no such thing as "infinity" in the real world (split)

[cladking]

 

 

You use counting numbers because there is nothing between them - guaranteed they have no liasons dangereuse.

 

 

 

I was merely pointing out that the infinity in which you believe extends in an infinite number of directions and their opposite directions as well. There are an infinite number of infinities and, no doubt, an infinite number of types of infinities. All of reality from this perspective is an infintesimal piece of something much larger.

 

It's hardly surprising that such a universe originated from an infintesimal point.

 

Meanwhile reality is so improbable that the odds against it are too large to really understand.

[Strange]

Meanwhile reality is so improbable that the odds against it are too large to really understand.

 

Please show how you calculated this.

 

I would assume the probability of reality is 1. But what do I know.

[cladking]

 

Please show how you calculated this.

 

I would assume the probability of reality is 1. But what do I know.

 

I could elaborate or explain post 17.

 

EVERYTHING has antecedents or pre-existence. A baby can't be born without parents and a grain of sand doesn't emerge into reality full blown. Even the most subtle force requires highly complex and mostly unknowable precedents.

 

If you see events and that which exists to be certainty (100% probability) then why can't anything be predicted in advance? Isn't our inability to predict the outcome of sub-atomic collisions always going to result in an inability to predict the future?

 

What are the odds that my bagel has the exact cellular and chemical composition that it actually has? Could the farmer who first cultivated wheat predict where any specific molecule of a fraction of the grain originated?

 

Perspective always affects what is seen. Metaphysics carefully excludes percieved reality like the nature or existence of a grain of sand but you look at it and then say not only that it exists but that the odds of its existence is a certainty. All of reality is preordained from your perspective. It is because it is because it is.

 

Somehow it seems unlikely that if you didn't get the point of post 17 that this one will be any better. Perhaps you'll at least notice I answered the question this time.

[Strange]

Perhaps you'll at least notice I answered the question this time.

 

If your dictionary defines "calculate" as waffle incomprehensibly, then yes.

[Delta1212]

I'd say the probability that it has the exact makeup that it has is 1.

 

The probability that it was now going to have that exact makeup as of one second ago may be slightly lower. And the probability of it currently having that exact makeup as of a billion years ago is lower still.

 

You can't assign a probability to something happening without some sort of context.

[studiot]

One should be careful about assigning a probability of 1 since its meaning may depend upon context.

 

A) P(E) = 1 on an "a priori" basis implies that E has always occurred and must always occur.

 

B) P(E) = 1 on an empirical basis means that means that E has always occurred (been observed to occur) but does not imply that E will occur in future - hence the common disclaimer in financial investment circles.

 

C) P(E) = 1 on a subjective basis means that we may or may not have any data about past occurrences, but we think it will occur in the future, but this is not a guarantee like A.

Edited April 24, 2016 by studiot

[Delta1212]

That's what I mean, though. Without some kind of context, any probability that you assign to anything is meaningless. You can't project single occurence events backwards or forwards. You can't talk about how many times they happened in the past or how many times they will happen in the future. So you need to define the context more strictly because we can't assume a lot of things about the problem that we could with, for instance, a coin toss.

[studiot]

 

You can't talk about how many times they happened in the past or how many times they will happen in the future

 

That is what Bayes Theorem is all about.

[BiotechFusion]

How about "it's impossible to have an infinite amount of information, mass, energy, momentum or other dimensional unit within a finite region of space-time of a non-zero metric" which also allows us to include technical conditions of the big bang where we supposedly had all the infinite mass and energy of the universe condensed into a point and also allows us to let the universe be infinite in size if it wants.

[Mordred]

Actually that's not quite right. The finite point is only our observable (finite) portion condensed to the smaller than an atom size. It doesn't model the infinite portion, it only models the region of shared causality of our observable portion and how it expands from there

[ajb]

How about "it's impossible to have an infinite amount of information, mass, energy, momentum or other dimensional unit within a finite region of space-time of a non-zero metric"

When we calculate such infinite things then the theory is understood to break down. For example, you get infinite renormalised energy-momentum tensors of quantum fields near CTCs. (In layman terms time machhines seem to break down!)

