Is infinity an illusion?

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Offline JP

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Re: Is infinity an illusion?
« Reply #100 on: 16/09/2013 16:13:04 »
Well put, dlorde.

I suspect a problem with 'absolute nothingness' is that it's scientifically useless. 

It's like thinking of the process of building models of the universe (or parts of it) as starting with a blank sheet of paper and writing down all the properties of the model on it.  Eventually, you'd hope to have a model that made predictions about measurable quantities in order to be scientifically useful.  If you want to ask 'what initial states of the universe are possible?' you'd be asking for what initial states you could write on the paper that, coupled with a set of laws you also write down, would match what can be observed/measured. 

The problem with 'absolute nothingness' is that it would be a completely blank piece of paper, which clearly in no way relates to measurements/observations we can make today.  Even if you could somehow have the 'initial state' of the universe be a blank part of the paper, you'd still have to have another part dealing with measurable quantities: position, time, energy, momentum.  Since the paper has something written on it, it's necessarily not dealing with 'absolute nothing.'

The 'nothing' that Lawrence Krauss and other scientists are talking about is similar to having the universe part of the paper blank, but the physical laws part of the paper covered with equations: quantum mechanics, general relativity, space, time, etc. We can start from a universe in a 'blank state,' but because physical laws describe the behavior of measurable properties of that blank state (energy, distance, etc.) we aren't describing 'absolute nothing.'

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Offline Bill S

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Re: Is infinity an illusion?
« Reply #101 on: 16/09/2013 18:31:55 »
Quote from: JP
If you can tell me why, scientifically, "can there be infinity in nature" depends on "can there ever have been nothing?"

That’s not quite what I said, JP.  As you accurately quoted, what I said was: “Does nature exist in infinity? The answer to that depends on the answer to “Can there ever have been nothing”?”

In other words: if something has always existed, then the Universe must be intimately linked to that something.  In fact, if causality is relevant to the situation, that something must be causally related to the Universe.

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Now, as for the question of whether there could have been nothing, most physicists would say no

That’s encouraging.  Would I be right in thinking that those who would say yes would claim that the Universe came from nothing? 

Would it also be the case that they would redefine nothing so as to make it something?

If nothing has a different meaning in science than it does in general parlance, I am neither qualified – nor anxious – to argue with that.  I think it would good if scientists who write Pop Sci books made that distinction clear to their readers, who, in general, will be non-scientists, but that’s another matter.

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The problem with 'absolute nothingness' is that it would be a completely blank piece of paper

Have we reached the stage where, if we mean nothing we have to say absolutely nothing, otherwise we are talking about something?

I like your analogy using the sheet of paper to represent nothing, but we might change the perspective slightly and consider that “absolutely nothing” is represented by no paper.  In that case there will be nothing to write on so we will never have our model universe, however we redefine nothing.

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Offline Bill S

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Re: Is infinity an illusion?
« Reply #102 on: 16/09/2013 19:03:50 »
Quote from: Pmb
See post #32 on page 2.

Thanks Pete, I had lost sight of that. 

What I said was “I feel sure you did not intend starting an etymological diversion”.  Obviously that was not as reassuring as it was intended to be.  :(

I always try to answer questions, but of late my visits to the computer have been brief and hurried, so I may have fallen short on occasions.  I think we are very close to the point where I shall have to look at how my thoughts on infinity have been influenced by this discussion.  Hopefully comparing older with newer thoughts will provide some answers. 


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Offline JP

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Re: Is infinity an illusion?
« Reply #103 on: 16/09/2013 19:29:51 »
Quote from: JP
If you can tell me why, scientifically, "can there be infinity in nature" depends on "can there ever have been nothing?"

That’s not quite what I said, JP.  As you accurately quoted, what I said was: “Does nature exist in infinity? The answer to that depends on the answer to “Can there ever have been nothing”?”

In other words: if something has always existed, then the Universe must be intimately linked to that something.  In fact, if causality is relevant to the situation, that something must be causally related to the Universe.
That argument works if you expect any two events in the universe to be causally connected, but clearly this isn't the case!  A star in our galaxy and a star outside the visible universe can both go supernova and these events have no causal connection to each other.  Now, you might say, if some event created all points in the universe, then those points must be causally connected to this event and thus to each other somehow.  But causality applies to events within our universe, and if some external event created the universe, it would not exist within the universe (since this event created the universe).  Therefore, there's no reason to impose causality on it. 

This is tough to get one's head around, but when dealing with ideas like the creation of the universe, our poor brains aren't very well equipped to deal with it.  We have a hard enough time thinking beyond our low velocities/accelerations and large size to accept relativity and quantum mechanics, let alone thinking about the creation of space and time themselves!

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Now, as for the question of whether there could have been nothing, most physicists would say no

That’s encouraging.  Would I be right in thinking that those who would say yes would claim that the Universe came from nothing? 

Would it also be the case that they would redefine nothing so as to make it something?

If nothing has a different meaning in science than it does in general parlance, I am neither qualified – nor anxious – to argue with that.  I think it would good if scientists who write Pop Sci books made that distinction clear to their readers, who, in general, will be non-scientists, but that’s another matter.

Yes.  As much as I respect Lawrence Krauss, I strongly dislike the title "A Universe from Nothing."  I haven't read it, but from hearing him speak about his ideas, I believe he's arguing that the universe came from quantum fluctuations.  But for quantum fluctuations to exist, quantum mechanics must exist and therefore there are properties to the pre-universe: at least the properties necessary to support some flavor of quantum mechanics.At any rate, there must be some physical laws existing that describe how to go from pre-universe to having the universe.

