# Is Infinity Possible?

• I

## Main Question or Discussion Point

Einstein mentioned that our universe if a finite spherical universe inside an infinite space. If this said infinite space is, as said, infinite, then infinity is possible? How do you explain the science of infinity?

• davenn

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phinds
Gold Member
Einstein mentioned that our universe if a finite spherical universe inside an infinite space. If this said infinite space is, as said, infinite, then infinity is possible? How do you explain the science of infinity?
I doubt Einstein said that since it is absolutely not in accordance with modern cosmology. There is no "outside". The universe is everything there is. It may be infinite in extent or it may not. Infinite seems to be the general consensus these days but it is not a known fact. If it is finite, the topology is not known.

• russ_watters and davenn
How do you explain the science of infinity?
Sorry, this question is not clear, you need to elaborate.

russ_watters
Mentor
How do you explain the science of infinity?
Infinity is a mathematical concept, not a scientific one.

Infinity is a mathematical concept, not a scientific one.
Infinity and related words refer to a set of conceptual abstractions which need not be restricted to mathematics. The question whether physical space is finite or infinite is not resolvable as simply a misapplication of the terms. It's a reasonable formulation of a question the correct answer to which is not known to be known.

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• russ_watters
Buzz Bloom
Gold Member
It's a reasonable formulation of a question the correct answer to which is not known to be known.
Hi sysprog:

I wonder if "the correct answer" is not only not known but also not scientifically knowable. I cannot imagine a scientific method that would result in certainty that that the universe was in fact infinite, or in fact finite. However, I think there are methods that can produce an approximation of the probability that the universe is infinite or is finite.

I understand that the universe model that best fits the currently available astronomical data gives a value for the average spacial curvature that is close to zero on the side that corresponds to a hyperbolic (infinite) spacial geometry. This value also comes with a range of error. From these values (and assumptions about the probability distribution) one can calculate the probability that the geometry is not hyperspherical, which means it is not finite.

I apologize for not citing a well known reference on this topic, and the numerical values, but I do not now have the time to look it up.

https://arxiv.org/pdf/1502.01589.pdfFrom abstract
The spatial curvature of our Universe is found to be very close to zero, with|ΩK|<0.005.​
6.2.4 Curvature
(49) The combined constraint shows impressive consistency with aflat universe: ΩK=−0.005+0.016−0.017(95%,PlanckTT+lowP+lensing).​

I confess I do not know the correct method for working with an with different value for + and -. I am making a guess that since the two values are close, if I use the average 0.0165 as standard deviation and assume a Gaussian distribution, then the probability will approximately be
P(ΩK > 0) ~= erf(0.005/0.0165) = ~erf(0.303) = ~0.332.​
Thus, based on the calculations of this reference, the probability is ~1/3 the universe is finite and ~`2/3 it is infinite.

Regards,
Buzz

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ZapperZ
Staff Emeritus
2018 Award
There are "infinities" in the mathematics everywhere that describe our world. This exists even in the electronics and materials that you use everyday (look up van Hove singularity in the density of states of material). In fact, if you look at ordinary conductors, the concept that produces Ohm's law requires that the single-particle spectral function be a delta function!

So why is everyone fixated only on "space" and such exotica?

Zz.

• • Pi-is-3, Steelwolf, Klystron and 3 others
I wonder if "the correct answer" is not only not known but also not scientifically knowable. I cannot imagine a scientific method that would result in certainty that that the universe was in fact infinite, or in fact finite.
It seems to me that proof of spatial finiteness in a spatially finite universe would be more likely to be attainable than would be proof of spatial infiniteness in a spatially infinite universe; if space is bounded, then we could imagine observing effects indicative of the existence of the boundary, but if space is unbounded, our not observing anything indicative of the existence of a boundary would not establish that there isn't one.

There are "infinities" in the mathematics everywhere that describe our world. This exists even in the electronics and materials that you use everyday (look up van Hove singularity in the density of states of material). In fact, if you look at ordinary conductors, the concept that produces Ohm's law requires that the single-particle spectral function be a delta function!

So why is everyone fixated only on "space" and such exotica?

Zz.
We also don't know whether time and space at any scale are ultimately continuous or discrete.

• russ_watters
Buzz Bloom
Gold Member
So why is everyone fixated only on "space" and such exotica?
Hi ZapperZ:

What causes my "fixation" is that I find it difficult to conceptualize about the geometry of the universe as being uncertain with respect to being finite or infinite. I am unaware of any other scientific question that has this particular uncertainty.

BTW, I added a reference and numbers to my previous post.

anorlunda
Mentor
What causes my "fixation" is that I find it difficult to conceptualize
There are plenty of examples of physics that are so unlike our daily experience that we can never conceptualize them. Evolution did not wire our brains to conceptualize everything However we can understand them via the language of mathematics.

• • pinball1970, Klystron and russ_watters
ZapperZ
Staff Emeritus
2018 Award
Hi ZapperZ:

What causes my "fixation" is that I find it difficult to conceptualize about the geometry of the universe as being uncertain with respect to being finite or infinite. I am unaware of any other scientific question that has this particular uncertainty.

BTW, I added a reference and numbers to my previous post.
But you are not the OP, who questioned the "science of infinity". I pointed out that one doesn't need to look at issues of "space time" to discover that "infinities" exist almost everywhere in the mathematics of our physics. So do you and the OP also have no problems in accepting those infinities in your conductors and semiconductors, but only have problems with your concept of the "geometry of the universe"?

I find this very puzzling. People seem to think that such "exotic" properties only occurs in "exotic" physics, without realizing that the very things they use everyday exhibit similar properties.