 

 

 

which also allows us to include technical conditions of the big bang where we supposedly had all the infinite mass and energy of the universe condensed into a point and also allows us to let the universe be infinite in size if it wants.

But this is not right, you have supposed wrong.

Edited April 28, 2016 by ajb

[BiotechFusion]

When we calculate such infinite things then the theory is understood to break down. For example, you get infinite renormalised energy-momentum tensors of quantum fields near CTCs. (In layman terms time machhines seem to break down!)

Infinity isn't a number, you can't count to it, so it's impossible for us to *count* any number of objects that total infinity. If an apparent approach to infinity arises, it doesn't necessarily (or ever) mean that there is physically an infinite amount of something in a finite region of space. Rather, it is a fallacy of the assumption firstly in the model's equivalence to the universe, secondly in the fallacious assumption that infinity is a number that can be obtained and thus thirdly the fallacy that infinity is a "result" of a model. For instance, we can *model* the increase in relative frequency of sound waves of an accelerating object as asymptotically skyrocketing towards infinity as an object approaches the speed of sound. But guess what? We never, ever, ever, ever, ever, ever, ever, ever, ever, ever, ever, ever, ever, ever, ever actually observe a sound wave of infinite frequency and we especially know we don't because the world is still here and the universe still exists, it was not destroyed by that infinite energy sound wave. Just because a function like 1/x approaches +/- infinity doesn't mean 1/0=+/-infinity and this error is exactly why mathematicians leave it as "undefined."

Another example: the inverse square law of gravity. Well, gravity might die out over distance at a rate of 1/x^2 (and something similar with charge), but guess what? Earth doesn't have infinite acceleration due to gravity at its core or anywhere around it or in it.

Yet another example: fusion. Technically, the repulsion between two protons should, according to your reasoning "be infinity" when the protons try to fuse together and come into contact with each other, thus preventing fusion. However, not only do we know fusion is possible, but we know that exact model is wrong and the reality is the repulsion isn't infinite and rather than protons tunnel through each other.

Even yet another example: Photons. Using the model that acceleration=force/mass, you'd come to the conclusion that a photon has "infinite acceleration." Well, we don't see photons accelerating past the speed of light so clearly that's wrong, we only see them being absorbed, emitted, decohered, constructed and scattered.

Even yet another example: posetive feedback loop. In certain systems of equations with solutions in the form of complex exponentials, we can see a positive feedback loop wherein the waves adding together at a certain resonance frequency supposedly producing indefinite constructive interference over time, so we should be able to bounce a few sound waves and destroy the Earth right? Well, again, even with the passage of indefinite time, a finite volume and a finite amount of matter and energy would eventually force that oscillator to become damped and you wouldn't get an infinitely large exponentially growing harmonic oscillation, just something that levels off at a finite amplitude, it's literally like the universe is built to prevent us from ever reaching infinite anything.

 

So, clearly, since infinity isn't an actual number, we can't measure it quantitatively. We can only assume if we choose to that an indefinitely large volume of space has an indefinitely large amount of matter and energy. Since infinity doesn't lie on a number line, it is impossible to count an infinite number of any units of any dimension, and since the basis for which we typically define physical reality is the culmination of dimensions in which space is formed and objects move within, we can't physically observe infinity in any finite region of space. "You can only have infinity if you already started with it," I think that's a pretty decent compromise like in the instance that we assume the universe is indefinitely large which allows infinity to "exist," just not measurably so.

 

Another thing to consider, especially in the case of the sound waves is that infinity usually gives some kind of violation in conservation laws. Just think about it: does it actually make sense that putting a finite amount of force into accelerating an object gives me a sound wave of infinite energy? I suspect the same is true with your quantum models and thus the reality is that due to the quantinization of space, time and pretty much everything, there is a finite maximum amount of energy and momentum and minimum amount of energy and momentum that a particle can have, like for instance Planck time and then dividing by Plank time. Since we can't have any time less time than Planck time and we can't travel less than a Planck length, the maximum speed of matter is probably something around 1 planck length per planck second.

