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Author Topic: Is infinity an illusion?  (Read 68841 times)

Offline niebieskieucho

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Re: Is infinity an illusion?
« Reply #75 on: 14/09/2013 21:40:07 »
I'm sorry to admit that haven't read all the posts of this thread. I have not enough time to do it. Nevertheless, I feel not contaminated by comments of the participants of this topic.
As regards to infinities, they appear in mathematics playing a useful role, but as far as reality is concerned, the idea of infinity vanishes, as in nature everything is finite. You can see mathematician deviding 100 by 13, but you will never see the final result. Infinity is a process of continuation of finite things. In this case 100 is finite number and 13 too and the finite figures can follow one by one without stopping.
In nature everything is finite. We cannot imagine infinite things, thus such in nature do not exist.

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« Last Edit: 14/09/2013 21:45:12 by niebieskieucho »
 

Offline JP

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Re: Is infinity an illusion?
« Reply #76 on: 14/09/2013 22:12:04 »
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]

Yes!  That's the issue at the heart of this thread (and it surprises me it's gone on so long).  I'd hope any physicist would admit that we don't know the answer to the question of whether infinities can exist in nature (examples would be the size of the universe, the infinitesimal sizes of point particles or the infinitesimal division of space if it is continuous).  There's interesting arguments on both sides of the issue, but science is based on evidence, and so far there's nothing convincing either way.  Certainly the lower or upper limit is so small or so large that we can plug infinities into many equations without introducing much error (indeed, the error must be so small that we can't currently measure it or we'd know the answer already!)

What surprises me is seeing so many arguments against infinity based on personal intuition.  Surely, intuition shouldn't guide debates in science.  If we'd relied on intuition, we wouldn't have quantum mechanics or relativity!  Surely it's not intuitive to anyone (at least anyone without serious training in those fields) that particles behave like waves or that time and distance measurements can vary between observers.  Sure, infinity may not be able to exist in nature, but let's admit there's no proof either way, and certainly both equations with and without infinities can match our measurements.  We keep infinities around because it's easier to use calculus than to compute everything in terms of finite differences.
 

Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #77 on: 14/09/2013 22:33:40 »
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.

Yes!  That's the issue at the heart of this thread (and it surprises me it's gone on so long).  I'd hope any physicist would admit that we don't know the answer to the question of whether infinities can exist in nature (examples would be the size of the universe, the infinitesimal sizes of point particles or the infinitesimal division of space if it is continuous).  There's interesting arguments on both sides of the issue, but science is based on evidence, and so far there's nothing convincing either way.  Certainly the lower or upper limit is so small or so large that we can plug infinities into many equations without introducing much error (indeed, the error must be so small that we can't currently measure it or we'd know the answer already!)

What surprises me is seeing so many arguments against infinity based on personal intuition.  Surely, intuition shouldn't guide debates in science.  If we'd relied on intuition, we wouldn't have quantum mechanics or relativity!  Surely it's not intuitive to anyone (at least anyone without serious training in those fields) that particles behave like waves or that time and distance measurements can vary between observers.  Sure, infinity may not be able to exist in nature, but let's admit there's no proof either way, and certainly both equations with and without infinities can match our measurements.  We keep infinities around because it's easier to use calculus than to compute everything in terms of finite differences.

I agree with all of the above. The discussion of infinity can become one of philosophy rather than hard science. In science we also have imaginary numbers which perform useful functions and no one would agree that they occur naturally.
 

Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #78 on: 14/09/2013 23:28:18 »
As my last word on this topic, in relativity we have relativistic beta and gamma which can be used to plot an exponential curve and relates to time dilation, length contraction and energy input. However a lot of physical systems and populations can be described by a logistical s curve which is finite. As most of the physical systems outside of relativity have this behavior then why the exclusivity of relativity? Is there any evidence against the exponential nature? Has anyone even thought about this?
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #79 on: 15/09/2013 18:14:57 »
Quote from: dlorde
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)?

You are, of course, absolutely right.  One of the difficulties inherent in talking about infinity is that our terminology is closely tied to the finite reality we perceive.  Some time ago I asked numerous people what they considered to be the difference between infinite and eternal.  The answers varied in form, but all came down to the same thing: eternity is infinite time and infinity is infinite space, or anything else.  Yet infinity is not a number of anything, including cubic metres of space, and eternity is not a vast expanse of time.  The introduction of time and space into the concept of infinity is, at best, a way of trying to imagine infinity.

