Is the Universe infinite or not?

[Robertphysics]

The reason why I have this question is because I’ve been thinking that the observable universe is filled with galaxies and planets mostly around stars , and we also have explored that there are a lot of black holes in the universe which if I’m correct are simply dead stars which once had energy to keep themselves in equilibrium.
Now since all of the universe we know is like this I think it would be logical to assume that the rest of it or the parts we don’t see, because either they are too far or are expanding away from us faster than light, are also the same , that is filled with stars and galaxies.
What confuses me is that if the universe is indeed infinite (no one knows just making an educated guess here) then doesn’t that give us a paradox like there is/was infinite amount of energy in the universe or in the singularity that started the big bang ?
Because if the observable universe is filled with stars and leftover radiation energy from the big bang then we could assume the rest of it is also in the same form and if it has no limits then that is basically a limitless amount of energy simply separated by a vast distance due to expansion in time and space but since it came from a singularity doesn’t that imply that this singularity must have had an infinite amount of energy in it in order for it to expand into an endless space filled with endless stars that undergo fusion etc?

P.S. But if it’s finite I guess we run into even more mathematical and philosophical problems than with an infinite one don’t we ?

 

[DrStupid]

What confuses me is that if the universe is indeed infinite (no one knows just making an educated guess here) then doesn’t that give us a paradox like there is/was infinite amount of energy in the universe or in the singularity that started the big bang ?

Yes, an infinite universe contains an infinite amount of energy. But where is the paradox?

 

[anorlunda]

I hesitate to answer because others on PF are much more expert than I on subjects like this. But try this argument.

Energy doesn't exist by itself. Energy is a property of particles or fields. If there is an infinite amount of particles and fields, that have energy, then why shouldn't energy also be infinite?

 

[jbriggs444]

Even in models which have a singularity, there is no transition from "singularity" to "expanding universe" over which energy is conserved.

 

[Chronos]

Multiplication and division by zero yields nonsensical results. I fail to see to any reason to take such derivations seriously. It more accurately reflects, imo, the failure of our mathematical conceptions to properly model the universe.

 

[Robertphysics]

Thank you anorlunda for pointing that out. Well the paradox is in exactly what jbrings444 wrote , that if we suppose the universe started out at singularity and if it's somehow infinite now then either it was at once finite in terms of energy and particles and then somehow along the way got infinite or it was infinite from the beginning simply the spacetime expanded as it went along and I guess still does. Both ideas sound somewhat odd.
Ok but if those models transition from singularity to infinite universe then what do they put in if they leave out energy conservation ?One way this would sound better is that say universe started out with some finite yet extremely large , ridiculously huge amount of particles and densities that simply grew larger colder over time as space expanded and entropy was busy doing its job. But this again doesn't make sense in the case if universe is infinite because then I assume all the stars and galaxies would be so spread out that we would have problems detecting any in the observable universe correct? Because basically one runs over the problem of how do you put a finite amount of matter into an infinite spacetime which is yet expanding.

Ok so just for clarity I would love to make a short list of possible scenarios , please feel free to add some if their not mentioned , I would love to hear what you think is the most probable one.1) Universe begins at singularity with a large but not infinite density and expands over time , cools and forms the galaxies and all other mechanisms that we are now familiar with.
It continues to expand but is not infinite. This probably runs into the questions (a-into what it expands and what is behind the “fence” , is it a loop even though it’s near flat or is here something else we haven’t yet understood and proven…)

2) Universe begins the same as a densely packed singularity and then expands into infinity. Obviously the problem with would be how can something finite simply turn into an infinite object , but if I understand correctly atleast it doesn’t violate energy conservation and other stuff because spacetime expands but the matter simply decays and undergoes entropy and is separated by ever greater distances yet it doesn’t imply matter should somehow be infinite together with spacetime.
3) Universe begins everywhere at once , but this again is confusing as what is meant everywhere , it it’s finite then that can be understood but if it’s infinite then eberywhere is a meaningless word I guess. Also if it begins everywhere at once then how come it was insanely dense and hot at the beginning because if something is very dense everywhere at once then how does it get less dense over time ? Did it start everywhere but not infinitely everywhere at once and then over time that everywhere expanded into infinity but this again brings us in a loop of the same problems encountered in previous questions.

Sorry for this being that long or maybe something which I could have read on Wikipedia

 

[jbriggs444]

Thank you anorlunda for pointing that out. Well the paradox is in exactly what jbrings444 wrote

But there is no model where the universe started out with a singularity. That's what I wrote.

 

[newjerseyrunner]

I'm not sure that it'll ever be possible to determine that something is infinite?

If you're in the middle of a swimming pool and can only see five feet in any direction, how could you determine if the pool was finite or not?

