Infinity -just maths or any physical existence?

[Vivek des]

Iam wondering whether 'infinity' has real physical existence or just a mathematical paradox? If it does have a physical existence why don't we come across any quantity which is physically eternal? Someone please help..

 

[phinds]

Iam wondering whether 'infinity' has real physical existence or just a mathematical paradox? If it does have a physical existence why don't we come across any quantity which is physically eternal? Someone please help..

"physically eternal" implies infinite time. Maybe there is no such thing, but that does not preclude the universe from being infinite in size. The universe is the only thing I can think of that could be infinite in size.

Mathematically, using today's models, the singularity at the center of a black hole has infinite density but it is generally believed that this is just a math thing that will go away if/when we get a valid theory of quantum gravity.

 

[arildno]

What is paradoxical about infinity as a mathematical object?
Counter-intuitive in many ways, sure. But paradoxical?

 

[ZapperZ]

Iam wondering whether 'infinity' has real physical existence or just a mathematical paradox? If it does have a physical existence why don't we come across any quantity which is physically eternal? Someone please help..

In many of the material that you use, there are properties in those material in which these infinities occur. The van Hove singularity, especially in the phonon density of states, makes itself known via the various property of the material. Similarly, the singularity in the density of states at the edge of the energy gap in a superconductor influences the property of the material.

BTW, why is singularity a "mathematical paradox"? There's nothing paradoxical about its existence in mathematics.

Zz.

 

[CompuChip]

If you are implying that every mathematical concept should have an occurrence in the real world, I disagree. It feels a bit like saying that since we have an alphabet, any combination of letters should be an English word.

 

[TumblingDice]

Iam wondering whether 'infinity' has real physical existence or just a mathematical paradox?.

That's either too few choices or a loaded question. The concept of infinity in physics goes at least as far back as Aristotle, who distinguished between two types of infinities:

1) Potential infinities, such as all positive integers - 1, 2, 3, ... the 'infinite future', or a potentially infinite universe.
2) Actual infinities, those that are localized/confined, like aspects of a black hole, or the infinite amount of points between any two points on a line in Euclidean geometry.

These are a few examples of infinity that may not fit well into either of the two categories you mentioned.

 

[No-where-man]

What is paradoxical about infinity as a mathematical object?
Counter-intuitive in many ways, sure. But paradoxical?

Interesting, the funny thing is I do not not find this counter-intuitive at all, I also do not find this paradoxical at all as well.

 

[Khashishi]

Plenty of our physical models have infinities. Whether these are real is something that cannot be answered. The models work, and that's all we can say.

 

[Hepic]

You can feel 'infinity'. You just need two mirrors. After put your body between mirrors(the first to show your face,and the second to show your back.),and look yourself. You will see infinite times your body.

 

[CWatters]

There was an article in New Scientist on infinity recently. Unfortunately you need a sub to see it here.. http://www.newscientist.com/article...-end-time-to-ditch-the-neverending-story.html

 

[phinds]

You can feel 'infinity'. You just need two mirrors. After put your body between mirrors(the first to show your face,and the second to show your back.),and look yourself. You will see infinite times your body.

Actually, you won't. If you angle the mirror enough so that you can actually SEE the back of your head the images will go off to the side and eventually run out. If you angle the mirror perpendicular to your view you can only see your face and no views of the back of your head.

 

[arildno]

Interesting, the funny thing is I do not not find this counter-intuitive at all, I also do not find this paradoxical at all as well.

Different kinds of infinities?
That a set is infinite if and only if it exists a bijective mapping between itself and a strict subset of it?

 

[Hepic]

Actually, you won't. If you angle the mirror enough so that you can actually SEE the back of your head the images will go off to the side and eventually run out. If you angle the mirror perpendicular to your view you can only see your face and no views of the back of your head.

Theoritically you can. You have not mirron 180 degrees,but less or more,so you can see your back and the next person,etc...

 

[arildno]

Theoritically you can. You have not mirron 180 degrees,but less or more,so you can see your back and the next person,etc...

Nonsense.
Besides, it would only be a feeling of a COUNTABLE type of infinity, not of an uncountable.

 

[DrGreg]

You can feel 'infinity'. You just need two mirrors. After put your body between mirrors(the first to show your face,and the second to show your back.),and look yourself. You will see infinite times your body.

Even if you had a mirror made of unobtainium that reflected 100% of the light without distortion, because of the finite speed of light you'd need to wait an infinite time to see an infinite number of images.