So his "nothing" is indeed "something" that has very precise properties!  Of course, the title "a universe from something" doesn't have the same ring to it.

(As an aside, even talking about pre-universe is problematic, since the universe defines all time that we know of, so it's questionable if time exists if the universe doesn't... Talk about mind-benders!)

Physicists don't ever really talk about "absolute nothing" (my definition, hence the quotes) which would be the absence of all properties of the model as well as the model itself--the "blank sheet of paper."  Since there would be no rules to cover quantum fluctuations or any other means of generating the universe, it wouldn't allow us to describe the creation of the universe.  Moreover, there would be no definitions of energy, time, distance or any other measurable quantity, which is why it's not useful to physicists!  We may be able to talk about it in metaphysics, but if it in no way relates to anything we can observer or measure, it's not useful to scientists.

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The problem with 'absolute nothingness' is that it would be a completely blank piece of paper

Have we reached the stage where, if we mean nothing we have to say absolutely nothing, otherwise we are talking about something?

I like your analogy using the sheet of paper to represent nothing, but we might change the perspective slightly and consider that “absolutely nothing” is represented by no paper.  In that case there will be nothing to write on so we will never have our model universe, however we redefine nothing.

[/quote]

:)

This is the problem with dealing with metaphysical concepts.  I like the blank paper, and I think it works so long as we say "whatever I write on this paper represents nature."  Then the only way we could describe a nature that is "absolute nothing" is to remove all properties from it, hence a blank sheet of paper.

We could say "we'd have to remove the paper," but then things get circular, because if the paper was on a desk, you'd now have an empty desk.  And you'd have to remove that desk.  Then you'd have an empty room, but you'd have to remove the room.  Then you'd have empty space, but you'd have to remove space.  Then you'd have an empty [whatever contains space], and you'd have to remove that, etc. etc. etc. 

It's an interesting metaphysical exercise, but I'm not sure it's of use to scientists.

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Offline Bill S

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Re: Is infinity an illusion?
« Reply #104 on: 16/09/2013 19:34:42 »
Quote from: dlorde
I'm open to be persuaded that my interpretation of the semantics is faulty

I think your interpretation of the semantics is spot on. 

Perhaps I should continue working on the wording of “the question”.  As I am confident you know what I am really asking, and as you obviously have a facility with words, and an enviable feeling for semantic rectitude, your help would be appreciated. 

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Offline yor_on

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Re: Is infinity an illusion?
« Reply #105 on: 16/09/2013 19:58:34 »
How about the Copenhagen model? In where consciousness is a non ignorable part of any 'system'. To make a measurement, as we think of it normally, consciousness must be involved, and so 'histories' as our definitions of a past, a 'now', and a future. What would a quantum computer have to say about those ideas?
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Offline dlorde

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Re: Is infinity an illusion?
« Reply #106 on: 16/09/2013 20:09:51 »
... As much as I respect Lawrence Krauss, I strongly dislike the title "A Universe from Nothing."  I haven't read it, but from hearing him speak about his ideas, I believe he's arguing that the universe came from quantum fluctuations.  But for quantum fluctuations to exist, quantum mechanics must exist and therefore there are properties to the pre-universe: at least the properties necessary to support some flavor of quantum mechanics.At any rate, there must be some physical laws existing that describe how to go from pre-universe to having the universe.

So his "nothing" is indeed "something" that has very precise properties!  Of course, the title "a universe from something" doesn't have the same ring to it.
Yes, pretty much; Krauss explains his views on the different 'levels' or semantics of nothing in this interview (click on 'Show' to the right of 'Transcript').

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Offline dlorde

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Re: Is infinity an illusion?
« Reply #107 on: 16/09/2013 20:33:09 »
How about the Copenhagen model? In where consciousness is a non ignorable part of any 'system'. To make a measurement, as we think of it normally, consciousness must be involved, and so 'histories' as our definitions of a past, a 'now', and a future. What would a quantum computer have to say about those ideas?
Strictly speaking, it's the Copenhagen Interpretation, and its principles don't invoke consciousness. But wave function collapse is fundamental, and is said to occur when an observer (a classical device) registers an outcome.

As Heisenberg said, "The observer has, ... only the function of registering decisions, i.e., processes in space and time, and it does not matter whether the observer is an apparatus or a human being; but the registration, i.e., the transition from the "possible" to the "actual," is absolutely necessary..." (my bolding).

Eugene Wigner and a few others proposed that minds were external observers, not amenable to QM, and minds perform the measurements that collapse the wave function. It is not a popular idea among physicists, but very popular in pseudoscience.

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Offline yor_on

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Re: Is infinity an illusion?
« Reply #108 on: 16/09/2013 20:59:01 »
A pleasure to see you here Dlorde :) As for any interpretation I, as always, get stuck on the question of 'observing'. I have an idea in where you can't separate a system of non conscious able 'observers' from one in where consciousness must be involved. Can a universe 'exist' without consciousness being involved?
=

Heh, as seems Heisenberg. It's the simplest explanation to me, assuming that logic is what defines a universe. Although :) I do like fantasy, and sometimes your fantasies might define physics, presuming you have a way to translate it into a logic.
« Last Edit: 16/09/2013 21:04:27 by yor_on »
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Offline dlorde

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Re: Is infinity an illusion?
« Reply #109 on: 16/09/2013 21:23:58 »
I think your interpretation of the semantics is spot on.
OK, good... 