Oh look, wikipedia, what a coincidence that basic logic didn't fail me

https://en.wikipedia.org/wiki/Speed_of_light

"Speed of light: Planck Length per Planck Time: 1"

The speed of light might seem like some barrier of infinity, but it's actually just the smallest possible length traveled in the smallest possible time.

 

 

Edited April 29, 2016 by BiotechFusion

[ajb]

BiotechFusion I am not understanding your point... you basically agree with me.

 

Infinity is not something that one expects to measure. When a physical theory gives an infinite result that is usually seen as the theory breaking down and no longer being a 'good' model for the whole parameter space. You are right that one expects a quantum theory of gravity to possibily regulate the infinites that are found in semiclassical gravity, maybe not.

 

Maybe you simply misunderstood me.

 

 

P.S. Guess what? I know that 1/0 is not equal to infinity. LOL

Edited April 29, 2016 by ajb

[Strange]

Oh look, wikipedia, what a coincidence that basic logic didn't fail me

https://en.wikipedia.org/wiki/Speed_of_light

"Speed of light: Planck Length per Planck Time: 1"

The speed of light might seem like some barrier of infinity, but it's actually just the smallest possible length traveled in the smallest possible time.

 

That seems backward (or at least circular). The Planck time is defined as the time taken for light to travel one Planck length (and there is "no reason to believe that exactly one unit of Planck time has any special physical significance"):

https://en.wikipedia.org/wiki/Planck_time

 

There is currently no evidence that space or time are quantised and my understanding is that in theories which are based on this idea the smallest lengths and times are far smaller than the Planck units.

[ajb]

There is currently no evidence that space or time are quantised and my understanding is that in theories which are based on this idea the smallest lengths and times are far smaller than the Planck units.

Rather general arguments suggest that space-time should have a cell structure known as Planck cells, which should be of the size of Planck volume. But without a full theory of quantum gravity it is hard to say much more.

[BiotechFusion]

 

That seems backward (or at least circular). The Planck time is defined as the time taken for light to travel one Planck length (and there is "no reason to believe that exactly one unit of Planck time has any special physical significance"):

https://en.wikipedia.org/wiki/Planck_time

It seems backwards but it's the way that we define space and time based on the speed of light being invariant. It also says "the Planck length is, in principle, within a factor of 10, the shortest measurable length – and no theoretically known improvement in measurement instruments could change that."

​So, it doesn't have a practical application because we don't use any technology that deals with such a small scale, but in terms of physics, if it's the smallest possible unit of length, that means there are limits to how distance can be traveled by a particle, which also means there are limits to what force a particle can exert, how much energy it can have and so on. But mostly, it is the smallest amount of time that can have any measurable meaning, so why be redundant and have an necessarily complicated theory with infinitely small values below the lowest possible physically relevant value that are impossible to observe? Why don't we just explain everything with god while we're at it since he's impossible to observe too?

 

 

 

There is currently no evidence that space or time are quantised and my understanding is that in theories which are based on this idea the smallest lengths and times are far smaller than the Planck units.

I suppose in terms of empirical data, the real answer is that nobody really knows because there certainly isn't evidence against planck time, we certainly don't have evidence that its possible to have infinitely small mass and infinite small energy, only that they are quantized at some point. But, the possible energies associated with a standard model has a strict correlation to the propagation of electro magnetic radiation, and since the energy of light is a function of frequency, only certain wavelengths of light can exist and thus only certain energies can exist. You could do the math for interpolated frequencies, but they would be meaningless to this universe.

So at this point it's not that Planck time and Planck length have to exist, but rather that you have redundancies in physics, things which are in no way needed for the universe to function as it does when you deal with lengths smaller than a Planck length and Planck time.

Ultimately you have to ask "if matter and energy is quantized, why not space?" It's already validated that light itself is quantized, so does it really make sense to mix and match what we know for sure is a quantized system of matter and energy with another system that can have all sorts of random transcendental scalars?