 

[No-where-man]

Plenty of our physical models have infinities. Whether these are real is something that cannot be answered. The models work, and that's all we can say.

The problem is, that so far, I have not seen any model that represents true infinity.

 

[phinds]

The problem is, that so far, I have not seen any model that represents true infinity.

Define "true infinity"

 

[ZapperZ]

The problem is, that so far, I have not seen any model that represents true infinity.

Huh?

In many of the material that you use, there are properties in those material in which these infinities occur. The van Hove singularity, especially in the phonon density of states, makes itself known via the various property of the material. Similarly, the singularity in the density of states at the edge of the energy gap in a superconductor influences the property of the material.

Did you miss that, or are you saying that those are not "true infinity"?

Zz.

 

[arildno]

Huh?



Did you miss that, or are you saying that those are not "true infinity"?

Zz.

Well.
Isn't it a distinction between a) finding results compatible with an existing singularity, and indeed derivable from regarding it as existent and b) To show the singularity's existence?

 

[ZapperZ]

Well.
Isn't it a distinction between a) finding results compatible with an existing singularity, and indeed derivable from regarding it as existent and b) To show the singularity's existence?

I don't see the distinction. How else do you show the existence of a singularity other than having a set of results that are compatible with the existence of it? How else do you show the existence of superconductivity than having a set of results that are consistent with the existence of superconductivity?

Zz.

 

[arildno]

I don't see the distinction. How else do you show the existence of a singularity other than having a set of results that are compatible with the existence of it? How else do you show the existence of superconductivity than having a set of results that are consistent with the existence of superconductivity?

Zz.

The distinction lies in that showing the actual existence of a singularity (or anything else not directly observable) requires that the (sum total of) effects we DO observe cannot be derivable from any other situation.

It might perfectly well be that this IS indeed, the case with the van Hove singularity, but I certainly think the distinction between compatibility of observations and necessary implication of existence from observations is a valid one.

Not a terribly important distinction, I will admit..
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"How else do you show the existence of superconductivity than having a set of results that are consistent with the existence of superconductivity?"

That any form of non-existence of superconductivity is theoretically incompatible with the results one has, perhaps?

 

[Vivek des]

Thank you everyone! :) even when most of your arguments were out of my knowledge it helped me .. Singularity, infinite time and everything thanks once again.!

 

[ZapperZ]

The distinction lies in that showing the actual existence of a singularity (or anything else not directly observable) requires that the (sum total of) effects we DO observe cannot be derivable from any other situation.

I still don't get it. We ARE still talking about physics, aren't we?

ALL of our models and theories have this type of verification. I mean, how do you show the existence of a quantum critical point, for example? You can't actually sit at that point and say "Ah, we're there!".

The theory shows that there is a singularity. The experiments are consistent with the theory, and even show signatures of such peaks (example: look at the density of states of a superconductor near the gap region). And there are NO other alternative theory in which such singularity does not exist to explain the body of data. What else can you conclude?

Zz.

 

[arildno]

"We ARE still talking about physics, aren't we?"
Sure, but this isn't abstruse philosophy, but is a perfectly valid point in standard maths:
For a trivial example, take the limit value V of a perfectly standard infinite sum.

Just because V is a value you measure, and indeed can predict to measure by adding an INFINITE terms of that sum, doesn't mean that adding a FINITE googoolplex of terms won't give just about V as your result.

Furthermore, as for singularities:
Does it always follow that just by postulating a singularity and get accurate predictions from that (for example, which is standard, modelling the vibrations of a metal bar as the results of a sharp hammer blow by means of the Dirac Delta function therefore prove that the magnitude of the force used was actually infinite, lasting 0 seconds?
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"And there are NO other alternative theory in which such singularity does not exist to explain the body of data. What else can you conclude?"
That IS, indeed, the sufficient criterion after which I asked.

 

[ZapperZ]

"We ARE still talking about physics, aren't we?"
Sure, but this isn't abstruse philosophy, but is a perfectly valid point in standard maths:
For a trivial example, take the limit value V of a perfectly standard infinite sum.

Just because V is a value you measure, and indeed can predict to measure by adding an INFINITE terms of that sum, doesn't mean that adding a FINITE googoolplex of terms won't give just about V as your result.

