position and after ~14 billion years it has increased in volume to all that we are able to perceive now.
zeffur7
Sep12-11, 03:11 PM
The observable universe is finite. The big bang happened about 14 billion years ago, so light from points in space that are 14 billion-light years away (actually 46 because of expansion) are just now reaching us and showing us the big bang. If we try to see farther than 46 billion light years away, we can't, because there is a wall of light caused by the big bang we are trying to see passed.
The unobservable universe may be infinite, but we can't know because we can't see it. But even if we could, how can you prove something like "infinite". It would take an infinite amount of time to measure something infinitely large.
Excellent points!
If the big bang originated as a singularity (which some theorize) can we estimate the volume of the observable universe at 1 billion year increments since the beginning?
If yes, what was the rate of expansion? Did 90+% of it expand in a nanosecond or how did it expand, if we know.
"...light from points in space that are 14 billion-light years away (actually 46 because of expansion) are just now reaching us and showing us the big bang. If we try to see farther than 46 billion light years away, we can't, because there is a wall of light caused by the big bang we are trying to see passed.
It seems to me that we should have been receiving light from the moment light was being created--which should include the light from the wall of light that you essentially describe as the barrier that we cannot see past. Light from points closer to us should arrive in shorter periods of time than light from points further from us. If the light we are now receiving is 14 billion years old, how can we be certain it is from the beginning of the big bang? Or do we make our estimate of the age of the universe based on the light wall barrier that you have described?
zeffur7
Sep12-11, 03:29 PM
... the rest of us have an interest in discussing the existance of things outside the OU,...
I'm digging your vibe, wo?/man :)
I'd like to see everyone's thoughts on the subject, as long as that have a modicum of sense with them.
I like the theory that the universe might be some weird 4-D shape. If you travel in the same direction on the 2-D surface of the earth, you would eventually end up in the same place. It's not infinite, but you would never find a boundary. If the universe were 4D it could be that you could keep going in one direction through 3D space, and in a similar way never find a boundary, just end up in the same place. I guess that would make it bounded in the 4th dimension, but unbounded in the other 3.
That may even lead to ideas like all of the other galaxies we see are just our own galaxy from the various times in the past, with the light having passed different distances through the whole universe before we see it again.
Pure speculation really, I don't think there's any evidence for it, there may in fact be evidence to the contrary. I just think it's quite a neat, wacky idea that seems to tie in quite nicely. How could it be tested?
I did not think I made such an assertion.
OK, I guess I misunderstood you.
... Consider the conjecture that the big bang was a singularity that began to expand at some position ...
That is a totally incorrect description of what is currently believed to be the case, in that there was no "position" in space that the expansion happened from, it happened everywhere at once.
yenchin
Sep12-11, 11:37 PM
I like the theory that the universe might be some weird 4-D shape. If you travel in the same direction on the 2-D surface of the earth, you would eventually end up in the same place. It's not infinite, but you would never find a boundary. If the universe were 4D it could be that you could keep going in one direction through 3D space, and in a similar way never find a boundary, just end up in the same place. I guess that would make it bounded in the 4th dimension, but unbounded in the other 3.
That may even lead to ideas like all of the other galaxies we see are just our own galaxy from the various times in the past, with the light having passed different distances through the whole universe before we see it again.
Pure speculation really, I don't think there's any evidence for it, there may in fact be evidence to the contrary. I just think it's quite a neat, wacky idea that seems to tie in quite nicely. How could it be tested?
Note that what you are talking about doesn't have to require extra spatial dimension, just imposing non-trivial topology will do. For example on some video game, you disappear into the right side of the screen and emerges from the left, effectively that world is *the same* as a cylinder, obtained by gluing left and right edges of the computer screen. Such a topological effect can be looked for via brute force statistical methods (like you say, essentially by looking for patterns which correlate at different directions, not just galaxies but also CMB), but we have not found anything conclusive yet. See e.g.
http://plus.maths.org/content/os/issue10/features/topology/index
http://www.csulb.edu/~scrass/Teaching/math355/articles/dodecaSpace.pdf
http://www.maths.lse.ac.uk/Personal/mark/topos.pdf
Infinitely large can expand to still be...well...infinitely large. For example, the set of all natural number has the same "size" as the set of all even natural numbers. Check out the idea of cardinality of infinite set.
yes i accept infinite can get bigger infinite. But no finite thing can become infinite after finite amount of time (or after finite number of steps). for example the sequence {nc},n=1 to infinity (where c is a positive real number, in case you want the sequence to grow faster you can choose a big c ) after any finite number of steps, never becomes infinity . then after 14 billion years how could the universe become infinite ? starting from a point?
my point is " some thing infinite can get bigger or smaller but it could have not been finite in the past, and will never become finite in the future "
I like the theory that the universe might be some weird 4-D shape. If you travel in the same direction on the 2-D surface of the earth, you would eventually end up in the same place. It's not infinite, but you would never find a boundary. If the universe were 4D it could be that you could keep going in one direction through 3D space, and in a similar way never find a boundary, just end up in the same place. I guess that would make it bounded in the 4th dimension, but unbounded in the other 3.
I like this idea too, and it's possible that 3D space at the last scatering surface was compact. You don't need 4D space, only 4D spacetime.
Constantin
Sep19-11, 05:20 PM
I see the Universe's "diameter" mentioned in two above posts.
I'm pretty sure the Observable Universe only has radius, and not diameter. To measure a diameter you need to be on the edge of the Universe (or any circle or sphere) and that's not possible in any version of the Universe. You can't simply multiply the radius by two and say it's diameter.
Constantin
Sep19-11, 05:35 PM
I'll quote these two above posted arguments as very convincing:
---
"how can you prove something like "infinite". It would take an infinite amount of time to measure something infinitely large."
"The observable universe is finite. Given that is the only part observationally accessible, the rest is scientifically irrelevant until an observationally detectable effect on the observable part is confirmed."
---
The first argument can be given against anything being infinite, not just the Universe.
I see the Universe's "diameter" mentioned in two above posts.