 

When a physical theory gives an infinite result

But see that's the thing, it never, ever does that, no model does that, infinity cannot be the defined result of any mathematical operation and thus it cannot be the result of any quantitative model. Like I said, you can "approach" infinity in which case looking at empirical data, you will never find we actually obtain infinity, we never see sound wave of infinite frequency, we never see infinite repulsion in atoms, we never see photons accelerating to infinite velocity, a vertical asymtote like that just means we don't have the data to determine the correct, finite value and this is exactly why you don't want to assume that the value an asymtote approaches is the physical value at the asymtotic singularity itself, hence why mathematicians say "undefined" rather than "infinity."

 

You are right that one expects a quantum theory of gravity to possibily regulate the infinites that are found in semiclassical gravity, maybe not.

Again, violation of conservation laws and just common sense, you can't have infinite momentum from a finite amount of mass and force and energy, because ultimately that's what we're dealing with, we don't measure infinitely small mass, we only measure finite and even quantized mass, so any model where something like mass is allowed to become infinitely small and thus produce a vertical asymtote as mass approaches zero is inaccurate, at least if we don't assume to begin with that there are infinitely small particles of infinitely small mass that make up mass-bearing particles. The same concept is true for energy and momentum, we don't observe infinitely small momentum and energy or infinitely big momentum and energy, only finite amounts. Does it really make sense to you that a quantized system of matter and energy could ever give you an infinite amount of any dimensional vector or scalar? It if does, I refer you to the fact that breaking the sound barrier does not destroy the universe with a sound wave of infinite frequency.

 

From our own empirical data, not even considering any sort of mathematics, it would appear infinite anything only exists when you already start with an infinite amount of something as a given, we have never measured an infinite amount of something within a finite region of space or in a finite complexity in the mechanics of our observations.

Edited April 29, 2016 by BiotechFusion

[ajb]

But see that's the thing, it never, ever does that, no model does that, infinity cannot be the defined result of any mathematical operation and thus it cannot be the result of any quantitative model.

You are simply wrong.

 

For example the electron self-energy in classical theory is known to give an infinite result. It maybe that the calculation involves taking some limits, but still you can get 'infinite values' for things within a theory. This as I have said, this usually signals that you are pushing the theory beyond its scope. The curvature singularities in general relativity are also undersood in this way.

 

 

Like I said, you can "approach" infinity in which case looking at empirical data, you will never find we actually obtain infinity....

Who said anything here about empirical data?

 

I agree that one will not measure infinity in any experiment. But that is not what I have been talking about. I have been talking about calculations within physical theoreis that produce infinities for things that you would like to be physical observables. Again, this usually taken as the theory breaking down.

 

 

Does it really make sense to you that a quantized system of matter and energy could ever give you an infinite amount of any dimensional vector or scalar?

You have to look at the calculations carefully. We can and do encounter infinities when looking at various models quantum or otheriwse.

 

 

 

It if does, I refer you to the fact that breaking the sound barrier does not destroy the universe with a sound wave of infinite frequency.

What?

 

 

From our own empirical data, not even considering any sort of mathematics, it would appear infinite anything only exists when you already start with an infinite amount of something as a given, we have never measured an infinite amount of something within a finite region of space or a finite complexity in the mechanics of our observations.

We do not expect to ever measure something as having an 'infinite value'. Everyone here agrees... so what the heck are you trying to argue about?

[BiotechFusion]

You are simply wrong.

It's basic math, infinity cannot be an actual result of a quantitative model, I don't know how else to break it down to you.

 

You are simply wrong.

For example the electron self-energy in classical theory is known to give an infinite result. It maybe that the calculation involves taking some limits, but still you can get 'infinite values' for things within a theory. This as I have said, this usually signals that you are pushing the theory beyond its scope. The curvature singularities in general relativity are also undersood in this way.

