How Does Multiverse Theory Make *Every* Universe Possible?

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Is every combination possible based off of uncertainty? When the big bang happens in another universe and one electron moves slightly differently because of uncertainty it changes everything. Is that why there are "infinite" number of universes?

When people say infinite do they really mean infinite? So is it actually true (if I were in another universe) that everything could be the exact same, but instead I'd be writing the answer to this question just because I figured it out before anyone else on the world or does that have implications that would make the multiverse different in different ways?
 
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It is not known whether there are an infinite number of universes.

In theory, however, it is often said that in an infinite multiverse, all possible realities play out. It's fun to imagine, say, two different universes with identical histories up until a particular point, when you suddenly decide to do something different in one of the universes. I think this is what you're getting at when you say "be the exact same". This is actually not possible if determinism holds. Sure, quantum uncertainty allows for identical pasts to have different futures, but there are limits: an electron might jump an energy level in one universe and not the other, but a human being won't suddenly decide to act differently because such macroscopic activities require a great number of quantum mechanical events over a relatively long time scale.
 
I would argue that macroscopic events can be changed across the entire universe by even the influence of the gravity of the electron jumping a tiiiiny bit further due to chaos theory.
 
What does chaos theory have to do with quantum transitions?
 
Not my scope of knowledge but I'd like to throw this in:

I read a book on bubble theory, the theory that the there are a number of universes, surrounded by an event horizon out of which no universe can observe the others.

Anyway, the author made a case for the differences in the universes occurring from variations of the fundamental forces after they separate. For example, in one universe, an instant after the big bang, matter and energy become distinct. An instant later, gravity, strong and weak nuclear force, and EM force become distinct. However in this universe, gravity is a fraction weaker than in ours, and so, theoretically, dust clouds never clump into planets or stars.
 
Yes, that kind of multiverse is particularly motivated by string theory (the so-called "landscape" of string vaccua) where each universe has different values of the fundamental constants. The string landscape, though embarrassingly vast, is not infinite.
 
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bapowell said:
What does chaos theory have to do with quantum transitions?
bapowell said:
Yes, that kind of multiverse is particularly motivated by string theory (the so-called "landscape" of string vaccua) where each universe has different values of the fundamental constants. The string landscape, though embarrassingly vast, is not infinite.
Any tiny movement in one area affects the entire universe. One electron moving a tiny bit differently changes everything in the universe. (wiki: "studies the behavior of dynamical systems that are highly sensitive to initial conditions")
 
noname2020x said:
Any tiny movement in one area affects the entire universe. One electron moving a tiny bit differently changes everything in the universe. (wiki: "studies the behavior of dynamical systems that are highly sensitive to initial conditions")
Sure, but that's not the same thing as having two identical universes up to a particular point at which something suddenly occurs on a macroscopic scale in one and not the other. Quantum physics will cause macroscopic differences, but these will take time to manifest.
 
bapowell said:
Sure, but that's not the same thing as having two identical universes up to a particular point at which something suddenly occurs on a macroscopic scale in one and not the other. Quantum physics will cause macroscopic differences, but these will take time to manifest.

I didn't say it wouldn't take time to manifest. Basically, my question is: Does multiverse theory claim that there are literally an infinite number of universes where I am a doctor in one that cures cancer and I'm a MMA fighter in another? Any wouldn't this mean there are a huge number of degrees of infinity?
 
  • #10
Multiverse theories are highly speculative at this time (there is no "multiverse theory"), and so we have no idea what the physics of the multiverse is. If you wish to postulate that there are infinite number of universes, each with different initial conditions (different positions and momenta of all the particles) then, yes, there will be a universe where you cure cancer and one where you are an MMA fighter providing that neither of these is physically impossible.
 
  • #11
In some multiverse theory there is infinite possibilities with different physical properties.

Weird for me as an atheist to accept. There could be a universe in which a God created everything in six days a few thousand years ago. As a paleontologist I'm am writing about it in that Universe with derision because it all seems silly... however, in an infinite number of universes there could be...

Yikes...gets too weird.
 
  • #12
Yes indeed, it does seem silly.

I certainly won't be subscribing to any multiverse theories until someone puts some hard facts on the table. That doesn't seem likely with multiverse theory any time soon.
 
