Parallel Universes?

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Stranger that fiction: parallel universes beguile science
by Annie Hautefeuille
Sun Dec 30, 2007

Is the universe -- correction: "our" universe -- no more than a speck of cosmic dust amid an infinite number of parallel worlds?

A staple of mind-bending science fiction, the possibility of multiple universes has long intrigued hard-nosed physicists, mathematicians and cosmologists too.

We may not be able -- as least not yet -- to prove they exist, many serious scientists say, but there are plenty of reasons to think that parallel dimensions are more than figments of eggheaded imagination.

The specter of shadow worlds has been thrown into relief by the December release of "The Golden Compass," a Hollywood blockbuster adapted from the first volume of Philip Pullman's classic sci-fi trilogy, "His Dark Materials".

In the film, an orphaned girl living in an alternate universe goes on a quest, accompanied by an animal manifestation of her soul, to rescue kidnapped children and discover the secret of a contaminating dust said to be leaking from a parallel realm.

Talking bears and magic dust aside, the basic premise of Pullman's fantasy is not beyond the scientific pale.

"The idea of multiple universes is more than a fantastic invention -- it appears naturally within several scientific theories, and deserves to be taken seriously," said Aurelien Barrau, a French particle physicist at the European Organization for Nuclear Research (CERN), hardly a hotbed of flaky science.

"The multiverse is no longer a model, it is a consequence of our models," explained Barrau, who recently published an essay for CERN defending the concept.

There are several competing and overlapping theories about parallel universes, but the most basic is based on the simple, if mind-boggling, idea that if the universe is infinite then logically everything that could possible occur has happened or will happen.

Try this on for size: a copy of you living on a planet and in a solar system like ours is reading these words just as you are. Your lives have been carbon copies up to now, but maybe he or she will keep reading even if you don't, says Max Tegmark, a cosmologist at MIT in Boston, Massachusetts.

The existence of such a doppleganger "does not even assume speculative modern physics, merely that space is infinite and rather uniformly filled with matter as indicated by recent astronomical observations," Tegmark concluded in a study of parallel universes published by Cambridge University.

"Your alter ego is simply a prediction of the so-called concordance model of cosmology," he said.

Another type of multiverse arises with the theory of chaotic inflation, which tells us that all these parallel worlds are expanding so rapidly -- stretching further and further in to space -- that they remain out of reach even if one could travel at the speed of light forever.

Things get even stranger when one brings the often counter-intuitive laws of quantum physics into the picture, these experts say.

In a landmark paper published in 1957 while he was still a graduate student at Princeton University, mathematician Hugh Everett showed how quantum theory predicts that a single classical reality should gradually split into separate but simultaneously existing realms.

"This is simply a way of trusting strictly the fundamental equations of quantum mechanics," says Barrau. "The worlds are not spatially separated, but exist as kinds of 'parallel' universes."

The borderline between physics and metaphysics is not defined by whether an entity can be observed, but whether it is testable, pointed out Tegmark.

There are many phenomena -- black holes, curved space, the slowing of time at high speeds, even a round and rotating Earth -- that were once rejected as scientific heresy before being proven through experimentation, even if some remain beyond the grasp of observation, he said.

He concluded that it was becoming increasingly clear that multiverse models grounded in modern physics could be empirically testable, predictive and disprovable.

http://news.yahoo.com/s/afp/20071230/sc_afp/scienceastronomycosmologyfilmbooksentertainment;_ylt=AjYGCTEc1hN1wY_VMInCcGgDW7oF

Wonder if each universe will have its own seperate God or Gods.

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Any dimensionality that is 90 degrees from all others is another dimension, but the question as to why we cannot access more than three is not addressed.

The logical extrapolation of a given scientific/mathematical theory does not in and of itself give it a basis for pragmatism.

