- #1
pelletboy
- 1
- 0
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.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?
pelletboy said:How do you explain the science of infinity?
Infinity is a mathematical concept, not a scientific one.pelletboy said:How do you explain the science of infinity?
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.russ_watters said:Infinity is a mathematical concept, not a scientific one.
Hi sysprog:sysprog said:It's a reasonable formulation of a question the correct answer to which is not known to be known.
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.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.
We also don't know whether time and space at any scale are ultimately continuous or discrete.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.
Hi ZapperZ:ZapperZ said:So why is everyone fixated only on "space" and such exotica?
Buzz Bloom said:What causes my "fixation" is that I find it difficult to conceptualize
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.
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.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 ...
sysprog said:We also don't know whether time and space at any scale are ultimately continuous or discrete.
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 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
Hi anorlunda:anorlunda said:There are plenty of examples of physics that are so unlike our daily experience that we can never conceptualize them.
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.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.
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.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.
Hi sysprog: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:sysprog said:It's common knowledge that there are infinities in the mathematics that describe physical phenomena.
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.Buzz Bloom said:Hi sysprog:sysprog said:It's common knowledge that there are infinities in the mathematics that describe physical phenomena.
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
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.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.
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.sysprog said:We also don't know whether time and space at any scale are ultimately continuous or discrete.
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 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.The volume of the Earth is not analogous to the volume of a finite universe.
Hi sysprog: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.
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.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.
Hi russ: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.
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.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.
Hi sysprog: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.
So, this is what I believe that I know at the present time.Buzz Bloom said:P(ΩK > 0) ~= erf(0.005/0.0165) = ~erf(0.303) = ~0.332.
Hi Russ:russ_watters said:Any property that has a zero value has an inverse property with an infinite value. E.g., resistivity/conductivity.
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.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."
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.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
I think it's exactly zero with superconductivity, but I'm not sure.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?
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.Buzz Bloom said:Do you know of any other physical context in which it is uncertain about infinite or finite?
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.
No, infinity cannot be measured or quantified in the traditional sense. It is a concept that goes beyond any finite number or quantity.
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.
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.
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.