  • #13
the quantum mutiverse is an interpretation of Quantum Mechanics, and as an interpretation it doesn't touch the physics of it (I know quantum mechanics in some good extend but I don't really care about the "multiverses") but it's a philosophical point of view. You can do quantum mechanics without getting involved in the different interpretations of it.

The multiverse in string theory is a different thing, and it doesn't apply to different moments or "measurements". I think it was applied at the beginning of the Universe when it was supposed to be a "stringy"-theory governed thing. In strings (if someone believes that this is a real physical theory- I don't) I think you can derive the number of those extra universes that were 'born' together with ours (so it's a "prediction" -bad I'd say- and not an "interpretation")...and that's why to people who tell me that sting theory predicted our Universe, I return that it predicted it together with a vast number of different ones...if I recall well some people found ~10500 ones, together with ours.
 
  • #14
I say to those who tell us that string theory predicted our universe:

No, because your models have 11 dimensions, whereas our universe only has 3.
 
  • #15
NIgelSmith50 said:
I say to those who tell us that string theory predicted our universe:

No, because your models have 11 dimensions, whereas our universe only has 3.
There's more to it than that. String theory predicts that extra dimensions are compactified, making them difficult to observe directly.
 
  • #16
I know what it predicts and I know that the extra dimensions are 'compactified'.

As I said, it is wrong because our universe has 3 dimensions.
 
  • #17
NIgelSmith50 said:
I know what it predicts and I know that the extra dimensions are 'compactified'.

As I said, it is wrong because our universe has 3 dimensions.

That's not a valid argument in physics.
I too try to remain sceptic but don't start criticizing for the sake of criticizing.

If you must point out flaws start with the absence of deSitter solutions.

Also we live in a universe with 3 spatial dimensions. Not 3 dimensions altogether, 4 dimensions is what we work with since Einstein's GR.

bapowell is correct (within the scope of string theory), the predicted size of these compactified (curled up) dimensions is (can be?) smaller than scales we can probe at this time.
 
  • #18
NIgelSmith50 said:
I know what it predicts and I know that the extra dimensions are 'compactified'.

As I said, it is wrong because our universe has 3 dimensions.

How do you know that our universe has 3 dimensions?
 
  • #19
Every time I hear this 'curled up dimensions' I cringe. Show me evidence for this please.

I know the universe has 3 dimensions because I exist in it.
 
  • #20
NIgelSmith50 said:
Every time I hear this 'curled up dimensions' I cringe. Show me evidence for this please.

I know the universe has 3 dimensions because I exist in it.

We don't have proof, we don't have prove against it either.
Within the confines of science this means we cannot dismiss the theory as false!

We keep with the theory because various reasons (this is my feeling about this).
One will be senior scientists don't want to abandon a theory they spent a significant part of their life on.
Another is the elegance of the theory (the idea is quite simple, the maths gets hard quite soon).

The extra dimensions are there for technical reasons and really make our starting point simple. (for example 11D sugra contains a graviton, gravitino and a 3-form gauge field, not that much particles).
The technical reasons are easy to see in modern books (I liked the treatment in Becker, Becker, Schwarz for bosonic strings).

But as you say, we only perceive 3+1 dimensions so we have a surplus of dimensions.
 
  • #21
We don't have proof against it?? Whatever happened to the scientific method?

I was asked how I know the universe has 3 dimensions like this was in any doubt. I don't accept the '3+1 dimensions'. The +1 dimension you refer to is not in any way equivalent to a spatial dimension.
 
  • #22
NIgelSmith50 said:
Every time I hear this 'curled up dimensions' I cringe. Show me evidence for this please.

I know the universe has 3 dimensions because I exist in it.
There is no evidence for "curled up" dimensions. They are simply a characteristic prediction of the theory. Atoms were speculated about millenia before they were observed: it would have been foolish to discard such ideas simply because no atoms were seen in ancient Greece.

You exist in the universe and interact with it via the fundamental forces. Hence your experience depends on their character. You take it for granted that these forces probe all of spacetime in such a way that humans can perceive all that there is.
 
  • #23
NIgelSmith50 said:
We don't have proof against it?? Whatever happened to the scientific method?
What proof do we have against extra dimensions existing at the Planck scale?
 
  • #24
JorisL said:
Within the confines of science this means we cannot dismiss the theory as false!

