Exploring the Science of Infinity: Is It Possible?

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In summary: I think that others share that difficulty.Do I understand correctly that if the universe is finite, the topology is not known, but if the universe is infinite, the topology is known (the Poincare dodecahedral sphere)?Regards,BuzzIn summary, the conversation discusses the concept of infinity in relation to the universe. Einstein's belief that the universe is a finite spherical universe within an infinite space is questioned, and the science of infinity is explored. It is mentioned that the universe may be infinite in extent, but this is not a known fact. The conversation also touches on the possibility of the universe being finite and the difficulty in determining its topology. The idea of infinity in mathematics and its presence in everyday materials is also mentioned
  • #1
pelletboy
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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?
 
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  • #2
pelletboy said:
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.
 
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  • #3
pelletboy said:
How do you explain the science of infinity?

Sorry, this question is not clear, you need to elaborate.
 
  • #4
pelletboy said:
How do you explain the science of infinity?
Infinity is a mathematical concept, not a scientific one.
 
  • #5
russ_watters said:
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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  • #6
sysprog said:
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 spatial curvature that is close to zero on the side that corresponds to a hyperbolic (infinite) spatial 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.

ADDED
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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  • #7
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.
 
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  • #8
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.
 
  • #9
ZapperZ said:
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.
 
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  • #10
ZapperZ said:
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.
 
  • #11
Buzz Bloom said:
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.
 
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  • #12
Buzz Bloom said:
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.
 
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  • #13
sysprog said:
... 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
 
  • #14
sysprog said:
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.
 
  • #15
Buzz Bloom said:
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.
 
  • #16
anorlunda said:
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
 
  • #17
sysprog said:
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.
 
  • #18
ZapperZ said:
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.
 
  • #19
sysprog said:
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
 
  • #20
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
 
  • #21
Buzz Bloom said:
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.
 
  • #22
sysprog said:
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.
 
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  • #23
sysprog said:
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.
 
  • #24
pelletboy said:
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.
 
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  • #25
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.
 
  • #26
sysprog said:
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.
Hi sysprog:

I think the confusion is between (a) the absence of a limit, or (b) having a infinite value for a property. In the universe example, the size (e.g volume) is either infinite or it is a finite value (possibly changing over time). For a photon, its frequency and its wavelength are never infinite (and also never zero). Do you get the distinction?

Regards,
Buzz
 
  • #27
Buzz Bloom said:
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.
The basic point of calculus is dealing with continuous change by incorporating infinities/infinitessimals. It would be hard to find a non-steady physical process that doesn't have to deal with infinity in its modeling.

Infinity is often regarded as way too exotic/mysterious and we're seeing a lot of that in this thread. That was largely the point of my first post.
 
  • #28
russ_watters said:
The basic point of calculus is dealing with continuous change by incorporating infinities/infinitessimals. It would be hard to find a non-steady physical process that doesn't have to deal with infinity.
Hi russ:

I get that the math deals with infinities. From many discussions here on the PF it has been made clear that in a small space in which some point has an infinite value for some property, such a point is called a singularity, and within a small space around the singularity it is said that the mathematics does not apply to the physics. It is in this sense that I am trying to make the point that aside from the possibly infinite size of the universe, there are no possible infinity values for physical properties.

Regards,
Buzz
 
  • #29
Buzz Bloom said:
...I am trying to make the point that aside from the possibly infinite size of the universe, there are no possible infinity values for physical properties.
I would think any property that has a zero value can have an inverse property with an infinite value, even if not always named/defined/useful. E.g., resistivity/conductivity.
 
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  • #30
sysprog said:
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.
Hi sysprog:

I have underlined "know" in the quote. This is to highlight what I understand to be a fundamental concept regarding all of science. The point is that "know" is a misleading word to use about science. In practice it has a usage meaning that is quite different from what is commonly intended as its meaning. In science a "fact" is believed to be true with a high degree of confidence, but also with the understanding that it is possible that at some future time (multiply reconfirmed) an observation with show that the fact is not true, or at least is not completely true. One excellent example from history is Newtonian mechanics.

A commonly used example of this understanding is that when a value is measured, or calculated from other measurements, an error range is also given. (See for example the values in the paper I cited in post #6.) The value and its error range allows a reader to calculate a probability that the actual value is in some specified range. I did that calculation in post #6.
Buzz Bloom said:
P(ΩK > 0) ~= erf(0.005/0.0165) = ~erf(0.303) = ~0.332.
So, this is what I believe that I know at the present time.
Based on the data described in the cited document, I know that the probability is ~1/3 that the universe is finite and ~2/3 that it is infinite.​
From my perspective this is qualitatively and scientifically different than, "We don't know, for example, whether the universe itself is a finite or infinite."