I'm pretty sure the Observable Universe only has radius, and not diameter. To measure a diameter you need to be on the edge of the Universe (or any circle or sphere) and that's not possible in any version of the Universe. You can't simply multiply the radius by two and say it's diameter.
Now that's just silly. The OU is not a physical object, it's just a way of describing the sphere which represents the fartherst out in any direction that we can "see". To say that it has a radius but no diameter is profoundly nonsensical.
zeffur7
Sep22-11, 04:44 PM
No one knows right now, our technology is to young to discover if the Universe is infinite or finite. The only thing we know is, it is expanding and we already proved that.
We also know that that expansion is accelerating.
zeffur7
Sep22-11, 04:49 PM
yes i accept infinite can get bigger infinite. But no finite thing can become infinite after finite amount of time (or after finite number of steps). for example the sequence {nc},n=1 to infinity (where c is a positive real number, in case you want the sequence to grow faster you can choose a big c ) after any finite number of steps, never becomes infinity . then after 14 billion years how could the universe become infinite ? starting from a point?
my point is " some thing infinite can get bigger or smaller but it could have not been finite in the past, and will never become finite in the future "
If the big bang reverses at some point & then become the big crunch (i.e. a singularity), what say ye of the min & max of that system, if it were true?
Tanelorn
Sep23-11, 12:55 PM
The observable universe is finite. Given that is the only part observationally accessible, the rest is scientifically irrelevant until an observationally detectable effect on the observable part is confirmed.
Chronos by observable universe do you count the CMBR sphere or just the highest redshifted galaxies?
The observable universe is shrinking all the time and eventually only our local group will be visible from our position. However isnt it pretty certain that the unobservable universe still exists both now and at that later time - unless we believe that the universe not homogenous and isotropic?
The observable universe is shrinking all the time and eventually only our local group will be visible from our position. However isnt it pretty certain that the unobservable universe still exists both now and at that later time - unless we believe that the universe not homogenous and isotropic?
Seems to me that statement is both right and wrong. The OU isn't actually shrinking in terms of the number of light-years it encompasses, but it IS "shrinking" in the way you mean, which is that it contains less and less stuff because everything is moving out of it.
What Chronos has said in other posts is that there basically ISN'T anything outside the OU because we can't TELL directly whether there is or not, but I think that's an overly restrictive point of view. I think the UN-observable universe exists now and will continue to exist but in practical terms, that doesn't seem to mean much since as Chronos always points out (correctly) we just can't detect it.
It's not at all clear to me that there will EVER be any way to detect it, although I have heard, vaguely, that there are some theories that say there will be / may be observational evidence left over from the earliest times after the singularity that we WILL be able to observe remnants of. I don't get how this works but it would be neat if such things ARE ever observed.
Tanelorn
Sep23-11, 01:40 PM
Perhaps I wasnt being clear. Try less of the matter in the universe will be observable in the future. However this wasnt the point I was trying to make.
If the big bang reverses at some point & then become the big crunch (i.e. a singularity), what say ye of the min & max of that system, if it were true?
then please give me the initial conditions to formulate the differential equations, then i will tell you the max and min
The observable universe is finite. The big bang happened about 14 billion years ago, so light from points in space that are 14 billion-light years away (actually 46 because of expansion) are just now reaching us and showing us the big bang. If we try to see farther than 46 billion light years away, we can't, because there is a wall of light caused by the big bang we are trying to see passed.
The unobservable universe may be infinite, but we can't know because we can't see it. But even if we could, how can you prove something like "infinite". It would take an infinite amount of time to measure something infinitely large.
Ok now tell me will you take infinite amount of time to say "The set of all natural numbers" is finite or infinite? :smile: Actually only if you wanna prove an Infinitely large thing as "Finite" you will take infinite amount of time
chrisbaird
Sep26-11, 11:28 AM
Ok now tell me will you take infinite amount of time to say "The set of all natural numbers" is finite or infinite? :smile: Actually only if you wanna prove an Infinitely large thing as "Finite" you will take infinite amount of time
I meant it is not possible to physically prove something is infinite. A mathematical proof is a different beast. We can go ahead and make mathematical models of the universe and from some postulates mathematically prove it is infinite. But to see if our model matches reality, we have to do physical experiments and make observations. No physical experiment can measure something infinite. If the universe is finite, then we could measure it. If the cosmic background radiation stopped coming at a certain point in time, that would tell us the universe is finite. The last glimpse of CMB radiation would be coming from the literal edge of the universe. Such a finding would shake the cosmology world up a bit, but I doubt it will happen.
... If the cosmic background radiation stopped coming at a certain point in time, that would tell us the universe is finite. The last glimpse of CMB radiation would be coming from the literal edge of the universe. Such a finding would shake the cosmology world up a bit, but I doubt it will happen.
Uh ... say WHAT? Could you elaborate on that, please. I'm certainly willing to believe it's just me, but that makes no sense to me.
chrisbaird
Sep26-11, 12:34 PM
Uh ... say WHAT? Could you elaborate on that, please. I'm certainly willing to believe it's just me, but that makes no sense to me.
That me try to do better. Imagine that the universe is finite spatially, and always has been, and is not periodic (it does not wrap around and connect to itself). In other words, imagine that there is a physical edge to the universe beyond which nothing exists. Shortly after the big bang, the cosmic background radiation is created effectively uniformly at all points in the universe and spreads out from each point in all directions. CMB radiation that travels a long ways before hitting a planet or space probe's camera needs a longer time to do so, and is thus absorbed/observed at a much later time than the big bang. The CMB radiation created at points in space close to the earth were absorbed long ago by the earth (or were not absorbed and long ago zipped away from the earth, out of our region of interest). But CMB radiation created at points very far away from the earth are just now reaching us and being detected. If there were a physical edge to the universe, there is a physical limit to points in space that were in existence to create CMB radiation. After enough time has elapsed that the CMB radiation created at one edge of the universe has had a chance to travel to the opposite edge of the universe, it will be gone. All of it will have been absorbed or flowed beyond the universe's edge at this point. (Unless the edge of the universe consists of giant and perfect mirrors, so that the universe in a giant resonant cavity.) While I do not believe this to be the case in reality, I am trying to imagine the implications of a finite universe. Have I gone wrong anywhere?
