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robram18
2010-Feb-18, 04:12 PM
Okay I'm quite new to learning in depth about the size of the universe. First post so apologies if it's a bit long-winded.

It would seem it is generally accepted that the universe is most likely to be infinate due to the lack of mass in the universe needed to curve it.

Using this assumption people and scientists talk of 'everything that is possible in physics will happen somewhere in our infinite universe'.

Now I find this difficult to grasp - Monkeys on typewriters - infinite amounts of people just like me. So whilst looking at various articles on the internet, this theory cropped up a few times.

The gist is that:
Infinity multiplied by an infinitismal number = a finite number.

Filling in the gaps with examples this would become:

Infinity multiplied by the sheer complexity of the conditions under which we have become intelligent creatures = a finite number e.g. 1 or 143 or 973 etc.

This idea seems to make a lot of sense to me. Multiplying the unimaginably massive by the unimaginably small = a finite number.

I wanted to know if this theory is very popular?
It doesn't seem to be mentioned all that often across the internet. People seem to prefer to entertain the possibility that there are an infinite amount of us!!!

Just an example to help get my point across (stolen from something else I read) -

The mile counter on a car is like the human brain. Brain cannot comprehend infinity and the infinitismal.
The mile counter cannot comprehend/register/show a number below 1 mile or above 999,999 (it simply has no room for it and has not been designed to encompass other numbers).

To the mile counter 0.25 miles is an infitismal number whilst 2 million miles is an infinite number. It cannot comprehend either.

However, 0.25 x 2,000,000 = 500,000. To the car mile counter this is a finite number.

An example of the infinitismal x infinity = finite?

Could this model be replicated by the human mind and the nature of infinity in our universe?

PetersCreek
2010-Feb-18, 04:34 PM
Are you presenting this as your own idea or did you read it somewhere? I'm no mathematician but the math doesn't look at all right to me. For instance, what does "the sheer complexity of the conditions under which we have become intelligent creatures" mean, numerically speaking? If it's a positive, real number then multiplying it by infinity still yields infinity.

robram18
2010-Feb-18, 04:40 PM
No not my idea at all, a combination of a few ideas and theories I've read from others and I'm very open to having it shot down! :)

I've added an example to my first post.

I am no mathematician. If this theory is fundamentally flawed in maths then please say so, I am not mathematically adept enough to know if it is.

The way it's been presented to me in the arguments i've read it just seemed more feasible to me than infinite planet earths and infinite me's..

And yes I am assuming that the conditions under which we've come to be intelligent creatures is infinitismally unlikely. Which is a number so close to zero it is impossible to imagine.

PetersCreek
2010-Feb-18, 05:39 PM
The odometer analogy is fatally flawed because the infinitesimal is not a quantity that simply falls below a threshold we can comprehend. Likewise, infinity is not some undefined quantity that's bigger than we can fit in our head. They have specific mathematical definitions, as hard as they may be to visualize or imagine.

With that said, here a few words from a moderator:

Take great care in editing your posts. Revisionism is taken very seriously here. You may correct errors within a reasonable amount of time but changing content later, especially after someone has replied, is a no-no. You should have provided your example in another post. If you haven't already done so, please famiarize yourself with our rules, linked in my signature below.

And by the way, welcome to the BAUT forums.

robram18
2010-Feb-18, 05:49 PM
Thanks PetersCreek. Didn't realise the editting rule, will bare that in mind in future!

So in short do mathematical laws mean that...

Infinity x infinitismal amount = infinity?

And there are no exceptions to this no matter how infinitismally small?

Swift
2010-Feb-18, 06:09 PM
So in short do mathematical laws mean that...

Infinity x infinitismal amount = infinity?

And there are no exceptions to this no matter how infinitismally small?
The only exception to that rule is when the infinitesimal amount is actually zero.

robram18
2010-Feb-18, 07:38 PM
I have another question.

Does the idea of an infinite universe comply with the idea of the big bang?

If the big bang was the beginning, then the size of the universe would be the speed of light mutiplied by the time since the big bang right? Which would give an actual size.

Granted we would never reach the edge, because us going faster than the speed of light breaks the laws of physics. However, this idea does mean that the universe does have an edge, albeit that it continues to expand beyond any physical means of 'catching it'.

So does that mean someone who believes in an infinite universe cannot believe in the big bang?

robram18
2010-Feb-18, 08:27 PM
Actually that question above can be ignored.
Realised I'm talking about the observable universe.

And that the universe itself expands faster than the speed of light.

Regardless though the universe would still have a 'size' would it not even if the expansion speed is unknown?
i.e. time since the big bang x speed of the expansion of the universe.

Given infinite time it would be infinitely big.

But given that there has been 13.7 billion years since the bang does this not mean at this moment our universe has a finite size?

Sorry if I'm being confusing, just find it interesting and want to get my head round it!

Murphy
2010-Feb-19, 02:06 AM
Would this question by any chance have been provoked by the recent BBC Horizon documentary about Infinity? (To Infinity and Beyond (http://www.bbc.co.uk/programmes/b00qszch))

Well whether you saw it or not, I did and was indeed very interested in some of the ideas in it. I'd heard most of it before and though I understood the ideas around the debate about whether the universe is infinite or finite, but some of the stuff in that show was quite perplexing to me.

