The Universe: Finite or Infinite?

[DevilsAvocado]

1
As a proponent of Mathematic Universe Hypotesis,
http://arxiv.org/abs/0704.0646
- this is very good reading,
I don't see any difference between physical and mathematical.

2
For that reason Newtonians gravity theory was not valid, because when applied to the infinite Universe, you got infinities. In General Realitivity you don't run into infinities even for the infinite Universe.

3
If a theory is a) self-consistent, b) is compatible with the observations I don't see reason to cry all the time "wow, but wait, the whole Universe is hanging in the nothingness! or wow, but it is infinite!" :)

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1) I love Max Tegmark :!), he is a brave man and the Grand Master of Mind-Blowing Theories!

• TOE - Theory of Everything
• ERH - External Reality Hypothesis
• MUH - Mathematical Universe Hypothesis
• CUH - Computable Universe Hypothesis

Tegmark probably has more intelligence in his left pinky TOE than I have in my whole brain, and obviously I cannot comprehend all of his Mathematic Universe Hypotesis.

But then again, I am the DevilsAvocado and I did complete my course at the http://www.youtube.com/watch?v=kQFKtI6gn9Y" , and therefore I naturally going to have objections about this.

"If a future physics textbook contains the TOE, then its equations are the complete description of the mathematical structure that is the external physical reality. We write is rather than corresponds to here, because if two structures are isomorphic, then there is no meaningful sense in which they are not one and the same."

Huum, isn't this 'maneuver' a little bit too easy to 'replace' the physical reality with math? Isomorphic is mainly a mathematical 'tool' (right?) for mapping between objects... isn't that 'cheating'?

Example: If you have a complete technical drawing of a house, and make a complementation with all scientific knowledge about the material, down to quarks - then Tegmark could call the technical drawing and the physical building isomorphic, right? But can Tegmark take his family and move into that Technical Drawing?? I say no.

"Wigner argued that 'the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious', and that 'there is no rational explanation for it'."

I DO admire all people who use extremely advanced mathematics to investigate and explore the world. They are my heroes!

At the same time, I think there is a little risk of losing perspective and getting 'lost in translation', and fall in love with the 'pure magic' of the tools you are working intensely with. For me, as layman, it feels extremely awkward that the physical world doesn't really exist - it's just equations...

In Erwin Schrödinger's book - What Is Life - from 1944 (old stuff I know! ) he wrote as a section header in Chapter 1:

PHYSICAL LAWS REST ON ATOMIC STATISTICS AND ARE THEREFORE ONLY APPROXIMATE

And if I'm not wrong; there is NOT today ANY mathematical equation that can describe what really goes on in the QM-world. All we calculate are probabilities, right? And Heisenberg's uncertainty principle doesn't give us much hope of ever getting rid of this 'trauma', right? So, how can (mathematic) approximations ever be the real physical world we live in??

Another side of this coin could be the EPR paradox, and the fact that Alain Aspect 1982 (almost?) performed a validation of Bell's theorem (Bell inequality). The world is random by nature. As far as I know, mathematics is NOT random by nature?

Tegmark's solution to banish randomness:
" ... so that the final state is a superposition of observers obtaining all outcomes, then in the limit of infinitely many bits, almost all observers will find their bit strings to appear perfectly random and conclude that the conventional quantum probability rules hold."

Huum, "a superposition of observers obtaining all outcomes" = Many-worlds interpretation ...??

If so, I not like...

The final objection is completely homemade, and feel free to laugh out loud!
What's the most natural geometric shape in the universe? Yes, circles/spheres. Not quadrates/triangles. What is the natural mathematic tool for handling circles and spheres?

3.14159265358979323846264338327950288 ... ... ... ... ... ... ... ...

Just a layman 'feeling' - but shouldn't ∏ be more 'exact/natural', if the Mathematical Universe Hypothesis is correct...??


- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
2) Is the reason for NOT running into infinities even for the infinite Universe, the fact that we can never get out of our local light-cone (event-horizon)? Or is this 'embedded' more 'fundamentally' in GR?


- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3) "b) is compatible with the observations"... Hehe, this is the Holy Grail of avoiding difficult questions! Business as usual, everything (observable) works, without any help of the turtles!

 

[DevilsAvocado]

Yes, it can, without any help of the turtles :)

Turtles all the way down
I think I've found the solution... The last turtle is not that big, and he has all the information at the fingertip!

 

[DevilsAvocado]

DevilsAdvocado, regarding the QM ManyWorlds you are a victum of popular junk about the MWI.

1. There are no 'MANY' universes in MWI - everything happens in the same universe, just some parts of the omnium (almost) loses an ability to communicate forming 'branches'
2. When I make an experiment with different outcomes, I don't 'split' the whole Unvierse. The effect propagates at speed of light (or slower) via experimentally observed process called 'Qunatum Decoherence'
3. MWI does not make any additional assumptions expect we already have in QM. In that sense it is minimalistic. It does not even postulate the existence of the other branches: all that is derived using the standard QM stuff + Quantum Decoherence

Okay, thanks for info.

And how do we relate Qunatum Decoherence to Tegmark's:
"a superposition of observers obtaining all outcomes"

To me it sounds like every observer is going to have their own bit...??

 

[Dmitry67]

DevilsAdvocado, regarding your objections, how do you know if you are living in the virtual reality or real reality? "complete technical drawing of a house" is not a good example for "virtual reality". So you can't live there.

The second part of your objections are rather constatation of fact that we don't know the 'Ultimate', TOE equations. Yes, this is true. But we hope we'll learn them soon.

And precise and deterministic laws of physics can lead to the appearence of randomness (MWI, BM)

 

[Dmitry67]

Okay, thanks for info.

And how do we relate Qunatum Decoherence to Tegmark's:
"a superposition of observers obtaining all outcomes"

To me it sounds like every observer is going to have their own bit...??

It depends on how you define the "observer"
After the schoedinger cat experiment:

You + closed box with 1/2 dead cat + 1/2 alive cat

So you can never see the superposition of cats
you get decoherenced with the box literally after you exchange few photons, and the system evolves into

1/2 Happy you observing alive cat + 1/2 Sad you observing dead cat

 

[DevilsAvocado]

DevilsAdvocado, regarding your objections, how do you know if you are living in the virtual reality or real reality? "complete technical drawing of a house" is not a good example for "virtual reality". So you can't live there.

The second part of your objections are rather constatation of fact that we don't know the 'Ultimate', TOE equations. Yes, this is true. But we hope we'll learn them soon.

And precise and deterministic laws of physics can lead to the appearence of randomness (MWI, BM)

Thanks. Virtual reality is cool, and could be one explanation for the "turtle problem". Can we be absolutely sure about the vastness of our universe in that case? I mean, is there any way to tell for sure (CMB, etc)?

TOE is very thrilling. I can't wait.

A deterministic law of physics sounds a little 'disturbing'. I like my free will...

 

[DevilsAvocado]

It depends on how you define the "observer"
After the schoedinger cat experiment:

You + closed box with 1/2 dead cat + 1/2 alive cat

So you can never see the superposition of cats
you get decoherenced with the box literally after you exchange few photons, and the system evolves into

1/2 Happy you observing alive cat + 1/2 Sad you observing dead cat

Yes, but then again Tegmark's MUH has a problem to banish the randomness in the Geiger counter?
Or, Curiosity Killed The Cat??

 

[Dmitry67]

In MWI free will is compatible with determinism.

Virtual reality is cool, but this is not what Max meant. The idea of Matrix is too popular, but what he is saying is much deeper.

Let me ask you - how you can tell the mathematical system from a physical one?

 

[Dmitry67]

Yes, but then again Tegmark's MUH has a problem to banish the randomness in the Geiger counter?

