The Naked Scientists

The Naked Scientists Forum

Author Topic: Is infinity an illusion?  (Read 68684 times)

Offline Bill S

  • Neilep Level Member
  • ******
  • Posts: 1828
  • Thanked: 12 times
    • View Profile
Re: Is infinity an illusion?
« Reply #25 on: 05/09/2013 22:13:10 »
Quote from: JP
....the idea of an electron orbiting an atom without spiraling into the nucleus....

For a long time that gave me problems; then I, sort of, got my head round the idea that it was the quantization of energy that prevented spiraling.  However, there was still the problem that if the electron was orbiting, it must be accelerating, so where was the energy coming from?  I suppose it's blatant thread drift to talk about it here, but am I right in thinking that we should no longer think of the electron as orbiting, but rather as being in any, or all, of an "infinite" (See! I just brought it back on topic) range of positions at the same time?

 

Offline alancalverd

  • Global Moderator
  • Neilep Level Member
  • *****
  • Posts: 4717
  • Thanked: 154 times
  • life is too short to drink instant coffee
    • View Profile
Re: Is infinity an illusion?
« Reply #26 on: 05/09/2013 23:02:12 »
Yes.
 

Offline Bill S

  • Neilep Level Member
  • ******
  • Posts: 1828
  • Thanked: 12 times
    • View Profile
Re: Is infinity an illusion?
« Reply #27 on: 06/09/2013 14:08:17 »
Great, but does that mean that the electron/wave is stationary, or is that too intuitive for thinking about QM?
 

Offline Bill S

  • Neilep Level Member
  • ******
  • Posts: 1828
  • Thanked: 12 times
    • View Profile
Re: Is infinity an illusion?
« Reply #28 on: 07/09/2013 21:02:25 »
Quote from: JP
In some cases such as the size of the universe, some theorists take it literally.  This is where I hedge my bets since you'd have to come up with a testable hypothesis to distinguish between an infinite universe or not.  As far as I know the question isn't settled. 

I run into a problem here.  If the Universe started at the BB, how could it be infinite?

I have been assured that it could have been infinite from the start.  However, I have yet to find an explanation as to how something infinitesimally small could be infinite.
 

Offline Bill S

  • Neilep Level Member
  • ******
  • Posts: 1828
  • Thanked: 12 times
    • View Profile
Re: Is infinity an illusion?
« Reply #29 on: 07/09/2013 21:23:32 »
While looking at the question of infinity I came across the Hartle-Hawking State.

http://en.wikipedia.org/wiki/Hartle%E2%80%93Hawking_state 

A few questions spring to mind.

Planck epoch = 0 to 10^-43 s.  This is a period of time; therefore time must have started at t=0.  Therefore time exists during the Planck epoch.  Do I have the right impression?

They suggest that “….if we could travel backward in time toward the beginning g of the universe, we would note that quite near what might have otherwise been the beginning, time gives way to space such that at first there is only space and no time.”

Does this statement imply that we would see that the condition of “space and no time” exists after t=0, or that we would be able to see beyond the BB?

 “….that at first there is only space and no time”.

Is this before or after the BB?

If there was a time when there was space but no time, how could this condition change?  Surely time is needed in order to allow change.  If there were a condition in which there were space and no time, there would be only space now, unless some outside influence “created” time.

They propose that “the universe is infinitely finite”!   I’m told I am the one with odd ideas about infinity. 

Is there a difference between “infinitely finite” and “unbounded”?
 

Offline Pmb

  • Neilep Level Member
  • ******
  • Posts: 1838
  • Physicist
    • View Profile
    • New England Science Constortium
Re: Is infinity an illusion?
« Reply #30 on: 08/09/2013 05:37:35 »
Quote from: Bill S
Over 40 years ago I had a long discussion with a maths teacher about infinity.  It culminated in his conceding that the series of whole numbers, although apparently unbounded in both directions, was not an example of true infinity.
Do you still believe this? If so, why? It certainly isn't true. Infinity quite litteraly means without bound. In this case for the sequence (not series) of whole numbers, by which I assume that you're referring to a sequence of numbers which increases without bound, then it's an infinite sequence. I don't understand how anyone could conclude otherwise. Please explain.

Quote from: Bill S
Imagine my elation when I saw, in the New Scientist an article suggesting that some physicists were trying to remove infinity from scientific – and even mathematical – calculations. 
Please post the reference to this article. I'd like to read it. I assume you've read it. Would that be a correct assumption?

Quote from: Bill S
This must raise the question: How can we test for infinity?  Surely such a test would require an infinite amount of information. 
That depends highly on what it is that we're trying to measure as being infinite. Can you give an illustrative example?
 