Tanelorn
Sep26-11, 03:36 PM
Chris, I think I understand what you are suggesting. If the universe has an edge and we are relatively near it, then eventually we would see no more CMBR in that direction because it had all passed us by. I suppose we can keep looking!
I think that the observable universe is small compared to the whole universe because the CMBR is so flat in every direction implying homogeneity. However, if there was an edge of some kind I would not expect it to be a sudden transition either, there again we cannot discount any possibility, however remote, when we cannot make any observations.
[QUOTE=Tanelorn;3524331] ... I think that the observable universe is small compared to the whole universe because the CMBR is so flat in every direction implying homogeneity.QUOTE]
I too think I now get what Chris is saying (and agree w/ him that it is unlikely), but I do NOT get the statement above. Why does homogeneity limit his suggestion in any way, or suggest that the U is much bigger than the OU ?
Tanelorn
Sep26-11, 05:46 PM
Phinds, ever since reading Penrose's estimate that the observable universe is just ~10-31 the size of the whole universe, I have been trying to build a mental picture of such a system.
It is pretty funny to think that the entire observable universe is an insignificant part of the whole universe.
Phinds, ever since reading Penrose's estimate that the observable universe is just ~10-31 the size of the whole universe, I have been trying to build a mental picture of such a system.
It is pretty funny to think that the entire observable universe is an insignificant part of the whole universe.
Seems quite reasonable to me, but of course the estimates vary all over the place and we don't really KNOW so it gets to be a somewhat theological (i.e. non-falsifiable) discussion.
I'm still interested in hearing your answer to my question of why you think the CMB homogeniaty implies anything about the size of the U beyond the OU.
zeffur7
Sep27-11, 02:21 AM
then please give me the initial conditions to formulate the differential equations, then i will tell you the max and min
In other words, it would be finite. :)
Drakkith
Sep27-11, 05:55 AM
In other words, it would be finite. :)
Only if the initial conditions were finite. There is no known way to tell currently.
Tanelorn
Sep27-11, 08:45 AM
I'm still interested in hearing your answer to my question of why you think the CMB homogeniaty implies anything about the size of the U beyond the OU.
I am saying that matter homogeneity on large scales of the Observable Universe itself, and the flatness of the CMBR suggests to me, and I believe many others, that the OU is small in size compared to the complete Universe. I think I said this already and I cant think of any better wording!
I am saying that matter homogeneity on large scales of the Observable Universe itself, and the flatness of the CMBR suggests to me, and I believe many others, that the OU is small in size compared to the complete Universe. I think I said this already and I cant think of any better wording!
Thanks. Actually, I worded my question very poorly. What was confusing me was actually the statement
If the universe has an edge and we are relatively near it, then eventually we would see no more CMBR in that direction because it had all passed us by.
but I think I get it now.
Tanelorn
Sep27-11, 09:17 AM
ok glad to help. Lots of if and buts there and a cynic might say that it still needs to be proved.
The only truth that counts is the one that can be scientifically proved.
Deuterium2H
Sep28-11, 01:38 AM
Yes, that is DEFINITELY a misconception when it comes to infinities. Do you have a problem with the following algebraic statement?
infinity + 1 = infinity
The thing represented by the word "infinity" is EXACTLY the same on both sides of the equation. If you can't get your head around this, then you will not get any further with the concept of infinity. This, by the way, is just an algebraic version of Hilbert's Hotel.
Careful...that is not technically correct. I don't know why I always get into Set Theory here on the Cosmology section, but it seems to come up a lot.
Infinity, in and of itself, is not a number. There are finite numbers (ordinals), and transfinite ordinals. There are finite sets, and infinite sets.
The first transfinite ordinal is omega "w"...which can be considered the next larger number after ALL the Natural numbers. It is the order type of the Set of all numbers preceding it, which is the Set of Natural numbers.
In accordance with Cantor's ordinal arithmetic, w + 1 = w is NOT true. w + 1 is the next ordinal which succeeds w. On the other hand 1 + w = w IS true.
So, a well ordered listing of ordinals that include the Naturals and extend to the first three transfinite ordinals would be: { 0, 1, 2, 3,..., w, w+1, w+2 }
We also know that that expansion is accelerating.
Have we measured that acceleration ? so that we are also able to calculate its(the acceleration) rate of change, huh:smile:?
chrisbaird
Sep30-11, 12:37 PM
Have we measured that acceleration ? so that we are also able to calculate its(the acceleration) rate of change, huh:smile:?
Yes, several times. The first time was in 1998 as reported here (http://iopscience.iop.org/1538-3881/116/3/1009/pdf/1538-3881_116_3_1009.pdf). Several years ago I attended a lecture by a member of this group, Dr. Kirshner, on these results and the presentation was amazing.
Have we measured that acceleration ? so that we are also able to calculate its(the acceleration) rate of change, huh:smile:?
Do you have some reason for thinking that we have not? The tone of your post seems to imply that. As Chris said, we have.
Maybe space-time’s a compact Lorentzian manifold :smile:
To measure a diameter you need to be on the edge of the Universe (or any circle or sphere) and that's not possible in any version of the Universe. You can't simply multiply the radius by two and say it's diameter.
And to measure the radius ?
Yes, several times. The first time was in 1998 as reported here (http://iopscience.iop.org/1538-3881/116/3/1009/pdf/1538-3881_116_3_1009.pdf). Several years ago I attended a lecture by a member of this group, Dr. Kirshner, on these results and the presentation was amazing.
Do you have some reason for thinking that we have not? The tone of your post seems to imply that. As Chris said, we have.
:smile:No i don't have . but i wonder how it's measured and i remember i read in a book that the acceleration is decreasing , if so please tell me whether the rate of change of the Acceleratrion is also measured and can we say that the acceleration will ever reach zero or keep on decreasing ?