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Perhaps I should continue working on the wording of “the question”.  As I am confident you know what I am really asking, and as you obviously have a facility with words, and an enviable feeling for semantic rectitude, your help would be appreciated.
This discussion has got me thinking again about infinity and nothing, and it now seems to me that absolute nothing (Krauss's 3rd 'nothing', which he kind of skirts around in the interview) is not a coherent physical concept, so there can't 'have been' absolute nothing, any more than 'not stamp collecting' is a hobby, or 'an absence of cotton' is a saleable commodity.

Krauss's 2nd nothing is no particles, or radiation, or even space itself, but the laws of quantum mechanics only - which allow space to appear as a quantum fluctuation:
Quote from: L.Krauss
... space itself is subject to quantum mechanical properties, including the fact that it can fluctuate in an out of existence, just like the particles within space can fluctuate in an out of existence. But if that's possible, you could start with no space itself and create the nucleus, the basis of the universe. You can literally have no space and no time and, poof, suddenly a space can appear and a time within that space.
I'm not qualified to speculate on how, or what it means, that the laws of QM can exist in the absence of spacetime.

Krauss's 1st nothing is the popular concept of 'empty space', the quantum vacuum, which, I think we agreed, doesn't really count as nothing in this context.

The idea of an infinite past doesn't really apply if, as in the 2nd nothing, time itself has a 'start' point. Hawking's (now obsolete) big bang to big crunch sphere model, with time running north to south, provides a visualization of this; where time starts at the north pole of the sphere, the universe expands, reaches a maximum size at the equator, and shrinks back to a big crunch at the south pole, where time ends. In this model, there is no 'before the big bang', in the same way there is no 'north of the north pole'.

Admittedly, it's difficult to conceive of time beginning without intuitively trying to imagine what was before that, but OTOH, is it really any easier to conceive of an infinite past?  I'm currently thinking of a self-contained, finite spacetime 'blob' that has no boundaries - i.e. no edge or 'outside' in either space or time; but I'm open to an infinite past given a plausible argument (and given that I can somehow distinguish it as a better model than a finite past!).
« Last Edit: 16/09/2013 21:53:53 by dlorde »

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Offline dlorde

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Re: Is infinity an illusion?
« Reply #110 on: 16/09/2013 21:47:08 »
A pleasure to see you here Dlorde :)
Thank you, and likewise, I'm sure ;)

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... Can a universe 'exist' without consciousness being involved?
All the indications are that consciousness (whether ours or alien) must have arrived somewhat after the big bang because, as far as we know, it takes a while to evolve (unless you want to speculate that a rapidly expanding ball of plasma and/or hydrogen can be conscious). Even the idea that consciousness is required to collapse a wave function doesn't preclude it. Also, what level of consciousness would it take to maintain the existence of the universe - would a rat do? a frog? And consider - is it reasonable to suggest the universe will cease to exist when the last consciousness dies?

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Heh, as seems Heisenberg. It's the simplest explanation to me, assuming that logic is what defines a universe.
Sorry, I can't parse that...
« Last Edit: 16/09/2013 21:51:37 by dlorde »

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Offline Bill S

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Re: Is infinity an illusion?
« Reply #111 on: 16/09/2013 21:58:31 »
Quote from: JP
"A Universe from Nothing."  I haven't read it

Don’t bother, unless you are keen to know why Krauss thinks God is an outdated concept!

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even talking about pre-universe is problematic, since the universe defines all time that we know of, so it's questionable if time exists if the universe doesn't...

Is it not necessary for time to exist in order that change may happen?  The change from “no Universe” to “Universe” would require time to exist in order to let the change happen; wouldn’t it?

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Now, you might say, if some event created all points in the universe, then those points must be causally connected to this event and thus to each other somehow.  But causality applies to events within our universe, and if some external event created the universe, it would not exist within the universe (since this event created the universe).  Therefore, there's no reason to impose causality on it.

“…then those points must be causally connected to this event and thus to each other somehow.”  I would accept that if something caused the Universe to come into being it would be causally connected to the Universe, which would include every point.  To argue that this implied that there was any causal link between individual points, apart from their having a common origin, would be very difficult to justify.  My sister and I have a common origin, but neither of us is causally responsible for the other. :)

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We could say "we'd have to remove the paper," but then things get circular, because if the paper was on a desk......

Not necessarily, because you are constructing the model, you do not have to include the desk in your model.  If you call the paper “nothing”, then you are in the same position as Krauss, you have to accept that your “nothing” is “something”.  Without the paper you really have nothing (unless you choose to add another “something”, like a desk), and with “nothing” you have nowhere to construct your universe.


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Offline dlorde

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Re: Is infinity an illusion?
« Reply #112 on: 16/09/2013 22:24:59 »
Is it not necessary for time to exist in order that change may happen?  The change from “no Universe” to “Universe” would require time to exist in order to let the change happen; wouldn’t it?

I'd agree that time is required for change, but if time itself begins with the universe, then (as I mentioned previously) there is no 'before', so there can have been no change. IOW it's only a problem if we assume a default timeline within which the universe begins (the intuitive view). Without that timeline, the universe just is, i.e. there's no process by which it 'comes into existence'; it is only from the point of view of its inhabitants that it 'begins' at time=0.

