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Author Topic: Is infinity a misconception?  (Read 58356 times)

Offline Bill S

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Re: Is infinity a misconception?
« Reply #50 on: 24/09/2014 20:02:59 »
Quote from: Pete
JohnDuffield is a major crackpot - Beware!!!!

The geological cognoscenti said that about Alfred Wegener. 

Many still say it about Warren Carey, but he is still a geologist of considerable stature.
 

Offline Bill S

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Re: Is infinity a misconception?
« Reply #51 on: 25/09/2014 20:01:46 »
In another thread; in response to my saying that there could never have been nothing, otherwise there would still be nothing now; JP pointed out that we could not make this claim because, outside the Universe conditions could exist in which something could come from nothing. He assured me that to substantiate my claim scientifically I would have to provide proof that such conditions could not exist.

Let’s apply this to the infinity argument.

Quote from: alancalverd
……an infinite number of rationals exist between the bounds of 0/1 and 1/1.

Is this a scientifically valid claim? 

How could anyone prove that there was not something that would prevent this from being a physical reality?  Smallest possible divisions, quanta etc? 

Can anyone identify an “infinite” point?   Of course not; in fact that is a ridiculous question.

If a physical infinity exists, it cannot exist within a finite universe – in fact the finite universe would have to exist within the infinite entity.
 

Offline Bill S

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Re: Is infinity a misconception?
« Reply #52 on: 25/09/2014 20:06:45 »
Quote from: evan
For example, relativity has many expressions like 1/√(1-v2/c2)

As v→c, 1/√(1-v2/c2) →∞.

Does 1/√(1-v2/c2) go to infinity, or to 0?
 

Online jeffreyH

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Re: Is infinity a misconception?
« Reply #53 on: 25/09/2014 20:26:17 »
Quote from: evan
For example, relativity has many expressions like 1/√(1-v2/c2)

As v→c, 1/√(1-v2/c2) →∞.

Does 1/√(1-v2/c2) go to infinity, or to 0?

When v^2 = c^2 the square root operates on zero. Within the currently known laws of physics V cannot exceed c so zero would be the limit when velocity is increasing. However we then end up with 1/0 which is undefined. I disagree with this equaling infinity. When v tends to zero the square root then is √(1-0/c^2). Then we have 1-0 and with the square root of 1 being 1 the whole expression is 1/1. So in this situation the limit is 1. We can equate this to multiplying by one which gives us 100% of an original value. This means that as the value tends towards undefined we end up with a decreasing amount of the original value until the mathematics eventually breaks down at undefined.
 

Online jeffreyH

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Re: Is infinity a misconception?
« Reply #54 on: 25/09/2014 20:33:00 »
Let us take a simple equation A*B = C. It follows that A = C/B. What if we set B to zero. A*B = C then becomes A*0 = 0. Now if A > 0 what is the meaning of A = C/B if C is also > 0? In this case and to make sense C has to tend towards zero and equal B when exactly zero. This is why were are missing a component in the relativistic equations. This does not mean that C and B are always equal but they must be equivalent when they reach zero. They must both cross the origin.
 

Offline Bill S

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Re: Is infinity a misconception?
« Reply #55 on: 26/09/2014 15:37:38 »
Jeff (is it OK to call you Jeff), I usually have to substitute numbers for letters to make sure I have grasped algebraic equations. 

In this case I get:

A*B=C     A=C/B     If A=2 & B=0

2x0=0        2=0/0 which makes no sense to me.

After that you lose me.  How do you get from C=0 to C tends towards 0
 

Offline JohnDuffield

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Re: Is infinity a misconception?
« Reply #56 on: 26/09/2014 16:05:46 »
...Let’s apply this to the infinity argument.

Quote from: alancalverd
……an infinite number of rationals exist between the bounds of 0/1 and 1/1.

Is this a scientifically valid claim?
No. Take a look at your ruler. There isn't an infinite number or amount of anything between the 0 and the 1. People who talk about dividing up that distance into some infinite subdivision are getting lost in abstraction. 

How could anyone prove that there was not something that would prevent this from being a physical reality?  Smallest possible divisions, quanta etc?
You can't disprove this sort of thing, just as you can't disprove fairies. 

Can anyone identify an “infinite” point? Of course not; in fact that is a ridiculous question.
It all gets very abstract and very ridiculous very quickly. But when you point this out, some guy who can't point to any supporting scientific evidence starts calling you names.

If a physical infinity exists, it cannot exist within a finite universe – in fact the finite universe would have to exist within the infinite entity.
I agree. There ain't no infinities in nature. None that we know about. And I don't see that changing any time soon.


Quote from: jeffreyH
...However we then end up with 1/0 which is undefined. I disagree with this equalling infinity...
Well said Jeffrey. We talk about infinite time dilation for the hypothetical guy travelling at c, but what it really is, is zero local motion.   
 

