Infinity

[pgrmdave]

If I remember correctly, mass is a measurement of how much a body curves space-time. A Black Hole is what occurs when a body curves space-time until it is parallel to itself. It was explained to me like a ball of metal on a blanket. The blanket bends around the metal, creating a slope. The heavier the metal, the steeper the slope, until at some point, the metal makes the slope parallel to itself. The reason that we cannot achieve infinite speed is due to the fact that it would require infinite energy, infinite mass, while it could, theoretically, be acheived by infinite speed, is not contingent upon it.

[Fishteacher73]

Or with some of the wormhole theories, would infinate mass puncture space-time (Alagorical to the rubber mat that is distored by mass as illustrating the curvature of space/time).

 

A line reaching out in infinity in both directions would allow for a curved existence. A ray on the other hand would only exist in a planar existence (a line could as well).

 

I think it is impossible for anything to be truly mass. Much like you integrate an equation to find the area below, it is only an aproximation as you reduce the intervals to *almost* zero. We can get in all practical terms to zero, but it still is not really zero. Just as with truly massive amounts that near infinity can mathmatically assumed to be, but they do not truly attain an infinite existence in a physical sense.

 

I think here is a distinction to mathmatical infinities and spatial infinities. I do not truly believe that there can be an emprically derived infinity aside from spatial ones. Anything infinite outside of mathmatical infinities would by default contain everything.

[C1ay]

I am not aware of any such observations that have not been corrected to match the perceived age of our universe. I will happily look at any such evidence.

 

This paper at NASA says,

 

"If we compare the two age determinations, there is a potential crisis. If the astronomers who estimate that 1/H0 is as small as 10 Billion years are correct, then the age of the Universe would be shorter than the age of its oldest stars. This contradiction implies that either the Big Bang theory is incorrect or that we need to modify general relativity by adding a cosmological constant.

 

Some astronomers believe that this crisis will pass as soon as our measurements improve. If the astronomers who have measured the larger values of 1/H0 are correct and the smaller estimates of globular cluster ages are also correct, then all may be well for the Big Bang theory."

 

As far as I know it is unresolved. It may simply be that we don't have the technology yet that we will need to make the correct determination. At any rate I don't think we have all of the evidence or information that we need to conclusively determine the age of our universe at this point. This conflict suggests to me though, that the answer may be bigger than any we have peviously imagined.

[C1ay]

I don't know that there can be an infinite direction without some kind of curvature of the direction.

 

Why not? I can imagine a straight line stretching infinitely in any direction. What would necessitate curvature of this line?

[RiverRat]

Did Hilbert not state … infinite is nowhere to be found in reality. It neither exists in nature, nor provides a legitimate basis for rational thought. ... The role that remains for infinite to play is solely that of an idea.

 

Infinite is easily described in the abstract (x +1).

 

I read at one point that a rationalization for infinity can be found in the dissection of ‘space’. Take a ‘foot’ of space and continually divide into subsets (1/2,1/4,1/8, … 1/100000000 etc). What would happen when the subset reaches the planck length? Does it become meaningless and thus ceases to be a product of infinity?

[Buffy]

I read at one point that a rationalization for infinity can be found in the dissection of ‘space’. Take a ‘foot’ of space and continually divide into subsets (1/2,1/4,1/8, … 1/100000000 etc). What would happen when the subset reaches the planck length? Does it become meaningless and thus ceases to be a product of infinity?

The infinity you describe is that of rational numbers (expressible as a fraction), which is greater than the infinity of integers but smaller than the infinity of real numbers or imaginary numbers as oulined in zadojla's post above. Mathematics is of course abstract, so can be used to discuss things that may not exist in the real world. The statement that "infinity does not exist in the real world" is true if you talk about measurement, since anything could be measured by the number of Planck Lenghts of its dimensions, and you can't measure anything smaller than a PL, but then nothing's smaller than a PL (we think).

 

Can you find the Hilbert quote? I'd love to look at that.

 

Cheers,

Buffy

[RiverRat]

Can you find the Hilbert quote? I'd love to look at that.

 

Hilbert … "On the Infinite," in Philosophy of Mathematics

 

I saw this referenced in a footnote once. I got bits and pieces of it photo copied from a relative that had an advanced math theory class.

[Tormod]

As far as I know it is unresolved. It may simply be that we don't have the technology yet that we will need to make the correct determination. At any rate I don't think we have all of the evidence or information that we need to conclusively determine the age of our universe at this point. This conflict suggests to me though, that the answer may be bigger than any we have peviously imagined.

 

C1ay, the paper you quote is very outdated. The age of the universe was determined - using the WMAP instrument - to be 13.7 billion years. This was in 2002.

 

Look here for one of the news stories from that time:

http://www.space.com/scienceastronomy/map_discovery_030211.html

[Tormod]

Why not? I can imagine a straight line stretching infinitely in any direction. What would necessitate curvature of this line?