Exactly, you start from infinity, you bring something from infinity which isn't a value that you can physically bring anything from and then on top of that you have to take a limit anyway, you can't actually reach infinity even in math. The field of an electron may possibly be allowed to extend indefinitely throughout space but even then it still only propagates at the speed of light. Your fallacy is that you are assuming that a few symbols on paper is reality itself, but any physicist would agree that a model is just a model, the universe is whatever it is independently from what we model it to be. But that's not even the worst of your comment, the worst is that you're ignoring that you were given infinite distance to begin with, which I said is an agreeable compromise. As long as you start with infinity as a given, you can have infinity, but if you do not start with infinity, don't expect to physically create anything remotely resembling an infinity. If you already start out considering the infinite distance of the universe, then of course you're likely going to get some kind of assumption where you are forced to assume some indefinitely large result like your boundary of integration or summation.

Like, for instance, if I start with the assumption that the universe has a non-zero density of matter and energy in proportion to volume, then I assume as a given that the universe is infinitely large, it is only then that I could conclude the universe has an infinite amount of matter and energy.

 

Who said anything here about empirical data?

Me, over and over again, that's the whole basis for this discussion is never actually confirming that an infinite amount of something exists in finite space which is why I said "ok, we can have infinite amount of something if we start off assuming an infinite amount of space..."

 

You have to look at the calculations carefully. We can and do encounter infinities when looking at various models quantum or otheriwse.

Well given a finite system to begin with, no, we encounter seeming vertical asymptotes or finite values that are assumed to occur with the indefinite growth of another value like time, even though we'll never be able to measure an infinite amount of time passing.

 

What?

Exactly what I said, we can *model* the relative changes in frequency of a sound wave as approaching infinity when a moving object approaches the sound barrier, but when an object actually breaks the sound barrier, even though it's a loud sound, it's not a sound of infinite frequency, even though your reasoning would suggest it has to be. Again, not only is infinity not a number, but a model is not reality, a model is just a model and it's something we use to make predictions easy.

 

We do not expect to ever measure something as having an 'infinite value'. Everyone here agrees... so what the heck are you trying to argue about?

Oh, so then you agree that your statement "you get infinite renormalised energy-momentum tensors of quantum fields near CTCs" is wrong? Seems like you're pretty immersed in the idea that we've measured an infinite dimensional value in physical reality despite the fact that infinity doesn't exist on a number line.

Edited April 29, 2016 by BiotechFusion

[ajb]

It's basic math, infinity cannot be an actual result of a quantitative model, I don't know how else to break it down to you.

 

Think about the electrostatic potential of a point like particle as r -> 0.

 

This tells you that it would take an infinite amount of energy to assemble an electron. We know this is wrong as we see electrons! This simply signals that we have pushed classical electrostatics too far and end up with a silly result.

 

Your fallacy is that you are assuming that a few symbols on paper is reality itself...

You are now lying.

 

I have never claimed that physical theoreis 'are' reality. In fact, I keep saying quite the opposite.

 

 

But that's not even the worst of your comment, the worst is that you're ignoring that you were given infinite distance to begin with, which I said is an agreeable compromise.

In our mathematical models this is okay, which is what we are talking about.

 

 

Oh, so then you agree that your statement "you get infinite renormalised energy-momentum tensors of quantum fields near CTCs" is wrong? Seems like you're pretty immersed in the idea that we've measured an infinite dimensional value in physical reality.

Nope... this was a statement about a calculation within semiclassical gravity.

 

 

You seem to like to argue for the sake of it!

[BiotechFusion]

Think about the electrostatic potential of a point like particle as r -> 0.

It doesn't matter for several reasons: One, you're assuming infinite distance exists to begin with. Two, we can't ever measure or test that potential is anything at infinite distance because we can't measure anything at infinite distance. Three, in our standard model, fields propagate at the speed of light, so a charged particle cannot have physical relevance at a distance beyond the length of a light second multiplied by the number of seconds that the particle has been in existence.

Fourthly, it's just a model that works with other models.

 

This tells you that it would take an infinite amount of energy to assemble an electron. We know this is wrong as we see electrons!

Oh no, some precious *model* wasn't a picture-perfect image of reality? How expected.

 

You are now lying.