You can dismiss it as "unscientific" ... by no means can string theory be considered a scientific theory in the common sense...
Up to now it's a department of mathematics, with a few attempts by some phenomenologists to give it some predictability (without success).
 
  • #25
ChrisVer said:
You can dismiss it as "unscientific" ... by no means can string theory be considered a scientific theory in the common sense...
Up to now it's a department of mathematics, with a few attempts by some phenomenologists to give it some predictability (without success).
Let's not get hung up on semantics. The question of whether or not the universe has more than 3 spatial dimensions is absolutely an empirical one. Whether string theory is "scientific" or not has nothing to do with it.
 
  • #26
bapowell said:
Let's not get hung up on semantics. The question of whether or not the universe has more than 3 spatial dimensions is absolutely an empirical one. Whether string theory is "scientific" or not has nothing to do with it.

What do you mean by empirical? The extra dimensions is not a problem since the theory can explain why we don't see them... The problem is the theory and whether it can give real answers for the Universe we live in.
 
  • #27
ChrisVer said:
What do you mean by empirical? The extra dimensions is not a problem since the theory can explain why we don't see them... The problem is the theory and whether it can give real answers for the Universe we live in.
From Oxford:

Emprical: Based on, concerned with, or http://www.oxforddictionaries.com/us/definition/american_english/verify#verify__2 by http://www.oxforddictionaries.com/us/definition/american_english/observation#observation__2 or experience rather than theory or http://www.oxforddictionaries.com/us/definition/american_english/pure#pure__2 http://www.oxforddictionaries.com/us/definition/american_english/logic#logic__2 .

Your comment was in response to JorisL's statement that a lack of evidence for extra dimensions is not evidence for the lack thereof. He is correct, and I'm saying that extra dimensions, as physical properties, are in principle measurable. What's "unscientific" about that?
 
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  • #28
Unscientific is the theory which cannot be falsified/verified by some experiment.
The whole statement of JorisL was:
We don't have proof, we don't have prove against it either.
Within the confines of science this means we cannot dismiss the theory as false!

I am saying that in the 1st line, the theory becomes unscientific. How can you then speak about the confines of science over it?
 
  • #29
ChrisVer said:
Unscientific is the theory which cannot be falsified/verified by some experiment.
The whole statement of JorisL was:I am saying that in the 1st line, the theory becomes unscientific. How can you then speak about the confines of science over it?
Why can't the existence of extra dimensions be falsified?
 
  • #30
bapowell said:
Why can't the existence of extra dimensions be falsified?

tell me an experiment that we should conduct to check for it...or sole predictions it can give so that we can indirectly check it...
 
  • #31
3+1 works perfectly well at macroworld-- pointer. On the other hand, quantum realm begs for multiplicity(universes/manyworlds and stuff) due to weird observables -- superposition. Somehow we don't have any success in making it classical (consistency issues with experiments). So we are forced to use probability and wavefunction evidently works pretty well. In consequence, a particle that could go up or down — all of the possibilities happen in "different worlds". These "different worlds" are in fact different parts of the same universal wave function, but for all intents and purposes their futures are entirely separate; the only way they could come to interact again is if both of them lead to situations that are completely indistinguishable on the particle level, in which case they would "interfere" constructively or destructively, making such an outcome more or less likely. MWI is an interpretative crossroad between science/unscientific and multiverse is way beyond that. I just stick to Meh..for now ^^. BTW what is cutoff?
 
  • #32
ChrisVer said:
tell me an experiment that we should conduct to check for it...or sole predictions it can give so that we can indirectly check it...
Missing energy in a collider.

Yes, I grant that at present we are woefully under the appropriate energy threshold to rigorously test this prediction. But that is not the point of this thread, which is in response to Nigel's comment that the absence of evidence for extra dimensions proves their absence. This is false, regardless of the feasibility of the experiment.
 
  • #33
ChrisVer said:
tell me an experiment that we should conduct to check for it...or sole predictions it can give so that we can indirectly check it...

