Originally posted by oxmixmudd
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Strange but True: Infinity Comes in Different Sizes
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Please explain what an uncountable infinity of universes would mean in physical terms.
Again and again, transfinite cardinals are an axiomatic concept. There are abstract mathematical concepts such as the cardinality of the "Reals" (the power of the continuum = c) being that of the power set of the integers, and that of the set of real-valued functions of a real variable = cardinality of the power set of the reals.
But so what?
How would this apply to physical reality?
Is there a reference?
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Originally posted by robrecht View PostAre you sure this is the article you meant to cite here? It does not seem to say that a multiverse is more likely than a universe.
But it does make some very interesting points. Though not definitively so, this point seems to run counter to your view: "The Casimir force is widely cited as evidence that underlying the universe there must be a sea of real zero-point energy. This argument follows from Casimir's analysis and prediction. It is not necessarily true, however. It is perfectly possible to explain the Casimir effect by taking into account the quantum-induced motions of atoms in each plate and examining the retarded potential interactions of atoms in one plate with those in the other.
This point may be interesting to some: "Zero-point energy behaves differently. For ordinary radiation, the ratio of pressure to energy density is w=1/3c2, which is customarily expressed in units whereby c=1, and thus the ratio is expressed as w=+1/3. But for zero-point energy the ratio is w=-1. This is owing to the circumstance that the zero-point energy density is assumed to be constant: no matter how much the universe expands it does not become diluted, but instead more zero-point energy is assumed to be created out of nothing."
In general, the idea that dark energy is in fact zero-point energy is very interesting. So thanks for that. A patent for tapping zero-point energy as a usable source of energy, what an incredible idea!
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Originally posted by shunyadragon View PostNo that is not the reason for the response cited. The question was; If a multiverse exists, what is the nature of the substrate of the multiverse.
It is not counter to my view.
I too have tried to engage you on this particular point before.אָכֵ֕ן אַתָּ֖ה אֵ֣ל מִסְתַּתֵּ֑ר אֱלֹהֵ֥י יִשְׂרָאֵ֖ל מוֹשִֽׁיעַ׃
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Originally posted by 37818 View PostLooking at an infinity being at the decimal point.
...000.000... or ...999.999... being the same infinity.
G64 not infinity ...987.000...
Gn where n is infinity. ...987.000... having no left starting digit. Is a smaller infinity than ...999.999... Infinity.
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Originally posted by robrecht View PostOK. I thought you were using that reference to support this statement of yours: "The belief that there would be only one universe, ours, is an extreme view. Since the more general view of science is that more universes within a multiverse matrix is possible, and more likely."
I too have tried to engage you on this particular point before.
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Originally posted by shunyadragon View PostThe predominate (sic) view in science is that our universe is not unique, it is the view of the multiverse, and the possibility, not certainty that our universe is one of many possible universes. Of course the concept of the multiverse is not proven nor certain. It is simply the dominant view.
And I SERIOUSLY doubt there's a reputable cosmologist that believes that the maths of transfinite cardinals applies to physical reality.
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Originally posted by shunyadragon View PostThe predominate view in science is that our universe is not unique, it is the view of the multiverse, and the possibility, not certainty that our universe is one of many possible universes. Of course the concept of the multiverse is not proven nor certain. It is simply the dominant view.אָכֵ֕ן אַתָּ֖ה אֵ֣ל מִסְתַּתֵּ֑ר אֱלֹהֵ֥י יִשְׂרָאֵ֖ל מוֹשִֽׁיעַ׃
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Originally posted by klaus54 View PostAgain, I've never seen ANY application of transfinite cardinals to physical reality. And according to your example of initial conditions, a countable infinity will also produce every possible arrangement of states according the (countable) infinity of universes. But, I don't understand the no-repeats thingy. Why couldn't one have repeats, or in fact repeats an unlimited number of times?
I can see where this is going though. Can you consider that something might be possible outside the confines of this universe that is not possible within this universe? That's all I'm looking at. I don't think there is anything wrong with my conclusion if the set of initial conditions for a universe derives from an uncountable continua. I'm not trying to say such a continua exists, just what the consequences would be if it does
Also, the standard assumption that in an infinite multiverse there are guaranteed repeats is based on the assumption the set of starting states for a universe is countable, and that the total number of possible states for that universe as it unfolds is finite over finite time due to the quantum nature of its 'basic building blocks'.
Interestingly, IF the number of states for a given universe is (countably) infinite over infinite time, and the number of possible universes is (countably) infinite, then what we have, over infinite time, is the set of all possible arrangements of the elements of a countably infinite set, which is the power set of the countably infinite set, which, as I'm sure you know, makes the cardinality of the multiverse over infinite time 2aleph zero or aleph one.
JimLast edited by oxmixmudd; 02-13-2016, 12:27 PM.My brethren, do not hold your faith in our glorious Lord Jesus Christ with an attitude of personal favoritism. James 2:1
If anyone thinks himself to be religious, and yet does not bridle his tongue but deceives his own heart, this man’s religion is worthless James 1:26
This you know, my beloved brethren. But everyone must be quick to hear, slow to speak and slow to anger; James 1:19
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Originally posted by shunyadragon View PostThe predominate view in science is that our universe is not unique, it is the view of the multiverse, and the possibility, not certainty that our universe is one of many possible universes. Of course the concept of the multiverse is not proven nor certain. It is simply the dominant view.