 

Good question. But that you can imagine it does not make it so. :(

 

Let's not resort to one-liners in the Lounge. The purpose of this forum was to spend time contemplating issues like this. There have been som good posts but so far I see only

 

a) further examples of numerical infinities

:( attempts to explain that the universe is infinite

c) discussion on whether multiple dimensions can make stuff infinite

 

The question about whether the infinitely small ends at the planck length is very interesting, because it implies that there is no infinity an the small scales ("going downwards"). C1ay has suggested that the universe never ends, although this is will be hard to prove.

 

But I still fail to see anything *physical*, and that is smaller than the observable universe, that can be proven to be infinite. Is it even possible?

[C1ay]

I still fail to see anything *physical*, and that is smaller than the observable universe, that can be proven to be infinite. Is it even possible?

 

I tend to think not. Considering that our own local universe is known to be finite it would seem that any physical infinity that it could itself contain would make it infinite as well.

 

This reminds me of a discussion I saw somewhere else wherein someone mentioned printing a googolplex. Someone else pointed out that there are not even a googol of atoms in the universe, thus if every atom were the ink to print one digit there would not only not be enough ink, there would be no atoms left to make the paper to print the ink on. As large as our universe is I felt this illustrated how small it really is compared to infinity.

 

 

I believe probably time is the only dimension in our universe that can have a magnitude of infinity and it cannot be observed. This leaves the only observable infinities to be those which are purely mathematical.

[Tormod]

I believe probably time is the only dimension in our universe that can have a magnitude of infinity and it cannot be observed. This leaves the only observable infinities to be those which are purely mathematical.

 

This is a very good statement. Yes, it appears that the only infinities we can claim to at least comprehend are mathematical. This has some philosophical implications, though, which is probably a whole new thread, on whether pure mathematics reflects reality or not.

 

I am still pondering the idea of whether a singularity is "inifitely small with infinite mass" or not. It seems impossible to me. Another thought then is whether the Big Bang really can come out of such a point. If C1ay one's idea about an infinite space in which our universe is correct - an idea I have read about in several books, although with different aspects (for example, multiverses with bubbles separated by nothing, or multiverses of different kinds of space floating in a higher-dimensional space, etc) - then a property of that space must have allowed singularities to exist.

 

It then follows that if our universe cannot have physical infinities of that kind, then the universe into which our own is expanding *cannot* be the same kind of "space" as our own.

[C1ay]

I am still pondering the idea of whether a singularity is "inifitely small with infinite mass" or not. It seems impossible to me. Another thought then is whether the Big Bang really can come out of such a point. If C1ay one's idea about an infinite space in which our universe is correct - an idea I have read about in several books, although with different aspects (for example, multiverses with bubbles separated by nothing, or multiverses of different kinds of space floating in a higher-dimensional space, etc) - then a property of that space must have allowed singularities to exist.

 

I cannot see infinite mass in an infinitesimally small point either. I can imagine a black hole growing larger and larger as it collects an enormous amount of mass like mass of our universe which could eventually cause some cataclysmic event that expels all of the mass into an expanding volume like that which we call the universe. I have never quite understood why a singularity was required for the big bang to occur.

 

It then follows that if our universe cannot have physical infinities of that kind, then the universe into which our own is expanding *cannot* be the same kind of "space" as our own.

 

I imagine the space is the same. Our universe is simply a subset of all matter and the space which contains it. Since the infinite space that contains our universe is itself, infinite, it can contain infinities. Since our subset is a finite collection, it cannot.

 

Imagine placing a one gallon pail of water with some marbles in it inside of a five gallon pail of water that also has some marbles. The water is space and the marbles are matter. It is easy to see that you could never put 2 gallons of marbles in the one gallon envelope that is the 1 gallon pail but that does not limit the larger envelope which is the 5 gallon pail from being able to contain 2 gallons of marbles. Both share the same space, the water. It is only the matter itself in the 1 gallon pail that is a subset of any matter that may be in the 5 gallon pail outside of the 1 gallon pail. A simplistic view but maybe it illustrates my vision better than earlier posts.

[Tormod]

I can imagine a black hole growing larger and larger as it collects an enormous amount of mass like mass of our universe which could eventually cause some cataclysmic event that expels all of the mass into an expanding volume like that which we call the universe.

 

I received this press release from NASA a few days back:

NASA OBSERVATORY CONFIRMS BLACK HOLE LIMITS

 

The very largest black holes reach a certain point and then grow no more. That's according to the best survey to date of black holes made with NASA's Chandra X-ray Observatory. Scientists also discovered previously hidden black holes well below their weight limit.

 

These new results corroborate recent theoretical work about how black holes and galaxies grow. The biggest black holes, those with at least 100 million times the mass of the sun, ate voraciously during the early universe. Nearly all of them ran out of "food" billions of years ago and went onto a forced starvation diet.

 

On the other hand, black holes approximately 10 to 100 million solar masses followed a more controlled eating plan. Because they took smaller portions of their meals of gas and dust, they continue growing.

 

"Our data show some super massive black holes seem to binge, while others prefer to graze," said Amy Barger of the University of Wisconsin and University of Hawaii. Barger is lead author of the paper describing the results in the latest issue of The Astronomical Journal. "We understand better than ever how super massive black holes grow."

