# Does Infinity exist in nature

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Well Does infinity exist in nature?

I have recently heard blackholes actually slowly die, they somehow radiate energy (I think in gravity waves).

Perhaps Black holes (not the event horizon, the "Actual Stuff") has a real size?

Also the bigbang seems to suggest our universe isnt endless, Just really really really big. So the universe Does not go for infinity.

Theres a Limited Speed, Mass/energy in the universe and Size.

If there is a limit on everything there is a limit on complexity.

Do we realy know of any instances in which infinity does exist, or have we created the concept?

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Well Does infinity exist in nature?

Generally it is believed that you will never measure anything to have an infinite value. So in that sense, infinities do not exist in nature.

Simply put, we can only measure real numbers. Infinity is not a real number.

That said, in a physical theory, that is a mathematical model we can have many non-observable constructs. These maybe infinite. For example, the vacuum energy density can be infinite in quantum field theory*. Only measurable energies are constructed as finite differences.

* It is a nieve calculation, but assuming a continuous structure at all scales etc you can show that the zero-point energy is infinite. In standard approaches it QFT you are then free to redefine the vacuum energy by subtracting off the zero-point energy giving a zero energy denisty.

Do we realy know of any instances in which infinity does exist, or have we created the concept?

Every concept in mathematical physics is man-made. Every concept ever is man-made.

So, in physics the presence of some (measurable) quantity blowing up to infinity is usually seen as the signature of the breakdown of a theory. This means theory is unable to cope with what it is being asked to do.

This can lead to new physics. For example the classical self-energy of an electron infinite. It would take an infinite amount of energy to construct an electron, yet we know they exist. The solution was found by applying quantum ideas to electromagnetic theory.

The presence of curvature singularities in general relativity should be viewed with this in mind. General relativity cannot be complete. There are situations where it does not seem to work. It is possible that quantum effects will remedy this.

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Cheers for the response.

Lol, how do you measure infinity thats a good point, i like that.

But yeh we still stuck with infinity as a man made concept

I want to know it exists or doesnt.

And i find it difficult to seperate infinity from 0, does nothing only exist in concept as well? (the only way i know to express infinity is to use the "number 0" in some form)

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It all starts to get very philosophical and metaphysical quickly.

Zero is a real number and we can measure things to have the numerical value zero. This may of course depend on how we set up our units and measure with with respect to what.

How would you define "exist" in this context?

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At first it might seem like zero has the same problem:

You can't measure "infinity," you can only measure "bigger than we can measure."

You can't measure zero, you can only measure "smaller than we can measure."

However, it's not really the same. As ajb says, zero is a real number, and infinity is not. And the problem in measurement is not actually analogous. With zero it's just a problem of precision. Any physical measurement you make is going to have a degree of precision and a margin of error. You can't measure "exactly zero" with unlimited precision, but you also can't measure "exactly three," for exactly the same reason. With infinity, you just have to say it's at least larger than the largest finite thing you can measure, which is, shall we say, infinitely imprecise.

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0 is a set with no elements.

1 is defined to be the union of 0 and the set that consists of 0 (which is the set with 1 element, zero.) So on and so forth.

Infinity is the set of all elements. Since there is no set within nature that consists of all the natural numbers infinity does not exist in nature.

Simple enough, eh?

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Does infinity exist in nature?

I do not think so. Numbers exist in mathematics which is an abstraction, simplification, and primitivization of nature in the human's mind. Example: you have N apples. It is an approximation to say so. In fact what is implied is that they are similar in all qualities - sizes, colour, etc., i.e., when one counts as an apple any particular apple regardless of difference. As soon as you try to describe the apples more precisely, it becomes insufficient to use only one number for it.

Similarly for all physical laws - they are approximate and primitive. Extrapolated too much, they may bring singularities (which is just an evident discrepancy).

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I may be wrong but I'm fairly certain that when an object moves faster than the speed of sound, the sound waves in front of the object are infinitely dense, so infinity does exist in nature.

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Yes it does, for example In the game of tic tac doe,No one wins ,no matter

how long you play, As far as Our universe goes the are 2 possibillitys,

(1) either our univerce has an abrupt end,or (2) It just keeps going, I believe that there is something supernatural,maybe God< involved here. If anyone here disagreese with me ,then tell me I want to know

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Yes it does, for example In the game of tic tac doe,No one wins ,no matter

how long you play, As far as Our universe goes the are 2 possibillitys,

(1) either our univerce has an abrupt end,or (2) It just keeps going, I believe that there is something supernatural,maybe God< involved here. If anyone here disagreese with me ,then tell me I want to know

I see no need for the supernatural, invoking the supernatural is always a mistake, it's like saying i cannot possibly know that so it must be God, so far every time that has been said it eventually becomes apparent god is not the answer. There are lots of answers to how and why the universe is how it is that do not need anything but math and the human mind to explain it. Of course you are welcome to believe anything you like.

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I may be wrong but I'm fairly certain that when an object moves faster than the speed of sound, the sound waves in front of the object are infinitely dense, so infinity does exist in nature.

