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Author Topic: Is infinity an illusion?  (Read 68416 times)

Offline Pmb

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Re: Is infinity an illusion?
« Reply #50 on: 11/09/2013 02:08:58 »
Quote from: lean bean
You may remember my reply to you here..  Reply #24.

Glad you mentioned that.  I'd lost track of that thread.  Going back over it may save some repetition.  :)
Same here.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #51 on: 11/09/2013 04:54:04 »
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Same here.

Could it be an age thing, Pete?
 

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Re: Is infinity an illusion?
« Reply #52 on: 11/09/2013 18:46:55 »
What happens when we extrapolate back far enough is that the models start predicting ever increasing density--a density that tends to infinity at some point in the past.  Most scientists take Bill's point of view here and believe that this infinity is an indication of a flaw in the model, not something that physically existed.
JP
I was answering old Bill's question about what began at the BB in the context  of size of universe being infinite or finite.

I did mention the equations breakdown because of the density of matter/energy.
Even if they didn't breakdown, in what way could they suggest anything about the universe being finite or infinite in size?  that was the context in which I answered old Bill's question on this thread.


I did say something on the other thread here, my reply #29... http://www.thenakedscientists.com/forum/index.php?topic=48385.25

:) :)




« Last Edit: 11/09/2013 18:55:16 by lean bean »
 

Offline JP

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Re: Is infinity an illusion?
« Reply #53 on: 12/09/2013 02:39:04 »
Lean bean, I wasn't criticizing your points.  I was trying to point out an interesting "infinity" that appears in the equations and how it ties in with Bill's idea that infinities are not generally physical entities.  It's interesting that a few infinities are taken seriously by physicists "infinitesimally small" and "infinitely large universe," while most are not "infinite density" as one example. 

Infinities are funny things.  Even with the equations predicting infinite density, you can still have an infinitely large universe that is ALSO infinitely dense.  It remains infinitely large no matter how dense it is.  That's one of the weird parts of infinity.  If something is infinitely big and you compress it, it's still infinitely big, only denser! 
 

lean bean

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Re: Is infinity an illusion?
« Reply #54 on: 12/09/2013 17:37:20 »
Infinities are funny things.  Even with the equations predicting infinite density, you can still have an infinitely large universe that is ALSO infinitely dense.  It remains infinitely large no matter how dense it is.  That's one of the weird parts of infinity.  If something is infinitely big and you compress it, it's still infinitely big, only denser!
Okey-dokey. :)

« Last Edit: 12/09/2013 17:40:01 by lean bean »
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #55 on: 12/09/2013 22:11:14 »
Quote from: JP
If something is infinitely big and you compress it, it's still infinitely big, only denser!

  If you start with an infinite amount of low density and compress this to an infinite amount of high density, who/what "creates" the extra density?  Where does it come from? 

OK, it's only theoretical, but what happens if you try to consider practical applications?
 

Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #56 on: 13/09/2013 02:18:09 »
If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom? That would mix finite and infinite.
 

Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #57 on: 13/09/2013 02:20:49 »
Also having infinite helium would preclude having infinite electrons, protons and neutrons. You would have split infinities.
 

Offline JP

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Re: Is infinity an illusion?
« Reply #58 on: 13/09/2013 03:25:20 »
Quote from: JP
If something is infinitely big and you compress it, it's still infinitely big, only denser!

  If you start with an infinite amount of low density and compress this to an infinite amount of high density, who/what "creates" the extra density?  Where does it come from? 

OK, it's only theoretical, but what happens if you try to consider practical applications?

Why is this a problem?  If the universe is actually infinite, it has an infinite amount of "stuff" so there would be no problem compressing it, having it get denser, and still having an infinite universe. 
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #59 on: 13/09/2013 09:31:03 »
If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom? That would mix finite and infinite.
Why would that be a problem?