Your comment is completely justified, but somewhat unhelpful in terms of discussion. 

Let me rephrase the question.  Can there ever have been nothing?  Or, perhaps:

If there had ever been nothing, could there be something now? 


 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #80 on: 15/09/2013 18:23:15 »
Quote from: Niebieskieucho
as far as reality is concerned, the idea of infinity vanishes, as in nature everything is finite.


I cannot agree that everything in nature is necessarily finite.  Everything we see, we perceive as finite, but that is only our perception, which, as scientists frequently point out, “ain’t  necessarily so”.

 

Offline Pmb

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Re: Is infinity an illusion?
« Reply #81 on: 15/09/2013 18:33:21 »
Quote from: niebieskieucho
In nature everything is finite. We cannot imagine infinite things, thus such in nature do not exist.
That's not necessarily true. At this point in time we don't know either way which is true and which is false.

In a temporally open system the universe will expand forever, the size of it becoming larger and larger with time, increasing without limit. That's the very meaning behind the term infinity.

In a spatially open system space itself is unbounded, the size has no limit.  That's the very meaning behind the term infinity. Also the amount of material in a spatially open system is infinite, the amount of material being unbounded and hence infinite.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #82 on: 15/09/2013 19:53:48 »
 
Quote from: JP
Yes!  That's the issue at the heart of this thread (and it surprises me it's gone on so long).  I'd hope any physicist would admit that we don't know the answer to the question of whether infinities can exist in nature

One of the reasons it has gone on so long is that we tend to talk across one another.  Apart from dlorde’s attempt to brush it under the carpet, who has actually responded to the question: “Can there ever have been nothing”?

Does infinity exist in nature?  I neither know, nor pretend to know.

Does nature exist in infinity? The answer to that depends on the answer to  “Can there ever have been nothing”?
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #83 on: 15/09/2013 20:09:54 »
Quote from: Pmb
In a temporally open system the universe will expand forever, the size of it becoming larger and larger with time, increasing without limit.

Agreed.

Quote
That's the very meaning behind the term infinity.

It is, undoubtedly, the “meaning behind the term infinity” used in that sense (in a language such as English in which correct usage is assessed on the basis of "common usage by educated people" it is always possible to argue for or against a particular usage) but, although unbounded, your for ever expanding universe could never become “infinite”, it will always be a finite, expanding universe.

BTW, in the 21st century it is not as easy to distinguish between educated and uneducated people as it probably was when the above criterion was formulated.

 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #84 on: 15/09/2013 20:12:45 »
Quote from: JeffreyH
The discussion of infinity can become one of philosophy rather than hard science

No comment.   :)
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #85 on: 15/09/2013 20:20:09 »
Quote from: Pmb
In a strong sense of the phrase (and not to come off as too arrogant), we know better.

This is one reason why "hitch-hikers" like me come to people like you, looking for answers, and why we are sometimes disappointed when questions seem to be evaded.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #86 on: 15/09/2013 20:26:12 »
Quote from: Pmb
Also the amount of material in a spatially open system is infinite, the amount of material being unbounded and hence infinite.

You might demonstrate that the amount of material in a spatially open system is unbounded; you might theorise that it could be infinite; but could you prove that it was infinite?
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #87 on: 15/09/2013 20:33:21 »
... Apart from dlorde’s attempt to brush it under the carpet, who has actually responded to the question: “Can there ever have been nothing”?
That wasn't the question I responded to, and rather than trying to sweep it under the carpet, I was hoping you might be able to explain how it made sense at all. You couldn't, so you changed the question to one that makes no more sense to me than the previous one.

How can nothing 'be'?
 

Offline niebieskieucho

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Re: Is infinity an illusion?
« Reply #88 on: 15/09/2013 21:09:33 »
Quote from: Niebieskieucho
as far as reality is concerned, the idea of infinity vanishes, as in nature everything is finite.

Quote
I cannot agree that everything in nature is necessarily finite.  Everything we see, we perceive as finite, but that is only our perception, which, as scientists frequently point out, “ain’t  necessarily so”.
What they consider could be infinite and on what grounds?
Nature (the universe) cannot be infinite, but if scientists claim otherwise, then it would mean that:
Finite matter of the universe is constantly expanding. It’s possible for some time.
Or
The universe is readily infinite. But it’s impossible, as anything real can be closed in a solid. Infinite universe could be compared to a solid without walls. Obviously such solid cannot exist. 
 