You'd have to close to an edge, we've looked in all directions as far as we can see, and there is nothing that looks like an edge.

 

[DrStupid]

If you're in the middle of a swimming pool and can only see five feet in any direction, how could you determine if the pool was finite or not?

In such situations Occham's Razor comes into play. Boundaries without any relevance for experimental observations should be excluded from the theory.

 

[newjerseyrunner]

In such situations Occham's Razor comes into play. Boundaries without any relevance for experimental observations should be excluded from the theory.

That's the point I was trying to make I guess. We can only see 13b light years +-1, so all we can know is that the universe is larger than that and that it looks the same in all directions so there is no indication of a special boundary in or near our Hubble bubble.

 

[DrStupid]

We can only see 13b light years +-1, so all we can know is that the universe is larger than that and that it looks the same in all directions so there is no indication of a special boundary in or near our Hubble bubble.

The preference for an unlimit universe results from the observation that the visible universe is flat.

 

[phinds]

... if we suppose the universe started out at singularity and if it's somehow infinite now then either it was at once finite in terms of energy and particles and then somehow along the way got infinite

That is not physically possible. Either it was and is infinite or it was and is finite.

 

[OCR]

...eberywhere is a meaningless word...

Eberywhere might not be meaningless, I'm not sure, nevertheless ...[COLOR=#black].[/COLOR]

Here's a little trick though, see the red squiggly line under eberywhere ?

And, see the the check mark in the dropdown ?... put a check mark at the same place in yours...

edit:
God, I hope nobody saw my spelling mistake...

 

[Aufbauwerk 2045]

Cosmology is not my field, so I will answer your question with some questions. I admit I am extremely skeptical of talking about the whole universe as if we understand it. I would like to hear from the experts who are up to date with the research on this topic. Perhaps, since I don't know much at all about cosmology, my questions will seem quite naive.

For example, what does it mean when we ask if there is an infinite number of particles in the universe? What is the physical meaning of such a question? Suppose we give an answer. Can we back up such an answer, assuming it makes some kind of physical sense, using the scientific method? I think the question itself is meaningless from the point of view of the scientific method.

What does it mean to say there is an infinite expanse of space? Or what does it mean to say there is a finite expanse of space? Is there a boundary or not? If there is a boundary, what lies beyond? Again, how do we back up our claim using the scientific method?

We can never physically count an infinite number of particles or physically measure an infinite expanse of space. I take the view that if we can't count or measure something, we have no right to speak about it in physics. It's not the same as saying there are an infinite number of prime numbers. Infinity in that sense is a mental construct. It is not a statement about nature.

We might say the surface area of the Earth is potentially infinite, because we can travel around it an infinite number of times. But that is not the same as saying the surface area is actually infinite. Aristotle long ago distinguished between potential infinity and actual infinity.

As I said, I do not claim any expertise at all. I look forward to a cosmologist shedding some light on this subject.

 

[PeterDonis]

What does it mean to say there is an infinite expanse of space?

That one could, in principle, travel indefinitely in the same direction without ever reaching a point one had been to before. Mathematically, that the manifold which describes "space" is not compact. An example would be ordinary Euclidean 3-space.

Or what does it mean to say there is a finite expanse of space?

That if you travel far enough, in any direction, you will eventually start reaching points you have been to before. Mathematically, that the manifold which describes "space" is compact. An example would be a 3-sphere.

Is there a boundary or not? If there is a boundary, what lies beyond?

No models of the universe include a boundary to space. The models in which space is finite have it as finite without boundary, like a 3-sphere.

I take the view that if we can't count or measure something, we have no right to speak about it in physics.

This is much too strong. We talk in physics about many things that we can't count or measure. For example, we can't count or measure quarks; we only know of their existence indirectly.

 

[Aufbauwerk 2045]

That one could, in principle, travel indefinitely in the same direction without ever reaching a point one had been to before. Mathematically, that the manifold which describes "space" is not compact. An example would be ordinary Euclidean 3-space.
That if you travel far enough, in any direction, you will eventually start reaching points you have been to before. Mathematically, that the manifold which describes "space" is compact. An example would be a 3-sphere.
No models of the universe include a boundary to space. The models in which space is finite have it as finite without boundary, like a 3-sphere.
This is much too strong. We talk in physics about many things that we can't count or measure. For example, we can't count or measure quarks; we only know of their existence indirectly.

Thanks for your reply but I am not satisfied. (At least not yet ...)

It is one thing to create a mathematical model in which one could in principle travel in the same direction, however that is defined, and never arrive at your starting point. I am not asking about a mathematical construct, but about actual nature. How would we ever prove that the indefinite travel scenario has physical meaning?

I don't mean we need to literally count particles one by one and get the exact number. If we have a huge box full of particles, perhaps we could never literally count the number of particles, but the number is still finite. My point is that it is meaningless to talk about an infinite number of real particles. As far as I understand, it is just a mathematical construct with no physical meaning.