MUH is unrelated to Schroedinger cat problem
MWI is.
Randomness is an illusion.
Both branches (deterministically) exist
Observer is each branch thinks that the outcome was random.

 

[DevilsAvocado]

In MWI free will is compatible with determinism.

Virtual reality is cool, but this is not what Max meant. The idea of Matrix is too popular, but what he is saying is much deeper.

Let me ask you - how you can tell the mathematical system from a physical one?

Well, I guess if we accept the possibility that we and the universe are a running simulation, then the mathematical system setting the rules, must be more real than the actual simulation!?

And I guess there is NO way to find out if we are real real, or simulated real, i.e. if the 'programmer' did his job.

If this is true; how can we ever find TOE?? The 'programmer' must be an idiot if he programmed his own 'weakness'?

If we are not simulated, then I say my Technical Drawing is a pretty good indicator.

Another (old) question that pops up in my head; Nick Bostrom is almost sure we are in a simulated reality, and that it's impossible to tell the difference between real reality and simulated reality.

Hence the (mathematical) simulation system/rules/programming must be 'govern' from outside the simulation, right? How can the 'simulation governors' (and here goes my turtles again! ) be absolutely sure they are not simulated as well?? And so on, and so forth, in all eternity... (And, does this make any 'real' difference...??)


Finally a new nut for you to crack:
If we are in a simulated reality - how you can tell a 'real' mathematical system that works, from a simulated mathematical system that is simulated to work?

 

[DevilsAvocado]

MUH is unrelated to Schroedinger cat problem
Both branches (deterministically) exist
Observer is each branch thinks that the outcome was random.

So "observer in each branch" is not the same as splitting observer worlds?

(I must be stupid )

 

[Dmitry67]

You're right, there is NO way to find out if we are PEFFECTLY simpulated. Then it is IRRELEVANT if we are simulated or not.And MAx suggests not to talk about the simulation.

For the same reason there is no difference between physical and mathematical - beings in the mathematical structure feel it perfectly physical and real.

 

[Dmitry67]

So "observer in each branch" is not the same as splitting observer worlds?

(I must be stupid )

You are split.
In order to split an observer in Andromeda Galaxy, that observer must look in the telesope and receive enough photons so there will be difference (even if he is not aware of it) for him between 2 outcomes - dead can and alive. So it is a physical process which requires information transfer

I am just busting the popular myth that 'any event splits the whole Universe'

 

[DevilsAvocado]

Okay I buy that, if we are PEFFECTLY simulated.

Though it could involve a risk for Max, since he base his argument on something that maybe looks a little like Catch-22:

1) There is NO way to find out if we are PEFFECTLY simulated.
2) Then it is IRRELEVANT if we are simulated or not.
3) For the same reason there is NO difference between physical and mathematical systems.
4) Hence there is NO way to prove physically if statement 3 is true or false.

This could be one level above my understanding. But I always thought that science required; first a theory, and then a physical experiment, approving or disapproving the theory? This seems impossible with MUH/CUH...?

 

[DevilsAvocado]

You are split.
In order to split an observer in Andromeda Galaxy, that observer must look in the telesope and receive enough photons so there will be difference (even if he is not aware of it) for him between 2 outcomes - dead can and alive. So it is a physical process which requires information transfer

I am just busting the popular myth that 'any event splits the whole Universe'

This must be true, because I feel split.

 

[Dmitry67]

This could be one level above my understanding. But I always thought that science required; first a theory, and then a physical experiment, approving or disapproving the theory? This seems impossible with MUH/CUH...?

Then, as you can not tell the difference between REAL or BEING EMULATED, or PHYSICAL and MATHEMATICAL there is no use to say that 'we are emulated'

The Ocamms razor is used then: if we can't prove that we are emulated, then we are NOT emulated. If we can prove that some magical substance makes mathematical formulas 'real', then there is no difference between physical and mathematical.

 

[DevilsAvocado]

Dmitry67, doesn't a PEFFECTLY simulated physical world looks disturbingly like God...?