Offline niebieskieucho

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Re: Is infinity an illusion?
« Reply #89 on: 15/09/2013 21:22:17 »
Quote from: niebieskieucho
In nature everything is finite. We cannot imagine infinite things, thus such in nature do not exist.
Quote
That's not necessarily true. At this point in time we don't know either way which is true and which is false.
There is no problem to make a diagnosis. If one cannot sketch an infinite universe (no matter scale and accuracy) such universe does not exist (as any real things can be sketched).
Quote
In a temporally open system the universe will expand forever, the size of it becoming larger and larger with time, increasing without limit. That's the very meaning behind the term infinity.
I need not to refer to needless, so-called parameter omega. The universe does not expand. It’s a closed system. I realize that it’s hard to imagine “empty” space ending sharp, but there is no other feasibility. It must end sharp. The problem is, that we cannot see spatial structure from the perspective of physical entities of the micro-world hence such limitation gives the impression that the universe is infinite which is impossible. Such is my stance and I am not going to change it. 
Quote
Also the amount of material in a spatially open system is infinite, the amount of material being unbounded and hence infinite.
As I said earlier it’s only our human (due to natural limitations) perception. In reality space =/= nothing (lack of space). That implies finiteness of the universe, in other words both the universal space and its content.
« Last Edit: 15/09/2013 21:24:55 by niebieskieucho »
 

Offline Pmb

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Re: Is infinity an illusion?
« Reply #90 on: 15/09/2013 21:37:23 »
Quote from: Bill S
Quote from: Pmb
In a strong sense of the phrase (and not to come off as too arrogant), we know better.
This is one reason why "hitch-hikers" like me come to people like you, looking for answers, and why we are sometimes disappointed when questions seem to be evaded.
I'm not entirely sure I understand what you mean here. But if I do then I don't think that you're being exactly fair here, Bill. You wrote
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.
And this is the what I was commenting on. It was a statement which I assumed you meant was true. It wasn't a question. Since I'm a "person of science" I assume that you're referring to people like myself, right? If so then I disagree. I know the difference between a mathematical singularity and a physical one. Other physicists know the difference too. I'll find where in the new version of Black Holes and Time Warps - Second Version by Taylor, Wheeler and Bertschinger talk about the difference. Right now I'lll simply point out where in Gravitation and Spacetime - Third Edition by Ohanian and Ruffini these authors speak of it. Starting on page 325 Chapter 8 is entitled Black holes and gravitational collapse. The title of Section 8.1 is entitled Singularities and pseudosingularities. On page 326 the authors write
Quote
It is important to realize that the Schwarzschild “singularity” at r = rS is not a physical singularity. The “singularity in Eqs. (8.2) and (8.3) is spurious – it is a pseudosingularity or coordinate singularity. It arises from an inappropriate choice of coordinates and can be eliminated by a change of coordinates.
This is a perfect example of a real infinity versus pseudoinfinity. The infinity only arises because of a poor choice of coordinate systems. I don’t know of any relativist who doesn’t know this very elementary fact of differential geometry. So who is it that you’re saying that they don’t know the difference between mathematical infinities and physical infinity? And what is it you yourself mean when you speak of real infinities versus a pseudoinfinity and isn’t it possible that it’s you who don’t know the difference? I’ve asked you to explain them to me above and you went off on something you called a etymological diversion which I had to go look up. I was unable to learn what that phrase meant and forgot to get back to you on that. So what does it mean anyway?

You then later said
Quote from: Bill S
An infinite series (sequence) exists only in the (presumably finite) mind of the mathematician as a useful concept.
Is this what you meant by an infinity that isn’t real? If so then I think that’s misleading. What you really mean is what I’d say a physicist would mean, i.e. non-material infinity. Real to a physicist means something doesn’t exist. Einstein’s field equations only exist in the mind. They can be applied in the material world but that’s different.

Then you write
Quote from: Bill S
I simply call attention to the fact that infinity is not a number,..
I don’t think that any physicist would or has said anything different to you, have they? Nobody could ever claim that I thought infinity was a number since I’ve never thought that. You then write
Quote from: Bill S
…the concept of infinity is of singular importance in thinking about the origin of the Universe.
which I agree with but don’t understand why you posted it.









 

Offline Pmb

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Re: Is infinity an illusion?
« Reply #91 on: 15/09/2013 21:53:47 »
Quote from: Bill S
Quote from: Pmb
Also the amount of material in a spatially open system is infinite, the amount of material being unbounded and hence infinite.