I guess I will need to leave this topic until next year.

 

[lifeonmercury]

What do you mean by physical meaning? Would you only accept the finding of an infinite universe after physically traveling trillions of light years to find you haven't returned to the same spot?

 

[anorlunda]

How would we ever prove that the indefinite travel scenario has physical meaning?

I think you just stepped over the line into nonsense philosophy which is not allowed by PF rules. How can you prove that you physically exist and aren't just a simulation in the matrix? -- nonsense.

But let me help you to express that in a more acceptable way. Hard science makes predictions which can be confirmed or refuted by observation. Science that can not produce refutable predictions is mere speculation. There is a lot of that tolerated by mainstream science. For example multiverse theories. They are tolerated in the hope that they will produce refutable predictions. But the support lasts only as long as the hope. Support for string theory seems to be weakening because it hasn't yet produced refutable predictions.

So, what are the hopes of cosmologists about finding refutable predictions relating to open/close/flat universe?

 

[PeterDonis]

How would we ever prove that the indefinite travel scenario has physical meaning?

You can't. But you can't prove that the "quark scenario" has physical meaning either, because you can't directly observe them. We believe quarks exist because our best current theory of elementary particle physics, the Standard Model, requires them to exist in order to explain what we observe. We similarly believe that the universe is spatially infinite because our best current theory of cosmology requires that in order to explain what we observe. Our level of confidence in the latter case is weaker than in the former, but the basic thought process is the same.

 

[Orodruin]

How would we ever prove that the indefinite travel scenario has physical meaning?

You do not prove things in physics. You prove things in mathematics, but in physics you attempt to describe how the world behaves in terms of a model. If your model is successful in describing what you observe then it lives to make another prediction. If not, it is discarded or modified. Note that even models that are known to not work in certain regimes may still be very good for describing how things work in some other regimes. For example, Newton's theory of gravity works quite well for most solar system dynamics apart from predicting small effects such as the perihelion precession of Mercury.

We also generally try to keep unnecessary assumptions out of the models and to make the models as "simple" as possible without losing predictive power. This is essentially Occam's razor. In order to be a scientific model, the model must also make definite predictions. If you have a model that can fit anything, it is not really predictive.

 

[Chronos]

How would you ever know you had completed a full circle in a wraparound universe? By the time you returned to your starting point, any and all recognizable reference points would be long gone and forgotten.

 

[PeterDonis]

By the time you returned to your starting point, any and all recognizable reference points would be long gone and forgotten.

There is nothing in the laws of physics that requires this. In principle one could leave a beacon or some other reference object that could last indefinitely.

 

[Chronos]

Just inserting a practical limit on the idea of circumnavigating the universe. I concede a few black holes might serve as reference points, assuming the universe is compact enough to permit circumnavigation before they evaporate.

 

[Aufbauwerk 2045]

Is there a cosmologist in the house?

I find this topic disturbing because I'm not sure how it fits into science at all. To hopefully ward off any unthoughtful responses to that statement, I'm not saying it does not fit into science at all.

To avoid confusion, I will try to make my questions a bit simpler.

(1) Do cosmologists follow the scientific method when they develop a theory which claims to answer the question "is the universe finite or infinite?"

(2) If the answer to question (1) is yes, as I would expect, then do they accept the idea of Karl Popper that a scientific theory must be falsifiable?

(3) If the answer to question (2) is no, then what is their criterion for saying their theory deserves to be called a scientific theory? I am not saying there is no criterion, only that I am curious what the cosmologists say it is.

(4) If they answer yes to (2), can they suggest any observation or experiment which would in some way support the falsification of their theory?

Many believe Popper's criterion is a good way to distinguish between science and pseudo-science. I am not saying if I agree or disagree. This is not about my personal viewpoints. I am asking others who know the subject for their viewpoints.

But on a personal level I am very interested in keeping a discussion of "is the universe infinite or not," which is the topic of this thread, on a scientific basis.

It's silly to say that to ask in what way a certain activity is following the scientific method is somehow engaging in pseudoscience. On the contrary, I am interested in how cosmologists see their methods fitting into the scientific method.

Just to be clear, and avoid ruffling any feathers, I am not saying for one moment that they are doing pseudo-science. I just want to understand how their field fits into the same scientific method as, for example, early 20th century experimental work in atomic physics, or if you prefer the search for the Higgs boson.

On a lighter note, I remember what one of my favorite physics professors said. (For those who value such things he was a Nobel laureate.) He was a theoretical physicist but not a cosmologist. His work was much more down to Earth and had tremendous applications in the real world. He said "the problem is that some people start talking about the whole universe, and they forget about y = x²."