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Offline JP

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Re: Is infinity an illusion?
« Reply #113 on: 17/09/2013 00:15:13 »
Is it not necessary for time to exist in order that change may happen?  The change from “no Universe” to “Universe” would require time to exist in order to let the change happen; wouldn’t it?
Maybe.  At the risk of sounding like a crackpot, a lot of advances in science require throwing out common sense ideas that we trust based on our place in the universe.  For example, particles were particles until we realized that on small scales they might not be.  Time and length measurements should agree between observers according to our intuitive view of the world--only they don't if we imagine traveling fast enough.

Similarly, the idea that time is fundamental might not be true--we're used to it because our brains work by turning energy into order, a process which necessarily follows an arrow of time.  If time is a quanta, which can pop out of some more fundamental "stuff," then our universe and our view that things evolve in time might just be due to the fact that our brains exist in a universe with time and require time in order to function.

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Now, you might say, if some event created all points in the universe, then those points must be causally connected to this event and thus to each other somehow.  But causality applies to events within our universe, and if some external event created the universe, it would not exist within the universe (since this event created the universe).  Therefore, there's no reason to impose causality on it.

“…then those points must be causally connected to this event and thus to each other somehow.”  I would accept that if something caused the Universe to come into being it would be causally connected to the Universe, which would include every point.  To argue that this implied that there was any causal link between individual points, apart from their having a common origin, would be very difficult to justify.  My sister and I have a common origin, but neither of us is causally responsible for the other. :)
I'd argue against the idea that something that "caused" the universe had to be causally connected to it.  Causally connected means something very specific about connections within space-time.  A cause of the universe would exist outside of, or at a more fundamental level than space-time, so there's no reason why causality need to apply to it.  In fact this cause would create space and time somehow, so I suspect it's impossible to apply an idea like causality to it.

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We could say "we'd have to remove the paper," but then things get circular, because if the paper was on a desk......

Not necessarily, because you are constructing the model, you do not have to include the desk in your model.  If you call the paper “nothing”, then you are in the same position as Krauss, you have to accept that your “nothing” is “something”.  Without the paper you really have nothing (unless you choose to add another “something”, like a desk), and with “nothing” you have nowhere to construct your universe.


But "not including the desk" is a property of the model.  ;)  I suspect there's little to be gained by trying to define metaphysical nothingness in terms of precisely what it doesn't contain.  Certainly I don't see how it's got any use in physics.

I don't literally mean we have paper, but if the paper defines the set of properties, then a blank paper would denote nothingness (a set devoid of all properties).  This is problematic, though, since "a set devoid of properties" has the property of being devoid of properties!

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Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #114 on: 17/09/2013 02:16:57 »
I wasn't going to reply to this again but if we consider Newton's third law.

Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body.

If we consider the universe to be a body in the sense that it has mass then what opposite effect did the creation of the universe have? The collapse of another universe of the same mass? That seems to be equal and opposite.

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Offline dlorde

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Re: Is infinity an illusion?
« Reply #115 on: 17/09/2013 11:23:12 »
I don't literally mean we have paper, but if the paper defines the set of properties, then a blank paper would denote nothingness (a set devoid of all properties).  This is problematic, though, since "a set devoid of properties" has the property of being devoid of properties!
Again, if you treat the absence of something as a thing in its own right, particularly as the same type of thing that is absent (in this case a property) when dealing with sets, you can get into all kinds of awkward and contradictory logical knots; for example, you can say that not only does the paper have the new property of being devoid of all properties, but it also has the property of being devoid of property A, the property of being devoid of property B, ...etc. This list can include all conceivable properties, not just the properties it would normally have (and, of course, the property of being devoid of all inconceivable properties too). It really doesn't work.

This kind of reminds me of Russell's Paradox (i.e. does the set of 'all sets that don't contain themselves' contain itself or not?), where Russell developed a type theory to separate types of sets and where they could be applied, that removed such self-referential loops.

Although, having said all that, there are physical instances where it is legitimate to treat the absence of something as a thing in its own right, such as the movement of 'holes' in semiconductors, but these are restricted contexts.
« Last Edit: 17/09/2013 11:34:01 by dlorde »

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Offline alancalverd

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Re: Is infinity an illusion?
« Reply #116 on: 17/09/2013 19:18:49 »
Although, having said all that, there are physical instances where it is legitimate to treat the absence of something as a thing in its own right, such as the movement of 'holes' in semiconductors, but these are restricted contexts.

Although somewhat off-topic, I must defend the existence of holes a a thing rather than a non-thing. If you observe the Hall effect in a p-type semiconductor it is obvious that the moving charge really is positive. In a biased p-n junction photodiode, it is clear that the drift velocity of the holes is lower than that of the electrons.
helping to stem the tide of ignorance

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Offline dlorde

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Re: Is infinity an illusion?
« Reply #117 on: 17/09/2013 22:14:20 »
Although, having said all that, there are physical instances where it is legitimate to treat the absence of something as a thing in its own right, such as the movement of 'holes' in semiconductors, but these are restricted contexts.

... I must defend the existence of holes a a thing rather than a non-thing. If you observe the Hall effect in a p-type semiconductor it is obvious that the moving charge really is positive. In a biased p-n junction photodiode, it is clear that the drift velocity of the holes is lower than that of the electrons.
As I said, it is legitimate in some contexts to treat them as things. In case of confusion, I was thinking of electron holes.

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Offline Pmb

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Re: Is infinity an illusion?
« Reply #118 on: 17/09/2013 23:07:01 »
I'd like to point out that there is a difference between things that exist that have no material existance such as credit.

Would you rather have nothing or have nothing as well as owe nobody anything?