You might demonstrate that the amount of material in a spatially open system is unbounded; you might theorise that it could be infinite; but could you prove that it was infinite?
I seem to have neglected from the beginning that physics does not have as its goal to be able to test whether something can be tested and the results prove something to be true. Science has never worked that way. It's not something that can be done in general. While it might be able to be done in certain cases it cannot be done in general.

It's well known that in physics nothing can ever be rigidly proven. Science has never been able to prove anything. That'd be like saying that the speed of light has been proven in all inertial frames. Since there are an infinite number of inertial frames how could that have ever been done in a finite amount of time?

Also, while one of the meanings of infinite is "without end" that is not the only one. It also means - http://www.merriam-webster.com/dictionary/infinite

Quote
Infinite - (1) having no limits (2) extremely large or great (3) extending indefinitely (4) endless <infinite space> (5)  immeasurably
To me immeasurably[/n] means <infinite amount of matter etc>

Quote from: Bill S
I have not offered to scan and post this as I'm sure it would infringe copyright. 
Oh well. However it'd probably be legal for a one time scan and e-mail. Some people do it all the time when they go to the library and want to share what they read in a magazine article. But no biggy. That probably mostly applies to research articles.

This thread is too long to cover all of these comments so I'll stop now.

 

Offline JP

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Re: Is infinity an illusion?
« Reply #92 on: 16/09/2013 01:39:33 »
Quote from: JP
Yes!  That's the issue at the heart of this thread (and it surprises me it's gone on so long).  I'd hope any physicist would admit that we don't know the answer to the question of whether infinities can exist in nature

One of the reasons it has gone on so long is that we tend to talk across one another.  Apart from dlorde’s attempt to brush it under the carpet, who has actually responded to the question: “Can there ever have been nothing”?

Does infinity exist in nature?  I neither know, nor pretend to know.

Does nature exist in infinity? The answer to that depends on the answer to  “Can there ever have been nothing”?

What scientific reason do you have for saying this?  My point is that much of what's being presented in this thread as obvious fact has no scientific merit.  If you can tell me why, scientifically, "can there be infinity in nature" depends on "can there ever have been nothing?" I can see how the two are related.  (I can see how they're related intuitively, but intuition is a poor guide when dealing with the creation of the universe and possible infinities, and certainly intuition isn't scientific.)

Now, as for the question of whether there could have been nothing, most physicists would say no.  It's hard to really consider the question in terms of current science, though, and may never be possible.  To develop a theory that uses nothing would be so difficult/impossible because it could have no properties, so what would our theory and equations tell us?  The moment we wrote an equation about now "nothing" behaves, it has properties and is no longer nothing.  To write an equation that tells us how the universe comes from "nothing" would also endow "nothing" with properties, hence it isn't nothing.  As far as I can tell, it's a scientific catch-22.  That doesn't mean that "nothing" can't exist, but we're probably not equipped to handle it scientifically yet (and maybe never will be). 
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #93 on: 16/09/2013 04:26:18 »
Quote from: dlorde
That wasn't the question I responded to, and rather than trying to sweep it under the carpet, I was hoping you might be able to explain how it made sense at all. You couldn't, so you changed the question to one that makes no more sense to me than the previous one.

How can nothing 'be'?

Dlorde, I appreciate your input, not just in this thread, but also elsewhere.  I have no intention of insulting your obvious intelligence by accepting your invitation to assume that you failed to understand what I meant by either of those questions.  I am not looking for a battle of words, but a discussion of something I believe is relevant to scientific thought. 

I will infer that you are not really trying to sink the discussion in a see of semantics.

Picking up on your last question, may I ask what "is" when no thing exists?
 

Offline Pmb

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Re: Is infinity an illusion?
« Reply #94 on: 16/09/2013 04:35:16 »
I'd like to give an example from general relativity: Let us consider a spacetime devoid of all matter. Consider two systems S and S' where S is an inertial system and S' a non-iniertial system which is rotating uniformly relative to the first system. Both systems are devoid of all matter and of infinite extent. There is a time depenance relavant here in the absense of matter since the inertio-gravitational field is time depenant. This qualifies as a system devoid of all matter and has a time dependance on it. Is this what one of you were looking for?
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #95 on: 16/09/2013 04:41:36 »
Quote from: Pmb
I'm not entirely sure I understand what you mean here. But if I do then I don't think that you're being exactly fair here, Bill.