Offline alancalverd

  • Global Moderator
  • Neilep Level Member
  • *****
  • Posts: 4717
  • Thanked: 154 times
  • life is too short to drink instant coffee
    • View Profile
Re: Is infinity an illusion?
« Reply #31 on: 08/09/2013 10:04:27 »
Great, but does that mean that the electron/wave is stationary, or is that too intuitive for thinking about QM?

The key phrase in your question was "think of". By no means the same as "is".

The wave function eloquently and adequately describes the behaviour of electrons in and around atoms, but an isolated electron  in a vacuum behaves delightfully like a charged particle. What it is, is an electron. 

As for measuring infinities, by definition, you can't.
« Last Edit: 08/09/2013 10:08:21 by alancalverd »
 

Offline Bill S

  • Neilep Level Member
  • ******
  • Posts: 1828
  • Thanked: 12 times
    • View Profile
Re: Is infinity an illusion?
« Reply #32 on: 08/09/2013 18:09:18 »
Quote from: Pmb
Do you still believe this? If so, why? It certainly isn't true. Infinity quite litteraly means without bound. In this case for the sequence (not series) of whole numbers, by which I assume that you're referring to a sequence of numbers which increases without bound, then it's an infinite sequence. I don't understand how anyone could conclude otherwise. Please explain.

I feel sure you did not intend starting an etymological diversion, but if you go back to the Latin root, infinite means without end.   A sequence, such as the whole numbers, has no end, so if it is something that is real, in itself, then it is infinite, within the strict literal meaning of the word, but in both archaic and modern usage the word infinite has acquired wider significance. 

However, the sequence of numbers is something which has no existence other than as a tool for counting objects.  3 x nothing and 300 x nothing are the same thing.  3 and 300 have significance only in respect of the things they enumerate.  3 apples exist, 300 apples exist; an infinite number may exist, but has no real meaning; an infinite number of apples cannot exist in any context that we could recognise as real.

An infinite series (sequence) exists only in the (presumably finite) mind of the mathematician as a useful concept.

I am not questioning the use or value of infinities in mathematics, nor the value, in calculations, of treating infinity as though it were a number.  I simply call attention to the fact that infinity is not a number, and that outside mathematical usage, the concept of infinity is of singular importance in thinking about the origin of the Universe.


 

Offline Bill S

  • Neilep Level Member
  • ******
  • Posts: 1828
  • Thanked: 12 times
    • View Profile
Re: Is infinity an illusion?
« Reply #33 on: 08/09/2013 18:43:10 »
Quote
Please post the reference to this article. I'd like to read it. I assume you've read it. Would that be a correct assumption?

 The article appeared in the New Scientist 17.08.2013.  As far as I am aware, the full article is available on line only to subscribers.  As a non-subscriber, I have access only to a hard copy.  I have not offered to scan and post this as I'm sure it would infringe copyright. 

Your assumption is correct, I have read the article; several times.  Your local library might well have back numbers of NS.
 

Offline Bill S

  • Neilep Level Member
  • ******
  • Posts: 1828
  • Thanked: 12 times
    • View Profile
Re: Is infinity an illusion?
« Reply #34 on: 08/09/2013 20:40:45 »
Quote from: Pmb
That depends highly on what it is that we're trying to measure as being infinite. Can you give an illustrative example?

Surely, whatever we are trying to measure will be either finite, in which case we will, in principle, be able to measure it, or it will be infinite, in which case we will be unable to measure it with any finite measuring tool. 

“Illustrative example”?  Suppose my back garden (yard)  is 20x15m and I want to turf it.  I can measure it, and I will know how much turf to order, and how much this will cost.

Now suppose I decide my garden has infinite length and width.  With only finite measuring instruments, how can I measure it?  How can I know how much turf to order?

You might argue that I need an infinite amount of turf.  True as that might be, mathematically; what does it mean in the real world?

If I go to a supplier and ask for an infinite amount of turf, I suspect I would exit his office very quickly.

However, if he is anxious for business and thinks “I might do well out of this nutter”; how does he work out how much to charge me?  £infinite, perhaps?  What chance does he have of getting that?  In fact, all this example illustrates is that discussing the concept of an infinite amount leads to talking rubbish.


I hope this will prompt you to provide an example of how this “depends highly on what it is that we're trying to measure as being infinite”.  I'm doing my best to see the other side of this, but it's hard going.  :)



 

Offline Bill S

  • Neilep Level Member
  • ******
  • Posts: 1828
  • Thanked: 12 times
    • View Profile
Re: Is infinity an illusion?
« Reply #35 on: 08/09/2013 20:53:13 »
Quote from: alancalverd
The key phrase in your question was "think of". By no means the same as "is".