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Offline dlorde

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Re: Is infinity an illusion?
« Reply #119 on: 17/09/2013 23:24:18 »
I'd like to point out that there is a difference between things that exist that have no material existance such as credit.
Credit is an interesting one, because it is a provisional or stand-in thing; which makes me wonder about virtual particles and other quantum fluctuations that have a notional quality, only occasionally resulting in 'real' things...

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Offline Bill S

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Re: Is infinity an illusion?
« Reply #120 on: 18/09/2013 01:26:10 »
Quote from: dlorde
Without that timeline, the universe just is, i.e. there's no process by which it 'comes into existence'; it is only from the point of view of its inhabitants that it 'begins' at time=0.


If it does not come into existence, then it has no beginning, so is it not, by what seems to be popular definition, infinite?

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Offline Pmb

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Re: Is infinity an illusion?
« Reply #121 on: 18/09/2013 01:56:11 »
Quote from: Bill S
If it does not come into existence, then it has no beginning, so is it not, by what seems to be popular definition, infinite?
No neccesarily. If you're educated in calculus then you're familiar with the concept of being bounded below but unbound above or bounded above but unbound below. Both of which are infinite. See http://mathworld.wolfram.com/Infinite.html

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Offline Bill S

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Re: Is infinity an illusion?
« Reply #122 on: 18/09/2013 03:46:06 »
Pete, if the Universe had no beginning, is it not unbounded in that direction, and therefore infinite?

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Offline Pmb

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Re: Is infinity an illusion?
« Reply #123 on: 18/09/2013 03:54:03 »
Pete, if the Universe had no beginning, is it not unbounded in that direction, and therefore infinite?
It is not temporally bounded, yes.

Let me expound on this a bit more since I just realized something. Something can have no lower limit and still be bounded. The value x in the relationship 0 < x < 1. This is bounded since we cannot decrease the value of x as much as we want to. The same thing holds for the upper limit.
« Last Edit: 18/09/2013 21:33:59 by Pmb »

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Offline dlorde

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Re: Is infinity an illusion?
« Reply #124 on: 18/09/2013 09:02:30 »
If it does not come into existence, then it has no beginning, so is it not, by what seems to be popular definition, infinite?
Depends what you mean by 'infinite' here. If time begins with the universe, there is no prior temporal extent because there is no prior time, so in what sense can it be temporally infinite? and I don't see that infinite spatial extent is a requirement.
« Last Edit: 18/09/2013 09:05:26 by dlorde »

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Offline Bill S

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Re: Is infinity an illusion?
« Reply #125 on: 18/09/2013 20:08:45 »
I’ve just found a few minutes to read the past dozen or so posts properly.  There are several points to which I must respond, but first, Dlorde’s last post raises a point which, in different guises, keeps appearing, but remains unresolved. May I suggest that, for the moment, we draw a line under all that has gone before and see what we can do with this.

 
Quote from: dlorde
  If time begins with the universe, there is no prior temporal extent because there is no prior time, so in what sense can it be temporally infinite?

For convenience, let’s use the term “eternity/eternal” here.

Is eternity a very long time?

My answer would be “no”, it is not.  In fact it is not time at all.  We are creatures of time so it is practically impossible for us to imagine timelessness.  As JP points out, our intuition is often wrong.  IMO it is intuition that makes us attach any temporal significance to eternity.  Eternity cannot be measured in seconds, millennia or any other temporal units. It is not time.

This brings us back to Dlorde’s question: “there is no prior temporal extent because there is no prior time, so in what sense can it be temporally infinite?”

I would argue that if there is a prior temporal extent, then we are not talking about eternity.  There is no such thing as “temporally infinite”.  Outside of mathematics, time and eternity are completely incompatible.  If you argue for no time before the Universe, then surely you are arguing for unmeasurable, indivisible eternity.

I know this seems to contradict my assertion that there would need to be time before the Universe to permit the change, but let's deal with one thing at a time.



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Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #126 on: 18/09/2013 21:49:11 »
Pete, if the Universe had no beginning, is it not unbounded in that direction, and therefore infinite?
It is not temporally bounded, yes.

Let me expound on this a bit more since I just realized something. Something can have no lower limit and still be bounded. The value x in the relationship 0 < x < 1. This is bounded since we cannot decrease the value of x as much as we want to. The same thing holds for the upper limit.

But what if we have ? <= x <= infinity? What is denoted by the question mark? Also can we insert equality for infinity?

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Offline Pmb

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Re: Is infinity an illusion?
« Reply #127 on: 18/09/2013 23:10:29 »
Quote from: jeffreyH
But what if we have ? <= x <= infinity? What is denoted by the question mark?
Also can we insert equality for infinity?
Equal signs in relationships involving infinity have no meaning.

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Offline AndroidNeox

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Re: Is infinity an illusion?
« Reply #128 on: 18/09/2013 23:41:31 »
While we cannot necessarily know whether any infinities 'exist', it's simple enough to show that they cannot be observed, and so have no directly detectable existence for us. Bell's Inequality, though, shows that the multiplicity of states for unobserved systems are real and measurable, but only while they are unobserved. Whether the totality of all possibilities is finite... I dunno.

Personally, I think that spigot algorithms (like the Bailey-Borwein-Plouffe, BBP, algorithm) could not work if we didn't exist within a background of infinite information. Just because pi can be described in terms of a few algebraic symbols doesn't mean that it possesses finite information. I find it telling that all such concise descriptions include terms, like e, which likewise cannot be fully described in finite information.

