The Universe: Finite or Infinite?

[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?

 

[Chronos]

Why is that surprising? You are solving for an indefinite integral.

 

[Dmitry67]

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

Not exists:
number of smth = 0

Not defined:
number of smth = FATAL ERROR.

 

[DevilsAvocado]

Not exists:
number of smth = 0

Not defined:
number of smth = FATAL ERROR.

Okay, thanks Dmitry6.

I was "hooked" on the "parallel" to:

ln(1E-100) = -230,258509338289
ln(0) = FATAL ERROR

(My "intuition" tell me that if you claim to create smth, then you probably also need a "creator", and that's not "likeable". On that I agree with +110%!)

Let's talk about:
1) "So the initial inflation may be a solution. But it is difficult to provide more details now."

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


Q1) If the universe is infinite; I derive from 1 that you accept the thought that spacetime/matter/laws was "spread" infinitely at t=0+1plank? I.e., it was NOT infinitely already "there", for some kind of "spontaneous symmetry breaking", right?

Q2) GR says that gravity slows down time. Could the extreme density at t=0 have made "room" for an "infinite inflation spreading" of CMB/laws?

Q3) If (the yet speculative) LQG is correct, then Q1 must also be correct, right? Since we are talking about the Big Bounce, right?

Q4) If Q1 is wrong: How can one singularity (Big Bang/Big Bounce) be infinite?

Q5) Is your opinion that an infinite universe needs to have the same CMB/Laws of physics?

 

[Dmitry67]

Q1. No, if universe in infinite now, it was ALWAYS infinite.
Q2. Time is slowed down for the objects inside gravity wells relatively to other observers outside. In the Universe, all observers were in the same conditions, and there were no 'outside' observers, so the answer is NO
Q3. Why? Big Bounce is compatible with both Finite and Infinite universes.
Q4. Singularity is not a point (while it is a point in some cases). Singluarity means 'some physical variable becomes infinite'. In infinite universe singularity (inifinite density) was just everywhere.
Q5. It is difficult to imagine how physical laws can be different in different areas or in different times. In both cases it would require some 'border line' with some laws on the left and another on the right.

 

[DevilsAvocado]

A fish cannot comprehend the existence of water. He is too deeply immersed in it. - Sir Oliver Lodge

Thanks Chronos! For the solution!
I must explain; I am a layman finding my way thru the "deep water"...
The background for this is (https://www.physicsforums.com/showpost.php?p=2466119&postcount=116":

... 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.

And Dmitry67 hated the word "created".
And the explanation for my clumsy way thru the "water" is maybe here https://www.physicsforums.com/showpost.php?p=2470490&postcount=123".

So, what's your opinion – is the universe Finite or or Infinite? (with all respect to the "deep water" )

 

[DevilsAvocado]

Q1. No
Q2. NO
Q3. Why?
Q4. In infinite universe singularity (inifinite density) was just everywhere.
Q5. it would require some 'border line' with some laws on the left and another on the right.

Thanks!

The good news:
Q5 is a BIG relief for me. I was struggling with the (nervous ) 'borderline' question here https://www.physicsforums.com/showpost.php?p=2462473&postcount=113".
At least some indication that 'layman thinking' works to some extent...

Q2: Thanks. Missed relativity in GR completely.

The bad news:
I think the answer for Q1, Q3 and Q4 is way over my present understanding...?

Q1: I 'my world', if you take the "Cosmology point of view/God’s eyes view/Bird’s view" of the universe at t=2, and then look again at t=200, you must see some difference in size, since we can prove that the universe is expanding at least 2c?? As you explained in https://www.physicsforums.com/showpost.php?p=2457103&postcount=72"; "Now expand this line to 200%: every point on then new line will be 2*X. All distances now doubled.". To me, if distances are doubled, it means that the overall (Bird's) size must also be greater? I can't get this into my head...

Q3: Same as Q1. (Big) Bounce to me, means something is getting bigger/smaller/bigger (in cosmology).