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Originally posted by oxmixmudd View PostMy point about initial conditions relates, say, to the constants of the universe - speed of light, gravitational constant etc. The properties that create the relationships between these constants do not have to be derived from a countable set. For example, pi, the ratio of a circumference to the diameter, is not a ratio that is found in a countable set of infinite numbers. So my point is that IF the 'constants' of a universe can in fact take on any of an uncountable set of relative value as the potential set of initial conditions for that universe, then each universe could in fact, even over countably infinite time, be a one off, something unique, something that did not repeat fully the expression of any other universe - assuming the number of created universes was countable.
I can see where this is going though. Can you consider that something might be possible outside the confines of this universe that is not possible within this universe? That's all I'm looking at. I don't think there is anything wrong with my conclusion if the set of initial conditions for a universe derives from an uncountable continua. I'm not trying to say such a continua exists, just what the consequences would be if it does
Also, the standard assumption that in an infinite multiverse there are guaranteed repeats is based on the assumption the set of starting states for a universe is countable, and that the total number of possible states for that universe as it unfolds is finite over finite time due to the quantum nature of its 'basic building blocks'.
Interestingly, IF the number of states for a given universe is (countably) infinite over infinite time, and the number of possible universes is (countably) infinite, then what we have, over infinite time, is the set of all possible arrangements of the elements of a countably infinite set, which is the power set of the countably infinite set, which, as I'm sure you know, makes the cardinality of the multiverse over infinite time 2aleph zero or aleph one.
Jim
{ETA: Or maybe not. But we know our (visible) universe has a finite number of states. Why would one posit otherwise for other universes?}
Why posit something, other than for SciFi, for which there is no conceivable physical model?
Also, it seems the boundedness of our visible universe plus the Planck time and length limits it to a finite number of states. Do you think the Planck limitation possibly does not exist in some other universe(s).
Anyway, my main point still stands. Uncountable infinities are abstractions that don't exist in any physical way in our universe. In reality in our universe, every number is finite due to the Planck limitations or in the technology of data storage capacity.Last edited by klaus54; 02-13-2016, 01:38 PM.
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Originally posted by klaus54 View PostI think this would be aleph_0 X aleph_0 = aleph_0 like the cardinality of Q X Q
{ETA: Or maybe not. But we know our (visible) universe has a finite number of states. Why would one posit otherwise for other universes?}
Why posit something, other than for SciFi, for which there is no conceivable physical model?
Also, it seems the boundedness of our visible universe plus the Planck time and length limits it to a finite number of states. Do you think the Planck limitation possibly does not exist in some other universe(s).
Anyway, my main point still stands. Uncountable infinities are abstractions that don't exist in any physical way in our universe. In reality in our universe, every number is finite due to the Planck limitations or in the technology of data storage capacity.
We know that countable and uncountable infinities do correspond to certain mathematical concepts, concepts that have critical application in the real universe. So they are 'real' in an abstract sense. This universe somehow supports the concepts, and yields to them. We also can reason about them in this universe. And in so many ways, they represent or allow us to describe and reason about realities, even if they are not physical realities. They are incredibly useful in reasoning about the real universe. limits is an application of reasoning about countable and uncountable infinities that most certainly have application in the real universe. From proofs of calculus to the concept of the impulse which supports the mathematics of transforms such as the laplace and fourier.
But I'm not arguing you are wrong in terms of this physical universe having some element that can be directly correlated with a physical uncountable infinity. I don't know of one either.
JimMy brethren, do not hold your faith in our glorious Lord Jesus Christ with an attitude of personal favoritism. James 2:1
If anyone thinks himself to be religious, and yet does not bridle his tongue but deceives his own heart, this man’s religion is worthless James 1:26
This you know, my beloved brethren. But everyone must be quick to hear, slow to speak and slow to anger; James 1:19
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Originally posted by oxmixmudd View PostWe often make discoveries by reasoning about possibilities based on what we know and extending into what we don't know. But I run into what I'm running into here often, and I honestly don't understand it. Why do people become annoyed with others speculate about what might be? The only reason not to speculate about what might be - in my mind - is if you already KNOW it can't be. So from my perspective there is nothing to be annoyed about. I don't think what we are discussing represents ignorance or foolishness, I not proposing a new theory, just questing the assumptions surrounding an existing hypothesis that has no physical proof. Don't see what the problem is.
We know that countable and uncountable infinities do correspond to certain mathematical concepts, concepts that have critical application in the real universe. So they are 'real' in an abstract sense. This universe somehow supports the concepts, and yields to them. We also can reason about them in this universe. And in so many ways, they represent or allow us to describe and reason about realities, even if they are not physical realities. They are incredibly useful in reasoning about the real universe. limits is an application of reasoning about countable and uncountable infinities that most certainly have application in the real universe. From proofs of calculus to the concept of the impulse which supports the mathematics of transforms such as the laplace and fourier.Last edited by shunyadragon; 02-13-2016, 02:41 PM.
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