The universe could be infinite in spatial volume and matter content. T or F?

[gcol]

Martin:: Help!

 

I don't see a problem with the balloon analogy, except in the limitations of the mechanics of a party balloon.

 

My balloon has no skin, requires no space for expansion.

 

It makes its own space. It is driven by its own internal forces.

 

It is complete within itself, containing all we know or can know. Our own cosmic balloon is all there is.

 

It may or may not achieve equilibrium.

 

It may or may not contract to a singularity.

 

Imperfect analogies lead to flawed reasoning

[Martin]

Martin:: Help!

 

I don't see a problem with the balloon analogy, except in the limitations of the mechanics of a party balloon.

 

My balloon has no skin, requires no space for expansion.

 

It makes its own space. It is driven by its own internal forces.

 

It is complete within itself, containing all we know or can know. Our own cosmic balloon is all there is.

 

It may or may not achieve equilibrium.

 

It may or may not contract to a singularity.

 

Imperfect analogies lead to flawed reasoning

 

I may be dense and not getting what you are saying, but what it sounds like is you have understood the balloon analogy perfectly and have identified where it breaks down.

 

In the case of the real world space is expanding by Einstein's GR equation, not because of some kind of air being pumped into a higher dimension space inside.

 

Any analogy has limits and if you push the analogy too far you get mistakes.

 

You have identified where the limits are---in the mechanical CAUSE of the expansion. A party balloon expands because of air being pumped in. That doesn't correspond to anything in cosmology.

 

We'd have to imagine a balloon with a vacuum inside it and a vacuum outside it. We'd have to imagine that something started it expanding and it continues by momentum which it's own tension has not yet overcome. Nobody would be happy with the analogy.

 

In first year physics one learns mechanics and it always comes down to some differential equation, as I expect you know. there is a D.E. for a pendulum and a D.E. for a cannonball, and for a spring, and for a water wave, and so on. The key to mechanics (as a branch of general physics) is to use the correct D.E. In this case it is the Einstein Field Equation or the simplified Friedmann equation derived from it.

 

People trust the E.F.E. because it works so well describing gravity effects, like orbits in the solar system, and light bending, and time variation in GPS locator systems etc. and astronomical events closer to home.

 

And the Friedmann equations predicted an expansion redshift and Hubble's Law before Hubble observed it----predicted that one would see either a prevailing redshift or blueshift, an expansion or a contraction.

 

So the general feeling is that the E.F.E. is right (except at singularities where it breaks down) and that it, or the Friedmann simplification, EXPLAINS the dynamics of spacetime geometry. When you have a differential equation (whether for spring or pendulum or whatever) and it works in many different contexts you tend to think of it as an explanation for the mechanics.

 

So when you say "Help!" what i tend to think is it is time for you to take a look at the Friedmann equations. There are just two and they are not much more complicated than the other mechanics equations you may have seen, in first year physics.

 

there's a spacetime metric and the spatial part of it has a factor a(t) which changes with time----called the scale factor. And the differential equation involves the timederivative a'(t) and the current value a(t) of the scalefactor. And also the current value of the energy density, rho(t).

 

the energy density is a useful thing to know about the universe----it is where you convert all the matter like stars and dust into the energy equivalent and take the average over a large volume of space and it comes out to something quite comprehensible-----0.85 joules per cubic kilometer.

 

and that small but comprehensible density actually determines to a large degree what a'(t) is going to be relative to the current value a(t)

 

that is what one of the two Friedmann equations says. The other talks about a"(t) the second time-derivative of the scale factor (the change in the rate of change).

 

I have these equations copied in LaTex somewhere in the Astro reference sticky thread. If you want, I will get them and we can discuss them some.

As I say they are not all that hard. if you are already used to simple D.E. like for pendulum or springbob that you get in college freshman physics.

 

I think once you notice what is wrong with the balloon analogy (that it doesnt tell you the mechanics, it only gives a visual image of expansion) then it is maybe time to throw out the analogy and look at the differential equation that actually does encapsulate the mechanics.

 

Either way is fine with me, if you want, we will. But also not is OK too.

============

 

EDIT. I looked at the Friedmann equations that i have copied in posts #4 and #19 of the Astro links-sticky

http://www.scienceforums.net/forum/showthread.php?t=4133

and I could see how they would look intimidating depending how one felt that morning

maybe you wont feel like making the transition from material (rubber) analog to D.E.

if you do, ask for help. we would start with the k=0 case (spatial flat, it is nearly flat anyway so that is almost right)

because one of the terms is zero

and we would start with no dark energy (no acceleration)

so then the solution is just a gradual deceleration but expansion never quite stops

with a D.E. always study the simplest case first.

 

and if you don't want to mess with it, that's fine too.

[Anu-Ki Ptah]

Oh I wanted to add, that I feel the border in my own observational research is merely dictated by a change in overall frequency. SO again it comes to a stop but one could not see it in a 3Dimensional state due to relative frequency value..

Through alteration of a universl frequency value of a given object or being it would thusly change its state of being.

To the next dimensional construct..

But if one is speaking in purely mystical terms then we have to say that if we have consciousness then we would be repositioned into the next highest vibratory state of being..which for our consciousness as it is.would be the fifth dimension ,(being that as we in our present state consist of both 3 dimensional and 4 dimensional properties, The mental state is the intangible 4d state in which i speak of.) in purely mystical termonology

 

BTW Martin..would you give me your opinion on my Theory of Atomic reverberation?

Not sure if you did already and my Internet is acting goofy so I can't look right now.

I'll check back however.

Thanks.

[bascule]

Do I think it could be infinite? Sure... how would I know?

