Extent of space (APOD 23 Mar 2006)

[Qev]

Why is there a finite number of Planck units of space at any given time, though? Just because something is countable (ie. made up of discrete units) says nothing about whether it extends to infinity.

I'll agree that an initially-finite, expanding universe would approach infinite size over infinite time, but at any given point in time would still be finite in size. However, the universe could quite conceivably have started out being infinite from its inception.

From my understand of quantum mechanics, it states that there is a smallest possible unit for just about everything. I fail to see how that implies that there must be a finite number of said units.

[Chris Peterson]

Infinity is a conceptual limit, it does not exist passed our imaginations.

I disagree. As a language construct, it is generally vague and ill-defined. But mathematically, it is rigorous, and there is no reason to think that in its mathematical senses it doesn't act as a proxy for something that exists in reality.

Quantum mechanics states "Everything" need to be measured in quantum units, at a finite time there is a finite number of planck's lengths in the universe, multiply that number by 10 it remains an integer but is transposed into a conceptual number because it's value doesn't exist in the universe.

Quantum mechanics does not say that. There is no requirement that there be a finite number of any quantum states/particles/lengths.

An infinite universe does not mean that the probability of every possible event is one.

Can you show me to logic this statement is based on?

My assertion is simple: the number of possible events might grow faster than the number of spacetime loci available to host them. That may be true, or it may not- so far, we don't know enough about the Universe to put it to some kind of test. In terms of pure mathematics, infinite spaces can grow at different rates- which is why some limits can be reached, but others cannot. I should point out that if you feel this statement can't be true, it is incumbent on you to falsify it.

[PassionateBomba]

Kovil,

"Infinity ; what a concept.
If the Universe is infinite, would that then indicate that there is no God?"


I think it proves there is. And He is much bigger than infinity. Which would be a term we haven't even conceived yet.

As you have watched these great minds argue how things are or are not, infinity is the premise of the equation they cannot calculate.
You are correct, man cannot create things bigger than himself. He can only stack smaller things onto one another. An aircraft carrier is merely many small things stacked up. In fact, in all of history, man has created nothing. No engine of any kind that can produce more energy than it consumes. For every celebrated creation of man, a blind eye has been turned that much, much, much more was destroyed in the process.

Back to the equation.
Has any of the calculations proved the origin of the Universe, Earth, Life? No. They have only generated hypothesis that in their collective collaboration overwhelms any other explanation, therefore it must be. Except for a few radicals that usually press on.
The moon formed in conjunction with the Earth. Nope, it came from the Earth. Nope, it was captured by the Earth. Nope, it was a collision. Nope, stay tuned. All of these concepts have been accepted as scientific fact, only to be disproved.
In science competition with religion, it stomped its feet to have its theories taught along side the facts. This has grown politically to the point that it is taught at the exclusion of the facts. This is scary because the theories being derived today have at their root, former theories.

This is dangerous because, when based in fact they did bring us the atomic bomb, irreversible pollution, famine, an unprecedented ability to bring ourselves to extinction. The universe in its calculation, brought beauty, life, perfection if you will. That the calculations being used to determine the universe has had the opposite results so far, should indicate even to a primary mind as my own, there is something elementary flawed in the calculation. That is, infinity.

Science says, we use 10% of our brain. If so, how do we know that. Has a brain been used at 100%? So the ability of our brain may also be infinite. As our most advanced thinkers show our primary nature, beckoning us to discover our own origin, we also have the same beckoning for the infinite. I have a hard drive of infinite storage, but my processor can only process a small percentage of that data, theory says, 10%.

You are infinitely more than you think you are, the universe is infinitely more than you think it is. Man armed with his scientifically proven limited ability to calculate, is not even going in the right direction, unless this is a brilliantly disguised effort at destruction.

That the universe is infinitely more than we can collectively imagine, yet it all behaves and exists according to very well established and proven sets of rules, proves beyond any doubt, calculation, concept, or theory; intelligence, ie God is at the helm, and He is infinitely much, much, more than the universe He has created.
Who or what He is, is something that the smartest and the ignorant will one day equally come to find out.

It is all that we can collectively think, times 10. Stay tuned. It will change.
Remember the motivation is power. Discover the basis of the universe you can harness it, control it. Man's creation = 0, Man's cures = 0, a Man's ability to control the thoughts of another man = priceless. And that friend, is the calculable value of infinity. Let he who has an ear, let him hear!

Love always,
PB

[Dr. Skeptic]

Infinity is a conceptual limit, it does not exist passed our imaginations.