Online jeffreyH

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Re: Is infinity a misconception?
« Reply #57 on: 26/09/2014 19:05:24 »
Jeff (is it OK to call you Jeff), I usually have to substitute numbers for letters to make sure I have grasped algebraic equations. 

In this case I get:

A*B=C     A=C/B     If A=2 & B=0

2x0=0        2=0/0 which makes no sense to me.

After that you lose me.  How do you get from C=0 to C tends towards 0

Sorry Bill that was rushed. You are right that when A = 2 then both C and B cannot both be zero. I set A to 2 to show that the only way round the division by zero was for C also to equal zero which then invalidates A. Anyway that was the point I was trying to make. In my view setting a denominator to zero means your value ceases to exist. Whatever the value be it radius, mass or anything else. In calculus this can be used as a limit in determining a derivative but to think of it actually representing a physical value is not at all useful.
 

Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #58 on: 26/09/2014 19:25:47 »
Quote from: JohnDuffield
I agree. There ain't no infinities in nature. None that we know about. And I don't see that changing any time soon.
Yet another ignorant comment again. The self energy of any point charged particle is infinite. See http://quantummechanics.ucsd.edu/ph130a/130_notes/node44.html

The mass/energy density of the universe is uniform so since a certain percentage of that matter consists of hadrons it follows that there are an infinite number of hadrons. All of these are infinite and known to all physicists who know what they're talking about.
 

Online jeffreyH

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Re: Is infinity a misconception?
« Reply #59 on: 26/09/2014 19:41:12 »
Quote from: JohnDuffield
I agree. There ain't no infinities in nature. None that we know about. And I don't see that changing any time soon.
Yet another ignorant comment again. The self energy of any point charged particle is infinite. See http://quantummechanics.ucsd.edu/ph130a/130_notes/node44.html

The mass/energy density of the universe is uniform so since a certain percentage of that matter consists of hadrons it follows that there are an infinite number of hadrons. All of these are infinite and known to all physicists who know what they're talking about.

What does the self energy correction say about the state of the field energy in the immediate vicinity of the electron?
 

Offline Bill S

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Re: Is infinity a misconception?
« Reply #60 on: 27/09/2014 13:17:32 »
Quote from: Pete
Even in classical electromagnetism, if one can calculates the energy needed to assemble an electron, the result is infinite, yet electrons exist. The quantum self energy correction is also infinite although it can be rendered finite if we accept the fact that out theories are not valid up to infinite energies.

Is this not tantamount to saying that we cannot work with infinities unless we modify them in some way; in which case they are not infinite?
 

Offline alancalverd

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Re: Is infinity a misconception?
« Reply #61 on: 27/09/2014 13:43:43 »

Quote from: alancalverd
……an infinite number of rationals exist between the bounds of 0/1 and 1/1.

Is this a scientifically valid claim? 

Interesting question. A hypothesis is scientifcally valid if it is (a) consistently predictive and (b) not disproved by experiment. It also has to be explanatory and consistent with previous observations. But a mathematical hypothesis is subject to absolute proof or disproof. So let's attempt an absolute proof. For any number a/b there exists a number a/(b+1) which is smaller and a/(b-1) which is larger. If b > a then a/b lies in the interval between 0 and 1. For any a there exists at least one  number a+1 > a so for any a I can define an appropriate b > a and hence numbers each side of a/b. There being an infinity of a there must thus be an infinity of a/b. 
 

Offline yor_on

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Re: Is infinity a misconception?
« Reply #62 on: 27/09/2014 14:57:28 »
Assume that for any point in a matrix there can be a defined distance. Then ask yourself how you can define it. By being 'inside' with it, measuring. 'Inside' is equivalent to the universe you're in, measuring on. Inside we need it, it's one of those things making macroscopic values work. It does not state what it should be from any thought up 'outside though. The simple solution to a outside is the idea of a universe as some physical entity, forming for example a sphere, or just a self enclosed barrier. If you instead define a 'outside' as being where distances won't hold anymore, then 'outside' can be thought of as a 'inside' too, but without arrow, and so without form.
=

Using that argument a distance becomes a sub division of another type of 'universe', where infinity loses its meaning, unless you want to define a infinity to anything lacking that arrow (clock). If you do, how will you treat the displacements between two 'ticks' on your clock? Also a question of discreteness.
« Last Edit: 27/09/2014 15:10:03 by yor_on »
 

Offline Bill S

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Re: Is infinity a misconception?
« Reply #63 on: 27/09/2014 16:44:06 »
Quote from: alancalverd
For any a there exists at least one  number a+1 > a so for any a I can define an appropriate b > a and hence numbers each side of a/b. There being an infinity of a there must thus be an infinity of a/b.

"Mathematical ‘existence’ meant only logical self-consistency and this neither required nor needed physical existence to complete it.  If a mathematician could write down a set of non-contradictory axioms and rules for deducing true statements from them, then those statements would be said to ‘exist’.”  John Barrow.

Your statement is a mathematical “truth” which neither requires nor needs physical truth to complete it.
 