Although I agree with your statement, I have to say you have lost me.  I think I may have expressed my meaning badly.  I’ll try again.

If we regard the electron as being in any, or all, of an "infinite" range of positions at the same time, do we regard the electron as being in motion, or stationary?  I then wondered if that question, in itself, was too intuitive to have a place in our thinking about QM.

 

Offline alancalverd

  • Global Moderator
  • Neilep Level Member
  • *****
  • Posts: 4717
  • Thanked: 154 times
  • life is too short to drink instant coffee
    • View Profile
Re: Is infinity an illusion?
« Reply #36 on: 08/09/2013 21:24:13 »
Disregarding "regard" for the time being, the wave function does not go to zero anywhere, so there is an infinitesimal probability that whatever it describes could turn up anywhere at all. So in principle, however large you make your search radius, it could be outside.

Turfing the lawn is an interesting question. If you rotate a hyperbola around the y axis you will generate a solid with a finite volume but infinite area, so a finite amount of water will flood a hyperbolic lawn, but you can never buy enough turf to cover it.   
 

Offline dlorde

  • Neilep Level Member
  • ******
  • Posts: 1441
  • Thanked: 9 times
  • ex human-biologist & software developer
    • View Profile
Re: Is infinity an illusion?
« Reply #37 on: 08/09/2013 23:08:30 »
Quote from: Bill S
Imagine my elation when I saw, in the New Scientist an article suggesting that some physicists were trying to remove infinity from scientific – and even mathematical – calculations. 
Please post the reference to this article. I'd like to read it...
This is as close as you'll get without a sub.: Infinity's end: Time to ditch the never-ending story?
It talks about the Tegmark's dissatisfaction with the 'measure problem' (that an infinite multiverse predicts everything), and confuses the size of the observable universe with the size of the universe, concluding that 'there's no room for infinity'. It mentions the problem of being unable to measure to infinite precision/accuracy, and of Wildberger's "rational geometry" that, replaces angles with a "spread" defined as a rational output extracted from mathematical vectors representing two lines in space. It mentions Zeilberger idea that the number line is a loop (i.e. that there is a biggest number that 'overflows' when you add 1!). All in all, it's a bit of a hashed together article about opinions on the fringes, although, to be fair, it does give some space to those who don't have a problem with infinity, or think the problem lies elsewhere.
 

Offline dlorde

  • Neilep Level Member
  • ******
  • Posts: 1441
  • Thanked: 9 times
  • ex human-biologist & software developer
    • View Profile
Re: Is infinity an illusion?
« Reply #38 on: 08/09/2013 23:21:53 »
If we regard the electron as being in any, or all, of an "infinite" range of positions at the same time, do we regard the electron as being in motion, or stationary? 
As I understand it, the wave function doesn't tell you that the electron is everywhere at the same time, but just tells you the probability of detecting it at any given point. What the electron is doing in between measurements is anyone's guess. As the wave function evolves, so the probability of detecting the electron at any given point may change. I expect you may infer, from successive measurements, that an electron has moved, although presumably that involves certain assumptions... 
 

Offline dlorde

  • Neilep Level Member
  • ******
  • Posts: 1441
  • Thanked: 9 times
  • ex human-biologist & software developer
    • View Profile
Re: Is infinity an illusion?
« Reply #39 on: 08/09/2013 23:23:05 »
Turfing the lawn is an interesting question. If you rotate a hyperbola around the y axis you will generate a solid with a finite volume but infinite area, so a finite amount of water will flood a hyperbolic lawn, but you can never buy enough turf to cover it.   
You could paint it green instead, by flooding it with green paint!  ;)
 

Offline JP

  • Neilep Level Member
  • ******
  • Posts: 3366
  • Thanked: 2 times
    • View Profile
Re: Is infinity an illusion?
« Reply #40 on: 08/09/2013 23:29:34 »
Disregarding "regard" for the time being, the wave function does not go to zero anywhere, so there is an infinitesimal probability that whatever it describes could turn up anywhere at all. So in principle, however large you make your search radius, it could be outside.

Just to nitpick--there can be zeros in the wave function, but they are essentially nodes of a standing wave (like the points in a standing wave on a string that don't move).  You're absolutely right that in principle, the wave function does extend out to infinity, though after a point there would be such a small chance of finding the electron that you'll never see it there in practice.
 

Offline Bill S

  • Neilep Level Member
  • ******
  • Posts: 1828
  • Thanked: 12 times
    • View Profile
Re: Is infinity an illusion?
« Reply #41 on: 09/09/2013 18:16:42 »
Quote from: alancalverd
If you rotate a hyperbola around the y axis you will generate a solid with a finite volume but infinite area

I could do with an explanation, here, please.  ???
 