(I no like, I no 'believer'...)

Edit: Forget this. Since we cannot prove we are simulated, we cannot prove God = same as 'yesterday'.

 

[DevilsAvocado]

Then, as you can not tell the difference between REAL or BEING EMULATED, or PHYSICAL and MATHEMATICAL there is no use to say that 'we are emulated'

The Ocamms razor is used then: if we can't prove that we are emulated, then we are NOT emulated. If we can prove that some magical substance makes mathematical formulas 'real', then there is no difference between physical and mathematical.

AHA! SOME MAGICAL SUBSTANCE MAKES MATHEMATICAL FORMULAS 'REAL'!

This is what I have been waiting for! Now it's even more interesting! This substance must be THE REALITY COMPUTER! Wow! This is even hotter than TOE! You could, with the help of mathematics and programming, build NEW WORLD'S!

Weird, spacey and (today) unscientific, but EXTREMELY COOL!

 

[Gan_HOPE326]

AHA! SOME MAGICAL SUBSTANCE MAKES MATHEMATICAL FORMULAS 'REAL'!

This is what I have been waiting for! Now it's even more interesting! This substance must be THE REALITY COMPUTER! Wow! This is even hotter than TOE! You could, with the help of mathematics and programming, build NEW WORLD'S!

Weird, spacey and (today) unscientific, but EXTREMELY COOL!

You are starting to sound worrying, you know...

But you're right, MUH is quite exciting. I just finished reading one of Tegmark's papers on the subject and... well... it gives substance to something I've always felt without being able to tell. There really is no difference between "information" and "reality", in some sense; if you have all of the information needed to describe reality, then you have... reality itself. Same goes for our physical laws. And what Tegmark calls Parallel universes of level IV are actually the last step of Copernican revolution: not only our Earth isn't the center of the universe, there's no reason to believe our universe is the center of the Multiverse either; i.e., our physical laws are not special in any way. There are worlds with repulsive gravity; or where gravity goes as the inverse of the cube of distance; or worlds with just one (ore one hundred) fundamental interactions. As long as they're internally coherent, there's no limit. Then it goes all back to ol' anthropic principle: we know this universe because this universe has laws fit to host life. Too complicated laws, for example, would probably give birth to a universe in which conditions vary on a very small scale in a practically unpredictable way, where complex structures like living beings would have an hard time existing; too simple laws simply wouldn't allow the diversity needed to generate life. What of an universe identical to ours but without the Pauli exclusion principle, to say one? Every atom would be identical; plus, gravity collapse would be quite easier. A chemically boring universe full of black holes: what a sh**ty place to live in !

But definitely, your magical substance is like ether; there's no need for it, so let's just throw it away. The deepest meaning of MUH is that we exist because our existence is mathematically coherent. WOW.

It also means that, since you can write a computer program with two AIs playing chess one against another, and a chessboard is a perfectly mathematically defined "world", that every single possible chess match is a world as real as ours.

(That goes for PAC-MAN, too )

 

[DevilsAvocado]

The observable universe appears to be temporally finite.

I do not see how a temporally finite universe can be infinitely large. A temporally finite universe can be unimaginably large, but, not infinite. Olber's paradox, imo, suggests an infinitely old universe should be in thermal equilibrium. This is not observed - e.g., :

Molecular Hydrogen in a Damped Lyman-alpha System at z_abs=4.224
http://www.arxiv.org/abs/astro-ph/0602212
. . . The high excitation of neutral carbon in one of the components can be explained if the temperature of the Cosmic Microwave Background Radiation has the value expected at the absorber redshift, T=14.2 K.

http://babbage.sissa.it/abs/astro-ph/0012222
The microwave background temperature at the redshift of 2.33771

Interesting thought about CMB. This arise further questions.