I disagree. As a language construct, it is generally vague and ill-defined. But mathematically, it is rigorous, and there is no reason to think that in its mathematical senses it doesn't act as a proxy for something that exists in reality.

Quantum mechanics states "Everything" need to be measured in quantum units, at a finite time there is a finite number of planck's lengths in the universe, multiply that number by 10 it remains an integer but is transposed into a conceptual number because it's value doesn't exist in the universe.

Quantum mechanics does not say that. There is no requirement that there be a finite number of any quantum states/particles/lengths.

An infinite universe does not mean that the probability of every possible event is one.

Can you show me to logic this statement is based on?

My assertion is simple: the number of possible events might grow faster than the number of spacetime loci available to host them. That may be true, or it may not- so far, we don't know enough about the Universe to put it to some kind of test. In terms of pure mathematics, infinite spaces can grow at different rates- which is why some limits can be reached, but others cannot. I should point out that if you feel this statement can't be true, it is incumbent on you to falsify it.

If the universe is infinite it cannot grow, infinity +1 still equals the same number. Do you see why infinity is a hard limit to grasp? Your use of ∞ is trying to state that 2∞≻∞, that is incorrect, a false statement.

If ∞ is an integer, then 1/∞ is a real number thus ≠ to 0. If the probability of an event is 1/∞ at a given time. If time the span of time for the event to take place =∞, then the equation becomes ∞/∞ which does =100%.

As I've stated before:

Take 1 second and divide it into half repeatedly until the smallest unit of time remains. If it can be divided ∞ times the result is 1/∞ single units.

Now take 100 billion years and repeat the process and again the result is 1/∞ units. So 1/∞ = both 1 second and 100 billion years - another false statement because: ∞ =|X|∞ (if |X|≻0)

The same procedure is also applicable to distances eg. 1 cm vs. 1 light year, mathematics requires quantum limits. Stating so, the universe also requires a quantum limit.

The (non)limit of infinity resides as a concept in the human imagination, nowhere else - along with "love" and "ugly" ... non-measurable concepts.


If the universe is infinite in size and/or age, math is an invalid tool to measure it.

[Chris Peterson]

If the universe is infinite it cannot grow, infinity +1 still equals the same number. Do you see why infinity is a hard limit to grasp? Your use of ∞ is trying to state that 2∞≻∞, that is incorrect, a false statement.

Sorry, but you don't understand infinity. It isn't a number. You can't apply mathematical operations to it. Your examples of adding to infinity, or dividing it into some number, are meaningless.

Mathematically, a space can have infinite volume and be expanding. Whether such a mathematical construct has a physical analog in the Universe is unknown, but hasn't been demonstrated to be impossible.

[kovil]

Energy, that which is neither createable nor destroyable . . . Energy truly is the Infinite !


In a tangential direction of thought; space, time and their inhabitant, energy, is studied here. (several equations of interest - see part 2)

http://www.journals.uchicago.edu/doi/pdf/10.1086/425155


The Astrophysical Journal, 616:643–668, 2004 December 1
# 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A.


THE COSMIC ENERGY INVENTORY
Masataka Fukugita
Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540; and Institute for Cosmic Ray Research,
University of Tokyo, Kashiwa 277-8582, Japan
and
P. J. E. Peebles
Joseph Henry Laboratories, Princeton University, Jadwin Hall, P.O. Box 708, Princeton, NJ 08544
Received 2004 June 3; accepted 2004 Auggust 9

ABSTRACT
We present an inventory of the cosmic mean densities of energy associated with all the known states of matter
and radiation at the present epoch. The observational and theoretical bases for the inventory have become rich
enough to allow estimates with observational support for the densities of energy in some 40 forms. The result is
a global portrait of the effects of the physical processes of cosmic evolution.

- - -

part 2

The current best value for the distance to the Galactic center is
R0 ¼ 7:94 0:42 kpc


velocity corrected for the solar proper motion is our adopted value of the circular speed of the Milky Way at the solar circle,
0 ¼ 234 13 km s1:


we estimate that the maximum rotation velocity of the Milky Way is Vmax ¼ 1:030 ¼ 241 13 km s1.

Identifying Vmax ¼ Vrot, we find
W20(MW) ¼ 502 30 km s1:


- - -

Appologies that the equations did not transfer well, (hasta la Vista baby, MSWindows); guess ya'll just have to click the link and read the 26 page original, or scan it a bit. The good part is at the end, the Appendix, and a great References section for future reference to some classic papers.

This is all standard mainstream thinking, but there is still good value in many of its thoughts, even if one is not mainstream in their perspective.