That's all I have to say about this topic, except that I look forward to comments by someone who is working in cosmology and can answer my questions.

Thank you for an interesting discussion. Now I'm back to y = x².

 

[jbriggs444]

(1) Do cosmologists follow the scientific method when they develop a theory which claims to answer the question "is the universe finite or infinite?"

If the finiteness or not of the universe were the only prediction of a particular theory then that would be a pretty worthless theory. It would also not be easily falsified.

It seems to me that you are holding theories of cosmology to a higher standard than you hold, for instance, Newton's universal law of gravity. $f=\frac{Gm_1m_2}{r^2}$ could be (and was) falsified without asking whether it supported arbitrarily large values of r.

 

[PeterDonis]

I am very interested in keeping a discussion of "is the universe infinite or not," which is the topic of this thread, on a scientific basis.

Then all your questions boil down to one: what, if any, evidence do we have that bears on the question of whether the universe is infinite or not? The answer to that is that we have plenty of evidence that constrains the parameter space of the standard hot big bang model of cosmology to a pretty narrow range, a range which makes it very unlikely, based on that model, that the universe is spatially finite, and very likely that it is spatially infinite. AFAIK there are no other models in serious contention with the standard hot big bang model in this area.

can they suggest any observation or experiment which would in some way support the falsification of their theory?

Sure, the observations that constrain the parameter space to a narrow range could have been different. The full parameter space is huge; the observations could have come out anywhere in it. But as a matter of fact, they came out where they did.

 

[eltodesukane]

"there is/was infinite amount of energy in the universe"
-- It is believe the total amount of energy is zero, the negative gravitational potential energy balancing the positive energy of matter, explaining how the whole universe could arise from an expanding infinitesimal quantum fluctuation.
https://en.wikipedia.org/wiki/Zero-energy_universe

 

[eltodesukane]

" And, see the the check mark in the dropdown ?..."
-- Where's the dropdown?

 

[PeterDonis]

It is believe the total amount of energy is zero, the negative gravitational potential energy balancing the positive energy of matter, explaining how the whole universe could arise from an expanding infinitesimal quantum fluctuation.

This is an example of why Wikipedia is not a reliable source. Gravitational potential energy is only well-defined in a stationary spacetime, and the spacetime of the universe is not stationary (because the universe is expanding).

 

[alexopth1512]

I find the question valid. And very difficult. And we have no tools right now to answer. And we have no rigid definition of universe. We shouldn't turn down the question if we stand stupid with no tools.

Another question that seemed a little silly was the Olbers' paradox, which actually is relevant to this one.

It could be infinite but then a singularity is not very likely, unless it is almost a singularity. with very very difficult to imagine substance and laws.

However, regarding the energy, there is no problem since the "universe" is expanding and we have an "horizon" where the relevant speed reaches the speed of the light, so no we won't be burnt from infinite energy. Or maybe this is the answer of nature to protect itself from its infinity.

 

[Peter Martin]

Multiplication and division by zero yields nonsensical results. I fail to see to any reason to take such derivations seriously. It more accurately reflects, imo, the failure of our mathematical conceptions to properly model the universe.

Division by zero is indeed undetermined but multiplication by zero is not. Zero times any number equals zero. But, for example, 12 divided by zero would have to be a number which when multiplied by zero equalled 12. But we've already agreed that that's impossible.

 

[Bandersnatch]

since the "universe" is expanding and we have an "horizon" where the relevant speed reaches the speed of the light

The cosmic event horizon is not coincident with the Hubble sphere. These two are the same only in universes devoid of matter and radiation, with dark energy component only (so called de Sitter universes).
In a universe like ours, the expansion rate falls down with time, allowing signals from beyond the Hubble sphere to reach us in finite time.

Notice how the Hs and EH tend to converge to a common value reflecting the universe becoming incereasingly dark energy-dominated.
(Graph source)

 

[Pjpic]

But on a personal level I am very interested in keeping a discussion of "is the universe infinite or not," which is the topic of this thread, on a scientific basis.Maybe there are different definitions for "universe" and for "infinity"; that might be causing some confusion. Even "is", might have different definitions (maybe it is limited to "only as far as we know" )

 

[PeterDonis]

I am very interested in keeping a discussion of "is the universe infinite or not," which is the topic of this thread, on a scientific basis.

See my post #26. I don't see what more we can say scientifically on the question than that.

 

[phinds]

But on a personal level I am very interested in keeping a discussion of "is the universe infinite or not," which is the topic of this thread, on a scientific basis.

addressed in post #26

Maybe there are different definitions for "universe" and for "infinity"; that might be causing some confusion. Even "is", might have different definitions (maybe it is limited to "only as far as we know" )

Only if you are making up your own definitions.

EDIT: I see Peter beat me to it.