1) To my understanding, we already have problems in propagating the almost perfectly smooth CMB to parts of the universe that (due to speed of light) never has been in physical contact. And the only(?) solution for this is the Cosmic Inflation Model.
Q1: If the universe is infinite – How can the infinite CMB be almost perfectly smooth? Can inflation really 'rescue' this scenario??

2) To my understanding, the laws of physics were created at the very first moment of Big Bang.
Q2: If the universe is infinite – The Cosmic Inflation Model must be overwhelmingly fast (i.e. infinite speed) to 'connect' all parts of an infinite universe, so that they all have the same laws of physics? Is this scenario really feasible??

Q3: If NO on Q1 or Q2 - Can we state that the universe cannot be infinite...?

(Dmitry67 & Gan_HOPE326 please pop in and comment)

 

[Gan_HOPE326]

Interesting thought about CMB. This arise further questions.

1) To my understanding, we already have problems in propagating the almost perfectly smooth CMB to parts of the universe that (due to speed of light) never has been in physical contact. And the only(?) solution for this is the Cosmic Inflation Model.
Q1: If the universe is infinite – How can the infinite CMB be almost perfectly smooth? Can inflation really 'rescue' this scenario??

2) To my understanding, the laws of physics were created at the very first moment of Big Bang.
Q2: If the universe is infinite – The Cosmic Inflation Model must be overwhelmingly fast (i.e. infinite speed) to 'connect' all parts of an infinite universe, so that they all have the same laws of physics? Is this scenario really feasible??

Q3: If NO on Q1 or Q2 - Can we state that the universe cannot be infinite...?

(Dmitry67 & Gan_HOPE326 please pop in and comment)

Let me see... just my opinion, but...

Q1) This CMB thing reminds me of the Olbers paradox... fact is, of course CMB comes only from parts of universe in our "event cone" - i.e., from a max distance of age of universe*speed of light. So it couldn't be infinite anyway, right? And if it WAS infinite, wouldn't that be just more reason for it to be smooth (it would be equally "infinite" from all directions, right?). The bigger the zone we receive CMB from, the smoother the radiation itself, assuming universe is more or less homogeneous.

Q2) For what I get, Inflaction IS overhelmingly fast. And yet, it's not given laws are the same in every tiny angle of this universe. There's what we call "Parallel Universes of level I": zones of our universe actually impossible to reach (out of our event-cone) where same laws hold, but with different fundamental constants. Not to speak about the possibility of different Inflaction bubbles...

Universe isn't infinite - to us. Because we are confined into our event-cone. Said this, there could be infinite unaccessible event-cones belonging to our universe, and infinite other universes with our same laws but different dimensionality and constants; or, speaking of MUH, infinite other mathematical structures internally coherent which then are universes on their own, with completely different laws. Enjoy your mind-trip, folks; you've just made your first step into madness .

 

[DevilsAvocado]

You are starting to sound worrying, you know...
...
But you're right, MUH is quite exciting. (That goes for PAC-MAN, too )

Hehe worrying, you ain't seen nothing yet!
MUH is very interesting, but my own private speculations are absolutely scandalous:

BUUH – Brain Utilize Universe Hypothesis
-------------------------------------------
We have already proven that size is irrelevant for objects in the universe. Therefore it's plausible to say that our observable universe is nothing more than a Brain, not a Brane.

Galaxy clusters are Neurons, and the Stars are Neurotransmitters, and thinking Individuals on planets are the actual Thoughts in the BUUH = Piece of cake, the BUUH hypothesis is proven correct.

Here's a MRI slice of my own BUUH as an undisputable
scientific proof, showing real Expanding Space & Dark Matter:

And here's a close-up on one Neuron in my BUUH, thinking:

( Safety description: This IS a joke, please do not banish me from this forum! :)

 

[DevilsAvocado]

Let me see... just my opinion, but...

Q1) This CMB thing reminds me of the Olbers paradox...

Q2) For what I get, Inflaction IS overhelmingly fast. And yet, it's not given laws are the same in every tiny angle of this universe. ...