Pete, I apologise if my answer offended you, I certainly intended nothing personal.  However, if you were to look back through this and other threads in which infinity has been discussed, I think you will find that almost every point I have tried to make about physical infinity has been countered by arguments involving mathematical infinities.

Quote
I know the difference between a mathematical singularity and a physical one.

Never in question, as far as I am concerned.  I understand that infinity is involved in the concept of singularities, but I am not aware that that is what we were talking about.
 

Offline Pmb

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Re: Is infinity an illusion?
« Reply #96 on: 16/09/2013 04:54:09 »
Quote from: Bill S
Pete, I apologise if my answer offended you, I certainly intended nothing personal. 
No worries my friend. I know that. :)

Quote from: Bill S
However, if you were to look back through this and other threads in which infinity has been discussed, I think you will find that almost every point I have tried to make about physical infinity has been countered by arguments involving mathematical infinities.
I disagree. To me a mathematical infinity is something like f(x) = limit(x->0) 1/x. A physical infinity is limit (r->0) kQq/r  where Q is charge on particle #1, q = charge on particle #2 and k = Coulomb's constant (not exactly sure of name). I think that a lot of people, including yourself, perhaps see both as being only mathematical where I see the former as mathematical since it pertains only to quantities which have a mathematical meaning whereas the second pertains to physical quantities and results in a physical force and the meaning of infinity has its usual meaning.

I'll speak only for myself now: When I say that I know this kind of thing what I'm saying is that I have a different opinion on the definition.
« Last Edit: 16/09/2013 05:00:03 by Pmb »
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #97 on: 16/09/2013 04:55:16 »
Quote from: Pmb
isn’t it possible that it’s you who don’t know the difference?

Yes, it is quite possible.

Quote
I’ve asked you to explain them to me above and you went off on something you called a etymological diversion

Pete, if you would remind me of the context (and post) in which I used the term etymological diversion in response to a question from you I will gladly try to clarify it.

Quote
Real to a physicist means something doesn’t exist.

You have lost me there, Pete.
 

Offline Pmb

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Re: Is infinity an illusion?
« Reply #98 on: 16/09/2013 05:06:23 »
Quote from: Bill S
Quote from: Pmb
isn't it possible that it's you who don't know the difference?
Yes, it is quite possible.
It's funny. I don't like talking to my friends with that tone. Sorry about that, Bill. :(
Quote from: Pmb
I've asked you to explain them to me above and you went off on something you called a etymological diversion.

Quote from: Bill S
Pete, if you would remind me of the context (and post) in which I used the term etymological diversion in response to a question from you I will gladly try to clarify it.
See post #32 on page 2.
Quote from: Bill S
Quote from: Pmb
Real to a physicist means something doesn't exist.
You have lost me there, Pete.
Yeah. Me too! LOL!! I think I meant to say that Real to a physicist means that something exists. I.e. in a sense they're synonyms.
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #99 on: 16/09/2013 12:40:31 »
I will infer that you are not really trying to sink the discussion in a see of semantics.
I'm trying to clarify and make sense what is being talked about, if only for my own understanding, and I think the semantics are central to that understanding.

Quote
Picking up on your last question, may I ask what "is" when no thing exists?
No thing 'is'. The problem for me here is that you're trying to treat an absence, a negation, as if it was something (some thing). But although it's used colloquially as if it were a thing, it's generally used relatively or comparatively regarding the absence of certain groups of things, e.g. "What's in the box? - nothing" means no objects, 'just air', or even 'just vacuum (empty space)'.  If there really was nothing at all in the box, its sides would have to be collapsed together, it would be flat; ironically, in this situation you wouldn't colloquially say "there's nothing in the box", because it isn't really a box when flat - a box always contains something.

So 'nothing' isn't a physical thing, it doesn't exist except as a concept. Physical existence is a property of things. If we're being strict about its meaning, i.e., beyond the colloquial, it seems to me that it doesn't make sense to treat it as something physical.

So a question like "what is there in the complete absence of anything?" can be answered with "nothing" only in a tautological sense, because an absence isn't something that physically exists. I suspect this is partly why physicists like Lawrence Krauss (A Universe From Nothing) don't literally mean 'nothing', but some kind of 'empty' spacetime that makes sense physically.

As I said, it seems to me that the semantics of 'nothing' are crucial to understanding what we're talking about. However, I'm open to be persuaded that my interpretation of the semantics is faulty.



 

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Re: Is infinity an illusion?
« Reply #99 on: 16/09/2013 12:40:31 »

 

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