[Case]

Energy, that which is neither createable nor destroyable . . . Energy truly is the Infinite !

If a quantity of something is neither increased nor decreased, then it is finite, isn't it? At least a constant quantity in itself is no reason to presume infinity.

In a tangential direction of thought; space, time and their inhabitant, energy, is studied here: The cosmic energy inventory.

Very tangential. No idea where you're going with this, though.

(several equations of interest)
part 2
The current best value for the distance to the Galactic center is R₀ = 7.94 ± 0.42 kpc
Our adopted value of the circular speed of the Milky Way at the solar circle, Ɵ₀ = 234 ± 13 km s⁻¹
Estimated maximum rotation velocity of the Milky Way is Vmax = 1.03 Ɵ₀ = 241 ± 13 km s⁻¹.
Identifying Vmax = Vrot, we find W₂₀(MW) = 502 ± 30 km s⁻¹

What is W₂₀, why do you find it so spectacular and how does it fit in with the current discussion?

This is all standard mainstream thinking, but there is still good value in many of its thoughts, even if one is not mainstream in their perspective.

Again, how does it fit in with the current discussion? I'm no expert in the field, so maybe I'm missing something, but I don't see the relevance yet.

[Dr. Skeptic]

If the universe is infinite it cannot grow, infinity +1 still equals the same number. Do you see why infinity is a hard limit to grasp? Your use of ∞ is trying to state that 2∞≻∞, that is incorrect, a false statement.

Sorry, but you don't understand infinity. It isn't a number. You can't apply mathematical operations to it. Your examples of adding to infinity, or dividing it into some number, are meaningless.

Mathematically, a space can have infinite volume and be expanding. Whether such a mathematical construct has a physical analog in the Universe is unknown, but hasn't been demonstrated to be impossible.

As Spock would say, " Your statement is illogical"

Sorry, I do understand the non-limit of Infinity. Your response contradicts itself, if a non-limit of infinity is reached it cannot expand. Limitless cannot expand, that is exactly what I mean when stating the limit infinity x 2 does not change its value. In an equation where 10 is a limit it can be multiplied by 2 for a limit of 20, because infinity isn't an integer a mathematical limit doesn't apply. For the size of the universe to be expanding it needs to be given a value measured as an integer, thus, for the universe to expand it must be finite.

Does any one else what to share an opinion on this?

[Chris Peterson]

Sorry, I do understand the non-limit of Infinity. Your response contradicts itself, if a non-limit of infinity is reached it cannot expand. Limitless cannot expand, that is exactly what I mean when stating the limit infinity x 2 does not change its value.

You are trying to use language to describe mathematics, and it doesn't work well. "[T]he limit infinity x 2 does not change its value" doesn't mean anything, or at best, it can mean any number of things. "Infinity" is not a number.

As I said, a space can be infinitely large and expanding. Two spaces can both be infinitely large, and one can have greater volume than the other. A one-dimensional space of infinite size would be all real numbers from negative infinity to infinity (that does not mean that the largest number in that space is infinity!). Another would be all the integers from negative infinity to infinity. The real number space is larger. You can apply a transform to either, essentially multiplying each value by a constant at a regular clock rate. That makes the space expand. It is an infinite space, growing larger.

There is no basis for saying that the Universe isn't behaving this way (but there are currently unfalsified cosmological arguments for a variety of contradictory possibilities).

[Qev]

Does any one else what to share an opinion on this?

I already have, but Chris is explaining it a lot better than I ever could.

[Dr. Skeptic]

The way I see it:

Infinity implies no limit or a non-existent limit.

Expanding implies an increase in the limit.

How can a limit that does not exist increase?

Only numbers can increase and infinity is not and does not attempt to imply a number.

It cannot be both ways. Infinity is like "compassion", it only exists as a concept in the human mind. In math, infinity can be approached as a limit yet not obtainable, to reach infinity would requires defining it as an integer which is contradiction in logic. Using infinity as an integer (as your statement suggests by proclaiming the "size" of the universe) is a violation of math.

The Planck's Length is the smallest measurable unit, anything that doesn't reside within the quantum value of a Planck's length does not reside in the measurable universe. There needs to be a finite number of Planck's Lengths for math to be a valid measuring tool. Saying that, the number of Planck's lengths does not need to be static, only an integer.

[Chris Peterson]

Infinity implies no limit or a non-existent limit.
Expanding implies an increase in the limit.
How can a limit that does not exist increase?

"No limit" comes close to making sense mathematically. But note that "no limit" is a condition, not a noun. "Expanding implies an increase in the limit" is where you have gone wrong. There is no substantive limit here.