Sir, you seem very unrealistically negative about the entire possibility of a multiverse. Just because there is not science to prove or disprove something does not negate it's potential existence. If you are so inclined to NOT believe in the possible future discoveries then just simply look to the past and give a thought to the potential future. At one point "the major scientific discoveries" of the world included first thinking the Earth was flat, then round, then they found planets and discovered the sun and all it's bodies orbited the earth...to think otherwise could possibly land you in prison or even executed...well we know the truth is planets orbits the sun...
Taking that into account at some point they thought only one sun, one solar system, one galaxy, etc...but come to find out there are trillions upon trillions of each.
In fact through out all of creation and existence itself there seems to be at least pairs of things all the way down to many of the very building blocks of matter itself. On top of that it seems existence itself is cyclical, things are born and things die, the remnants either create new similar life, a different life or both. It stands to reason then that this single universe that we are fixated on only needs a little more time, technology and science to prove there is actually more than one. I can actually envision trillions upon trillions of universes all being born, living and dying in this natural process of physical existence and our universe in all it's enormity is only a single thing that will also one day pass away and bring about a new and different universe in it's wake. This may also give more credence to the big bang theory by supplying a location of the bang before it 'banged'. Maybe the death of a previous universe was the bang that created this one...maybe two universes collided to make the bang. So much to be discovered yet that we shouldn't close our minds to ever...
so my request to you is ...Give me science/theory or opinion that can prove or disprove the above. The important thing here is to never stop questioning right?
 
  • #34
noname2020x said:
Is every combination possible based off of uncertainty? When the big bang happens in another universe and one electron moves slightly differently because of uncertainty it changes everything. Is that why there are "infinite" number of universes?

When people say infinite do they really mean infinite? So is it actually true (if I were in another universe) that everything could be the exact same, but instead I'd be writing the answer to this question just because I figured it out before anyone else on the world or does that have implications that would make the multiverse different in different ways?

There is an argument that infinite universes is the simplest. Alternatively, there should be a reason for whatever the finite number might be, whereas infinity needs no reason.

I'll leave you guys to argue where the burden of proof should lie.
 
  • #35
C.E. said:
Sir, you seem very unrealistically negative about the entire possibility of a multiverse.

I am. I am unrealistically negative to un-realism . Since that question touches the matter of "belief" and is untestable, it's viable for me to believe whatever I like. And the multiverse theories are so well untestable built, that they give me this freedom...so it's not me who has the problem with being "suspicious", it's the theory's problem that allows for such suspicion to rise.

C.E. said:
Just because there is not science to prove or disprove something does not negate it's potential existence.

Just because there is no science to prove or disprove it, it is unscientific. As a philosophy would be.
and by no means I want to say that being non-scientific is bad (maths is not bad), it's just a state.

C.E. said:
f you are so inclined to NOT believe in the possible future discoveries then just simply look to the past and give a thought to the potential future. At one point "the major scientific discoveries" of the world included first thinking the Earth was flat, then round, then they found planets and discovered the sun and all it's bodies orbited the earth...to think otherwise could possibly land you in prison or even executed...well we know the truth is planets orbits the sun...
Taking that into account at some point they thought only one sun, one solar system, one galaxy, etc...but come to find out there are trillions upon trillions of each.

The fact that we only learn the theories that successfully described the world, doesn't mean that theories are a priori correct. In fact even when you pick up one theory by proving it experimentally, all the rest that were invented to give answers to the same questions are pushed back. So you can say that for one theory to be right, one or more were wrong/unrealistic.
How are the stars an indication that a multiverse exists?

C.E. said:
In fact through out all of creation and existence itself there seems to be at least pairs of things all the way down to many of the very building blocks of matter itself. On top of that it seems existence itself is cyclical, things are born and things die, the remnants either create new similar life, a different life or both. It stands to reason then that this single universe that we are fixated on only needs a little more time, technology and science to prove there is actually more than one. I can actually envision trillions upon trillions of universes all being born, living and dying in this natural process of physical existence and our universe in all it's enormity is only a single thing that will also one day pass away and bring about a new and different universe in it's wake. This may also give more credence to the big bang theory by supplying a location of the bang before it 'banged'. Maybe the death of a previous universe was the bang that created this one...maybe two universes collided to make the bang. So much to be discovered yet that we shouldn't close our minds to ever...

Of course I cannot prove/disprove that statement, as it's philosophical and not scientific. I could only accept/deny it. Also in order to avoid a philosophical discussion (at least in a thread- if you want PM me), it's better to leave it at this: I personally deny it..
For me questions make sense if I can find someway to prove them right or wrong. A multiverse cannot be proven because you can't actually go to some other universe (as long as you are not 'high') and/or work with it. If the question by itself lacks this feature, I consider it "something else". Maybe it's fun for some coffee break discussion, or after a Star Wars movie, or working with it in a pure mathematical way, but it's not a scientific question...
 
