Can the Universe possibly be finite?

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rgold

Trad climber

Poughkeepsie, NY

Dec 15, 2011 - 11:56am PT

Dingus, I don't know what you mean by infinitesimals. The manifolds in question that are potential models for the universe are differentiable manifolds and so are capable of hosting calculus. Mathematicians spent quite a lot of time eliminating the naive concept of infinitesimals from playing any logical role in calculus, only to have Abraham Robinson demonstrate that there is a way to logically include them, if you are prepared to expand your concept of the real numbers. In any case, one can still insist there is no such thing as an infinitesimal and lose nothing in terms of mathematical results. It follows that compactness is not in danger from any mischief infinitesimals could possibly cause.

As for the big bang, of course at the instant of creation there is a space-time "singularity," since the entire system is, mathematically, a single point. Since a single point is also a compact space, there is still no logical conflict.

Jennie

Trad climber

Elk Creek, Idaho

Dec 15, 2011 - 12:56pm PT

Another happy analogy of the expanding universe (from ASTR -101) uses the expansion of a sponge, As the sponge expands all points within it move away from each other.

Sigh! … no analogy is perfect…unlike a sponge which has a center…the universe has no center. All points in space are equivalent.

There is no identifiable point of origin of the big bang. (We are in a sense "inside" the big bang). Portions of the universe are disconnected from us, because it would take longer than the age of the universe for light to reach us from these distances.

But no matter how trancendent a telescope we built … our view is blocked. The “omg, I’m so excited” era immediately after the big bang and up through 300,000 years, matter in the universe was so hot that it only existed as a yummy soup of protons, neutrons, electrons, photons other subatomic particles. Looking back through time, to this period, light would be scattered in a fog through which we could not observe.

Dingus McGee

Social climber

Laramie

Dec 15, 2011 - 01:01pm PT

rgold,

perhaps it is that my naive view of singularities needs more sophistication to bring this concept up to current math thinking.

So regardless of what type of a distribution there is at the singularity all the formalities of integrate-able functions on compact spaces hold?

Do distributions exist within singularities? Or are all gradients infinite within any singularity?

That is, it seems all of space and time (we measure) were contained within this singularity. So the compact space we talk of arose out of this singularity.

Mighty Hiker

climber

Vancouver, B.C.

Dec 15, 2011 - 01:24pm PT

So whether or not the universe is finite, will this thread be finite or infinte? Is SuperTopo the universe? If so, why isn't FatTrad receding at the speed of light?

immediately after the big bang and up through 300,000 years, matter in the universe was so hot that it only existed as a yummy soup of protons, neutrons, electrons, photons other subatomic particles

And a ton of slander and mental speculations...

rrrADAM

Trad climber

LBMF

Dec 15, 2011 - 01:33pm PT

Rradam,
So space is expanding everywhere. There is no edge.
Ok that is a new concept for me

Everything is expanding or stretching
That's a wild concept

Everything isn't stretching/expanding... It is space that is expanding.

How does "nothing" get stretched though....
What is it expanding out of
Do we have any ideas about this?

Great question. Who says space is "nothing"? That's how we think of it, intuitively, but our intuition is often wrong at the quantum level, counterintuitive in fact... Lots of ideas, but nothing testable as of yet (Loop Quantum Gravity, String Theory, Twister Theory, etc)... Space is most likely granular at the quantum level. Since we accept that mass/energy warp spacetime (GR), and that warpage of spacetime is what we percieve as gravity since energy/mass responds to that curvature, one must ask the same question... If it is warping spacetime, then what is "it" that is warping?

Like a friend of mine once said:
"Gravity isn't the engine that drives the car, it's the racetrack."

Or, like John Wheeler said:
"Matter tells space how to bend; space tells matter how to move."

That's what we see, and this even needs to be taken into account with the GPS satellites, as they do experience time dilation due to SR and GR... If they weren't time corrected, the system would work. So, we do understand it enough to be able to accurately correct for it.

rrrADAM

Trad climber

LBMF

Dec 15, 2011 - 01:41pm PT

D... Sorry if I was sloppy in my words, as I never mean't to imply anything as fact, other than what we see... An expanding universe, and the effects of gravity. Those we see, and are testable. Also, high energy physics is able to reproduce conditions of what the universe would be like at about 10^-6 seconds, thus we have some good experimental evidence to support the BB Theory, from well before nucleosynthisis to the present.