This is not correct. What happens when you go twice or three times the speed of sound? Is the air compacted to two or three times infinity?

Infinity, other than as a mathematical representation, has never been conclusively been shown to exist, only very, very large numbers.

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The first is an object moving below the speed of sound. The second is an object moving at the speed of sound. The third is an object moving faster than the speed of sound. The fourth is the sound barrier. Notice how in the second, there are five circles and the sound barrier is tangent to all of them, so there are five waves taking up no space between them. Their density is 5/0... or infinity

Merged post follows:

Consecutive posts merged

The image isn't showing up, so here's a link.

If that doesn't work, here's the URL: http://upload.wikimedia.org/wikipedia/commons/7/7d/Sound_barrier_chart.svg

EDIT: Also, there are such things as larger and smaller infinities.

Edited by benedictusk
Consecutive posts merged.

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wouldn't infinite density make a black hole? Even a single atom at infinite density would be a black hole.

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Generally it is believed that you will never measure anything to have an infinite value. So in that sense, infinities do not exist in nature.

Simply put, we can only measure real numbers. Infinity is not a real number.

That said, in a physical theory, that is a mathematical model we can have many non-observable constructs.

Maybe one can interpret the question wider, and ask wether the real numbers exist in nature?

This questions can be motivated by the observation that if we do not talk about symbolic mathematics, but actual numerical computations in the context of predictions etc, pretty much without exception all our representations of any real number is truncated, and the set of rela numbers is also truncated to a finite set, in a computer for example.

That makes for an interesting reflection also if nature itself, say one proton responding to an electron, if each subsystem can only code finite amount of information, then that may suggest that somehow the continuum models we often use contains a redundancy.

Continuum models, tend to contain an infinite and uncountable set of possibilities. And it seems ambigous to see howto compare two infinite set of possibilities. Usually the only sensible way to do this is with limits, but the choice of limiting procedure rarely connect to physics - maybe they should?

I for one think it's doubtful wether contiuum models has a justified place in a fundamental reconstruction of physics and a theory of QG.

If we admit that real numbers are just a mathematical tool, could it be that, there exists a better mathematical tool with LESS redundancy that we chould use?

Then maybe the infinities that we know to appear in some calculations just wouldn't appear in the first place.

/Fredrik

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IMO infinity is a human concept.

I guess changing the concept you can always get rid of infinity.

Simple geometrical example.

Angle.

_Can be defined by degrees, from zero to 360, making the whole circle.

_Can also be defined as a slope (used to describe the slope of a road): a distance divided by a height. A slope of 8% corresponds approximatively to an angle of 5 degrees (tangent 5~= .08). A slope of 100% is equal to 45 degrees.

And 90 degrees corresponds to a slope infinite.

Here we can easily understand that the concept "slope" is not applicable for all angles. The problem of infinite slope is not a problem of the road, nor a problem of the angle: it is a problem arising from the concept.

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I guess changing the concept you can always get rid of infinity.

Simple geometrical example.

Angle.

_Can be defined by degrees, from zero to 360, making the whole circle.

_Can also be defined as a slope (used to describe the slope of a road): a distance divided by a height. A slope of 8% corresponds approximatively to an angle of 5 degrees (tangent 5~= .08). A slope of 100% is equal to 45 degrees.

And 90 degrees corresponds to a slope infinite.

Here we can easily understand that the concept "slope" is not applicable for all angles. The problem of infinite slope is not a problem of the road, nor a problem of the angle: it is a problem arising from the concept.

The perspective I insinuated above is not cured by this example. If you consider the state space or allowable states. It's infinite regardless of wether you picture angles or slopes.

So the deeper issue of "infinity" is deeper than there mere extension of all finite real numers to include also $\infty$. It has to do with how to measure sets of distinguishable possibilities. Does it make sense to consider an infinite of physically distinguishable states?

This is IMO the more interesting side of the issue, that goes beyond the angle vs slope example you raise.

Now, if you combine this question with the meaning of probability and in particular subjective bayesian probability. Then the question seems to get also physical interpretations that is not just human concepts. Does the action of two interacting systems, really reflect a continuum of distinguishable possibilities or not?

/Fredrik

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Maybe one can interpret the question wider, and ask wether the real numbers exist in nature?

This is an interesting question.

The thing is no-one has ever seen a number. We have seen one apple, two cars, three monkeys, 100 gold coins etc...

So, it is a very reasonable question and the answer I think is no.

Numbers are used for counting. We "see" them as a "map" from collection of physical objects to the real line. We interpret that number as a measure the amount of elements of that collection. (The cardanality of the set more mathematically. Then of course we need to model our physical collection with a mathematical set (or class).)

If you recall the number books you read as a very young child, this process is reversed. Numbers are in effect defined as a measure of the number of elements of a collection of physical objects.

This simple idea already mixes the real world with the mathematical world. We have the physical world as a collection of things and to it we associate a real number in the mathematical world. Numbers, the mathematical world and counting physical objects are deeply intertwined.

This association of physical and mathematical is what theoretical physicists do all the time. It is a source of much confusion.