Q4: I can imagine an extremely large singularity, but not infinite. In 'my world' you need to concentrate/contract matter to make a singularity, hence moving it from other parts towards a more common center. Only solution to this (for me) is to 'create' more matter, so that the density increases globally/infinitely. But that's not feasible... I think?

 

[Dmitry67]

I think the thing which puzzles you is the behavior of infinite sets.
You try to apply the concepts of 'total mass' or 'total volume' to infinite sets, while it is well known that such measures are not applicable.

There are 3 ways to compare sets:
1. measures, like length or volume. You can use it when sets are finite, or areas are finite, and when sets are 'smooth' enough
2. number of dimensions (when some spatial metrics is defined on the sets). Space can be infinite;
3. cardinality. cardinality is applicable to any sets, nothing is required. If Axiom of Choice is accepted, then any sets can be compared using cardinality.

You always think about #1, while it is not applicable for infinite set.
When all sizes in the universe are doubled, and you believe then now it is 'twice is size', ask yourself, on what level are you talking: 1,2, or 3. If 1, then you can't use it for infinite sets.

To challenge your intuition, what set is 'bigger': a line or a 3D volume? Common sense tells us, that there are 'much more' points in 3D space then there are on the line. Yet, both sets have the same cardinality: you can map all points of a line to 3D space and all points of 3D space to a line so no point will be left and there will be 1-to-1 relationship. So you can't trust common sense.

 

[Dmitry67]

I can imagine an extremely large singularity, but not infinite.

Why not?
Say, density P=1/t everywhere in 3D space.
So P(X,Y,Z)=1/t
Here is an example of singularity infinite in size at t=0

 

[Chris Davison]

Hi everyone, I return after a couple of years,

Does the Universe have a limited life span or permanent existence? Is it limited or infinite in size? Is Earth the only inhabited planet? Has there ever been a period when no life of any sort existed anywhere in the Universe?

We can have a useful idea of the size of a lake or a forest, even of a state or country; however, looking away from Earth into space stretches the imagination to the extreme. Aware of my limitations I submit the following:

A choice needs to be made between finite and infinite size and between finite and infinite life-span.Without an understandable explanation as to what lies beyond the limits; my choice is for infinite in both cases.The finite-size view seems to be assuming a state of “absence of everything” at the edge of an Island-Universe. The finite-life view requires this same “absence of everything” before and after a limited life-span and it must also require a super-power capable of both universal creation and destruction. This power is not required if the assumption is made that the Universe had no origin and will always exist.Of course, infinite size and lifespan are not understandable concepts in the same way as the size of a lake or wood. This leads to the basis of my argument—in English, finite means limited, and to say that the Universe is limited is to say that once the limit is reached all trace of everything disappears including dimension; Now this is more difficult to accept than to assume infinite lifespan and size—It is reasonable to ask those who claim limited size and lifespan to explain how space and material came into existence from nothing, how it will disappear again, and to explain the situation beyond the edge of a finite-sized Universe; otherwise, are we not forced into the conclusion that the size and lifespan of the Universe are unlimited?

Barely detectable distant galaxies are very near objects indeed in a limitless Universe: they are as closer than the next grain of sand on an infinitely large beach. Although our tiny microcosm ( the detectable universe) will follow universal laws there has not been proof,observational or otherwise, of big-bang expansion.Infinite size contradicts the big-bang theory because the "proof" of the "Big Bang" is in part observational and the flawed calculations "proving" the "Big Bang" are based on the assumption that the Universe is finite in size and lifespan.also of course the Law of Conservation of Mass completely contradicts the "Big Bang" theory.In a Universe of infinite size, if there was a “bang” it was a local mini-bang, big only by our microscopic standards and not connected with”the origin”of a Universe that had no origin.

The Universe cannot expand or contract: these terms do not apply to infinite size, something of infinite age cannot be evolving with time. Matter: in one form or another always occupies infinite space and is not an“island” otherwise the “beyond the island” question remains. Only the components of space are subject to curvature not space itself; otherwise an understandable explanation of “curved nothing”is required.