Offline Bill S

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Re: Is infinity a misconception?
« Reply #64 on: 27/09/2014 16:49:16 »
Yor_on.  Your last post seemed to say something interesting; I just wish I knew what it was.   :(
« Last Edit: 27/09/2014 16:52:25 by Bill S »
 

Offline alancalverd

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Re: Is infinity a misconception?
« Reply #65 on: 27/09/2014 17:04:49 »

Your statement is a mathematical “truth” which neither requires nor needs physical truth to complete it.


Exactly so. The fact that you would run out of patience long before you ran out of possible subdivisions of the set of rational numbers between 0 and 1 does not however negate the assertion that the set is itself (a) infinite (b) larger than the set of integers and (c) not a continuum.
 

Offline Bill S

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Re: Is infinity a misconception?
« Reply #66 on: 27/09/2014 17:11:27 »
Quote from: Pete
JohnDuffield is a major crackpot - Beware!!!!

If that's based on his posts in this thread, I guess I'm in danger of acquiring the same label.

Crackpots of the world unite,
Our limit is the skies;
Won’t they be pissed if we are right,
And win a Nobel Prize?



 

Offline JohnDuffield

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Re: Is infinity a misconception?
« Reply #67 on: 27/09/2014 17:16:43 »
Yet another ignorant comment again. The self energy of any point charged particle is infinite. See http://quantummechanics.ucsd.edu/ph130a/130_notes/node44.html
Geddoutofit. The electron energy is 511keV. Not infinite. And you can diffract electrons. They aren't point particles. 

The mass/energy density of the universe is uniform so since a certain percentage of that matter consists of hadrons it follows that there are an infinite number of hadrons. All of these are infinite and known to all physicists who know what they're talking about.
What!? It doesn't follow that there's an infinite number of hadrons, they don't have infinite energy. And you don't have a clue what you're talking about.
 

Offline Bill S

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Re: Is infinity a misconception?
« Reply #68 on: 27/09/2014 17:25:57 »
Quote
Exactly so. The fact that you would run out of patience long before you ran out of possible subdivisions of the set of rational numbers between 0 and 1 does not however negate the assertion that the set is itself (a) infinite (b) larger than the set of integers and (c) not a continuum.

Absolutely!  These assertions are correct, but can exist only in the, presumably finite, minds of rational beings. 

A circular square centred on the bisector of the infinite side of a physically impossible triangle can exist in your mind, but, as you indicated, that does not make it a physical reality. 
 

Online jeffreyH

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Re: Is infinity a misconception?
« Reply #69 on: 27/09/2014 18:24:31 »
We pass through grass behush the bush to. Whish! A gull. Gulls. Far calls. Coming, far! End here. Us    then. Finn, again! Take. Bussoftlhee, mememormee! Till thous-endsthee. Lps. The keys to. Given! A way a lone a last a loved a long the


riverrun, past Eve and Adam's, from swerve of shore to bend of bay, brings us by a commodius vicus of recirculation back to Howth Castle and Environs.
 

Offline Bill S

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Re: Is infinity a misconception?
« Reply #70 on: 27/09/2014 20:40:45 »
“I done me best when I was let. Thinking always if I go all goes. A hundred cares, a tithe of troubles and is there one who understands me?"

Then there's the Three quarks for Muster Mark!

And we're back to physics.

 

Offline chiralSPO

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Re: Is infinity a misconception?
« Reply #71 on: 27/09/2014 21:20:30 »
Infinities are very useful mathematical concepts. We can never observe an infinity in the real world, but that does not necessarily mean that there isn't any physical infinity, it is just a restriction on our ability to observe and verify.

Infinitesimals are also very useful mathematically. I am not sure if quantization rules out any possibility of a physical infinitesimal, or just out ability to observe one.

A photon with zero energy would have an infinite wavelength. But again, even if it made sense for such a thing to exist, how could it be observed?
 

Online jeffreyH

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Re: Is infinity a misconception?
« Reply #72 on: 27/09/2014 22:22:07 »
“I done me best when I was let. Thinking always if I go all goes. A hundred cares, a tithe of troubles and is there one who understands me?"

Then there's the Three quarks for Muster Mark!

And we're back to physics.

You are a cut above the rest Bill.
 

Offline Bill S

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Re: Is infinity a misconception?
« Reply #73 on: 27/09/2014 23:11:23 »
Quote from: Jeff
You are a cut above the rest Bill.

I could be a crackpot, though, couldn't I?   ;D
« Last Edit: 27/09/2014 23:15:48 by Bill S »
 

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Re: Is infinity a misconception?
« Reply #74 on: 28/09/2014 00:45:11 »
Quote from: Jeff
You are a cut above the rest Bill.

I could be a crackpot, though, couldn't I?   ;D

I think we all have that potential.  :P
 

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Re: Is infinity a misconception?
« Reply #74 on: 28/09/2014 00:45:11 »

 

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