Can anything else be used? For sure there are other mathematical objects to think about than numbers and many of them do play an important role in physics. However, if one wants to measure something then I feel we are trapped in using real numbers.

There is something very special about real numbers and our physical world. This I believe comes down to the notion of cardanality and counting. In tern this means there is something very special and fundamental about real manifolds.

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I agree it's an interesting question, and about real numbers are not in nature etc.

So to the question, what can we do then?

However, if one wants to measure something then I feel we are trapped in using real numbers.

There is something very special about real numbers and our physical world. This I believe comes down to the notion of cardanality and counting. In tern this means there is something very special and fundamental about real manifolds.

Here I disagree a bit about us beeing trapped.

There is an undeniable utility of real numbers as a means of "continous counting" when it comes to sets so large that the continous view in a certain sense gets simpler and are accurate for most practical purposes, even though in a fundamental sense the the continuum is not quite one-2-one with reality.

But what I think, there are IMO good reasons also to think that there is more here, and there may be a connection between "counting", in particualr "counting evidence" and probability theory and which at a deep level connects to physics. In particular in the foundation of QM, the physical basis of probability is still somewhat unclear. The frequentists interpretation and ensembles of systems are not quite satisfactory, although in some domains it's good enough.

Another issue is to understand what "information" and relative information means, given that this seems to be a fundamental concept to QM. And certaainly here we have a deep connection between QM - information - counting.

One possible subjective bayesian view is that the "counting" could be seen as one system "counting" expected states of fellow systems in it's environment, and that this counting, when combining it with idea of information capacity bounds etc, may yield predictions that is related to constrained cardinality of state spaces.

So one alterantive, to beeing trapped in real numbers, is to try to make a reconstruction of the counting, and during the course get a reconstruction also of information theory that is not based on continuum probability.

After all, if we are to develop a theory of counting, and counting evidence to be used in desicion making in particular, the real numbers are IMO not a natural starting point. The integers are more natural and thus possible "more physical".

I still one can still understand the enormous succes of calculus as introduced by newton and leibnitz in physics, but the reason for that success does not contradict the possibility that this framework isn't of uniersal utility.

But maybe we have a bit lost ourselves in the contiuum formalism due to it's success.

There is a book by ET Jaynes "probability theory - the logic of science" where he by following an idea that he is to argue on counting evidence and rating degrees of belief, and he shows that by independent reasoning he is naturally lead to the koglomorov axioms of probability theoyr.

But very early he just makes an assumption that "degree of belief" is represented by real numbers, so he puts on that the set of possible beliefs forms a continuum! That's something I object to, and I think it's even wrong if you consider the set of possible beliefs as "distinguishable possibilities" to a physical observer/system. It doesn't make sense to consider a "mathematical observer".

/Fredrik

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It sounds like one is thinking about the fundamentals of set theory, foundational mathematics, logic and topos theory. This is outside my area of expertise. However, I do know that people are looking into such things with the reformulation of quantum theory in mind.

Chris Isham is one man that comes to mind here.

Topos theory has also been applied in differential geometry and geometric mechanics, (something else I am interested in) . However, it has yet to become widely known and I am very ignorant of this direction.

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I guess it depends what you are measuring as 'infinity'. Is the universe infinite, or merely a spec of time on the grand scheme of things? Personally, I do not believe anything is 'infinite'

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If we look a bit abstract to the question i think there is proof of infinity in nature. For example the immortal jellyfish - turriopsis nutricula. In theory this creature is immortal thus its lifespan is infinite if the habitat allows it. For me infinity is possible if we are talking about time span and things that last infinitely. But consider this : infinity is too long...something will interrupt the process. I think that the concept of infinity is hard to grasp due to the limits of the human mind. I am open to the concept of theoretical infinity it appeals to me a lot more than nothingness

P.S. This is my first post in these forums i hope you can cope with my English and that my manner of writing is tolerable. Happy to be here and any feedback and suggestions on my posts are welcomed!

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There is no need to look far. You can find infinity between zero and 1, if you wish.

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You can't measure zero, you can only measure "smaller than we can measure."

there are 0 oranges in my fruit bowl.

Merged post follows:

Consecutive posts merged

The first is an object moving below the speed of sound. The second is an object moving at the speed of sound. The third is an object moving faster than the speed of sound. The fourth is the sound barrier. Notice how in the second, there are five circles and the sound barrier is tangent to all of them, so there are five waves taking up no space between them. Their density is 5/0... or infinity

Merged post follows:

Consecutive posts merged

The image isn't showing up, so here's a link.

If that doesn't work, here's the URL: http://upload.wikimedia.org/wikipedia/commons/7/7d/Sound_barrier_chart.svg

EDIT: Also, there are such things as larger and smaller infinities.

this is only a crude representation. As the pressure builds up on the front point, the air itself can no longer be considered using ideal gas approximations and the fluid dynamics becomes more complex. The pressure does not increase to infinity.

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there are 0 oranges in my fruit bowl.

Are you sure? Maybe there is a tiny flake from a previous apple sitting in the bottom of the bowl that you just haven't noticed.

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