Regards,
Buzz
 
  • #31
russ_watters said:
Any property that has a zero value has an inverse property with an infinite value. E.g., resistivity/conductivity.
Hi Russ:

Thank you. You make a good point. I understand that it is commonly said that at some very cold temperatures the resistivity of some material becomes zero. (I.e., superconductivity.) If that is true, then that is a good and useful example, and I will need to adjust my perspective. Just a few questions to clarify my understanding.
Is it "certain" that the the resistivity becomes zero rather than just a very small positive value.​
Is there any substance and condition with zero conductivity?​

Regards,
Buzz
 
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  • #32
Buzz Bloom said:
So, this is what I believe that I know at the present time.
Based on the data described in the cited document, I know that the probability is ~1/3 that the universe is finite and ~2/3 that it is infinite.
From my perspective this is qualitatively and scientifically different than, "We don't know, for example, whether the universe itself is a finite or infinite."
Fair enough; however, I wasn't using 'know' in the sense of epistemic certainty, either. In my opinion, if in future we know whether space as we experience it is or is not curved enough (and does or does not have other characteristics sufficient) to make it topologically closed, while that would be a very significant piece of new knowledge, and would weigh strongly in favor of a finite theory, would not ipso facto resolve the question of finiteness or infiniteness of space, in any of the senses of 'know' that you have referenced.
 
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  • #33
Buzz Bloom said:
Hi russ:

I get that the math deals with infinities. From many discussions here on the PF it has been made clear that in a small space in which some point has an infinite value for some property, such a point is called a singularity, and within a small space around the singularity it is said that the mathematics does not apply to the physics. It is in this sense that I am trying to make the point that aside from the possibly infinite size of the universe, there are no possible infinity values for physical properties.

Regards,
Buzz
We know that the speed of light is finite, and we also know with high precision what its speed is, but we don't know its maximum frequency, or even for sure that it has a maximum frequency, although I think that we may learn in future that there is in fact physically a finite maximum frequency, and minimum time interval, and minimum distance, and to some degree of precision what those physical limits are.
 
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  • #34
Buzz Bloom said:
It it "certain" that the the resistivity becomes zero rather than just a very small positive value.
Is there any substance and condition with zero conductivity?​
I think it's exactly zero with superconductivity, but I'm not sure.

Another example: Light transmittance/absorbance. AKA Beer's law:
https://teaching.shu.ac.uk/hwb/chemistry/tutorials/molspec/beers1.htm

Incidentally, I've been using Beer's Law totally incorrectly.
 
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  • #35
Buzz Bloom said:
Do you know of any other physical context in which it is uncertain about infinite or finite?
Conditions at ##r=0## in a Schwarzschild black hole? It's a reasonable conjecture that some other physics is involved at sufficiently small values of ##r## to keep everything finite, but that is certainly not observationally confirmed and there is no compelling candidate theory.
 
<h2>1. What is infinity?</h2><p>Infinity is a concept that represents something that has no end or limit. It is often used in mathematics and physics to describe quantities that are unbounded or never-ending.</p><h2>2. Can infinity be measured or quantified?</h2><p>No, infinity cannot be measured or quantified in the traditional sense. It is a concept that goes beyond any finite number or quantity.</p><h2>3. Is infinity a real or theoretical concept?</h2><p>Infinity is a theoretical concept that is used to help us understand and describe certain phenomena, but it does not exist as a physical entity in the real world.</p><h2>4. How is infinity used in science?</h2><p>Infinity is used in various fields of science, such as mathematics, physics, and cosmology. It is often used to describe the behavior of systems that have no boundaries or limits, such as the universe or the concept of time.</p><h2>5. Is it possible to fully comprehend or understand infinity?</h2><p>It is debatable whether it is possible for humans to fully comprehend or understand infinity. Our brains are limited to thinking in finite terms, so it may be difficult for us to grasp the concept of something that has no end or limit.</p>

1. What is infinity?

Infinity is a concept that represents something that has no end or limit. It is often used in mathematics and physics to describe quantities that are unbounded or never-ending.

2. Can infinity be measured or quantified?

No, infinity cannot be measured or quantified in the traditional sense. It is a concept that goes beyond any finite number or quantity.

3. Is infinity a real or theoretical concept?

Infinity is a theoretical concept that is used to help us understand and describe certain phenomena, but it does not exist as a physical entity in the real world.

4. How is infinity used in science?

Infinity is used in various fields of science, such as mathematics, physics, and cosmology. It is often used to describe the behavior of systems that have no boundaries or limits, such as the universe or the concept of time.

5. Is it possible to fully comprehend or understand infinity?

It is debatable whether it is possible for humans to fully comprehend or understand infinity. Our brains are limited to thinking in finite terms, so it may be difficult for us to grasp the concept of something that has no end or limit.

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