Quote
Also having infinite helium would preclude having infinite electrons, protons and neutrons. You would have split infinities.
Again, why would would that be a problem? In an infinite universe, you could have an infinite number of galaxies containing an infinite amount of all the natural elements, and an infinite amount of relatively 'empty' space containing an infinite amount of hydrogen & helium at very low densities.
 

lean bean

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Re: Is infinity an illusion?
« Reply #60 on: 13/09/2013 17:40:54 »
  If you start with an infinite amount of low density and compress this to an infinite amount of high density, who/what "creates" the extra density?  Where does it come from? 
OK, it's only theoretical, but what happens if you try to consider practical applications?

who/what? Spacetime. It's a weird one Bill.
If it's spacetime determining the density, then in an infinite universe you have a contracting spacetime increasing density and expanding spacetime lowering density, but no change to size of universe... It's something like I was trying to convey earlier in the other thread #29
http://www.thenakedscientists.com/forum/index.php?topic=48385.25

My wording there
Quote
‘then what happens in the context of an infinit universe when it is run backwards so that each observable universe ‘closes down’ to its respected point? How many points in an infinite universe? The equations break down ‘everywhere’? singularity everywhere? My sentence ‘an infinite expanse in a state of singularity’ could read as ‘an infinite expanse in an indefinable state.’
This infinity stuff is just so weird. :)
« Last Edit: 13/09/2013 17:42:52 by lean bean »
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #61 on: 13/09/2013 17:58:43 »
Quote from: JH
If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom? That would mix finite and infinite.
Also having infinite helium would preclude having infinite electrons, protons and neutrons. You would have split infinities.

Do I detect a hint of a "kindred spirit"; someone who has thought beyond mathematical infinities and found something astonishing?

Are you a scientist?
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #62 on: 13/09/2013 18:13:45 »
Quote from: JP
Why is this a problem?  If the universe is actually infinite, it has an infinite amount of "stuff" so there would be no problem compressing it, having it get denser, and still having an infinite universe.

By definition, compressing something is making it smaller, but leaving it with the same amount of “stuff”.  If you could compress infinity; which I believe you can’t; you would produce a “smaller infinity”, which, outside mathematics, is nonsense.  If you could do that, your “smaller infinity” would have to be contained in a “larger infinity”; again, nonsense; so more “stuff” would have to come from somewhere to fill the "larger infinity". 

Why can we not unite relativity and QM?  It’s because infinity finds its way into the equations and produces nonsense.
 
 

Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #63 on: 13/09/2013 18:18:36 »
Quote from: JH
If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom? That would mix finite and infinite.
Also having infinite helium would preclude having infinite electrons, protons and neutrons. You would have split infinities.

Do I detect a hint of a "kindred spirit"; someone who has thought beyond mathematical infinities and found something astonishing?

Are you a scientist?

I am what you could call a computer scientist if such a thing exists. I have been thinking about infinity since I was 12 and I'm now 53. To me infinity seems to be a singular term and inconsistent with reality. I feel it is more akin to zero than we imagine. Zero could also be considered a singular term although both have a different meaning and application in mathematics. They are abstract and in my opinion break down when applied to perceived reality causing all sorts of paradoxes.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #64 on: 13/09/2013 18:21:35 »
Quote from: JH
If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom?

Please explain this, Jeffrey, I've been trying, on a number of discussion forums, for about three years, to make that point!
Changing just one word in the above quote would take the argument to a whole different level, but let's take one step at a time.
 
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #65 on: 13/09/2013 18:29:28 »
Quote
I have been thinking about infinity since I was 12 and I'm now 53.

I started thinking seriously about infinity when I was 19, and I'm now 73.  Between us we chalk up quite a few years of thinking.  :)
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #66 on: 13/09/2013 18:33:25 »
Quote from: LB
This infinity stuff is just so weird. :)

Agreed, but it is a problem only if you get stuck in "mathematical infinities".
 

Offline JP

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Re: Is infinity an illusion?
« Reply #67 on: 13/09/2013 18:56:23 »
Quote from: JP
Why is this a problem?  If the universe is actually infinite, it has an infinite amount of "stuff" so there would be no problem compressing it, having it get denser, and still having an infinite universe.