Most of the thinkers who describe themselves as pragmatists consider practical consequences or real effects to be vital components of both meaning and truth. http://en.wikipedia.org/wiki/Pragmatism

xingu wrote:

There are several competing and overlapping theories about parallel universes, but the most basic is based on the simple, if mind-boggling, idea that if the universe is infinite then logically everything that could possible occur has happened or will happen.

This is false logic and absurd, you cannot say that one infinity is bigger than another infinity, thus infinity does not mean that everything that could possibly occur has happened or will happen.

It's infinitely unlikely that our universe, at it is now, will be recreated in its absolute entirety even given infinity; again you cannot say that one infinity is bigger than another infinity.

That our universe, at it is now, could be recreated in its absolute entirety is possible in the sense that it's not entirely impossible, but that does not mean that even given infinity, such an event will happen.

Note that the limits of the English language expose Man's preconceptual contradictions, not the underlying concepts.

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There's an infinite number of infinities.

Annie just needs something to write about and with a handle like "Hautefeuille " one might understand her predicament.

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You need to commit to the time required to pop your corn properly, or in the alternative, if you do not want to commit the time, commit yourself.

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Two comments;

First infinities are a concept, not a number, so don't rush to apply mathematical operations reserved for numbers - e.g. sizing or ordering - on them. You need special fields of maths to "size" or "order" or "rank" an infinity - and what this operation means is strictly defined in such a sub-branch of mathematical study.

In these specialised fields specific infinities can be sized and ranged. Most commonly this can be used in set sizing (sets of numbers expanding from a source to infinity, whose members conform to some field operation - so you are comparing field operations over a range), limit theory, non-cartesian geometry, integration over infinities in multiple co-ordinate is often trivial, etc... The key point is not to throw around or inter-mix infinities with numbers - this is an absolute no go! Operations like +, -, *, /, =, >, < etc are field operations on numbers; infinities are ideas of boundlessness of some degree, not numbers - so don't apply field operations on them!

Secondly for us to exist seems there must be some sort of infinity somewhere - infinite time (e.g. collapsing / rebounding universe), infinite space (Hubble bubbles everyone - each with different properties), dimensional permutations (SuSy, Super gravity, string theory, membrane theory), infinitly varying laws of physics altering over one or more of the dimensions, infinite luck, infinte God, or my favourite - infinite complexity (a.k.a. scale relativity and the fractal universe) this theorum ponders whether existence is fractal at all "levels of reality" - so our existence as concious aware beings stems simply becuase we are at a level of reality conducive to intelligent life forming - and being fractals there is no smallest or largest only endless geometry.

Charming!

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Very charming and over my head.

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Infinities can be compared, since the word infinities, at least in my mind, implies the cardinalities of infinite sets rather than the sets themselves, so we can say that beth-null < beth-one.

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As an example using three infinite sets. Let X be the set of all positive numbers, Y is the set of all positive even numbers and Z is the set of all odd positive numbers.

What is the meaning of:

1) is X a larger set then Y?

2) does X have more members than Y?

3) is the sum of all the members of Y plus one 1 equal to the sum of all the members of Z?

4) is the sum of all the members of X = the combined sums of the members of Y and Z?

* * * * *

Is A larger, have more than, equals, is A +/- 1 are all field operations on numbers. Change numbers to defined infinities and you still have to be very, very careful doing field operations on them.

For all those above operations I would say it depends ... on other data specifying or implied in how the set grows and more importantly how it is compared (esp 3) to give any answer with meaning.

3. looks like it should ask is sum (Y) equal, bigger or smaller than sum (z), or alternatively is sum (Y) + (infinity * 1) = sum (Z).

Does this even start to show how messy and error prone mixing operations on numbers in a filed and infinities can be?

Even for qu 4. I would say - it depends how you count and how the sets grows, there is no final number you are comparing so what is really beings asked is an ordering question on a infinity that is constructed by summing sets that start respectively from 2 and 1 and grow outwards.