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  • #36
infinite is used far to much in science. I can see that there could be other universes it makes sense we once thought there was one planet then one solar system and so on so one day someone might find other universes but to say there is other Me's out there doing everything I do up until a decision I make and Alternate me makes is so far fetched It is almost impossible. For starters just measuring water boiling isn't possible it is so random imagine the odds odds of two identical big bangs.But other universes with planets and stars all made of anti matter and things like that are cool to imagine out there. As for not being able to see them . We don't know what our universe is expanding into mabye light cannot travel through or mabye it will get here one day.
 
  • #37
To avoid getting bogged down in whether or not multiverse theories are testable from a philosophical viewpoint or if the universe can be infinite, first be sure that you understand the distinction between the observable universe and the global universe in cosmology.

https://en.wikipedia.org/wiki/Shape_of_the_universe
 
  • #38
On the evidence of this debate, it seems that there is indeed an abandonment of the scientific method with regard to multiverse theory.

Not only do supporters of the hypothesis fail to offer any real science, but they seem to revel in the non-argument of proving a negative. I therefore have no alternative but to dismiss it on the same grounds that I would dismiss a religious belief.

This topic should be moved to philosophy or religion since it is clearly not science.
 
  • #39
NIgelSmith50 said:
On the evidence of this debate, it seems that there is indeed an abandonment of the scientific method with regard to multiverse theory.

Not only do supporters of the hypothesis fail to offer any real science, but they seem to revel in the non-argument of proving a negative. I therefore have no alternative but to dismiss it on the same grounds that I would dismiss a religious belief.

This topic should be moved to philosophy or religion since it is clearly not science.

This is a very common misconception.

Multiverses are predictions of other theories, not postulates. Some of these theories are widley accepted, others remain controversial. To understand why, you'll need to understand some Inflationary Cosmology and the Relative State Formulation of Quantum Mechanics. To discuss them, I'd suggest that you start a thread in the Cosmology or Quantum Physics subforum respectively. But be warned discussions on the Interpretations of Quantum Mechanics become very heated there, usually resulting in someone getting upset and the thread getting closed.

If you want a fuller understanding of the subject then I'd recommend Tegmark's recently published book, Our Mathematical Universe.
 
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  • #40
This topic seems to have gone a bit off track from the original question. The question is in the metaphysics domain, which I like to ponder about so I'll try to give it a shot.

noname2020x said:
Is every combination possible based off of uncertainty? When the big bang happens in another universe and one electron moves slightly differently because of uncertainty it changes everything. Is that why there are "infinite" number of universes?

When people say infinite do they really mean infinite? So is it actually true (if I were in another universe) that everything could be the exact same, but instead I'd be writing the answer to this question just because I figured it out before anyone else on the world or does that have implications that would make the multiverse different in different ways?

First of, I'll restrict my definition of multiverse to a (possibly infinite) number of universes operating under the same physical laws. So gravity, all forces and constants would be the same. Another assumption is that behaviour at the quantum level is truly random (adhering to the law of probabilities), and not a result of our ignorance of the true underlying principles.
In such a multiverse it is possible for every single plausible (meaning, not breaking any laws of physics) outcome to be realized. Most universes would have evolved so differently that Earth would never have formed in them. Others (a vast minority, since it is enormously improbable) would have evolved almost identical to ours with only 'slight' differences. You could be an MMA fighter or a doctor in one of those. But is it the real you then though? It means you chose another path in life, which implies you're wired differently or shaped by different experiences in this universe, so it would not really be you. Plus your path and experiences in life would be completely different than in this universe.
Every different action, however small it may be, will make the future of that similar universe diverge more and more from that of this one. It all boils down to chaos theory really. The state of each universe is extremely sensitive to the initial conditions (big bang), the closer the initial conditions of a universe are to that of ours, the more it will resemble ours. But the further you go in time, the more tiny differences accumulate and the more each universe diverges from the other.

So, to answer your question more direct, yes, every combination based of uncertainty is possible and the outcomes are, for all intends and purposes, infinite. This is ofcourse all just hypothetical :)
 
  • #41
I don't think that the idea of multiverse wants the laws of physics to remain the same. I think that different string vacua would result in different parameters (?) and so different laws.
 