It cannot be both ways. Infinity is like "compassion", it only exists as a concept in the human mind.

I see no basis for that statement. It is a philosophical position, not a physical or mathematical one. The fact that the human mind can't fully grasp the concept of infinity in a physical way does not mean that something physical- the Universe- can't be infinitely large.

The abstract "infinity" might be seen as a concept. "Infinitely large" is not.

In math, infinity can be approached as a limit yet not obtainable, to reach infinity would requires defining it as an integer which is contradiction in logic.

That is simply untrue. When you are working with mathematical limits, "infinity" can, and often is reached. That's basically what it means to have a converging limit! This does not require treating infinity as an integer, or any other kind of number.

The Planck's Length is the smallest measurable unit, anything that doesn't reside within the quantum value of a Planck's length does not reside in the measurable universe. There needs to be a finite number of Planck's Lengths for math to be a valid measuring tool.

I fail to see what the possible existence of a minimum length unit in the Universe has to do with anything. Note that the "measurable Universe" is finite, so naturally there would be a finite number of spatial quanta. The entire Universe, however, can be infinite, contain an infinite number of spatial quanta, and math continues to work just fine.

[Pete]

There needs to be a finite number of Planck's Lengths for math to be a valid measuring tool.

Kind of like how there needs to be a finite number of integers for math to be a valid measur... oh, wait.

[makc]

The way I see it:

Infinity implies no limit or a non-existent limit.

Expanding implies an increase in the limit.

How can a limit that does not exist increase?

every patch of space has its finite volume and diameter, so they can expand by some finite value at a time, no problems with that, right? now, infinite number of such patches added together - an infinite universe - would expand infinitely fast.

[Dr. Skeptic]

Well put Makc.

I see no basis for that statement. It is a philosophical position, not a physical or mathematical one. The fact that the human mind can't fully grasp the concept of infinity in a physical way does not mean that something physical- the Universe- can't be infinitely large.

The abstract "infinity" might be seen as a concept. "Infinitely large" is not.

You can conceive infinity but it can't be measured, it can't be divided, it can't be added to, it can't be put on paper, it cannot be placed in a ratio, it cannot manipulated by integers in any way - its simply the intellectual concept "If there is no limit". Quantum mechanics has set limits to the large and small of the universe including its age, if you would like to pose your evidence where infinity resides I'm open to listen.

[Chris Peterson]

You can conceive infinity but it can't be measured, it can't be divided, it can't be added to, it can't be put on paper, it cannot be placed in a ratio, it cannot manipulated by integers in any way - its simply the intellectual concept "If there is no limit". Quantum mechanics has set limits to the large and small of the universe including its age, if you would like to pose your evidence where infinity resides I'm open to listen.

Quantum mechanics has nothing at all to say about either the size or age of the Universe. "Infinity" is pretty meaningless in this conversation; "infinite" is not.

The simple fact is that no cosmologist will deny the possibility that the Universe is infinite in extent, even if they don't consider it the most likely scenario. Nothing in physical or mathematical theory prevents it. It's also the case that this will probably never be settled by observation, since the majority of the Universe, infinite or not, lies outside the observable Universe.

[Dr. Skeptic]

You can conceive infinity but it can't be measured, it can't be divided, it can't be added to, it can't be put on paper, it cannot be placed in a ratio, it cannot manipulated by integers in any way - its simply the intellectual concept "If there is no limit". Quantum mechanics has set limits to the large and small of the universe including its age, if you would like to pose your evidence where infinity resides I'm open to listen.

Quantum mechanics has nothing at all to say about either the size or age of the Universe. "Infinity" is pretty meaningless in this conversation; "infinite" is not.

The simple fact is that no cosmologist will deny the possibility that the Universe is infinite in extent, even if they don't consider it the most likely scenario. Nothing in physical or mathematical theory prevents it. It's also the case that this will probably never be settled by observation, since the majority of the Universe, infinite or not, lies outside the observable Universe.

Sorry, it has everything to do with the size and age of the universe, I think you might need to re-assess your perception of how all the pieces of the universe fit together, a model that allows for empirical data to co-exist with infinity relies on over simplified and contradictary science.

The universe cannot be infinite, (implying static) and expanding at the same time. I'm not limiting the logic to the Zeno's Paradox senario, all though it helps, mostly on the principles of entropy and why our universe is not a homogeonous haze of "stuff" as entropy would predict injecting infinity into the equation.

[Chris Peterson]

The universe cannot be infinite, (implying static) and expanding at the same time.