By definition, compressing something is making it smaller, but leaving it with the same amount of “stuff”.  If you could compress infinity; which I believe you can’t; you would produce a “smaller infinity”, which, outside mathematics, is nonsense.  If you could do that, your “smaller infinity” would have to be contained in a “larger infinity”; again, nonsense; so more “stuff” would have to come from somewhere to fill the "larger infinity". 

Why can we not unite relativity and QM?  It’s because infinity finds its way into the equations and produces nonsense.
 

The problem you've gotten yourself into here is that in the sense used to talk about the universe, compressing does not mean "getting smaller" by definition.  I could take the set of all real numbers and divide each number in it by 2.  I would be "compressing it" in that any two numbers will get closer to 0, but the set is still infinite and contains all real numbers. 

The idea of an infinite universe that could be more or less dense than it is currently while still remaining infinite is very similar.  The distance between any two points would increase or decrease, but if there was an infinite amount of stuff to begin with, you'll still have an infinite amount of stuff after "compressing" it.

You don't get yourself into trouble with conservation of density because there isn't any such law.  You don't violate conservation of energy or mass because in any region of the universe you look at, the conservation laws hold.  It's only when you look at an infinite region where you might have problems, but conservation laws aren't even defined over infinite regions, so that's not a problem either.

It might be the case that infinity is non-physical, but the argument that you couldn't have an expanding (or compressing) infinite universe doesn't forbid an infinite universe.
« Last Edit: 13/09/2013 19:03:15 by JP »
 

Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #68 on: 13/09/2013 19:03:54 »
Quote from: JH
If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom?

Please explain this, Jeffrey, I've been trying, on a number of discussion forums, for about three years, to make that point!
Changing just one word in the above quote would take the argument to a whole different level, but let's take one step at a time.
 

The problem is infinity does occur in equations. In that sense it has to be explained. Zero was first introduced into the numbering system in India. How long ago I do not recall but it revolutionized mathematics and introduced base numbering systems.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #69 on: 14/09/2013 05:30:33 »
Quote from: JP
The problem you've gotten yourself into here is that in the sense used to talk about the universe, compressing does not mean "getting smaller" by definition.  I could take the set of all real numbers and divide each number in it by 2.  I would be "compressing it" in that any two numbers will get closer to 0, but the set is still infinite and contains all real numbers.

Shades of Hilbert’s Hotel here. The only reason the HH scenario appears to work is that you can never reach infinity.  Once you start moving guests, you never stop, so no one is without a room, but someone is always in transit.  I suspect David Hilbert had a sense of humour.

1> 0.5
2> 1
3> 1.5
Etc.

In what sense are the numbers compressed?

You are still using mathematical approximations to try to explain physical infinity.


 

Offline Pmb

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Re: Is infinity an illusion?
« Reply #70 on: 14/09/2013 06:23:22 »
Quote from: JH
If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom?

Please explain this, Jeffrey, I've been trying, on a number of discussion forums, for about three years, to make that point!
Changing just one word in the above quote would take the argument to a whole different level, but let's take one step at a time.
 
Hi Bill,

Don't bother with claims from people who refuse to elaborate or clrarify what they mean. It's a trademark of pseudoscience and should be avoided at all costs.

I don't understand the problem you have with infinity. Could you clarify it for me?

Let me start from the basics:

Definition:

Infinite - )a) having no limit (b) without bound.

Obviously infinite is not a number as one can easily see from the definition. Under nomal situations it cannot take the place of a variable in an algebraic equation. Consider as an exmaple either the mass or charge density of a point particle. Both the mass and the charge are finite but since the mass/charge density = limit as vokume goes to zero of the ratio mass/volume, the mass/charge density is infinite, meaning that as the volume is made smaller and smaller the ratio mass(charge)/volume increases without bound. So in nature there does exist quantities which are infinite. The functions which describe densities of these types are called distributions and are defined using the Dirac delta function.