:smile:No i don't have . but i wonder how it's measured and i remember i read in a book that the acceleration is decreasing , if so please tell me whether the rate of change of the Acceleratrion is also measured and can we say that the acceleration will ever reach zero or keep on decreasing ?
I'm on shaky ground here so I hope someone who actually knows what they are talking about will chime in. What I THINK I remember reading is that the acceleration is decreasing asymptotically to a non-zero value and that the acceleration will never drop below that value so we DO seem to be on track for the universe dying by ice, not fire.
How do we know space is not infinite?
In science we can't know beyond what is observed/measured. The observable universe has a finite radius. You only can speculate beyond that.
IF our universe is infinite, would that rule out the possibility that other universes exist?
IF our universe is infinite, would that rule out the possibility that other universes exist?
Since there is not the slightest knowledge HOW other universes might exist, the question doesn't have much meaning. My guess is it's irrelevant since our universe isn't thought to be expanding INTO anything, it's not like we're going to use up all the room.
... it's not like we're going to use up all the room.[/QUOTE]
Heh..., here I go again...
Where is this "room"?
... it's not like we're going to use up all the room.
Heh..., here I go again...
Where is this "room"?[/QUOTE]
It's the non-existant stuff "outside" our universe that we're not going to use up all of, thus crowding out other non-existant universes. That's my story and I'm sticking with it !
That's my story and I'm sticking with it !
Okay, thanks, phinds!
But please be careful, I assume you know that you can get your license pulled for talking like that...
Justaman
Oct14-11, 11:35 PM
It is. There is no beginning, and no end, only transition. Same with time.
Justaman
Oct14-11, 11:42 PM
IF our universe is infinite, would that rule out the possibility that other universes exist?
One universe, lots of space, infinite potential for infinite configurations beyond that which has become visible to us as of yet.
It is. There is no beginning, and no end, only transition. Same with time.
Personal theories are not allowed on this forum. You should read the rules. This is a physics forum, not a theology forum.
maggiemaeu
Oct16-11, 03:14 PM
Well, it just seemed to me that if space was already infinite, it would be meaningless to consider that it was becoming infiniter. Anyway, thanks -- I read about Hilbert's Hotel, no joy. I evidently have a personel conceptual problem with infinity, possibly stemming from incorrectly thinking that if something increases, it increases from a defined point in space and time. and the amount of increase would be measured from that point.
assuming the definition of infinity in use here is immeasurably great, then it makes sense to imply that it has a defined starting point to measure from. however, the word is in my opinion and possibly in fact a paradox, so saying anything about measuring infinity or infinity getting bigger is just contradictory. that is not to say it's not argueable though.
maggiemaeu
Oct16-11, 03:20 PM
Personal theories are not allowed on this forum. You should read the rules. This is a physics forum, not a theology forum.
not neccessarily a personal theory; could simply be a professional theory you obviously haven't heard of yet. that is one explanation of many that i have heard concerning infinity. dont mean to cause trouble :)
[QUOTE=maggiemaeu;3562002] ... the word is in my opinion and possibly in fact a paradox, so saying anything about measuring infinity or infinity getting bigger is just contradictory. QUOTE]
ANOTHER Personal theory and this one DEFINITELY contrary to the facts.
Justaman
Oct16-11, 08:04 PM
Personal theories are not allowed on this forum. You should read the rules. This is a physics forum, not a theology forum.
Hi Phinds- my statement wasn't intended to be theological in any way- quite the contrary actually.
Quite simply, I don't think time ever began or will end, and that space continues for an infinite distance in all directions.
Considering infinite, how does time either start or end? With the freezing of a cesium atom? I don't think so, as the duration of it's condition is still real. Even beyond observable space (expanding at light speed) if no matter exists beyond some distance, wouldn't an object that moves into this space continue indefinitely until acted upon? How we currently measure time and space may become obsolete, but I don't think this suggests a beginning or end to either.
With infinite time comes infinite possiblities, so it seems unlikely to me that all matter sat in singularity eternally until 13B yrs ago.
Rather, I think (there I go again) the expansion/contraction cycle is a continuous and infinte process- the contraction cycle including material collisions of increasing frequency with decreased proximity, arriving at and passing a "central gravitational point" (thus entering expansion phase) at inconsistent intervals around the central (and dynamic) point.
This would then mean that expansion/contraction exists with or without a "big bang" event, and that all matter only occasionally (though repeatedly) forms an instantaneous singularity that, once again, "bangs".
Not even light could escape the gravitational pull at singularity, so the OU would be quite small. Would this mean that space-devoid of matter even 2 feet away- would be finite? I personally would not consider it so, making it infinite in all directions correct?
Assuming infinity of space and time, it seems likely that an infinite number of expansion/contraction/big bang cycles would be occuring at all times, of course located well beyond our OU, but part of a larger "universe".
As with cells in our body, it seems these universes must occasionally interact with/effect each other in some way, just as cells in our own body do.
Associated by proximity, would this then make our universe part of a finite "organism" which, on a universal scale taken to infinity, co-mingles with an infinite population of similar "organisms"? And so on, and so on...
I think so. But there I go again...
Sorry to go on so in responding.
Constantin
Oct16-11, 09:11 PM
It's easy to imagine time as finite. Actually it's much harder to imagine anything as being infinite. How do you imagine an infinite thing ?
Your problem arises from not being able to imagine time having limits. These limits, edges of the time dimension, beginning and end of time.
But if you consider time being just another dimension, you might find that easier.
Imagine the normal space dimensions. The Observable Universe is finite.
It has a center, any observer being at the very center of his own Observable Universe. And it has an edge, the furthest away it is possible to see. That edge is moving away and the Universe is expanding, but it's still finite.
Same thing with time. It has a beginning, the Big Bang. And an edge, the "current moment". The "current moment" is continuously moving, same as the edge of the Observable Universe. So the time spent since the Big Bang keeps increasing, but it's still finite.
Also don't consider the future as part of the time dimension. The future doesn't exist, yet.
If you imagine this analogy between space and time dimensions, you'll find it easier to understand the concept of finite time or space.
