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What is the consensus on whether or not nature actually has functional infinities such as an absolute singularity, or the multiverse itself as a whole, or even some potential for reality always existing in some state (a context from which spacetime or other can emerge).

Given renormalization for instance to deal with infinities that come up in quantum mechanics, does the act of doing so mean we don't think those can actually be a physical reality?

jazamm
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    Do you mean like the infinite density at the center of a black hole? Or the infinite force two point particles would exert on each other if infinitely close to each other? Or the possibly infinite size of the universe? If so, no. The solution to the General Relativity field equations give an infinite density, but this shows we need a better theory than GR. If you put charges close enough together, you need quantum mechanics to describe the forces, and the particles turn out not to be classical points. We can't see how big space is. expect it is at least 500 time bigger than the part we see. – mmesser314 Feb 25 '24 at 14:59
  • How about the slope of a vertical line? – PM 2Ring Feb 25 '24 at 18:39
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    Related: https://physics.stackexchange.com/q/24934/2451 , https://physics.stackexchange.com/q/590774/2451 , https://physics.stackexchange.com/q/455726/2451 , https://physics.stackexchange.com/q/261340/2451 and links therein. – Qmechanic Feb 26 '24 at 09:13
  • @mmesser314 well, any of those such things, even one, that is thought to be a physical reality? Whether they come from QFT or GR, are there any infinities such as an infinite size of the universe, that are considered plausible? If not, why not? Why do such imply we need a better theory, as opposed to just that the theory is correct, and the circumstance actually is infinite? – jazamm Feb 26 '24 at 09:22
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    Two more related questions. – J.G. Feb 26 '24 at 09:24
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    It's a good question, and I have voted to reopen, but I suspect it's one of those questions that is a matter of opinion. For what it's I don't believe infinities exist in the real world apart possibly from the size of the universe. But other physicists may have different opinions and there is no way to tell who is correct. – John Rennie Feb 26 '24 at 09:27
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    Rule of thumb is infinities imply an incomplete theory. Consider the Ultraviolet Catastrophe. The infinities of the Schwarzchild solution to Einstein's field equations at the event horizon were an artifact of coordinates. Renormalization of Quantum Field Theory also gets rid of infinities in a way that can't be done with gravity. – R. Romero Feb 26 '24 at 09:34
  • @JohnRennie thank you the range of opinions from a few physicists is what would educate me. That range and from whom, would be a good sample to help me form my own view and what to teach kids. I tend to agree w/ your view but it's wiser of me to see what the majority here says before I teach it. Without this kind of survey of qualified physicists, there is no other way for non-experts to make an informed opinion for themselves on this topic. I need to see what several experts think. – jazamm Feb 26 '24 at 10:02
  • @jazamm I voted that the question should be reopened i.e. I want the question to be reopened. You have misread my comment. – John Rennie Feb 26 '24 at 10:03
  • @R.Romero understood thank you, I suppose what I'm asking is why "Rule of thumb is infinities imply an incomplete theory." - Rather than that occasionally, a few of those are just the fact? – jazamm Feb 26 '24 at 10:05
  • @JohnRennie ah beg pardon, thank you kindly, response edited for those considering. Cheers. – jazamm Feb 26 '24 at 10:06
  • This question is simply asking for opinions on a statement; it should not have been reopened. – Kyle Kanos Feb 26 '24 at 15:53
  • Fields that fall off as 1/r have an infinite discontinuity at the origin (r=0). How is that handled? E.G. a point charge at the origin. – user45664 Feb 26 '24 at 17:38
  • @KyleKanos Respectfully this forum is not here only to serve physicists, but also to better inform the public as to your consensus. So getting those opinions as to how we should interpret what theories mean, as well as what we should teach our kids, seems extremely important. As a science communicator I have a duty to make sure I don't misrepresent what experts believe, and this is one of the only (and best) tools available for that. There are so many colloquialisms out there leaving wrong impressions already, which you folks must understandably find problematic. All best mate! – jazamm Feb 27 '24 at 06:07

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Sensible physicists never believe idealized mathematical models. We employ them to capture (sometimes extremely successfully) aspects of real phenomena, but mathematics isn't real. It exists only in the human mind.