They stated for instance that if the Universe is infinite, then there has to be other Earths out there somewhere (in-fact an infinite number of Earths). Now I'd heard of the Many-Worlds theory of Quantum Mechanics (or whatever it's officially called), which states that there should be an infinite number of Universes alongside our own and in many of these (an infinite number?) there will be an alternative version of Earth.

I can just about grasp that concept (I used to watch Sliders (http://en.wikipedia.org/wiki/Sliders) after all), but the idea that there would actually be other Earths in our own physical Universe was new to me. That if you were able to set off in a spaceship and journey fast and far enough, you would encounter planets that were almost exact copies of Earth (i.e. down to the people living on it, etc). But of course you would still encounter many more planets not like Earth, and you would find many Earth's which were nothing like our Earth (like there being no people on some, etc). But if the Universe is infinite, then there is an infinite amount of planets, and an infinite subset of them will be Earths!

Now that's a damn difficult thing to get your head around. I have some significant problems with this way of thinking about it though (Similar to what robram18 is saying), such as...

If there is an infinite amount of matter in the universe, where was it all at the Big Bang? Surely an infinity amount of matter will take up an infinite amount of space? (no matter how tightly it's packed). But then there would have been no "room" for the universe to expand into? An infinite amount of matter would take up all space, no just some fraction of it, right?

I think I can only conclude like what the astronomer says in the program, that a finite Universe is the only one we can understand and make sense of. I don't know, anyone else want to take a try at explaining this?

robram18
2010-Feb-19, 08:23 AM
Yes I did watch the Horizon programme a while back, and have been watching a few documentaries from Channel 4 aswel. On top of reading internet articles etc.

Great post btw.

I agree that I too can grasp there being identical earths if there are parallel universes.

But yeah I struggle to think that that is possible within our own universe on the basis that surely...
the time since the big blind x the speed of expansion = an actual size (albeit bigger than the what we could ever see).

infinite time in this equation would see infinite earth's. But we live within time, 13.7 billion light years, the best measurement we can give it currently.

Maybe that translates as 130 trillion big bang speed years, nobody knows. But that'd still be a finite number.

If time is endless then yes Earth would copy itself over and over eventually. I'd agree in this model that everything that can happen 'will happen'. I would not agree that everything that can happen 'has already happened'.

In opposition, if Big Crunch theory or Big Rip or whatever is in fact true, then this ending of time would mean a finite universe.

For me the idea of time is key.

If time is infinite I'd believe that the universe edge will expand infinitely and therefore earths would recreate somewhere down the line.

If time is finite the universe has to be also finite.

DrRocket
2010-Feb-20, 05:15 AM
Wou

They stated for instance that if the Universe is infinite, then there has to be other Earths out there somewhere (in-fact an infinite number of Earths). Now I'd heard of the Many-Worlds theory of Quantum Mechanics (or whatever it's officially called), which states that there should be an infinite number of Universes alongside our own and in many of these (an infinite number?) there will be an alternative version of Earth.

I can just about grasp that concept (I used to watch Sliders (http://en.wikipedia.org/wiki/Sliders) after all), but the idea that there would actually be other Earths in our own physical Universe was new to me. That if you were able to set off in a spaceship and journey fast and far enough, you would encounter planets that were almost exact copies of Earth (i.e. down to the people living on it, etc). But of course you would still encounter many more planets not like Earth, and you would find many Earth's which were nothing like our Earth (like there being no people on some, etc). But if the Universe is infinite, then there is an infinite amount of planets, and an infinite subset of them will be Earths!

That sort of thing is often stated. It demonstrates nothing more than a lack of understanding of the theory of probability on the part of he who said it. I does show the ingenuity of some string theorists in declaring victory as a result of the total failure of the theory to live up to its promise of singling out a clear set of unified physical laws on the basis of mathematical consistency.

The highlighted assertion in your post is based on a gross misapplication of the law of large numbers from probability theory. It is commonly associated with notions of a "multiverse", something else for which there is absolutely no evidence.

First, the openness or closedness (proper terminology for infinitude or finiteness) of the universe, is irrelevant. What is relevant is the existence of some sort of meaningful probability distribution on the universe, that is related to the physics thereof. If the universe is "infinite" (i.e. open) then there is a serious problem with trying to define a meaningful probability measure on it that has anything to do with physics. The more perceptive of the people who contemplate the possibility of a "multiverse" recognize this problem and it has a name -- the measure problem (http://physics.berkeley.edu/index.php?option=com_dept_management&act=events&Itemid=451&task=view&id=735).

The Law of Large Numbers implies, among other things, that in an infinite number of independent trials, any outcome of positive probability will occur, and in fact will occur infinitely many times. This has absolutely nothing to do with whether or not the universe is open.