Universe isn't infinite - to us. Because we are confined into our event-cone. ...

Okay, sounds fair. But there is one word that physically separates our lives from never happened – almost. If the CMB is to smooth, there would never been any galaxies, stars and planets, only a smooth fog of particles. If the CMB is too clumpy, there would only be black holes.

As I understand this; the CMB we see is a result of low entropy + almost smooth energy/particle distribution, shortly after Big Bang, which is extremely special initial conditions. Change this just a little bit, and you get a completely different universe. Infinity alone could never give us this (I think?).

Yes, we could argue different CMB and different Laws in different parts (light-cones) of an infinite universe. But then you run into another extremely difficult problem:

Where do we 'cut off' CMB & Laws, for new ones!?

I mean, even in an infinite universe all parts connects with the neighbor to neighbor to neighbor to neighbor, etc, etc. And at least one neighbor will always be exactly between two different neighboring CMB & Laws...

What CMB & Laws should we expect in this weird Light-cone 2!?

<-------- CMB/Law 1 -------> ? CMB/Law ?? <-------- CMB/Law 3 ------->
<-----> Light-cone 1 <-----> Light-cone 2 <-----> Light-cone 3 <----->

I could be terribly wrong, but as I see it, the only way to have an infinite universe is by truly Parallel Universes (bubbles), with completely separate Big Bang's...??

Hence, One Universe with One Big Bang cannot be infinite!

(Can I have the Nobel Prize now, please? )

 

[DevilsAvocado]

Q1) This CMB thing reminds me of the Olbers paradox...

P.S.
You probably already have seen it. If not, there are some extremely cool "baby-pictures" of Our Universe (CMB) at The Wilkinson Microwave Anisotropy Probe (WMAP).
D.S.

http://map.gsfc.nasa.gov/

 

[Gan_HOPE326]

P.S.
You probably already have seen it. If not, there are some extremely cool "baby-pictures" of Our Universe (CMB) at The Wilkinson Microwave Anisotropy Probe (WMAP).
D.S.

http://map.gsfc.nasa.gov/

Yeah, I know. As for why this CMB is distributed like this, and why is it that the density of matter in the universe is perfect for creating stars and planets (instead of random dust or black holes) I can only answer what science answers today, that is... I don't know. God knows. Maybe. If He exists, anyway. Man, this is confusing .

There always is the anthropic principle (other universes exist where the initial distribution was different; but because of this, they have no sentient beings to observe them).

About your "light cone" question... maybe laws change gradually? So slowly that it takes thousands of light cones to find significant differences? And of course this would mean they change over time, too... but, after all, it wasn't me who came out with this theory. I only read it today - so I can't really defend it thoroughly. There surely are more qualified persons for this.

And since we don't really know what the heck Big Bang actually was, well, it could have been one, or ten, for one or ten or hundred universes, who knows? Can we tell that one Big Bang can't generate an infinite number of finite universes? All I think I can say is: we live in a pragmatically finite universe, that is, our light-cone. For what we know, there could be nothing outside of it; and we just couldn't tell the difference. Without a seriously believable TOE we can't really state anything on universe in general. And how can we tell if a TOE really is "of everything", since we don't know everything? The only thing I can think of is, after all, mathematical elegance. After the many proofs of physical reality perfectly fitting with mathematics, the least I expect from a good TOE is to be simple and beautiful. In exploring what we can't possibly measure and observe, after all, our logic and even our aesthetic sense can be our only weapons.

 

[DevilsAvocado]

Yeah, I know. As for why this CMB is distributed like this, and why is it that the density of matter in the universe is perfect for creating stars and planets (instead of random dust or black holes) I can only answer what science answers today, that is... I don't know. God knows. Maybe. If He exists, anyway. Man, this is confusing .

Thanks for bringing this down to earth, very wise.