Justaman
Oct16-11, 09:29 PM
The Observable Universe is finite.
It has a center, any observer being at the very center of his own Observable Universe. And it has an edge, the furthest away it is possible to see. That edge is moving away and the Universe is expanding, but it's still finite.
Thanks, I well understand this, and how it serves to assert that the entire universe (consisting of everything beyond our OU) is indeed infinite. Since the OU that exists at the edge of my OU is twice as far away from me...and so on.
Same thing with time. It has a beginning, the Big Bang. And an edge, the "current moment". The "current moment" is continuously moving, same as the edge of the Observable Universe. So the time spent since the Big Bang keeps increasing, but it's still finite..
It's clear that a finite number of seconds have passed since the last big bang, but not that time did not exist/advance prior to it. So all matter in the universe existed in a single point and then simply exploded? How long would it have maintained this state? Of course, that duration would have been real and measurable.
Constantin
Oct16-11, 10:41 PM
There's no proof there was anything before the Big Bang. So it's pure speculation.
Just use the concept "what you can't see does not exist". It simplifies things quite a lot and avoids speculation.
We can't see before the Big Bang, so nothing existed before that. We can't see beyond the edge of the Observable Universe, so nothing exists beyond that edge.
Can't get simpler than that.
Constantin
Oct16-11, 10:48 PM
"So all matter in the universe existed in a single point and then simply exploded?"
Matter did not exist at the very beginning, just a huge amount of energy. That energy created the matter.
Drakkith
Oct16-11, 10:53 PM
Quite simply, I don't think time ever began or will end, and that space continues for an infinite distance in all directions.
That's fine. Current models don't care whether the universe is actually infinite or whether it wraps back on itself or something.
With infinite time comes infinite possiblities, so it seems unlikely to me that all matter sat in singularity eternally until 13B yrs ago.
Nonsense. If something is impossible now, it is impossible always. The sun has zero chance of violating conservation of energy and suddenly losing all of it's mass and energy and turning into a bowl of soup. As for all matter sitting in a singularity until 13 billion years ago, I don't know of anything in the standard model that says it did. In fact the model simply stops making predictions past a certain point. There are several other theories that try to go beyond the standard one and predict what happened during and before the big bang but none of those are accepted yet.
Rather, I think (there I go again) the expansion/contraction cycle is a continuous and infinte process- the contraction cycle including material collisions of increasing frequency with decreased proximity, arriving at and passing a "central gravitational point" (thus entering expansion phase) at inconsistent intervals around the central (and dynamic) point.
Unfortunately our observations show that unless something changes this is not the case.
This would then mean that expansion/contraction exists with or without a "big bang" event, and that all matter only occasionally (though repeatedly) forms an instantaneous singularity that, once again, "bangs".
I don't know what you call sudden expansion of the universe from a possible singularity, but I believe it's called the Big Bang.
Not even light could escape the gravitational pull at singularity, so the OU would be quite small. Would this mean that space-devoid of matter even 2 feet away- would be finite? I personally would not consider it so, making it infinite in all directions correct?
Our knowledge of physics breaks down at the singularity point, so there's no way to answer your question.
Assuming infinity of space and time, it seems likely that an infinite number of expansion/contraction/big bang cycles would be occuring at all times, of course located well beyond our OU, but part of a larger "universe".
As with cells in our body, it seems these universes must occasionally interact with/effect each other in some way, just as cells in our own body do.
Associated by proximity, would this then make our universe part of a finite "organism" which, on a universal scale taken to infinity, co-mingles with an infinite population of similar "organisms"? And so on, and so on...
None of this even makes any sense. I recommend that you take some time and understand current models of the universe before posting anything like this nonsense again. And remember that PF isn't the place for personal beliefs or theories.
Constantin
Oct16-11, 11:00 PM
A very good argument against the repeated "expansion/contraction/big bang cycles":
Evidence shows the Universe is expanding at an accelerated rate, so it will never contract again.
Justaman
Oct16-11, 11:09 PM
A very good argument against the repeated "expansion/contraction/big bang cycles":
Evidence shows the Universe is expanding at an accelerated rate, so it will never contract again.
Begs the question: What's out there, pulling it? I mean this in a purely scientific way. But obviously a topic for a different board. Sorry for the intrusion...
Thanks all, very interesting (and at times entertaining) thoughts.
Drakkith
Oct16-11, 11:25 PM
Begs the question: What's out there, pulling it? I mean this in a purely scientific way. But obviously a topic for a different board. Sorry for the intrusion...
Thanks all, very interesting (and at times entertaining) thoughts.
http://en.wikipedia.org/wiki/Cosmological_constant
maggiemaeu
Oct17-11, 04:11 PM
[QUOTE=maggiemaeu;3562002] ... the word is in my opinion and possibly in fact a paradox, so saying anything about measuring infinity or infinity getting bigger is just contradictory. QUOTE]
ANOTHER Personal theory and this one DEFINITELY contrary to the facts.
sorry, didn't mean it as an opinion, just presenting a problem in the arguement. honestly, there are many definitions of the word that are contradictory. the fact being that infinity is an argueable word, you have to narrow it down a little more. how could this be contrary to the facts? it is a fact that the word has different meanings and which ones you use is your business, not mine. all i'm saying is that specifics are needed in discussing infinity to avoid confusion.
i do admit i should have been more careful about how i conveyed that.
maggiemaeu
Oct17-11, 04:21 PM
A very good argument against the repeated "expansion/contraction/big bang cycles":
Evidence shows the Universe is expanding at an accelerated rate, so it will never contract again.
is this the theory that states there are multiple events similar to the big bang? sorry, i'm not sure:blushing::uhh:
[QUOTE=phinds;3562085]
sorry, didn't mean it as an opinion, just presenting a problem in the arguement. honestly, there are many definitions of the word that are contradictory. the fact being that infinity is an argueable word, you have to narrow it down a little more. how could this be contrary to the facts? it is a fact that the word has different meanings and which ones you use is your business, not mine. all i'm saying is that specifics are needed in discussing infinity to avoid confusion.
i do admit i should have been more careful about how i conveyed that.