The way that the theorem is misapplied is to assume, based on the apparent ability of string theory to produce something on the order of 10^500 (the number varies with the author and I have seen it as high as 10^1000) potential sets of physical laws, that all such potential "universes" must actually exist, and be a part of a multiverse. That multiverse is then somehow construed to consist of infinitely many "pocket universes" obeying one or another of those laws. Then the Law of Large Numbers is applied to this infinitude of pocket universes, to conclude that any set of physical laws and initial conditions must occur infinitely often -- without any apparent means of definining the probability measure for this to make sense.

It is absolutely impossible to have a probability measure in which infinitely many disjoint events can have equal probability. This is because the sum of the probabilities over a complete set of events must be 1, and the sum of anything positive taken infinitely many times is infinity.

So, in short, the assertion that you saw is more of the complete nonsense being promulgated in the name of string theory. It is pretty much lunacy to assert that there are 10^500 consistent sets of physical laws based on the "beauty" of a theory that has yet to be defined rigorously, that has made ZERO new predictions, and that cannot even explain the details of our little corner of the universe. I personally would be a lot more impressed if the proponents could demonstrate clearly ONE set of physical laws that explains the fundamentals of the physics that we observe, than I am by the statement that there are 10^500 of them (none of which have been defined clearly let alone proved to be consistent) and that the one that describes our situation must be in there somewhere.

01101001
2010-Feb-20, 07:05 AM
If the big bang was the beginning, then the size of the universe would be the speed of light mutiplied by the time since the big bang right? Which would give an actual size.

That would limit the size of the observable universe to various quantities depending on distance measure (Wikipedia (http://en.wikipedia.org/wiki/Distance_measures_(cosmology))), but it wouldn't constrain the size of the entire universe (nor even require it to be finite). There's no speed-of-light limit on expansion.

noncryptic
2010-Feb-22, 02:58 PM
If the big bang was the beginning, then the size of the universe would be the speed of light mutiplied by the time since the big bang right?

Only if the 'edge' of the Universe would be moving away from the 'center' at the speed of light, during all of the age of the universe.

But we do not know that it does that. In fact we know it does not do that.

What we do know is that within the universe, over a sufficiently large distance, space does expand at the speed of light (and even faster). But that is not the same thing as the whole universe 'growing' at the speed of light.
In reality the expansion rate measured 'end-to-end' would be much larger than the speed of light, if we could measure that. How fast that is depends on the size of the universe, which we do not know.

To complicate matters further, there is the era of inflation when the very young universe expanded at a rate much faster than the speed of light.
Also there are strong indications that the rate of expansion is not constant throughout the lifetime of the universe; expansion appears to be accelerating.

Jens
2010-Feb-23, 08:16 AM
If time is finite the universe has to be also finite.

I would totally agree here. The exception would be if the universe were created already infinite in size. But that doesn't seem to make sense. But I would agree that if the universe started with the big bang, it could not be infinite in size.

J Riff
2010-Mar-01, 01:14 AM
Maybe space is infinite, but matter isn't .. or is that theoretically possible ? Then we wouldn't have all those other earths to worry about at least.

Bearded One
2010-Mar-01, 02:24 AM
Maybe space is infinite, but matter isn't .. or is that theoretically possible ? Then we wouldn't have all those other earths to worry about at least.A problem I see with that is that it would mean that there is an infinite amount of empty space. That would mean the Universe doesn't look basically the same everywhere. Our occupied portion would be an anomaly and not be typical.

IsaacKuo
2010-Mar-01, 04:07 PM
The exception would be if the universe were created already infinite in size. But that doesn't seem to make sense. But I would agree that if the universe started with the big bang, it could not be infinite in size.
The realm of mathematical possibilities is weirder than you think.

It is possible, in principle, to start with a "big bang", have a period of finite size, and then go to infinite size. Actually, this might be the case if the "big rip" theory is correct.

For simplicity, consider a universe which is simply a hypersphere with a certain radius that changes with time. Thus, we can chart the size of the universe simply as a function of radius over time.

You're probably thinking of a simple curve, like r=100t. This starts of at 0,0. And it goes up from there...always a finite value.

Okay, but what about a curve like r=t/(1-t)? This starts of at 0,0. And it goes upward...and it accelerates upward...and it zooms upward off to infinity by the time it gets to t=1!

Of course, if everything stretches out evenly, then this is bad news for anyone living in the universe by time t=1. According to the "big rip" theory, something like this happens. Stretching keeps on going up on smaller and smaller scales until even atoms get ripped apart by space expansion.

But if stretching is uneven, then we could be in a part of the universe which is not as stretched out...it's theoretically conceivable that other parts of the universe have stretched out to infinity already.

HENARRY JAYA
2010-Mar-04, 05:24 AM
You're right Adrian. . And scientists also believe that there are parallel universes all around us. and in an example, there can be a dinosaur sitting right beside you right now but invisible because the dimensions that it lives in is different than yours.
I believe God's angels are also in a different universe that's why we can't see them but they can see us.

Jens
2010-Mar-04, 05:29 AM
I believe God's angels are also in a different universe that's why we can't see them but they can see us.

That doesn't make much sense. If they can see us but we can't see them, then they'd have a bit of a hard time getting us to know that they exist. And people wouldn't have written a book about them.

Also, your post seems to be moving into the dangerous territory of religious discussion. This thread is about implications of the universe being infinite.