Is the Universe Infinite?

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hmm, i think it don't, and in the same time, it do, maybe it don't have a limit, also it's expanding all the time,
but i think there's more after it,
it is infinity, but, it could be there another stage,
for example, you can find two places in a one places, that's what we can call, dimentions.

i had a topic about this subgect,
here's the link
http://sciforums.com/showthread.php?t=98645

 

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I don’t want it moved.

I personally have a significant learning base upon which I speculate but it seems that unless I give the details of my self-learning it leaves my speculations open to the same degree of criticism as fantasy and idle speculation. If I say I am self taught the criticism is that I went to Wiki, and unless I can convey the depth and detail of the foundations of my understanding I am still not qualified to speculate in the minds of some.

I’ll respond to your topic here, give some details of the foundation of my reply, and let the chips fall where they will. For this reply the self learning can be traced back to the early 1990‘s. I bought Penrose’s book, “The Emperor’s New Mind”, concerning computers, minds, and the laws of physics. My critics will call that Pop literature and not sufficient for a foundation of understanding. But I am college educated at a Big Ten University, a graduate in Finance and a retired financial executive who has had a continual and growing interest in science.

In Penrose’s book there are two chapters that make up about half of the book. One is call, “The Classical World”, and the other is, “Cosmology and the Arrow of Time”. The reason I mention Penrose is because you referenced the Big Bang and acknowledged that as the start of the universe in post #10. The Big Bang Theory is not considered speculation as much as it is considered the Standard Cosmology. Big Bang Theory is very specific about a few important things. One is the math. General Relativity math tracks back to a singularity and that is not said with a bad connotation. It simply is fact. A mathematical singularity occurs when spacetime beings. The Big Bang is the slang term applied to the beginning of spacetime and the name caught on more from press coverage than from the intentions of Einstein and others who developed it. Penrose does a good job of explaining it.

I mention Penrose’s book chapters on classical science and then relativity because in the period right after General Relativity first came out, or at least by around 1915, classical physics and the current cosmology of the day were based on a Euclidean coordinate system and Newtonian laws of gravity among other classical physics that has been evolving since Plato. Plato thought of the real world as made up of certain geometrical shapes but said the shapes were the ideal which the real world never quiet lives up to. General Relativity is the modern day equivalent to the view that reality is not Euclidean and Newtonian because those coordinate systems and analytical tools cannot cope with the realities of a relativistic world. Spacetime came into being to account for the tiny by pervasive differences between what could be explained classically and what couldn’t.

Penrose conveys the thinking that started with Einstein’s GR and the important application of tensor equations. He, in layman’s terms describes the WEYL and RICCI tensors which he capitalized in the text just like I did here. I am not shouting when I capitalize those terms. He explained how the Einstein Field Equations apply to a relativistic universe that we have come to embrace.

Phase space comes into play and at relativistic speeds and distances things happen to space and time that make the classical tools insufficient to explain. So General Relativity replaced the classical equations with WEYL, RICCI and relativistic coordinate systems, but the math that all of that is built on has specific characteristics. One of the characteristic is the beginning singularity. That means that unless you go down to the level of quantum mechanics which GR does not traditionally do, you have the beginning of spacetime with a singularity that essential implies zero volume of space containing infinite energy density, i.e. the mathematical singularity.

So when you say Big Bang was the beginning as you did in post #10 you are placing the discussion of the question, “Is the universe infinite”, right in the relativistic view point of GR and the singularity at the beginning. So from that context the space and time emerged in unison and are connected and as the singularity began to expand, spacetime inflates. My view is that the volume increases from the zero volume of the singularity and as it increases the energy density of the universe declines proportionately. The expansion is covered in Big Bang Theory by Alan Guth’s Inflationary Theory, also described in a book that I have borrowed from the library on several occasions. It describes exponential expansion from the singularity to a volume billions of light years across with the superluminal expansion taking place at around 10^-30 seconds after the Big Bang event.

That expansion is still going on today as you have acknowledged.

So to address the question in the OP from that foundation, it can be said that the universe is infinite in the context that the universe is all there is, there can be no “outside” to the universe because that is an oxymoron; the universe is all there is and it is inflating and expanding and it is infinite in space but spatially finite. Maybe that sounds like a contradiction and if so maybe someone will help explain it.

But if that is a proper characterization of the answer from the perspective of General Relativity, then that is where the discussion between Euclidean coordinates and relativistic coordinates comes in. Euclidean space is infinite spatially and if an event similar to the Big Bang occurred, but not as a relativistic singularity, but as perhaps a common event within the Euclidean geometry of a greater universe and an infinite time continuum, then the answer is yes, the universe is infinite in space, our expanding patch of space is finite and growing in volume, and beyond our finite expanding patch of space the Euclidean leaves the discussion open for speculation about what might be beyond.