The Universe does not have an “edge” or an “age”and any component or change would take an impossible infinite time to “cross” the Universe. (Of course, the expression”to cross”does not apply to infinite distance) Unlimited space, time and material have always and will always produce life at various levels; However, conditions required to produce life will occur infrequently by our standards and contact is unlikely. The nearest of a endless number of examples could well be located too far away for any form of communication.


I like and recommend Dr Rhawn Joseph's YouTube video on this subject:





Chris Davison

 

[Dmitry67]

Sorry, is it poetry or physics?

 

[DevilsAvocado]

Why not?
Say, density P=1/t everywhere in 3D space.
So P(X,Y,Z)=1/t
Here is an example of singularity infinite in size at t=0

This is spacey!

I have to think some more before 'computing' infinite sets... And jump on to the much easier part – infinite singularity!

Okay, maybe it’s because I think in 'pictures' and you think (the right way) in mathematics, that this doesn’t work for me. I’m going to try to get as close to your math as possible.

The density of a material is defined as its mass per unit volume:

$$\rho = \frac{m}{V}\,$$

I take it the same rule goes for the (infinite) universe? Ok, then if we then take the '2D Balloon Surface' as an analogy for universe, and use the Earth as the balloon (and forget about mass 'inside', and place all mass on the surface of Earth instead, and hope that it will work? ).

Now the surface of Earth will weigh 5.9736 × 10e24 kg at a radius of 6371 km (still hope that it will 'hold'!? ). For this to turn into a singularity, we use the Schwarzschild solution:

$$r_{s} = \frac{2GM}{c^{2}}$$

I skip the math , and pick the right answer from the web, and we get that the radius has to shrink from 6371 km to 9 mm (peanut-size), for the Earth mass to turn into a singularity!

Maybe this is not applicable on a 3D space? But I hope you see what I aiming at? The shrinking of volume to get higher density, to finally reach the Schwarzschild 'border'... and then I remember that you just mentioned that volume is not applicable to infinity, man this is weird...

But, now another question pops up! In an infinite universe, with infinite matter – how can you avoid the thing from turning into a singularity immediately at t=0+1plank... Schwarzschild would go bananas??

 

[DevilsAvocado]

Sorry, is it poetry or physics?

Ehhh well... right now my brain is somewhere in-between infinite poetry and finite physics... I think?

 

[DevilsAvocado]

Hi everyone, I return after a couple of years,

[Disclaimer: I’m only a layman]

Hi Chris, lots of questions and I’m going to give it a try:

"Does the Universe have a limited life span or permanent existence?"
We can’t tell yet, and the word existence is hard to put on the universe. What we do know is that the age of universe is 13.73 ± 0.12 billion years, since Big Bang. This is measured physically by the expansion using type Ia supernovae, temperature fluctuations in the CMB, and the correlation function of galaxies.

"Is it limited or infinite in size?"
Ask Dmitry67. (could be either)

"Is Earth the only inhabited planet?"
No one has called yet... But, my personal feeling is NO. The nearest galaxy Andromeda contains one trillion (10¹²) stars, and our own Milky Way contains 400 billion stars. There are probably more than 100 billion (10¹¹) galaxies in the observable universe (46.5 billion light-years). And we have found exoplanets (a lot!). So, it looks like a terrible waste of material if Earth was the only planet with excellent forums like this one!

"Has there ever been a period when no life of any sort existed anywhere in the Universe?"
Yes, definitely. From Big Bang until about 400 million years there were no stars = no life.

"...there has not been proof,observational or otherwise, of big-bang expansion"
Wrong. Actually in 1998 the http://en.wikipedia.org/wiki/Supernova_Cosmology_Project" published evidence that the expansion of the Universe is accelerating!

"Only the components of space are subject to curvature not space itself; otherwise an understandable explanation of “curved nothing” is required."
Wrong. The gravity from a massive object (such as a galaxy cluster or black hole) is warped space-time, bending everything in it – including the paths followed by light rays from a bright background source, creating Gravitational Lensing.