Infinite does not in any way imply static.

[Qev]

An infinite universe can expand just fine. 'Expansion' is simply an increase in distance between any two points over a period of time. The distance increases, and the universe continues to be infinite. There's no such thing as 'infinity pressure' closing in on everything and preventing it from expanding. Just because this isn't intuitive doesn't mean it isn't the case.

You keep saying that quantum mechanics somehow outlaws an infinite universe, but can you provide a precise explanation of how it outlaws this? Without referencing mathematically invalid constructions like 1/∞?

[craterchains]

, , , or in other words, "That dog won't hunt."

[Dr. Skeptic]

An infinite universe can expand just fine. 'Expansion' is simply an increase in distance between any two points over a period of time. The distance increases, and the universe continues to be infinite. There's no such thing as 'infinity pressure' closing in on everything and preventing it from expanding. Just because this isn't intuitive doesn't mean it isn't the case.

You keep saying that quantum mechanics somehow outlaws an infinite universe, but can you provide a precise explanation of how it outlaws this? Without referencing mathematically invalid constructions like 1/∞?

1/∞ is exactly why the universe cannot be infinite.

As Makc stated:

every patch of space has its finite volume and diameter, so they can expand by some finite value at a time, no problems with that, right? now, infinite number of such patches added together - an infinite universe - would expand infinitely fast.

I will add, the rate of expansion would also increase exponentionally at an infinite rate. Infinity cannot represent anything in the natural world- its nosensical to try.

[Dr. Skeptic]

The universe cannot be infinite, (implying static) and expanding at the same time.

Infinite does not in any way imply static.

Then I would like you to explain to me the mechanics on how you can increase the limit on a limitless value - I can't see it.

Quantum mechanics and the string theory can explain why the universe doesn't need to be infinite and why it needs a limit, also why these limits exist.

Note: Space/Time cannot exist without Mass/gravity, Space/Time doesn't need to infinite if Mass/Gravity isn't.

[Qev]

1/∞ is exactly why the universe cannot be infinite.

1/∞ makes about as much mathematical sense as 1/pomegranate. ∞ is not a number, you cannot divide 1 by ∞. And you still haven't provided an explanation of exactly why quantum mechanics supposedly invalidates an infinite universe.

As Makc stated:

every patch of space has its finite volume and diameter, so they can expand by some finite value at a time, no problems with that, right? now, infinite number of such patches added together - an infinite universe - would expand infinitely fast.

I will add, the rate of expansion would also increase exponentionally at an infinite rate. Infinity cannot represent anything in the natural world- its nosensical to try.

There's nothing wrong with that sort of expansion in an infinite universe, though. As the distance between two objects goes towards infinity, the rate of expansion between them does so exponentially. Why is this a problem? There's no fundamental limit to how quickly spacetime can expand.

Then I would like you to explain to me the mechanics on how you can increase the limit on a limitless value - I can't see it.

It sounds like you're arguing that 'infinity' is some fixed, very large value; that because the universe is infinite, there's somehow 'no room' for the universe to expand. It isn't like that. It's infinite. It has no upper bound. This doesn't restrict expansion in any way.

(Bear in mind that I'm not saying the universe is infinite, because we just don't know for sure. The current best theories seem to indicate that it is, though.)

[Chris Peterson]

Then I would like you to explain to me the mechanics on how you can increase the limit on a limitless value - I can't see it.

I don't know what to say, except that you need to review a first year calculus text. You don't seem to understand either limits, nor the mathematical meaning of infinity. This discussion is nothing more than philosophy without a common mathematical language, and that is clearly lacking here.

[Dr. Skeptic]

Then I would like you to explain to me the mechanics on how you can increase the limit on a limitless value - I can't see it.

I don't know what to say, except that you need to review a first year calculus text. You don't seem to understand either limits, nor the mathematical meaning of infinity. This discussion is nothing more than philosophy without a common mathematical language, and that is clearly lacking here.

I'm fully aware of the definition of infinity, infinity is simply no limit. Equations using infinity extrapolate "As the limit of infinity is approached". Infinity in no way suggests an empirical value, stating the universe is infinite is doing just that, by stating its expanding is implying an empirical value: Size of the universe = X, the rate of expansion is Y, time = t

delta X = XYt

What happens if any of these values are assigned infinity?

How can you insert infinity as a limit in a valid equation to define the rate of expansion in the above equation?


Empirical measurements of the universe are meaningless if the universe is infinite.

If the "Whole" cannot be measured, how can a "Part" be measured based on the same measuring criteria?

Note: Double standards are not allowed in physics.