 

http://chandra.harvard.edu/photo/2005/bhlock/

[C1ay]

The very largest black holes reach a certain point and then grow no more. That's according to the best survey to date of black holes made with NASA's Chandra X-ray Observatory. Scientists also discovered previously hidden black holes well below their weight limit.

 

These new results corroborate recent theoretical work about how black holes and galaxies grow. The biggest black holes, those with at least 100 million times the mass of the sun, ate voraciously during the early universe. Nearly all of them ran out of "food" billions of years ago and went onto a forced starvation diet.

 

That's a thought provoking article. For me it creates more questions. For black holes that reach 100 million solar masses do they just quit taking in more matter? Does their gravity suddenly switch off? If two galaxies collide where the black hole at the center of each is 75 million solar masse to begin with, what happens? Does a black hole that exceeds this limit lead to a cataclysmic event? How many eons will pass before mankind has the technology and the knowledge to really understand the implications?

 

It would seem to me that this implies that the theorized singularity that lead to the big bang was not any kind of black hole itself since it's mass was that of our entire universe. It would certainly seem that it would have been black though since it's gravity would have to have exceeded any of the black holes we know of. What kind of object could it have been?

 

This is going to require quite a bit more contemplation to theorize what these limits might mean.

[Tormod]

So far nobody has ever observed such a thing as a singularity. I think the idea that the big bang grew out of one is problematic. I have sort of always subscribed to that idea but it makes less and less sense.

 

Maybe I should read up on string theory - they avoid all kinds of singularities and infinities.

[Turtle]

___I heard a talk the other night by Michio Kaku on the radio & he was saying that it is now observed that black holes spin. Further he said that this makes a ring down past the event horizon & that they now speculate matter is spewing out the other side as a 'white' hole. Our universe may in fact be a white hole he said.

___Very interesting to listen to him.:cup:

[geko]

I actually think that infinite is quite an abstract term to begin with. There's definiately a difference i think between a physical infinity and a mathematical one. I personally think that an argument for or against infinity is a logical one (which could also be based on semantics). For example:

 

If we take the physical one and have a look at the definition it says that infinite = having no limits or boundaries in time, space, extent or magnitude. If taken literally this would mean that 'infinity' doesnt actually exist.

 

The universe for example cant be infinite because our knowledge says it has a beginning and it's still expanding. If it's expanding it's getting bigger. So it wasnt infinite in size to begin with, otherwise infinity has a value. Also, the volume of the universe could be worked out, couldnt it? How many seconds in 13.7 billion years? Multiply that by the speed of light, factor in the early acceleration and deacceleration, and you have it's length, bredth and width. Volume could be worked out from this, no?

 

Theoretically and mathematically we can say that x+1 represents infinity, but physically this cannot be accomplished. The numbers could not be written down because the universe isnt big enough. A computer couldnt begin the task because existentially it has nothing to work with and nowhere to begin. Theoretically it is said that a 'never-ending' string of 1's = infinity, but yet this has never been accomplished because from a inventry point of view it's impossible.

 

It's almost as though 'infinity' was incorporated into mathematics to make things work and get rid of the absurd infinities that various equations throw up. I have no idea about this but is this not a sign, if infinity canot be physically accomplished, that there's something wrong with the equations?

 

Anyway, semantically there's also a difference between 'big' and 'small' types of infinity. 'Infinite' usually denotes large, where as infintesimal' denotes small. Infintesimal doesnt exist because to our knowledge it's restricted to the planck length. So the argument towards something being infinately small is a flawed one to our level of understanding to begin with i feel and shouldnt be bothered with. Of course, our knowledge could be wrong, which therein i think lies the problem.

 

ie. time is argued sometimes as being infinite in direction. Whether forward or backward, 'something' will always exist. But this argument actually conventionally depends on what theory we subscribe to. Eg. if you think that our universe is the only one then we cannot argue for time to be infinite i feel because, to put it bluntly, we dont know. We dont know if the universe will end, or how or when, so arguing for infinite time under this stance is attempting to argue with knowledge that we dont really have. If it collapses back on itself or degrades or falls apart and our universe no longer exists (remembering that our universe is all that does exist), time ceases.

 

Like wise with multi-universe theories. It could be argued that the above is inaccurate because even if this universe ceases, other universes will continue, which highlights that existence continues and therefore time. But stating, from this, that time is infinite is again claiming knowledge we dont have as these, all of these, may end in time as well.

 

Apart from the mathematical notion of infinite, which can only be contemplated or worked with by the imagination, i think we're left with having to come up with a new definition of infinite. Off the top of my head i would propose that infinite = outside of time and space, unquanifiable and unknown. A physcial example of infinity (this type) would be maybe what the universe is expanding into. The universe expands into infinity.

 

This will obviously be seen as nonsense by many, but i do personally feel that it's more reasonable because to use the notion of infinity when [all that we know is finite] is nonsense, even if it does help solve absurdities.

 

 

.....

 

Im sure i had something else to say as well but after writing that i seem to have forgotten...