Offline dlorde

  • Neilep Level Member
  • ******
  • Posts: 1441
  • Thanked: 9 times
  • ex human-biologist & software developer
    • View Profile
Re: Is infinity an illusion?
« Reply #42 on: 09/09/2013 21:27:46 »
Quote from: alancalverd
If you rotate a hyperbola around the y axis you will generate a solid with a finite volume but infinite area

I could do with an explanation, here, please.  ???
Torricelli's Trumpet (Gabriel's Horn).
 

Offline alancalverd

  • Global Moderator
  • Neilep Level Member
  • *****
  • Posts: 4717
  • Thanked: 154 times
  • life is too short to drink instant coffee
    • View Profile
Re: Is infinity an illusion?
« Reply #43 on: 09/09/2013 23:50:38 »
Apologies! Of course, you have to rotate it around an asymptote, not the y axis. Pretty neat trick, though, ain't it?
 

lean bean

  • Guest
Re: Is infinity an illusion?
« Reply #44 on: 10/09/2013 13:30:56 »
Quote from: JP
In some cases such as the size of the universe, some theorists take it literally.  This is where I hedge my bets since you'd have to come up with a testable hypothesis to distinguish between an infinite universe or not.  As far as I know the question isn't settled. 

I run into a problem here.  If the Universe started at the BB, how could it be infinite?

I have been assured that it could have been infinite from the start.  However, I have yet to find an explanation as to how something infinitesimally small could be infinite.
Bill, what are you saying was infinitesimally small?  the universe or the observable universe?

 

Offline Bill S

  • Neilep Level Member
  • ******
  • Posts: 1828
  • Thanked: 12 times
    • View Profile
Re: Is infinity an illusion?
« Reply #45 on: 10/09/2013 15:28:53 »
Torricelli’s Trumpet is another example of a mathematical infinity, with which I have no argument.  I have a little trouble understanding how the volume could be finite; unless there is a mathematical “finiteness” similar to a mathematical “infinity”.  I’m very willing to accept that that may just be my lack of understanding, though.
 

Offline Bill S

  • Neilep Level Member
  • ******
  • Posts: 1828
  • Thanked: 12 times
    • View Profile
Re: Is infinity an illusion?
« Reply #46 on: 10/09/2013 15:37:53 »
Quote from: lean bean
Bill, what are you saying was infinitesimally small?  the universe or the observable universe?

We may be slipping into a terminological pitfall, here.  What do cosmologists believe began its existence at the BB; the universe or the observable universe?
 

lean bean

  • Guest
Re: Is infinity an illusion?
« Reply #47 on: 10/09/2013 18:42:31 »

We may be slipping into a terminological pitfall, here.  What do cosmologists believe began its existence at the BB; the universe or the observable universe?

What began its existence at the BB was a determinable space and time universe, before that equations breakdown. I think It's the density of matter/energy that brings about a breakdown of equations (singularity) not whether the universe is finite or infinite in size.
I know you like the following link...  http://www.astro.ucla.edu/~wright/infpoint.html
:)
You may remember my reply to you here..  Reply #24.
http://www.thenakedscientists.com/forum/index.php?topic=48385.0





« Last Edit: 10/09/2013 18:50:10 by lean bean »
 

Offline JP

  • Neilep Level Member
  • ******
  • Posts: 3366
  • Thanked: 2 times
    • View Profile
Re: Is infinity an illusion?
« Reply #48 on: 10/09/2013 21:13:35 »
This comes back to the original point of the post.  We got to the idea of "big bang" because we can only measure the universe where we have measuring devices (for cosmology, the relevant devices are mostly particle colliders and telescopes).  This limits the data we can collect.  From this data, we can figure out physical laws governing the universe.  By extrapolating back in time, we can try to figure out what the universe was like in the past.  This assumes, of course, that laws don't change in time and we're also limited to theories that match our current evidence.  For conditions far outside of what we can observe, we can't be sure our models are correct.

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. 


« Last Edit: 10/09/2013 23:50:09 by JP »
 

Offline Bill S

  • Neilep Level Member
  • ******
  • Posts: 1828
  • Thanked: 12 times
    • View Profile
Re: Is infinity an illusion?
« Reply #49 on: 10/09/2013 22:26:41 »
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.  :)
 

The Naked Scientists Forum

Re: Is infinity an illusion?
« Reply #49 on: 10/09/2013 22:26:41 »

 

SMF 2.0.10 | SMF © 2015, Simple Machines
SMFAds for Free Forums