There is nothing contradictory about infinity being able to get bigger. It can and does. This is a standard part of any reasonable definition of infinity and if you think otherwise, you might find it interesting to study up on the subject.
Constantin
Oct17-11, 04:50 PM
Mathematically infinity can get bigger, smaller, and you can joggle with it in different ways.
But can you give any example in physics of something that was proven to be infinite ? Because I don't believe there is such an example.
Mathematically infinity can get bigger, smaller, and you can joggle with it in different ways.
But can you give any example in physics of something that was proven to be infinite ? Because I don't believe there is such an example.
I believe that most (but by NO means all) models have the universe as infinite AND haveing size added to it all the time but that IS the only thing I am aware of.
And I think that talking about infinity getting bigger or smaller is probably incorrect. You can add to it or take away from it, but that does not change the fact that it is just "infinity".
khemist
Oct17-11, 10:10 PM
A simple way to think of infinity.
Consider all the real numbers -> 1, 2, 3, 4, etc...
One would certainly consider that an infinite set (give me any number, and I can get another number by simply adding 1). Now, take all the real even numbers -> 2, 4, 6, etc...
That is certainly an infinite set as well, but it has half the values as the original set!
A simple way to think of infinity.
Consider all the real numbers -> 1, 2, 3, 4, etc...
One would certainly consider that an infinite set (give me any number, and I can get another number by simply adding 1). Now, take all the real even numbers -> 2, 4, 6, etc...
That is certainly an infinite set as well, but it has half the values as the original set!
No, it's the same number. It SEEMS like half as much but that's that thing about infinity ... you can't treat it in normal mathematical operations as though it were like other numbers. Half of infinity is still infinity, as is twice infinity. Very UNintuitive.
khemist
Oct18-11, 01:53 PM
No, it's the same number. It SEEMS like half as much but that's that thing about infinity ... you can't treat it in normal mathematical operations as though it were like other numbers. Half of infinity is still infinity, as is twice infinity. Very UNintuitive.
That is what I am saying.... Although the even set has half the numbers, it is still infinity. Read what I wrote a bit more closely :)
That is what I am saying.... Although the even set has half the numbers, it is still infinity. Read what I wrote a bit more closely :)
DOH ! misinterpretaion alert !!! (by ME, I mean, not you)
maggiemaeu
Oct19-11, 06:20 PM
[QUOTE=maggiemaeu;3564061]
There is nothing contradictory about infinity being able to get bigger. It can and does. This is a standard part of any reasonable definition of infinity and if you think otherwise, you might find it interesting to study up on the subject.
i grudgingly admit you're right here. anything you recomend reading?:redface:
[QUOTE=phinds;3564083]
i grudgingly admit you're right here. anything you recomend reading?:redface:
I've been away from formal study to long to have any idea what's a good text these days. Others here can undoubtedly give you some good advice. If you don't get anything in this thread, start another specifically asking for advice on math books discussing infinities (there is a heiarchy of them, named "aleph null" (the "normal" infinity) "aleph 1" and so forth.
zeffur7
Nov27-11, 02:57 PM
A simple way to think of infinity.
Consider all the real numbers -> 1, 2, 3, 4, etc...
One would certainly consider that an infinite set (give me any number, and I can get another number by simply adding 1). Now, take all the real even numbers -> 2, 4, 6, etc...
That is certainly an infinite set as well, but it has half the values as the original set!
Another, and perhaps easier way to consider infinity is simply the following:
1. Infinity = the state or quality of being infinite.
2. Infinite = not finite, boundless, unlimited, indefinite, immeasurably/exceedlingly great.
e.g.: the dimensions of the universe/multiverse.
1. Infinity = the state or quality of being infinite.
a meaningless tautology
2. Infinite = not finite, boundless, unlimited, indefinite, immeasurably/exceedlingly great.
uses words where you should use math as zeffer7 did
e.g.: the dimensions of the universe/multiverse.
purely speculative on your part --- unproven and at present unprovable
Deuterium2H
Nov28-11, 02:39 PM
People following this thread might also be interested in another thread entitled "If the Universe is infinite, does that mean everything must exist somewhere".
Here is a link:
http://www.physicsforums.com/showpost.php?p=3062488&postcount=101
Using Set Theory, I argue that this is not necessarily the case. Some interesting ideas discussed in that thread.
I might add that this issue is stumbled over by a great number of leading physicists. Most recently, Brian Greene in his current PBS/NOVA show "The Fabric of the Cosmos". He makes the same logical error (IMHO) that is common in the infinite, "multi-verse" hypothesis...claiming that an exact duplicate of himself exists either in our infinite Universe, or in any of an infinite multiverses. The previously cited thread/link explains the pitfalls in this reasoning.
PatrickPowers
Nov29-11, 12:07 AM
I completely understand this concept, but would be astounded if it ever turned out to be the case. I DO believe it possible that the universe has the topology that you suggest but even if it does, the thought that it could be small enough that the light would actually reach us from both directions just strikes me as so unlikely as to be silly.
This possibility has been studied by astronomers with negative results.
PatrickPowers
Nov29-11, 12:16 AM
People following this thread might also be interested in another thread entitled "If the Universe is infinite, does that mean everything must exist somewhere".
Here is a link:
http://www.physicsforums.com/showpost.php?p=3062488&postcount=101
Using Set Theory, I argue that this is not necessarily the case. Some interesting ideas discussed in that thread.
I might add that this issue is stumbled over by a great number of leading physicists. Most recently, Brian Greene in his current PBS/NOVA show "The Fabric of the Cosmos". He makes the same logical error (IMHO) that is common in the infinite, "multi-verse" hypothesis...claiming that an exact duplicate of himself exists either in our infinite Universe, or in any of an infinite multiverses. The previously cited thread/link explains the pitfalls in this reasoning.
Yes, Greene is stumbling into a common fallacy.
1) I exist, therefore the probability of my existing is greater than zero.