 

[Chronos]

Thanks Chronos! For the solution!
I must explain; I am a layman finding my way thru the "deep water"...
The background for this is (https://www.physicsforums.com/showpost.php?p=2466119&postcount=116":


And Dmitry67 hated the word "created".
And the explanation for my clumsy way thru the "water" is maybe here https://www.physicsforums.com/showpost.php?p=2470490&postcount=123".

So, what's your opinion – is the universe Finite or or Infinite? (with all respect to the "deep water" )

Thanks for the easy out, my view is the universe is observationally finite. I avoid speculating beyond that because it cannot be falsified.

 

[Dmitry67]

But, now another question pops up! In an infinite universe, with infinite matter – how can you avoid the thing from turning into a singularity immediately at t=0+1plank... Schwarzschild would go bananas??

Look at the formula for Schwarzschild raduis. Do you see something strange? r is propotional to M. Intuitively one could expect r^3 (as volume).

So yes, you must compress Earth to 6mm to make it a black hole. Now make Earth (using the same material) 10 times bigger (radius of equator). It is now 1000 times heavier, as we assume the same density, and volume increases as r^3. So Schwarzschild raduis will be 6meters. It contains 1000'000'000 more space, then before to accommodate 1000 time more mass, so the density of that object, to be converted into a balckk hole, is 1000'000 times less now!

As you see, for a constant initial density, Schwarzschild radius grows as r^3 of the object radius. So, it 8always* catches with an actual raduis! It means, that you can make a black hole of any material without compressing to - from ground, earth, air, and even interstellar gas, you just need to make a big enough volume of that material.

Einstein was the first who had realized that. For the infinite Unvierse it means that it collapses into black hole now matter how low an average density is. That is why he introduced the lambda, trying to save the Universe.

However, it is applicable to the static universe only, if Universe if expanding, then its density depends on an average density and rate of expansion. So, regrding 'why it does not form singularity immediately' - because it MUST be expanding!

 

[Dmitry67]

The density of a material is defined as its mass per unit volume:

$$\rho = \frac{m}{V}\,$$

I take it the same rule goes for the (infinite) universe?

Yes, you just use it 'locally', for small volumes here and there, you don't need (and you cant) to calculate the nominator and denominator for the WHOLE universe.

 

[DevilsAvocado]

It means, that you can make a black hole of any material without compressing to - from ground, earth, air, and even interstellar gas, you just need to make a big enough volume of that material.

Einstein was the first who had realized that. For the infinite Unvierse it means that it collapses into black hole now matter how low an average density is. That is why he introduced the lambda, trying to save the Universe.

However, it is applicable to the static universe only, if Universe if expanding, then its density depends on an average density and rate of expansion. So, regrding 'why it does not form singularity immediately' - because it MUST be expanding!

Thanks a lot. I feel shivers down my spine... maybe there is small possibility for me to really understand this... I’m going to take my calculator and actually solve the equations... this is maybe not as hard as I imagine from start... fantastic...

I’ll be back. Thanks again.

 

[DevilsAvocado]

Thanks for the easy out, my view is the universe is observationally finite. I avoid speculating beyond that because it cannot be falsified.

That’s probably a healthy approach to the problem. On the other hand, we have really 'bad fishes' in 'the water', who doesn’t even care there’s an http://en.wikipedia.org/wiki/Multiverse" ...

 

[DevilsAvocado]

Yes, you just use it 'locally', for small volumes here and there, you don't need (and you cant) to calculate the nominator and denominator for the WHOLE universe.

Okay thanks. That, my brain is slowly accepting.

 

[naeemakhtar]

re:universe:Finite or infinite.
i have gone through the all dicussion on the finiteness or infiniteness of the universe.When we talke about finiteness or infiniteness then we percieve a goematrical figure describing (length,area or volume) terms of the numbers.Whole dicussion revolves arroud some definte geomatrical figures(which maths has discoverd) to comprehend the structure of the universe,do we excuse to accept the probablity of existence of some undiscovered geomatrical figures or shapes which could have potential to explain the struture of the universe at BB(big bang) and transition in it explicitly.or Mathematics
is insufficient to cater the qustion.