This is extremely complicated questions (especially for an amateur like me ). I've done some reading on other threads in this forum, https://www.physicsforums.com/showthread.php?t=225329". This is clearly a very sensitive matter for professionals, and I can certainly understand this. Lots of hard work, and then have to deal with zillion of crackpots on the web, saying: Well, it's all wrong! My Guru gave me the real solution in a dream last night, and I know it's true, I feel it it's true – and I can prove it with my mantra!

You could go mad for less.

Not to "mess-up" things more, I'm going to start with a "disclaimer", before saying anything more:

• I am a layman/amateur.
• I have no real education in cosmology or physics (one introduction-course in astronomy).
• I read popular-science.
• I spend time on the web, searching and reading about cosmology & physics.
• I do not understand the advanced math, required for modern science.
• I admire all hardworking people who spend a great part of their lives, struggle to solve the mysteries of nature – to the benefit for all of us (guys drinking beer and watching football).
• I do accept physics as practiced by the scientific community (of course).
• I am not religious, and I believe that religion should not have any part in science (or politics).
• I think it is important that scientist do all possible to communicate new science to the public.
• I like to question subjects (that could be questioned by a layman), if they don't make sense to me.
• My only hope in the complexity of science: "If you can't explain it simply, you don't understand it well enough." -- Albert Einstein
• I am curious.

(After this, I do hope I'm not going to be banned for continuing this discussion...)

The Anthropic principle works, even if my humble opinion is – works to easy... Or to quote Sir Roger Penrose:

It tends to be invoked by theorists whenever they do not have a good enough theory to explain the observed facts.

Gradually changed laws might work... even if there are severe problems... for instance the Fine-structure constant (α), characterizing the strength of the electromagnetic interaction, which holds electrons and protons together in atoms, and hold atoms together to make molecules. The "logical" value of this constant is α = 0.08542455 and if α were > 0.1 stellar fusion would be impossible.

(Life in Light-cone 2 would be "interesting" if α ≈ 0.1 ...)

The "LightConeQuestion" bothers me. In the PF thread above https://www.physicsforums.com/showpost.php?p=2175640&postcount=41":

If the big bang happened everywhere at the same time, then the problem I have with an initially infinite universe, is how was such an event synchronised? An initially infinite universe would require infinitely fast signals to coordinate a simultaneous start time everywhere and that would require a hitherto unknown FTL signalling mechanism. The requirement for the big bang to start everywhere simultaneously is a requirement that comes from the constraint that the universe is homogenous on large scales.

In short, it would seem that an initially infinite universe requires faster than light communication or rejection of large scale homogenous principle.

And no answer from PF Science Advisors, or any other guru? Why??

I think this a very fair question. If Inflation handles this comfortably – why not tell us? And if not, what on Earth is the meaning of not communicating that?? I do not understand this.

I do understand that we are talking about some very important theories in cosmology and physics: Einstein's field equations, Friedmann–Lemaître–Robertson–Walker metric, Cosmological principle, Cosmological inflation, Lambda-CDM model. And that it all works, mathematically.

Wikipedia – Universe – http://en.wikipedia.org/wiki/Universe#Solving_Einstein.27s_field_equations":

This metric [FLRW] has only two undetermined parameters: an overall length scale R that can vary with time, and a curvature index k that can be only 0, 1 or −1, corresponding to flat Euclidean geometry, or spaces of positive or negative curvature. In cosmology, solving for the history of the universe is done by calculating R as a function of time, given k and the value of the cosmological constant Λ, which is a (small) parameter in Einstein's field equations.

... if k is zero or negative, the universe may have infinite volume, depending on its overall topology. It may seem counter-intuitive that an infinite and yet infinitely dense universe could be created in a single instant at the Big Bang when R=0, but exactly that is predicted mathematically when k does not equal 1.

An infinite volume, infinitely dense, created in a single instant, homogeneous and isotropic to an observer at all times in the future and in the past, with the same CMB and Laws of physics, propagated thru (infinitely fast!?) inflation.

Sweet Mother of Jesus – Can someone please explain this to me?