You have to show you are checking along the way with equal items. So if Y "grows" from its start in groups of say 3 elements at a time and Z "grows" froms its start in groups of say 7 elements at a time and X grows in groups of 11 at a time then most of the time if you where do to a check point count summing to infinity the groups would not be comparable in the number of elents they had so their sums wouldn't add up.

* * * * * * *

So now a very famous example to ponder:

What percentage of all positive integers start with first digit 1 and what percentage starts with 9?

Who here expected each digit would occur exactly 1/9 of the time?

Who here perceives there is no answer?

Answer - (to 1 decimal place) 1 occurs 30.1% as a percentage of all infinite positive integers (with a base ten number system) whereas 9 occurs as the first digit only 4.6% of the time.

This is the famous John Bell result (alah only counting or summing numbers in logarithimic sizings gives a consistent answer - all other "bucket" sizes you could uses to measure the fraction of occurrence as the size so teh sample (multipler of the bucket or sample size) as it grows to infinity gives inconsistent results) - and this result is now being used by forensic auditors as it pervades all data sets - cut any way - to catch cheats!

So not just the end result, but the way you get there is critically important when you do operations on infinite sets!

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g__day wrote:

As an example using three infinite sets. Let X be the set of all positive numbers, Y is the set of all positive even numbers and Z is the set of all odd positive numbers.

What is the meaning of:

1) is X a larger set then Y?

2) does X have more members than Y?

3) is the sum of all the members of Y plus one 1 equal to the sum of all the members of Z?

4) is the sum of all the members of X = the combined sums of the members of Y and Z?

* * * * *

Is A larger, have more than, equals, is A +/- 1 are all field operations on numbers. Change numbers to defined infinities and you still have to be very, very careful doing field operations on them.

For all those above operations I would say it depends ... on other data specifying or implied in how the set grows and more importantly how it is compared (esp 3) to give any answer with meaning.

3. looks like it should ask is sum (Y) equal, bigger or smaller than sum (z), or alternatively is sum (Y) + (infinity * 1) = sum (Z).

Does this even start to show how messy and error prone mixing operations on numbers in a filed and infinities can be?

Even for qu 4. I would say - it depends how you count and how the sets grows, there is no final number you are comparing so what is really beings asked is an ordering question on a infinity that is constructed by summing sets that start respectively from 2 and 1 and grow outwards.

You have to show you are checking along the way with equal items. So if Y "grows" from its start in groups of say 3 elements at a time and Z "grows" froms its start in groups of say 7 elements at a time and X grows in groups of 11 at a time then most of the time if you where do to a check point count summing to infinity the groups would not be comparable in the number of elents they had so their sums wouldn't add up.

* * * * * * *

So now a very famous example to ponder:

What percentage of all positive integers start with first digit 1 and what percentage starts with 9?

Who here expected each digit would occur exactly 1/9 of the time?

Who here perceives there is no answer?

Answer - (to 1 decimal place) 1 occurs 30.1% as a percentage of all infinite positive integers (with a base ten number system) whereas 9 occurs as the first digit only 4.6% of the time.

This is the famous John Bell result (alah only counting or summing numbers in logarithimic sizings gives a consistent answer - all other "bucket" sizes you could uses to measure the fraction of occurrence as the size so teh sample (multipler of the bucket or sample size) as it grows to infinity gives inconsistent results) - and this result is now being used by forensic auditors as it pervades all data sets - cut any way - to catch cheats!

So not just the end result, but the way you get there is critically important when you do operations on infinite sets!

Please note that I'm using beth numbers, not integers. All the sets you listed are of the same cardinality, so there are bijections mapping X to Y to Z and back again. If there is no bijection mapping one set to another, then one set's cardinality is strictly larger than the other.

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I suggest you go watch the 3 hour "documentary" on the string theory which in terms explains the possible existence of parallel universes. the documentary is called "The Elegant Universe". You may watch that show online at http://www.pbs.org/wgbh/nova/elegant/program.html

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