Typically we define all physical quantities in nature using four basic quantities which themselves cannot be defined in other terms. They are distance, time, mass and charge. These are called "kinematic variables" while things like velocity/speed, acceleration, current, momentum, energy, angular momentum etc. are defined in terms of kinematic variables. These are called dynamnic variables.

There are often disagreement on what are to be though of as representing "real" quantities while all other are derived quantities and as such concepts which exist only in the mind. However that in no way makes them useless.

So to begine with please let me know if you agree with the above and if you don't then please elaborate on it explaining what you agree with and disagree with. Then we can go from there.

Thanks, Bill!
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #71 on: 14/09/2013 14:55:10 »
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I don't understand the problem you have with infinity

 I think my “problem” with infinity is one of persuading people of science that there is a difference between mathematical infinities and physical infinity.  There is a strong tendency to think that anything outside mathematical infinities smacks of philosophy/theology, but such is not necessarily the case.

I agree with your explanations.  I would take issue with nothing in your last post, but it doesn’t address the major point I am trying to make.

Time is very short at the moment, but I will come back to it later.  Perhaps, if we can take one point at a time, we can achieve some clarity. 
 

Offline Pmb

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Re: Is infinity an illusion?
« Reply #72 on: 14/09/2013 15:17:27 »
Quote from: Bill S
I think my “problem” with infinity is one of persuading people of science that there is a difference between mathematical infinities and physical infinity.
In your mind, what is the difference between a mathematical one and a physical one.

My own personal feeling is that this is no problem with scientists. In a strong sense of the phrase (and not to come off as too arrogant), we know better. We know that the answer all depends on definition. The author of the book I'm proof reading goes through great lengths to make sure the reader understands this regarding the event horizon of a black hole and the singularity at the center. The former is only a mathematical singularity which can be "transformed" away while the other is "real" and can't be transformed away.

Quote from: Bill S
There is a strong tendency to think that anything outside mathematical infinities smacks of philosophy/theology, but such is not necessarily the case.
I find that to be confusing. Can you give me a solid example? Thanks.

Quote from: Bill S
I agree with your explanations.  I would take issue with nothing in your last post, but it doesn’t address the major point I am trying to make.
Which is?

Quote from: Bill S
Time is very short at the moment, but I will come back to it later.  Perhaps, if we can take one point at a time, we can achieve some clarity. 
Okay. Let's start with the point that you'd trying to make.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #73 on: 14/09/2013 19:46:51 »
Quote from: Pete
Okay. Let's start with the point that you'd trying to make.


My starting point was asking the question: “Can there ever have been a time when there was nothing?”

When I first met that question, as a child, the answer, “No”, was cited as a proof of the existence of God.  Later, when I began to think seriously about this, I realised that the question applied to science as much as it did to theology.  One could neither prove, nor disprove the existence of God, but the existence of something eternal/infinite was another matter.

Logically, I could see no way in which, if there had ever been nothing, there could be something now.  There is quite a lot of literature around that suggests that the Universe represents the ultimate “free lunch” – it came from nothing. 

Avidly I sought out anything I could find that might explain this “something from nothing”.  The most recent book being “A Universe from Nothing” (L M Krauss).  I found this the most disappointing, to date.  His most quotable quote has to be: "When I say nothing, I don't mean nothing......"

Unlike Krauss, when I say nothing, I mean nothing: no space, no time, no matter, no energy, no quantum "something" to fluctuate; absolutely nothing.

The question remains, and perhaps we should make it the first point: “Can there ever have been a time when there was nothing?” 

I think not, but I’m open to persuasion.
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #74 on: 14/09/2013 21:00:05 »
The question remains, and perhaps we should make it the first point: “Can there ever have been a time when there was nothing?”
I'm not sure the question makes sense. How can there be time if there is nothing (assuming 'nothing' is the absence of anything, not just 'empty' space)?
 

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Re: Is infinity an illusion?
« Reply #74 on: 14/09/2013 21:00:05 »

 

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