Favorite quote, again :

If you can't explain it simply, you don't understand it well enough. -- Albert Einstein

 

[Dmitry67]

1
I think this a very fair question. If Inflation handles this comfortably – why not tell us? And if not, what on Earth is the meaning of not communicating that?? I do not understand this.

2
Wikipedia – Universe – http://en.wikipedia.org/wiki/Universe#Solving_Einstein.27s_field_equations":


An infinite volume, infinitely dense, created in a single instant, homogeneous and isotropic to an observer at all times in the future and in the past, with the same CMB and Laws of physics, propagated thru (infinitely fast!?) inflation.

Sweet Mother of Jesus – Can someone please explain this to me?

1
Inflation handles the problem to some extent. However, the initial inflation must be described using Quantum gravity theory, which is not ready yet. So the initial inflation may be a solution. But it is difficult to provide more details now.

2
The wiki article is confusing. I hate the word "created" they used. The function ln(x) is defined for x>0 only, but it does not mean that ln(x) is somehow "created" at x=0.

creation uses the notion of time (not existed at t1, but existed at t2) which is not aplicable to the Big Bang. The theory of Big Bang does not cover the Big Bang event.

Except for this, yes, our Universe can be infinite spacially, and when you approach t=0, it becomes more and more dense until the known laws of physics hold. It is incorrect to say, however, that at t=0 it was "infinitely dense"

 

[DevilsAvocado]

1
Inflation handles the problem to some extent. ...

2
The wiki article is confusing. I hate the word "created" they used. ...

Thanks a lot! For taking the time!

1
Okay, that does explain why. Thanks.

2
Extremely interesting! I think it was Edward Witten who mentioned "spontaneous symmetry breaking" when he was talking about Big Bang.

If we bring this down to "layman-levels", could one say that?

A) At t-1 nothing existed; no time, no space, no matter and no laws of physics.

B) At t0 everything existed; time, space, matter and laws of physics.

C) Since time didn't exist "between" t-1 and t0, "virtual" matter had "all the time" in the world to "spread infinitely" in "virtual space"? Like "symmetry breaking" when a (perfect) lake goes from water to ice – the water is already there, and when the (perfect) temperature goes below 0°C – the whole lake freeze simultaneously (i.e. not spreading the ice from "one corner to another"). This "lake" can be infinite and still "freeze" simultaneously at t0.

Is this what happen at Big Bang, maybe?

(I know that current theories [QG <> GR] cannot yet go all the way down to t0, but is this the "working model" with "spontaneous symmetry breaking"?)

 

[Dmitry67]

If we bring this down to "layman-levels", could one say that?

A) At t-1 nothing existed; no time, no space, no matter and no laws of physics.

B) At t0 everything existed; time, space, matter and laws of physics.

No
Say, Universe is defined at t from 0 to +INF
Then at t=-1 the question "did smth exist" is non applicable, because theory is not defined for t<0.

I want to accent the defference between 2 cases:
1. at t=-1 nothing existed
and
2. at t=-1 specetime is not defined

In case #1 you get a 'creation' at t=0
In case #2 nothing is created.

Very likely, in string theory, or LQG the vary nature of time is different few plank times after t=0.

 

[DevilsAvocado]

In case #1 you get a 'creation' at t=0
In case #2 nothing is created.

Aha... what is the difference between "not defined/defined" and "not exist/exist"?

(as for spacetime that is)


Edit:
Maybe a stupid question... Let's formulate it this way:

"2. at t=-1 specetime is not defined"
"In case #2 nothing is created."

Yes, nothing is created, but spacetime goes from undefined to defined, so you could argue that the definition of spacetime is "created" at t=0 , ... or ...?

Is guess it's the natural logarithm ln(x) that is the underlying foundation for this way of formulating the "event" (stupid question again)? You'll never be able to break thru the "0-wall" at t=-1 ... and therefore it's not that bright to talk about something as "not existing" at t=-1, right?