 

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Thanks Quantum Wave.
I'm in the same position as you.
When I was at school, I never realised that mathematics and physics were interesting.
I was also very bad at history, which is now one of my favourite subjects.

While in English, you studied the greatest writers such as Milton, Keats, and Shakespeare, in Maths you did algebra, and in Physics you did tedious experiments in Specific gravity and conductivity. When describing our Physics experiments, our Physics teacher made us do it in the past historic tense.
By the time I left school they were starting to include nuclear physics, and I started to get interested, but it was too late.

Hopefully they have changed the way schools operate now.

 

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They must have. I can tell from how bright and interested some young posters are. Keep an eye on Science Man and some of the other high school students who are looking to focus on math and physics. There are lots of young people who luv to show up the old guys. Too bad there won't be any Social Security left for them,

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. Just kidding about that...

Now Captain, how about you give us your view to your own question, "Is the universe infinite?"

 

I would say no, but I'm prejudiced.
I don't really like infinity.

One problem with it would be why the universe we see is so clumpy.
If there is infinite space, then why doesn't every particle have infinite space distancing it from every other particle?

 

because there are an infinite number of particles?

 

I don't think you can have an infinite number of particles in a finite universe can you?

 

Check out the Big Rip. My understanding is that in Big Bang Theory, given a positive cosmological constant, the universe will expand forever. Eventually the energy density will be so sparse that even the most stable particles will decay and the energy density will equalize across the endlessly expanding universe.

 

Captain Kremmen was talking about an infinite universe.

 

He was talking about infinite space and saying if that was the case why aren't particles all evenly spaced across it. Are you equating infinite space with an infinite number of particles in space?

 

There would be plenty enough space in an infinite Universe for an infinite number of particles to be infinitely distant from each other.

 

Not really. No two particles can be an infinite distace from each other.

 

Why not?

 

Because any distance that can be marked by two points in space is a finite distance. Think of two points on a line. The line can be infinitely long, but the two points must be a finite distance apart.

 

I believe this thought experiment underlies Einstein's idea of material particles at essentially infinite distance from any large gravitational mass.

If the particles are also infinitely separated there is no gravitational interaction, and the universe looks smooth. Therefore by induction, the universe doesn't consist of material particles infinitely separated, since the universe isn't smooth except at nearly infinite scale. Therefore our universe can't be infinite in size.

Note the qualifier "our universe". That's the one we get to observe--as Einstein pointed out there is only logical deduction, and the fact the universe looks logical to logical observers doesn't "prove" anything about the universe, except that observers are logical and see what appears to be a logical universe. We can't say that this logic is universal, only that it appears to be.

 

I think that argument is an argument against infinity existing at all.

Whatever distance you measure between two points, you can always put another point an inch further away and take away the first.
Ad infinitum.

 

That is a good point, however it doesn't mean that the line is not infinite. Suppose you do what you are suggesting but in the opposite order. Instead of putting another point an inch further away and then removing the first point, try taking away the point you are replacing before you replace it an inch further down the line.

Before you replace it, now measure the line from the single remaining point and you will find the line is infinite in length. There you have an infinity.

Another infinity that you might know about and not realize it is associated with the Big Bang. Theoretically, the Big Bang universe started with an infinity. The singularity that mathematically represents the beginning point in spacetime. A point has no volume, and BBT is interpreted by some to say that the total energy of our expanding universe occupied a point in space, i.e. infinite energy density in zero volume.

 

Yes infinite density, not infinite mass or infinite energy.
Also the theory can only track it back so far, so even infinite density may not be the case.

 

What about that back track. If the universe did start as a singularity meaning infinite energy density in zero volume then space itself started from zero volume and has inflated to the current volume. That volume is finite, and the matter and energy in it is finite. Your are right that BBT does not include space being infinite in volume and it doesn't include matter or energy to be infinite in quantity.

But if as you allow for, the universe does not track back to infinite energy density as in the singularity, then that means that some volume of space, however tiny, must have existed at the instant of the Big Bang, and the total energy that exists today must have occupied that tiny volume of space. Then that set of circumstances would eliminate the infinite energy density issue but raises an issue with the source and size of the space and the history of the energy.

If space and time did not begin with the singularity then the energy that occupies the tiny pre-existing space was not created with the Big Bang and that could confirm the idea that energy cannot be created or destroyed, but if it is true that energy cannot be created or destroyed then a new infinity comes up; energy could have always existed. There are implications from that which open the door to pre-conditions to the Big Bang. Since we cannot know about anything beyond the event horizon, we cannot know about, test, or confirm any pre-conditions and so the best consensus we have is Big Bang Theory.

You can Google "alternative cosmologies" and you will get idea of models that accept the possibility of pre-conditions, none of which can over come the black out on information imposed by the event horizon. Anything said about pre-conditions or beyond the event horizon is speculative.

 

The universe is expanding at an accelerated rate. If it is expanding it requires it to not be infinite.