2) In an infinite set, any event with probability greater than zero occurs infinitely many times.
The fallacy is in line 1. The probability that Greene exists could be zero.
To see this, consider the natural and real numbers. The probability that a real number is equal to a natural number is zero. Nevertheless the natural numbers exist.
So with probability zero, nevertheless the natural numbers and Greene exist.
Tanelorn
Nov29-11, 08:01 AM
Patrick is it useful though to say that the probability of anything at all existing is zero? Seems like a flaw in statistics to me :)
The probability that Greene exists could be zero.
BUT ... if it WERE zero, he would not exist and he DOES exist, so in this universe, it is NOT zero. In fact, in this universe, the probability of his existing is one.
Your argument about the numbers seems nonsensical but it could be that I'm just not following what you mean.
The satement "with probability zero ... the natural numbers ... exist" is what seems nonsensical. In a system where the probability of something existing is zero, it will NOT exist and if it does exist, then the probablity of it existing is one. I doubt you would argue with that, so what exactly ARE you arguing?
Deuterium2H
Nov29-11, 03:36 PM
Yes, Greene is stumbling into a common fallacy.
1) I exist, therefore the probability of my existing is greater than zero.
2) In an infinite set, any event with probability greater than zero occurs infinitely many times.
The fallacy is in line 1. The probability that Greene exists could be zero.
To see this, consider the natural and real numbers. The probability that a real number is equal to a natural number is zero. Nevertheless the natural numbers exist.
So with probability zero, nevertheless the natural numbers and Greene exist.
Hi Patrick,
No sure if you had an opportunity to read through the thread/link I provided. Not sure I agree with your beginning argument, as in this universe, we are pretty sure Brian Greene does exist, and therefore the probability of his existence is in fact one (1). However, your subsequent argument is spot on. Specifically, that there does NOT exist a one-to-one correspondence (bijection) between the Set of Natural numbers and the Set of Reals. The argument in the topic I linked to ("If the Universe is infinite, does that mean everything exists somewhere"), in summary, is that an infinite set does not imply the exhaustion of all possible "members". In other words, it is NOT a sufficient condition that an Infinite universe means that everything exists somewhere.
As a specific example, the Set of all Natural Numbers (N) has the exact same size (Cardinality) as the set of all Rational Numbers (Q). They are both infinite sets containing the exact same number of members. However, you will never find the rational number one third (1/3 = .3333) in the set N. In other words, even though N is infinite, and exactly equal in size to Q, it does not exhaust all the numbers...that is to say, there are an infinite number of Rational numbers that are not members of the infinite set N
Essentially, the same argument applies to the "infinite universe / multiverse". Just because something is infinite, does not mean it is exhaustive.
-------------------------------------------
Getting back to the second part of your post...as a further example in support of your argument:
As a thought experiment, consider a hypothetical lottery machine that contains bouncing ping pong balls, each representing a Real number...and includes all the Real numbers. When one goes to select a random ping pong ball / number (again think of the vacuum-based lottery machines), the chances of getting a Natural number is zero. In fact, the chances of getting a Rational number is also zero. Perhaps even more mind blowing, the chances of getting an Algebraic Irrational number (e.g. Square Root of 2) is also zero. Someone might ask, well what is left? When you grab that ping pong ball, you have a 100% probability of picking a Transcendental Irrational.
a meaningless tautology
Wrong. It point to the definition of infinite. That in itself is useful.
uses words where you should use math as zeffer7 did
By 'zeffer7' I imagine you errored.
The words that I used to define 'infinite' are accepted terms for defining 'infinite"--they are quite easily found in any high quality dictionary.
purely speculative on your part --- unproven and at present unprovable
"Infinity" is unproven and unprovable... what's your point??
Drakkith
Dec4-11, 02:12 AM
"Infinity" is unproven and unprovable... what's your point??
I think he means that saying infinity is the dimensions of the universe/multiverse is unproven and unprovable.
PatrickPowers
Dec4-11, 06:53 AM
BUT ... if it WERE zero, he would not exist and he DOES exist, so in this universe, it is NOT zero. In fact, in this universe, the probability of his existing is one.
Your argument about the numbers seems nonsensical but it could be that I'm just not following what you mean.
The satement "with probability zero ... the natural numbers ... exist" is what seems nonsensical. In a system where the probability of something existing is zero, it will NOT exist and if it does exist, then the probablity of it existing is one. I doubt you would argue with that, so what exactly ARE you arguing?
It has to do with measure theory, which is the basis of modern axiomatic probability theory. Measure theory was created to deal with infinite sets. You start out with your measure space, which is the set of all possible events, and has measure one. Then assign nonnegative measures to the subsets. The measure of a subset is equal to the probability that an event chosen from the measure space will be a member of the subset.
If the measure space is infinite then often the probability of every event is zero. Think of choosing one of the natural numbers with each number equally likely (something you can't actually do in real life.) The probability you will chose the natural number n is zero for every natural number. So if you could choose one natural number n, then even though the probability is zero nevertheless you have that number. You have proved that it was not impossible for you to chose that number. So "impossible" and "probability zero" are NOT the same thing.
Probability zero means that the probability is less than any positive number. Only zero remains. But it IS possible. (It would be silly to clutter the measure space with impossible events. What would be the point?)
Let's say you have the real numbers on the interval [0,1] and you imagine you can choose one of those real numbers with all numbers equally likely. The probability you will choose 0 is zero. But it's not impossible.
On the other hand, of you somehow DO choose zero then the conditional probability that you chose zero is 1. The conditional probability of X given X is always one. The conditional probability the Brian Greene exists given that Brian Greene exists is one.
If Brian Green were in a finite Universe then his assertion that the probability that he exists is greater than zero seems reasonable. You could theoretically count the number of planets n and then say that the chance that Greene exists is 1/n. That's more than zero. But in an infinite Universe I don't accept it. The conditional probability that Brian Greene exists given that Brian Greene exists is one, so this gives us no information other than that it is not impossible for him to exist. But as you have seen, this tells us nothing about his probability. In an infinite universe it is perfectly OK for him to have probability zero.