  • #42
ChrisVer said:
I don't think that the idea of multiverse wants the laws of physics to remain the same. I think that different string vacua would result in different parameters (?) and so different laws.

I excluded universes with different parameters because the main argument would still be the same. The only difference is that the number of universes similar to ours would be vastly smaller in comparison to the whole plethora of universes in the multiverse.
Also admittedly I know very little about string theory so I don't know what restrictions it might pose on a multiverse or the laws of its individual universes.
 
  • #43
ChrisVer said:
I don't think that the idea of multiverse wants the laws of physics to remain the same. I think that different string vacua would result in different parameters (?) and so different laws.

Some types of multiverse have exactly the same physical laws as our universe, others do not. Examples of those that do are those specifying the region of spacetime beyond our cosomlogical horizon and by the MWI.
 
  • #44
Not just string theory where you get universes with different parameters: "Discrete quantum gravity: a mechanism for selecting the value of fundamental constants" http://fr.arxiv.org/abs/gr-qc/0306095 - given this is a minimal combination of GR and QM it might be more general?

"Smolin has put forward the proposal that the universe fine tunes the values of its physical constants through a Darwinian selection process. Every time a black hole forms, a new universe is developed inside it that has different values for its physical constants from the ones in its progenitor. The most likely universe is the one which maximizes the number of black holes. Here we present a concrete quantum gravity calculation based on a recently proposed consistent discretization of the Einstein equations that shows that fundamental physical constants change in a random fashion when tunneling through a singularity."

Still you have to give way to the fact that universes like ours fall in a narrow set of parameters.
 
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  • #45
craigi said:
This is a very common misconception.

Multiverses are predictions of other theories, not postulates. Some of these theories are widley accepted, others remain controversial. To understand why, you'll need to understand some Inflationary Cosmology and the Relative State Formulation of Quantum Mechanics. To discuss them, I'd suggest that you start a thread in the Cosmology or Quantum Physics subforum respectively. But be warned discussions on the Interpretations of Quantum Mechanics become very heated there, usually resulting in someone getting upset and the thread getting closed.

If you want a fuller understanding of the subject then I'd recommend Tegmark's recently published book, Our Mathematical Universe.

Your opening two sentences are a clear contradiction.

If the theories are controversial, as you acknowledge, it is not a great basis for multiverse theory. Postulates would be a more applicable term based on your own logic.
 
  • #46
NIgelSmith50 said:
Your opening two sentences are a clear contradiction.

If the theories are controversial, as you acknowledge, it is not a great basis for multiverse theory. Postulates would be a more applicable term based on your own logic.

You'll have to explain where you see the contradiction, because I can't see how you're reading what I wrote.

If you're not sure how a multiverse is predicted by Inflationary Cosmology, String Theory and the Relative State Formulation of Quantum Mechanics, then I recommend that you start there, rather than getting bogged down with semantics. It'll all become much clearer, instead of getting confused about which are theories, which are postulates and which are predictions.
 
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  • #47
Do you have any source explaining the MV in Inflationary Cosmology?
Because the other sources have not satisfied me... strings is maths (so no real connection to nature and the universe, leave aside the prediction of more)...if we find SUSY I might become less of a skeptic (without leaving my skepticism until the end)... and Everret's idea is just an interpretation of QM and not a theory which can make measureable predictions (it's more like a philosophy, in a worse "position" than strings)
 
  • #48
ChrisVer said:
Do you have any source explaining the MV in Inflationary Cosmology?
Because the other sources have not satisfied me... strings is maths (so no real connection to nature and the universe, leave aside the prediction of more)...if we find SUSY I might become less of a skeptic (without leaving my skepticism until the end)... and Everret's idea is just an interpretation of QM and not a theory which can make measureable predictions (it's more like a philosophy, in a worse "position" than strings)

Sure. Start off with Tegmark's recent book 'Our Mathematical Universe'. It deals with the multiverse in all forms of which we are aware of to date. From there you should be looking toward the work of Guth and Linde for more detail from an Inflationary Cosmology perspective.

Regarding predictions of Everettian QM, you should look for work by Deutsch. Unfortunately, this is behind an internet paywall, so you may need to find an alternate source, if you don't want to pay and don't have access to an academic library.
 
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