And, "BINGEL" is my namo, not Bingo! =]

Mike Bolte

Trad climber

Planet Earth

Dec 15, 2011 - 11:31pm PT

Jenny - you can think of the "center" of the Big Bang as the beginning of time in a four-space kind of way.

Rich, you meant "geocentric" not "heliocentric".

Ed Hartouni

Trad climber

Livermore, CA

Dec 15, 2011 - 11:43pm PT

As for the big bang, of course at the instant of creation there is a space-time "singularity,"

the singularity represented by the "Big Bang" is in time only

rgold

Trad climber

Poughkeepsie, NY

Dec 16, 2011 - 02:09am PT

Rich, you meant "geocentric" not "heliocentric".

Yup.

the singularity represented by the "Big Bang" is in time only

Care to elaborate? What precisely is a singularity? And how can a (differentiable) manifold have a singularity in one parameter (whatever that means) and not have a singularity?

Ed Hartouni

Trad climber

Livermore, CA

Dec 16, 2011 - 03:48am PT

perhaps a bit to imprecise... and it's too late to get it right tonight...

the Friedmann models for cosmology have a relationship between the acceleration of the radius of the universe, and the radius related by the equation of state, so:

3Rdoubledot = -4πG(ρ + 3p)R

so you can solve for R(t)

the spatial extent of the universe in this model is determined by its age...

in the former cosmology
if ρ + 3p > 0 then Rdoubledot/R < 0 the acceleration is negative

at present R > 0, and Rdot > 0

so R(t) = 0 at some time in the past, you could define this as t=0

the current cosmology has ρ + 3p < 0 and an expanding universe...

Dingus McGee

Social climber

Laramie

Dec 16, 2011 - 09:03am PT

Ed,

so at some time in the past is there an R = 0 for this model? For some initial conditions? i.e. at t=0 we have to choose an R dot not= 0 to get change.

When R is identically zero(this is a singularity in space) you get no acceleration at t=0. So(by one set of IC's) there had to have been an R velocity which means the Big Singularity (space wise) lasted only an instant or infinitesimal amount of time?

Dingus McGee

Social climber

Laramie

Dec 16, 2011 - 09:06am PT

Ed,

How does the matter-energy that was at the site of the Big Bang sort of t=0 differ from the matter-energy in a Super Black Hole?

It seem that the gravity field would have collapsed in a Big Bang locale but not in the Black Hole Region?

Could the central region of a Big Black Holes be exploding like the Big Bang explosion but the exposion is not big enough to blow the Black Hole Apart? At some pressure the gravity field must collapse?

Dingus McGee

Social climber

Laramie

Dec 16, 2011 - 11:04am PT

Ed,

this Fredmann cosmological (explosion-pressure) model assumes that the matter-energy state in Big Bang Singularity exhibits inertia as we know it in this t>>0 space we live in. Does the matter-energy state of Big Bang region near t=0 exhibit inertia?

Ed Hartouni

Trad climber

Livermore, CA

Dec 16, 2011 - 11:47pm PT

1) so at some time in the past is there an R = 0 for this model? For some initial conditions? i.e. at t=0 we have to choose an R dot not= 0 to get change.

if ρ + 3p > 0 then the solution for R(t) goes through 0 at some point, and depending on the equation of state, you can calculate that time from the current conditions.

However, the "dark energy" provides a negative pressure p which makes ρ + 3p < 0.

So it is an interesting question how all this goes together.

if the universe is dominated by cold non-relativistic stuff the time since the singularity R(t)=0 there R(t0)=R(now), t0= 3/2H0

where H0 is the Hubble constant... but that gives a universe that is too young.

If the universe is dominated by relativistic matter, then t0=1/2H0

and if by vacuum energy t0 is infinite... the de Sitter universe.

There are epochs in the universe when relativistic matter dominates, where cold non-relativistic matter dominates and where vacuum energy dominates...

As far as initial conditions at the time of the singularity, that is a matter of speculation.

Inflation happens early, but certainly after the t=0 moment.

2) How does the matter-energy that was at the site of the Big Bang sort of t=0 differ from the matter-energy in a Super Black Hole?