There are two ways to identify a specific piece of information: calculate it or look it up. Calculation would correspond to the pre-BBP method of starting at 3 and working along the string (3.14...) to the desired digit. Spigot algorithms don't behave that way. A spigot algorithm finds any desired digit of the irrational number in a fixed number of steps, just as a look-up algorithm does (it takes essentially the same computational effort to identify the 100th word on the 10th page of a book as it does to identify the 10th word on the 100th page).

When the BBP algorithm was first proposed, theoretical physicists argued that it could not work because a finite (and small) amount of computation could access an unlimited quantity of information. Then, when BBP was proven to be correct, they all shut up. I don't think they should have. I think they were right and the fact that spigot algorithms work actually reveals something fundamental about reality.

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Offline dlorde

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Re: Is infinity an illusion?
« Reply #129 on: 19/09/2013 09:26:19 »
For convenience, let’s use the term “eternity/eternal” here.

Is eternity a very long time?

My answer would be “no”, it is not.  In fact it is not time at all.  We are creatures of time so it is practically impossible for us to imagine timelessness.  As JP points out, our intuition is often wrong.  IMO it is intuition that makes us attach any temporal significance to eternity.  Eternity cannot be measured in seconds, millennia or any other temporal units. It is not time.
...
I would argue that if there is a prior temporal extent, then we are not talking about eternity.  There is no such thing as “temporally infinite”.  Outside of mathematics, time and eternity are completely incompatible.  If you argue for no time before the Universe, then surely you are arguing for unmeasurable, indivisible eternity.
There seem to be two subtly different relevant definitions of eternity; one being an infinite or unbounded extent of time, the other being timelessness. The former is the more general definition, the latter used more in a theological context (the 'afterlife', etc).

If we take eternity to mean timelessness, rather than infinite time, then I would broadly agree with what you say - except that I don't see why you assert 'There is no such thing as “temporally infinite”'. The extent of time into the future may be infinite - we can't know, but it does seem there will be no big crunch, just continuing expansion (although there is talk of a 'big rip' if the acceleration of expansion continues).

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Offline Bill S

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Re: Is infinity an illusion?
« Reply #130 on: 19/09/2013 15:14:34 »
Quote from: Dlorde
There seem to be two subtly different relevant definitions of eternity; one being an infinite or unbounded extent of time, the other being timelessness. The former is the more general definition

Reality (whatever that might be) is surely not a matter of democratic “vote”.  As a "general definition" it is a handy approximation, but that may be all it is. 

Quote
the latter used more in a theological context (the 'afterlife', etc).

This is unfortunate, because it is off-putting to most scientists, but Julian Barbour (for example) would certainly disagree that timelessness is not a scientific concept.

Quote
I don't see why you assert 'There is no such thing as “temporally infinite”'.

I refer you to extracts from my previous post. 

“Is eternity a very long time?     My answer would be “no”, it is not.  In fact it is not time at all……..  Eternity cannot be measured in seconds, millennia or any other temporal units. It is not time.”

“I would argue that if there is a prior temporal extent, then we are not talking about eternity. ……… time and eternity are completely incompatible.  If you argue for no time before the Universe, then surely you are arguing for unmeasurable, indivisible eternity.”

Quote
The extent of time into the future may be infinite - we can't know

Unbounded, perhaps, but it can never become infinite.


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Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #131 on: 19/09/2013 16:33:30 »
Quote from: jeffreyH
But what if we have ? <= x <= infinity? What is denoted by the question mark?
Also can we insert equality for infinity?
Equal signs in relationships involving infinity have no meaning.

That is the problem. Only infinity can equal itself. It can be considered as 1 where this represents "the whole thing" rather than a numerical value.

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Offline JP

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Re: Is infinity an illusion?
« Reply #132 on: 19/09/2013 18:49:05 »
Quote from: jeffreyH
But what if we have ? <= x <= infinity? What is denoted by the question mark?
Also can we insert equality for infinity?
Equal signs in relationships involving infinity have no meaning.

That is the problem. Only infinity can equal itself. It can be considered as 1 where this represents "the whole thing" rather than a numerical value.

That isn't true.  If I take the whole set of real numbers, it has infinite elements.  If I remove from it all the natural numbers, what remains is clearly not all the real numbers, yet it still has infinite elements.  Hence, infinity = infinity makes no sense and as Pmb said, it has no meaning.

This is why in calculus, when you see infinity appear, it appears at limits in integrals or in taking a limit.  It does not appear in algebraic statements where numbers would appear.  This is because it is not a number and does not have the properties of a number.

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Offline JP

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Re: Is infinity an illusion?
« Reply #133 on: 19/09/2013 18:58:08 »
Quote from: Dlorde
There seem to be two subtly different relevant definitions of eternity; one being an infinite or unbounded extent of time, the other being timelessness. The former is the more general definition

Reality (whatever that might be) is surely not a matter of democratic “vote”.  As a "general definition" it is a handy approximation, but that may be all it is. 

Quote
the latter used more in a theological context (the 'afterlife', etc).

This is unfortunate, because it is off-putting to most scientists, but Julian Barbour (for example) would certainly disagree that timelessness is not a scientific concept.

Quote
I don't see why you assert 'There is no such thing as “temporally infinite”'.

I refer you to extracts from my previous post. 

“Is eternity a very long time?     My answer would be “no”, it is not.  In fact it is not time at all……..  Eternity cannot be measured in seconds, millennia or any other temporal units. It is not time.”

“I would argue that if there is a prior temporal extent, then we are not talking about eternity. ……… time and eternity are completely incompatible.  If you argue for no time before the Universe, then surely you are arguing for unmeasurable, indivisible eternity.”