So now that you supposedly have gotten used to this definition, I can also say that in an infinite Universe I expect the probability that the Earth exists is zero, the probability that the visible Universe exists is zero, etc. One would expect that the bigger and more complicated something is, the lower the probability.
Now let's confuse things further. If you have an infinite set with all events equally likely, then ANY finite subset has probability zero. So even if a jillion Brian Greenes exist in an infinite Universe, his probability is STILL zero. Compared with infinity, it's insignificant. If you got in your incredible space ship and toured a million worlds a second, the probability that you would find an alien Brian Greenes would be zero. A jillion divided by infinity is still zero.
Now to really put the zap on your mind, there are plenty of infinite sets with probability zero. The prime numbers are a good example. If you pick a natural number with each such number equally likely then the chance it is prime is zero. Suppose a Brian Greene is on every prime numbered world. So if you got in your incredible space ship and toured a trillion million worlds a second for a billion years, the probability that you would find one of that infinite set of alien Brian Greenes would STILL be zero. That's how big infinity is.
Think about it for a while. Get used to it. You will realize that this has to be true, otherwise the measure of your measure space becomes infinite instead of one. And that simply will not do. Probabilities are ALWAYS 0 through 1. That's the norm.
PatrickPowers
Dec4-11, 07:04 AM
I think he means that saying infinity is the dimensions of the universe/multiverse is unproven and unprovable.
Unproven certainly. But I hesitate to say unprovable. Bell came up with that theorem, so anything seems possible.
On the other hand you can say that physics never proves anything, and there is no arguing with that.
I think he means that saying infinity is the dimensions of the universe/multiverse is unproven and unprovable.
yes, that's exactly what I was saying
Patrick, I can't argue with your math, but to me it seems useless (because mutually contradictory) to say that something has zero probability of occuring yet it can occur. To me it seems that the language breaks down under such nonsense regardless of what the math says.
Blueyes5804
Dec21-11, 11:52 AM
I've been watching Stephen Hawkings "Universe" recently and have a perspective I'd like to share. I'm not a trained scientist, just a curiosity junkie. As you mentioned, science is theorizing the universe is expanding and will eventually grow cold and dark as galaxies just continue to move apart.
I'm wondering if the universe may work in a different way. Like... what if there are hot and cold areas, like the scientists say there are, and the hot areas expand while the cold areas contract, and somewhere in all this hot cold dynamic it's really staying pretty much the same size, just moving around within it's own parameters. Also, what if the hot areas (because they're expanding) kind of fold, twist and turn into their cold neighbors space, warming them up, and therefore, making the uv self renewing. what if? jus sayin. :=D
Blueyes5804
Dec21-11, 11:59 AM
I would like to know where, in the universe, are we. the milky way I mean. are we in the middle, in the suburbs, out on the farm? where exactly? any ideas?
Tanelorn
Dec21-11, 12:01 PM
Blueyes such a situation might fall foul of Isotopy and homogeneity requirements. It is not a preferred solution to believe that somewhere, even very far beyond the observable universe, is much different to our own local space - well at least for certain scales.
Blueyes5804
Dec22-11, 08:28 PM
Thank you for your reply Tanelorn. Let me see if I understand what you're saying. You're saying that the universe adheres to scale. okay. but i still think it could work the way I think it might. In our own world this same thing happens, as the earth twists, turns and roils, renewing it's crust as it devours it. it is self renewing. animated. living. I think of space as a landscape. an environment. different from our own, but a landscape still. self renewing.
by the way. do you know what neighborhood we live in in the universe? are we close to the core? on the edge? somewhere in the suburbs? Do you know if that's been figured out?
Drakkith
Dec22-11, 08:50 PM
I think of space as a landscape. an environment. different from our own, but a landscape still. self renewing.
by the way. do you know what neighborhood we live in in the universe? are we close to the core? on the edge? somewhere in the suburbs? Do you know if that's been figured out?
There is no edge, no center, no suburbs to the best of our knowledge.
Blueyes5804
Dec22-11, 09:54 PM
Thank You. so you're saying there is no "map" of the universe, and because of that, no galactic gps for us. ty. just wondering.
Thank You. so you're saying there is no "map" of the universe, and because of that, no galactic gps for us. ty. just wondering.
There is a map of the OBSERVABLE universe and it even has a center (WE are the center by definition) but that doesn't tell us about the rest of universe, just our little bitty part of it.
You said "no galactic gps". I assume you meant "no universe gps". Our galaxy is a staggeringly trivial part of the universe and we have a fair bit of knowledge of where things are in our galaxy (the Milky Way).
skippy1729
Dec23-11, 12:58 AM
I would like to know where, in the universe, are we. the milky way I mean. are we in the middle, in the suburbs, out on the farm? where exactly? any ideas?
Here is a nice picture of where we are: http://n-a-s-a.tumblr.com/post/13461282020/are-there-any-data-and-visualizations-that-graphically
Outer suburbs, close to the farms.
Skippy
Blueyes5804
Dec23-11, 02:46 AM
just went to the NASA link. O M G! ty
Blueyes5804
Dec23-11, 02:48 AM
How typical that we would think we are the center of the universe! reminds me of when we thought the sun revolved around the earth! lol ty for all the feedback. I find it really interesting!
Drakkith
Dec23-11, 02:02 PM
How typical that we would think we are the center of the universe! reminds me of when we thought the sun revolved around the earth! lol ty for all the feedback. I find it really interesting!
We don't think we are at the center of the Universe. But we KNOW we are at the center of the OBSERVABLE Universe. Here: http://en.wikipedia.org/wiki/Observable_universe
In Big Bang cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light (or other signals) from those objects has had time to reach us since the beginning of the cosmological expansion. Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction—that is, the observable universe is a spherical volume (a ball) centered on the observer, regardless of the shape of the universe as a whole. Every location in the universe has its own observable universe which may or may not overlap with the one centered on the Earth.
vBulletin® v3.8.7, Copyright ©2000-2012, vBulletin Solutions, Inc.