I wish I was but you're not understanding that everything you're saying is just based off of another model, used to work with results from another model, that's all those tensor fields are, new models to explain other models.

 

In our mathematical models this is okay, which is what we are talking about.

It's actually still not "ok" in math, it's only ok to take a limit, it's really just our own arbitrary abstraction of what infinity is as an object or value that is the basis for our supposedly logical arguments, I was probably being way too generous with that compromise, I shouldn't give people false hope about obtaining infinity like that.

 

Nope... this was a statement about a calculation within semiclassical gravity.

Oh, so then you do admit the fallacy that we measured an infinite amount of a dimensional unit?

 

You seem to like to argue for the sake of it!

You seem to like assuming you solved everything for the sake of it.

 

Even if infinity does exist, we can never measure it as being so, we can only make assumptions from models wherein we take limits to it.

 

See, the problem is you're not actually proving anything. The OP may not be right, we can't really assume infinite anything does or doesn't exist not only because the concept of infinity seems to be outside of our current methodology of reasoning, but even if it did, we wouldn't know it, we wouldn't be able to measure it. The only thing we can do is assume it exists, and that's where your issue comes in: you're using the assumption that infinity exists based on some model as a proof that infinity exists.

Edited April 29, 2016 by BiotechFusion

[Strange]

You seem to be saying that because we can't measure an infinite value in reality that it therefore means that infinity does not exist in mathematics. That is clearly wrong. Infinities occur in many places in mathematics. When that is in a physical theory then it generally means that the theory is no longer applicable.

[Delta1212]

You seem to be saying that because we can't measure an infinite value in reality that it therefore means that infinity does not exist in mathematics. That is clearly wrong. Infinities occur in many places in mathematics. When that is in a physical theory then it generally means that the theory is no longer applicable.

We assume.

[BiotechFusion]

You seem to be saying that because we can't measure an infinite value in reality that it therefore means that infinity does not exist in mathematics. That is clearly wrong. Infinities occur in many places in mathematics. When that is in a physical theory then it generally means that the theory is no longer applicable.

We can have mathematical objects which we arbitrarily label as infinity, but mathematically you cannot have infinity as a result of an operation on a finite number. Infinities don't actually "occur" anywhere in elementary mathematics, it really is that we're just arbitrarily defining it as a mathematical object and abstracting it to elementary algebra and transcendental calculus to try and reconcile some irregularities in our models and even then we still have problems when we do that, we can't ever just "have" infinity, we can only take a limit to it. In a sense, infinity is even more made up than our own number system itself and hence there are people who say "infinity doesn't exist."

So, "does infinity exist?" Well, infinity is just a mathematical object we made up, and even though within math it's not perfect, we'll assume for the sake of this point that it is perfectly abstracted to confines of elementary operations. A reasonable question would follow that,

"If there was no space, time, or anything that physically existed, would a number or mathematics still exist? Can I inherently measure a number on its own without physical representation?"

If yes, then there's a reasonable claim that infinity exists as well.

Edited April 29, 2016 by BiotechFusion

[Strange]

We can have mathematical objects which we arbitrarily label as infinity

 

Not exactly arbitrary.

 

However, there is another thread on exactly this subject already so I don't see any point in rehashing it here. Infinity is well defined in mathematics (even if that is based on choosing some "arbitrary" axioms).

But that is getting off the topic of the the thread which was that infinity doesn't exist "in the real world" (whatever that means).

Edited April 29, 2016 by Strange

[BiotechFusion]

 

Not exactly arbitrary.

 

However, there is another thread on exactly this subject already so I don't see any point in rehashing it here. Infinity is well defined in mathematics (even if that is based on choosing some "arbitrary" axioms).

But that is getting off the topic of the the thread which was that infinity doesn't exist "in the real world" (whatever that means).

Well, does math exist independent from our own construction of it to model reality? Can math ever perfectly model reality or will reality always have a discrepancy from our models?

 

Btw I don't think you deserve a -1, it's a relevant point.

Edited April 29, 2016 by BiotechFusion