Quote
The extent of time into the future may be infinite - we can't know

Unbounded, perhaps, but it can never become infinite.



Bill, what scientific reasons do you have for claiming that time can be unbounded but not infinite?  In fact, given that time can be measured by numbers "1 second, 2 seconds, 3 seconds..." wouldn't unbounded time necessarily mean infinite time?  You'd at least have all the natural numbers of seconds, and that's an infinite set.

I don't know if anyone has scientifically defined "eternity," but if I were to do so, I'd define it akin to "infinity."  It describes a concept of something increasing without bound, just as taking a limit as some variable goes to infinity does.  In this sense, eternity and infinity are very closely linked.  Whether one can exist or not is another question and one that we can't answer scientifically (yet).

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Offline JP

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Re: Is infinity an illusion?
« Reply #134 on: 19/09/2013 21:33:35 »
One other interesting thought (as long as I'm spamming the thread and it's well into the speculative rather than concrete science): in statistical mechanics, we talk of microstates of a system, each of which corresponds to a single possible arrangement of the particles that make up a system.  From that point, you can derive entropy and enforce an arrow of time by looking at the probabilities involved in going from one microstate to the next.

One could imagine that the universe is represented by something akin to a single microstate, and that space and time might be emergent properties due to considerations of how these universe-states are linked together.  I think this is similar to what Julian Barbour argues (though I haven't read any of his works).  If this were the case, then time wouldn't really have a meaning when we look deeper than our universe, and it's an emergent property based upon how our minds work and the ordering of states through which our minds pass.

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Offline Bill S

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Re: Is infinity an illusion?
« Reply #135 on: 19/09/2013 22:42:09 »
Quote from: JP
In fact, given that time can be measured by numbers "1 second, 2 seconds, 3 seconds..." wouldn't unbounded time necessarily mean infinite time?  You'd at least have all the natural numbers of seconds, and that's an infinite set.

You will always be able to counter any argument about infinity by quoting mathematical infinities and regarding them as being the same as the one non-mathematical infinity, if such a thing exists.  In mathematics I am happy to believe that finite things like individual numbers can become infinite, but apart, perhaps, from the example Pete gave, on which I am not qualified to comment, I know of no physical thing that, being finite, can become infinite.

Consider, for example, speed.   John Gribbin says: :  “So if a tachyon were created in some violent event in space, it would radiate energy away furiously…..and go faster and faster, until it had zero energy ……and was travelling at infinite speed”.  At what point could you say: the speed is now infinite?  What is infinite speed?

Quote
  It describes a concept of something increasing without bound

Precisely – increasing without limit, but never becoming infinite.  At any stage in its increase it is a number, and infinity is not a number.  I thought we had agreed on that.

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Offline dlorde

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Re: Is infinity an illusion?
« Reply #136 on: 19/09/2013 23:13:57 »
... I know of no physical thing that, being finite, can become infinite.

Consider, for example, speed.   John Gribbin says: :  “So if a tachyon were created in some violent event in space, it would radiate energy away furiously…..and go faster and faster, until it had zero energy ……and was travelling at infinite speed”.  At what point could you say: the speed is now infinite?  What is infinite speed?

Quote
  It describes a concept of something increasing without bound

Precisely – increasing without limit, but never becoming infinite.  At any stage in its increase it is a number, and infinity is not a number.  I thought we had agreed on that.

These ideas go way back to ancient times - Aristotle & co. said that infinities are potential rather than actual.

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Offline Bill S

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Re: Is infinity an illusion?
« Reply #137 on: 20/09/2013 04:02:24 »
Quote from: dlorde
These ideas go way back to ancient times

So do I, doesn't mean I'm wrong.  :D

Potential infinity?  Now there's an interesting concept.  If it is a potential infinity, it isn't infinite.  If it isn't infinite, it's finite.  If it's finite it can't become infinite.  How can it be potentially infinite? 

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Offline dlorde

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Re: Is infinity an illusion?
« Reply #138 on: 20/09/2013 10:18:34 »
Quote from: dlorde
These ideas go way back to ancient times
So do I, doesn't mean I'm wrong.  :D
Of course not ;)

Quote
Potential infinity?  Now there's an interesting concept.  If it is a potential infinity, it isn't infinite.  If it isn't infinite, it's finite.  If it's finite it can't become infinite.  How can it be potentially infinite? 
Quoting from the article I linked:
Quote
An actual infinity is something which is completed and definite and consists of infinitely many elements, and according to Aristotle, a paradoxical idea, both in theory and in nature. In respect to addition, a potentially infinite sequence or a series is potentially endless; being a potentially endless series means that one element can always be added to the series after another, and this process of adding elements is never exhausted.
The way I see it, he calls it potential because it can't be directly demonstrated or enumerated, it can only be inferred from its definition or properties. This doesn't mean it's finite, just that, by definition, it's not physically completed or actualised. So while the digital representation of pi is an infinite series of digits, you'll only ever see a finite decimal approximation.

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Offline Bill S

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Re: Is infinity an illusion?
« Reply #139 on: 20/09/2013 18:42:28 »
It’s many decades since I studied Latin, but I’m fairly sure that:-

Potentiale = potential; from potens = able or able to….

So to be potentially infinite something must be able to become infinite.

I think that "quasi infinite" might be a less confusing term, but I’m not going to argue with the use of “potentially infinite” for things like numbers; I just think it is important that we all know what we mean. 