Furthermore, as for singularities:
Does it always follow that just by postulating a singularity and get accurate predictions from that (for example, which is standard, modelling the vibrations of a metal bar as the results of a sharp hammer blow by means of the Dirac Delta function therefore prove that the magnitude of the force used was actually infinite, lasting 0 seconds?
---------------------------------
"And there are NO other alternative theory in which such singularity does not exist to explain the body of data. What else can you conclude?"
That IS, indeed, the sufficient criterion after which I asked.

I am still missing things here.

The theory contains points with singularity. I mean, one can't just say there is a singularity out of thin air. There is a difference between APPROXIMATING something to be a singularity, versus a theory that has, in it, such singularity. Again, I point to the BCS density of states, quantum critical point, etc. In fact, look at the single-particle spectral function, and figure out under what condition do you get back the beloved Drude model that gives you Ohm's law (hint: something diverges to a singularity for a quasiparticle with infinite lifetime!).

The issue of no other alternative being a sufficient criteria is puzzling. This just isn't a criteria to accept the presence of singularity, but also the criteria for the validity of anything in physics. I didn't argue for the presence of a singularity based on a theory that had other alternative! Look at my starting point: the accept theory contains such a description!

If there are other means of describing the experimental results, then forget about trying to validate the singularity. It is the theory that has problems!

Zz.

 

[arildno]

"
The theory contains points with singularity. I mean, one can't just say there is a singularity out of thin air. There is a difference between APPROXIMATING something to be a singularity, versus a theory that has, in it, such singularity."
I am glad you make this addition, and that it is a NECESSARY FEATURE of the theory in question that such singularities occur, (rather than merely googoolplex numbers).

That is more than sufficient criterion for me to accept their existence when combined with the theory having a high prediction and precision rate.

 

[phinds]

arildno, you have 11,000+ posts. How is it you do not understand how to use the quote button ?

 

[No-where-man]

Define "true infinity"

I was actually hoping that someone will show what kinds of infinity models in mathematics exist so far?
I take hypersphere for an example, which is not truly infinite at all, when you look at it more thoroughly. But, I was hoping someone tell me what other mathematical models exist?

I also do not understand models of point particles, how can they exist if they have no spatial extension, they have a lack of space-if that was the case, no particle would exist no matter how small/tiny it is, even if we talk about points.
A point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context. For example, from far enough away, an object of any shape will look and behave as a point-like object-but that only means that point particles are simply very, very small/tiny, they do have size/diameter/dimension (one dimensional), but they still take up space.
You need a lot of energy to increase the size of such small particles-the last time I read.

 

[No-where-man]

I don't see the distinction. How else do you show the existence of a singularity other than having a set of results that are compatible with the existence of it? How else do you show the existence of superconductivity than having a set of results that are consistent with the existence of superconductivity?

Zz.

Finally, someone, who speaks my language.

 

[TrickyDicky]

Isn't it a distinction between a) finding results compatible with an existing singularity, and indeed derivable from regarding it as existent and b) To show the singularity's existence?

Yes, and it's a clear distinction in science. Not only applicable to singularities. One can only wonder what makes such a straightforward distinction so hard to understand.

 

[AlephZero]

Well.
Isn't it a distinction between a) finding results compatible with an existing singularity, and indeed derivable from regarding it as existent and b) To show the singularity's existence?

Yes, and it's a clear distinction in science.

Really? Please explain how science can "show the existence" of anything whatever, except by "finding results that are compatible with its existence".

The map is not the territory.

 

[No-where-man]

Really? Please explain how science can "show the existence" of anything whatever, except by "finding results that are compatible with its existence".

The map is not the territory.

This reminds me on Copenhagen's school. How can I know that results of the data prove that you (or anyone else) exist behind the computer...
We all know we all exist, but according to Copenhagen's school this is not the case because I'm not observing you and you're not observing-so how can you know I exist behind your computer, and how can I know that you exist behind my computer.
Obviously there is something wrong with this hypothesis, or it needs to be extended, because despite all the experiments show, Moon (and everything else) does exist even when none is observing it.

 

[TrickyDicky]

Really? Please explain how science can "show the existence" of anything whatever, except by "finding results that are compatible with its existence".

The map is not the territory.

No, first please explain how making the distinction quoted in my post contradicts in any way what you write above.

If the first part of your first sentence refers to a) and the second refers to b), the distinction just points out that b) is a necessary condition but not a sufficient condition for a).

 

[CompuChip]

Really? Please explain how science can "show the existence" of anything whatever, except by "finding results that are compatible with its existence".

The map is not the territory.

Well, b) implies a) but generally a) is all we can do :-)