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- Thread starter Vivek des
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"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.

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arildno

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Counter-intuitive in many ways, sure. But paradoxical?

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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.

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CompuChip

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TumblingDice

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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.

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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.

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Khashishi

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CWatters

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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.

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arildno

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Different kinds of infinities?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.

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

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

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arildno

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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.

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DrGreg

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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.

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

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

Define "true infinity"

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

Huh?

ZapperZ said: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.

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arildno

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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?

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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.

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arildno

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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 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.

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?

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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

Zz.

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arildno

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"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.

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.

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"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.

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.

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