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Offline Bill S

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Re: Is infinity an illusion?
« Reply #140 on: 20/09/2013 18:50:51 »
Quote from: dlorde
So while the digital representation of pi is an infinite series of digits, you'll only ever see a finite decimal approximation.

I have seen it argued that pi cannot be infinite as it is the ratio of two finite numbers.  I'm not sure that I agree with the logic, but in any case it is a mathematical infinity, so it is not just the digital representation that is an approximation, it is the "infinity" itself.

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Offline dlorde

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Re: Is infinity an illusion?
« Reply #141 on: 20/09/2013 19:12:53 »
I have seen it argued that pi cannot be infinite as it is the ratio of two finite numbers.  I'm not sure that I agree with the logic, but in any case it is a mathematical infinity, so it is not just the digital representation that is an approximation, it is the "infinity" itself.
I don't quite follow; pi itself is exactly the ratio of circle circumference to diameter - a value which is a little over 3; there's nothing infinite about that - except that being an irrational number, the value can't be expressed as a simple fraction, so its decimal representation is infinite.

IOW, the value is finite, but its expression isn't.
« Last Edit: 20/09/2013 19:14:25 by dlorde »

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Re: Is infinity an illusion?
« Reply #142 on: 20/09/2013 19:23:36 »
.
For convenience, let’s use the term “eternity/eternal” here.

Eternity cannot be measured in seconds, millennia or any other temporal units. It is not time.

Bill, sorry to butt in, but can you describe what you mean here by eternity without using the concept of duration?  Or, do you mean time is not eternity because it had a beginning, so to speak?
« Last Edit: 20/09/2013 19:25:23 by lean bean »

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Offline Bill S

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Re: Is infinity an illusion?
« Reply #143 on: 21/09/2013 00:38:34 »
Nothing to apologise about, LB, it’s an open thread, not a clique.  The more contributors the better. 

Can I define eternity without using the concept of duration?  Probably not, but I’ll have a go.

We have evolved in 3D of space and 1D of time, so it is extremely difficult for us even to think about timelessness or changelessness. Fred Alan Wolfe might be able to find a yogi who can do it; he might even be able to do it himself, but most of us can’t.

For thousands of years people have been thinking about infinity/eternity, but no one has developed a terminology that is not linked to finite dimensions.  Infinity and eternity became differentiated because philosophers needed to think about spatial and temporal extent. 

My contention is that infinity cannot be measured in units of anything, and eternity cannot be measured in units of time. 

At risk of being accused of repetition, I would say: infinity is not a very big number, in fact it is not a number at all, and eternity is not a very long time, it is not time at all.   That’s probably as close as I can get to answering your question.
 
Quote
do you mean time is not eternity because it had a beginning, so to speak

I assume time, as we perceive it, had a beginning.  Any time now, I imagine there will be some searching questions on that subject, so I would rather wait a while before getting into that.   


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Offline Bill S

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Re: Is infinity an illusion?
« Reply #144 on: 21/09/2013 00:53:20 »
Quote
so its decimal representation is infinite

So, in common with mathematical infinities in general, it is unbounded, but can never become infinite.

Numbers need to be attached to things as adjectives need to be attached to nouns.  On their own, numbers are just concepts in the mind, so even if you could imagine an infinite number, which you probably can't, it would have no physical significance, unless you could produce an infinite number of objects.

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Offline dlorde

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Re: Is infinity an illusion?
« Reply #145 on: 21/09/2013 01:12:28 »
Quote
so its decimal representation is infinite

So, in common with mathematical infinities in general, it is unbounded, but can never become infinite.
It's value is bounded - e.g., it's between 3.1 and 3.2, but perhaps one could say it is indefinite (I don't know how mathematicians describe such things). It's decimal representation is infinitely long, so unbounded, so it can't be fully expressed that way.

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Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #146 on: 21/09/2013 01:33:06 »
How about an infinite time and dimension that is on the equivalent of a mobius strip. Continuous, joined up and unbounded. You would never get back to the same point even though it is connected.

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Offline yor_on

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Re: Is infinity an illusion?
« Reply #147 on: 21/09/2013 18:40:23 »
This one Dlorde.

""The observer has, ... only the function of registering decisions, i.e., processes in space and time, and it does not matter whether the observer is an apparatus or a human being;"

Observers, do they need a consciousness, and what defines a consciousness?
A arrow?

If I assumed the universe to be a representation of a quantum computer :) Which isn't that far from the idea of multiple universes created as a wave function breaks down, also assuming that this 'universe' contains it all.

Would a observer need to be 'locked' (to be conscious) under a arrow?
How do we define consciousness?
« Last Edit: 21/09/2013 22:09:32 by yor_on »
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Re: Is infinity an illusion?
« Reply #148 on: 21/09/2013 18:55:22 »
Jeffery, as long as we define a arrow, every point of my journey, from birth to death, must be unique. You don't need a Möbius strip for that one. In a four dimensional universe, allowing time to define a position with the other three, everything must be unique. That 'now' experienced something never coming back, unless I assume that the arrow can be played backwards. From that assumption I also must make one more to make it work. The one in where the other three room dimensions has no 'individuality', unless a arrow becomes involved.
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Offline Bill S

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Re: Is infinity an illusion?
« Reply #149 on: 21/09/2013 19:24:48 »
Quote from: dlorde
It's decimal representation is infinitely long, so unbounded, so it can't be fully expressed that way

Quote from: Bill S
On their own, numbers are just concepts in the mind
 

Please don’t think I’m objecting to the use of “infinity” in maths, as long as one realises that they are mathematical "infinities".