John Doty
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  • Whether or not this is true, that is a philosophical position that the physics itself does not require you to embrace. – David C. Feb 26 '24 at 15:25
  • @DavidC.The history of physics does. Galileo's experiments remain as fundamental physics even though the mathematics of gravity theory have changed drastically. Mathematical physics is a shifting story we tell about the phenomena: who sanely believes it? – John Doty Feb 26 '24 at 15:32
  • Well, for instance, I think a case could be made that Einstein really believed his General Relativity in such a way. – David C. Feb 26 '24 at 15:34
  • @DavidC. Einstein's beliefs seem to have been a bit shifty and unstable (this is not a criticism). – John Doty Feb 26 '24 at 15:37
  • @DavidC. Einstein saw GR as an incomplete component of a more comprehensive field theory, and attempted to construct one. – John Doty Feb 26 '24 at 15:41
  • Fair enough. But he nonetheless believed in the existence (at least possible existence) of such a theory, which would not have some future replacement.

    Physicists (like Einstein) who believe the universe is fundamentally logical and thus fundamentally mathematical and understandable, are likely to believe that mathematics itself is in some sense "real". I disagree with those who wish that all physicists would embrace the same philosophy of physics or of mathematical physics; a diversity of philosophical perspectives is a good thing.

     – David C. Feb 26 '24 at 15:45
  • @DavidC. I don't think that demoting physics to a mere branch of mathematics is a good thing for physics. – John Doty Feb 26 '24 at 16:01
  • @JohnDoty well for instance to the extent that it continues to let us accomplish tasks, I do myself at least interpret GR to mean that spacetime itself is indeed literally curved in nature, beyond just the math used to model it as such. – jazamm Feb 27 '24 at 05:45
  • @jazamm And 19th century physicists who had mastered Newtonian gravity thought that it was the absolute truth. – John Doty Feb 27 '24 at 14:16
  • @JohnDoty Physics is mathematics, but with units. To describe reality, physicists developed the concept of physical quantity, which is a product of number and unit. The first is mathematical, the second is physical. A physical theory describes the relation between various physical quantities using equations, which can always be made dimensionless. In that form we they are pure mathematics. Therefore, I would say that it is fair to say that mathematics is the language of physics. – JanG Mar 12 '24 at 16:50
  • @JanG Mathematics is a tool of physics, but it has its imperfections. Mathematics needs axioms, but the physical world doesn't provide them. Mathematics scales very badly: even the three body problem is a challenge, but galaxies have no trouble moving billions of stars around. – John Doty Mar 12 '24 at 17:07
  • @JohnDoty I won't argue with that, but if I can describe a physical model in terms of some equation I am happy with it. How to find the corresponding solution is an another issue. One can always use numerical methods for that. – JanG Mar 12 '24 at 19:29
  • @JanG You can always use numerical methods? You really believe that? Your assignment is to compute the Fano factor for silicon. – John Doty Mar 12 '24 at 20:16
  • @JohnDoty Please have understanding that I will not even try that. Physics and mathematics are two different "things", but describing physical phenomena in terms of physical quantities we use mathematics as a tool. – JanG Mar 15 '24 at 17:15
  • @JanG Yes we use mathematics as a tool. An unfortunately clumsy and blunt tool, but it's the best we have. – John Doty Mar 15 '24 at 20:17
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Experience suggests infinities aren't real. Misuse of The Partition Theorem implied runaway energies at certain frequencies due to heating, The Ultraviolet Catastrophe. By some primitive analyses, the night sky should be super bright. It isn't because the universe is expanding and its age is finite. Infinities disappear in QFT, giving us the most accurate theory we have. The infinities at the event horizon of a black hole vanish with a change of coordinates.

As to arguments that infinity exists with some physical manifestation, the center of a black hole has infinite density, but there's reason to believe that is suspicious apart from suspicion of infinities. General relativity is silent on the uncertainty principle which is a bad sign. Apparently some physicists believe the singularity truly has infinite density.

Due to a theorem from Paul Dirac, if there is a magnetic monopole anywhere in the universe, it is expected that electric charge would be quantized. If it doesn't matter where that monopole is, does it suggest it's effects propagate at infinite speed?

R. Romero
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