Zz.

Buzz Bloom
Gold Member
... proof of spatial finiteness in a spatially finite universe would be more likely to be attainable than would be proof of spatial infiniteness in a spatially infinite universe; if space is bounded, then ...
I believe you have a misunderstanding about finiteness. The surface of the Earth is finite but it has no boundaries. A finite universe is similar except that the finite space is three dimensional rather than two.

Regards,
Buzz

ZapperZ
Staff Emeritus
2018 Award
We also don't know whether time and space at any scale are ultimately continuous or discrete.
That has no connection with what I wrote. I don't need to know such thing to show you that there are infinities in the mathematics that describe the semiconductors that you are using to write this on your modern electronic devices.

Zz.

I believe you have a misunderstanding about finiteness. The surface of the Earth is finite but it has no boundaries. A finite universe is similar except that the finite space is three dimensional rather than two.

Regards,
Buzz
In the sense in which I was using the terms 'bounded' and 'boundary', the volume of the Earth is bounded, and the surface of the Earth is its boundary.

Buzz Bloom
Gold Member
There are plenty of examples of physics that are so unlike our daily experience that we can never conceptualize them.
Hi anorlunda:

I agree with the above quote, but you missed the critical point to my reason for "fixation". It is the uniqueness of this particular uncertainty. Do you know of any other physical context in which it is uncertain about infinite or finite? (Please do not use QM interpretations as an example. I have given up on trying to conceptualize in that context.)

Regards,
Buzz

jbriggs444
Homework Helper
In the sense in which I was using the terms 'bounded' and 'boundary', the volume of the Earth is bounded, and the surface of the Earth is its boundary.
But the point stands. Looking for evidence of finiteness by looking for a boundary is misguided. Finite but unbounded spaces (such as the surface of the earth) exist. We can never prove that the Earth's surface is finite by looking for an edge.

What we could do would be to get out our surveying equipment and look for triangles with internal angles that add to more than 180 degrees. Or we could just sail around the world.

That has no connection with what I wrote. I don't need to know such thing to show you that there are infinities in the mathematics that describe the semiconductors that you are using to write this on your modern electronic devices.

Zz.
It's common knowledge that there are infinities in the mathematics that describe physical phenomena. We don't know whether anything physical is actually infinite. Your post questioned why there appeared to be a fixation on extension of space as to whether it is finite or infinite, and I presented an example of similarly unknown matters on the smallness scale as distinguished from the largeness scale; just as we don't know whether the universe is infinitely large, we don't know whether distances or durations can be infinitely or infinitesimally small.

Buzz Bloom
Gold Member
In the sense in which I was using the terms 'bounded' and 'boundary', the volume of the Earth is bounded, and the surface of the Earth is its boundary.
Hi sysprog:

I apologize for my failure to be clearer. The volume of the earth is not analogous to the volume of a finite universe. However, the surface is a two dimensional analogue of the three dimensional hyper-surface of a four dimetional sphere. The interior volume of the four dimensional hypersphere is not part of the universe. It is only the three dimensional hyper-surface which approximates the shape of a finite universe based on a general relativity (GR) model.

Regards,
Buzz

Buzz Bloom
Gold Member
It's common knowledge that there are infinities in the mathematics that describe physical phenomena.
Hi sysprog:

I would appreciate seeing an example of such physical infinities. I am guessing there may be another misunderstanding that I may be able to explain.

Regards,
Buzz

sysprog said:
It's common knowledge that there are infinities in the mathematics that describe physical phenomena.
Hi sysprog:

I would appreciate seeing an example of such physical infinities. I am guessing there may be another misunderstanding that I may be able to explain.

Regards,
Buzz
What is the highest possible frequency, or shortest possible wavelength, of light? We can say mathematically that as frequency goes to 0, wavelength goes to infinity, and vice versa, but we don't know what physically is the shortest or longest possible time or distance.

russ_watters
Mentor
Infinity and related words refer to a set of conceptual abstractions which need not be restricted to mathematics. The question whether physical space is finite or infinite is not resolvable as simply a misapplication of the terms. It's a reasonable formulation of a question the correct answer to which is not known to be known.
I agree that the specific question about the universe is in the realm of physics, but the one I responded do, as worded, seemed broader. We've had similar discussions such as "does infinity exist in the real world?" IMO, it is a useful descriptive tool, but the question leads to more problems than answers and is better left go.

• hutchphd
russ_watters
Mentor
We also don't know whether time and space at any scale are ultimately continuous or discrete.
Right. This is a commonly argued example that I just find so unnecessary. Many/most models assume infinitely divisible - whatever - but I see no real value in a debate over whether, for example, the infinitenumber of points on a ruler is physically "real". More often than not, this leads to misunderstandings such as Zeno's paradox.

Einstein mentioned that our universe if a finite spherical universe inside an infinite space. If this said infinite space is, as said, infinite, then infinity is possible? How do you explain the science of infinity?
It would be remiss to not mention here the name Georg Cantor who showed there are infinitely many kinds of infinity. He has pre-worried about some of this for you. Wrap your head around that........here's a start:
https://www.britannica.com/science/transfinite-number
His primary works are relatively approachable without too much pain.

• Klystron
The volume of the earth is not analogous to the volume of a finite universe.
It could be if we regard the space-distortional effects of mass as part of what is on a universal scale a mere local phenomena set. We don't know, for example, whether the universe itself is a finite or infinite Euclidean or non-Euclidean space, inside which everything so far observable to us is a mere speck.