 

Do I think it's actually infinite? No. Not only do I not particularly like the idea for what can only be chalked up to "gut" reasons, but as far as my layman brain can comprehend all attempts to measure omega have suggested that this is not the case. If I understand the physics stuffins correctly, an infinite universe would have to be spatially flat.

 

This brings up a curious point though: if the universe is infinite with infinite matter, does that mean the Big Bang just represented a massive drop in the universe's density? I'm reminded of Hilbert's Paradox of the Grand Hotel... in a hotel with infinite rooms, it's possible to algorithmically rearrange the occupants (with a superprocess) such that you can always obtain more empty rooms. Is something like that what would've happened with space in the event of a Big Bang in a universe with infinite volume?

[Martin]

Do I think it could be infinite? Sure... how would I know?

 

Do I think it's actually infinite? No. Not only do I not particularly like the idea for what can only be chalked up to "gut" reasons, but as far as my layman brain can comprehend all attempts to measure omega have suggested that this is not the case.

 

that strikes me as eminently reasonable

If I understand the physics stuffins correctly, an infinite universe would have to be spatially flat.

 

If the only two possibilities are Omega = 1 and Omega > 1 (flat or positive curvature like a sphere) then that's right.

 

For several years now the measurments seem to disfavor Omega < 1, or even to rule it out. The error bars at least as far back as 2003, that I've seen, have been on the non-negative side. So one tends to forget that there is a theoretical possibility of an infinite negative curvature universe.

 

I think one can fairly say that an infinite universe would have to be flat or else negative curvature (which I find hard to picture) and the negative curvature case is currently not given much consideration or credence.

 

This brings up a curious point though: if the universe is infinite with infinite matter, does that mean the Big Bang just represented a massive drop in the universe's density? I'm reminded of Hilbert's Paradox of the Grand Hotel... in a hotel with infinite rooms, it's possible to algorithmically rearrange the occupants (with a superprocess) such that you can always obtain more empty rooms. Is something like that what would've happened with space in the event of a Big Bang in a universe with infinite volume?

 

Massive drop in density is a good way to put it, Bascule.

 

the thing that makes the density defined is the assumption of uniformity

(basically the Copernican principle that our sample isn't special in some way).

the distribution of matter LOOKS roughly homogeneous and isotropic on average and so one makes the ASSUMPTION that it really is, and so the average density is defined

 

the tricks in Hilbert's hotel have to do with moving stuff around IIRC. If you don't have uniformity then you can show the density is not well-defined. Inifinite mass divided by infinite volume can be whatever you want. Or whatever Hilbert's hotel clerk wants it to be.

 

I can't answer your question about a possible rearrangement of infinite mass at the time of, say, a bounce. It is an interesting (perhaps even strange) idea. For my part, I still think of infinite universe as logically possible but as time goes on I am getting deeper into the rut of thinking finite. So it is hard for me to speculate about that infinite big bang or big bounce possibility.

[Eureko]

I have no clue about it. I just voted for a finite space from what I know from reading Hawking.

If there was a beginning, and it started there and continued growing, how could it become now infinite? It should have grown over everything growable! Weird to imagine. I think it must be finite.

Me declino a pensar que también tiene una masa finita.

[antimatter]

I have no clue about it. I just voted for a finite space from what I know from reading Hawking.

If there was a beginning, and it started there and continued growing, how could it become now infinite? It should have grown over everything growable! Weird to imagine. I think it must be finite.

Me declino a pensar que también tiene una masa finita.

 

So you voted false?

Think about it; the entire universe is made up of an infinite amount of three dimensional spaces, so wouldn't all of these planes have an infinite volume?

And since they have an infinite volume, couldn't an infinite amount of matter occupy the space?

I'm not entirely sure either, but it just sort of helps to think about it as an infinite number of spaces rather than one space.

[Riogho]

But isn't space NOT infinite? Arn't we watching it expand?

 

And isn't the dark energy that perturbs throughout the entire universe actually decreasing in density with time, therefore it isn't infinite?

[antimatter]

The universe IS expanding, that is true, but the space inside the universe is infinite.

 

Do you mind giving a source for that?

[Shadowwalker]

In standard cosmology, matter is assumed to be distributed throughout all space more or less uniformly. So if space is infinite volume, the amount of matter is infinite. If space is a boundaryless finite volume then the amount of matter is finite as well.

 

In neither the finite or infinite case is there any edge or boundary to space, and since the region occupied by matter coincides with the whole of space there is no edge or boundary to the occupied volume either.

 

the question of space infinite or finite has not been resolved yet.

 

What is your opinion? Do you think space volume could be infinite?

 

Actually it is all theory so no one can truthfully answer as to what is the answer it is just one of the mysterious unknowns of the world we try to understand.

[Klaynos]

Actually it is all theory so no one can truthfully answer as to what is the answer it is just one of the mysterious unknowns of the world we try to understand.

 

I suggest you learn what a theory is in physics before you make comments like that:

 

http://en.wikipedia.org/wiki/Theory#In_physics

[doG]

I said true. Why?

 

Much of the thread here tries to compare one infinity with another. This is like dividing by zero, meaningless. For example, the set of positive integers, 1, 2, 3, .... is infinite but there is also an infinite number of infinite sets between any two integers. The makes the set of positive integers an infinite set of infinite sets of infinite sets. Obviously all infinities are not the same if any of them can contain others within themselves.

 

Most advocates I've encountered that believe in a finite universe rely on evidence from the CMBR, a result of the theorized Big Bang. Consider though, is it possible that the Big Bang occurred in a larger infinite volume of space? If so would the CMBR simply represent the limit of our observational ability with everything beyond the event horizon lying outside of our observational limit?

 

The OP asked if the universe "could" be infinite in volume and matter. Without supporting evidence that it can't then it would seem to be possible that it could.