We don't know what the state of matter is inside a black hole, we don't have a quantum theory of gravity, which is required to answer that sort of question. The differences are that at t=0 and after, there was sufficient kinetic energy (pressure) to overcome the potential energy (gravity) and set the entire universe into expansion.

Inflation is a way to very the Hubble "constant" and cause the universe to expand exponentially, the end of that inflationary period is the restoration of the system to a ground state, a transition out of the "false vacuum"....

while this may sound fanciful, the finger prints of this are in the cosmic microwave background in the fluctuations that are observable in the sky today.

In a black hole, the matter collapses because the gravitational energy overcomes the "Pauli pressure" of electrons, then of nuclear matter... but what happens after that is not yet accessible to us.

3 Singularity exhibits inertia as we know it in this t>>0 space we live in. Does the matter-energy state of Big Bang region near t=0 exhibit inertia?

the energy balance of the universe is nearly zero (it is zero for all intents and purposes). This is often referred to as the "flatness problem" but what it says is that the kinetic energy of the universe equals the potential energy.

To have this the density of the universe has to equal the critical density, which it does... and it has not changed much since t=0.

rmuir

Social climber

From the Time Before the Rocks Cooled.

Dec 17, 2011 - 10:51am PT

Space is incredibly inconceivably large.

"You keep using that word. I do not think it means what you think it means."

rgold

Trad climber

Poughkeepsie, NY

Dec 17, 2011 - 12:49pm PT

If infinity cannot "be," then there is some time after which there is no time.

Ed Hartouni

Trad climber

Livermore, CA

Dec 17, 2011 - 12:50pm PT

which, of course, begs the question, "what is time?"

Ed Hartouni

Trad climber

Livermore, CA

Dec 17, 2011 - 01:23pm PT

"So where does the idea and math for the destruction of anti-matter in the early stages of the big bang come from."

if you look around you, you do not see matter and anti-matter annihilating, say, look for the 511 keV X-rays of electron-positron annihilation.

Those X-rays are a signature of matter and anti-matter being around one another.

So look a bit farther away, nothing...

Look even farther away, still nothing....

Where ever we look in the universe, no matter how far back, we don't see anti-matter in the same quantities as matter.

We infer from this that there is an asymmetry which would treat anti-matter differently than matter. In the very early times of this universe, the energy density was sufficiently high that the elementary particles were what there was, and they were interacting with each other... the slight asymmetry in the interactions caused the anti-matter to disappear faster than the matter.

What does the math looks like?

It depends on what theory you would subscribe to in order to explain the asymmetry.

The asymmetry cast in the language of "The Standard Model of Particle Physics" is called the "Strong CP-problem" and the most elegant solution (at least from our perspective now) is the possibility that the QCD lagrangian admits a term which would cause a violation of the "charge conjugation" (C) and "parity" (P) symmetries... the overall symmetry CPT (T is "time reversal") is thought to be inviolate for deep reasons.

The axion is a particle which comes out of this theory of Roberto Peccei and Helen Quinn (in 1977).

The discovery of the axion at a particular mass and "coupling" (read "charge" but it is not electromagnetic charge) would provide both an explanation for CP-violation and the Dark Matter of the universe... we'd kill two birds with one stone, so to speak.

TWP

Trad climber

Mancos, CO

Dec 17, 2011 - 03:05pm PT

If the universe is infinite, when did it become infinite?

Conversely, if the universe is finite, when did it become finite?

A finite or infinite time ago?

How could we possibly tell the difference? Especially since we believe our universe began a mere 13.7 billion years ago. We have no way to detect an event PRIOR to that time.

I believe "our universe" began 13.7 billion years ago as an indefinitely small space and mass and has expanded ever since.

This possiblity means countless other universes - like at point of beginning infinitely small in space and mass - originated both before and after the event horizon of the beginning of "our universe."

I believe we have no way of "going beyond/before" the origin of our universe and can realize that amongst the multiverses, "ours" is one amongst perhaps an indefinite (but not infinite) number of other universes.

Why do I say "indefinite" instead of "infinite" "number of other universes?"

Because if more universes can still be created from an infinitely small space and mass, then at some point in time, there will be "one more" - and thus was NOT infinite the moment before that "next" universe came into existence.

If the universe became infinite a finite time ago, then there is a time "before" and "after" the universe became infinite. But how long? Infinite or finite? Gets hairy no matter how you try to unpeel the onion.