Strange but True: Infinity Comes in Different Sizes

[shunyadragon]

Frank - I think we are talking past each other? Do you have a preconcieved notion of what I must believe about the universe/multiverse because of my Christian faith?


Jim

No

[klaus54]

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?

[shunyadragon]

Are 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.

No 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.

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!

It is not counter to my view.

[robrecht]

No 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.

OK. 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.

[shunyadragon]

Looking 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.

Further comment. This type of infinity only exists within a greater temporal or infinite time frame.

[shunyadragon]

OK. 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.

The 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.

[klaus54]

Further comment. This type of infinity only exists within a greater temporal or infinite time frame.

This is your unsupported opinion.

Transfinite cardinality is an abstract not a physical concept.

[klaus54]

The 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.

Science is based on testable evidence not "dominant views".

And I SERIOUSLY doubt there's a reputable cosmologist that believes that the maths of transfinite cardinals applies to physical reality.

[robrecht]

The 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.

As you may recall, I have no objection to this view, but what I have asked you to support in the past is your view that a multiverse is more probable. There are multiple ways of modeling something that might be called a multiverse in a variety of ways, but I'm not sure that 'we' are able to determine the probability of a multiverse vs a universe.

[oxmixmudd]

Again, 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?

My 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 2^{aleph zero} or aleph one.


Jim

[Adrift]

The 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.

The dominant view by who? I thought the multiverse theory was purely hypothetical. If it's the dominant view of astronomers and physicists, do you have any surveys or reputable data to back that up? The only dominant view I'm aware of concerning the origins of the universe is the Big Bang.

[shunyadragon]

This is your unsupported opinion.

Transfinite cardinality is an abstract not a physical concept.

All concepts of infinity are derived as abstract concepts in various math proofs. I am refering to how they would apply in reality IF they existed.

[klaus54]

My 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 2^{aleph zero} or aleph one.


Jim

I 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.

[oxmixmudd]

I 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 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.

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.


Jim

[shunyadragon]

We 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.

I was not annoyed, your hypothetical situation remains unlikely, and weak as klaus54 noted.

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.

The above is a little unclear and needs to explained. First, the universe does not 'somehow support nor yield to them.' Math concepts are derived in the abstract, and than they are used as part of a tool box of math in support hypothesis and theories.