How many particles are in the entire (rather than just the observable) universe?  I would guess that if the universe is open, or infinite, then there is a countable infinity of particles. But if the universe is closed, or finite, then there is only a finite number of particles.  Is this correct? Or could a finite universe have a countable infinity of particles or an infinite universe an uncountable infinity of particles.
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It is often quoted that the number of atoms in the universe is 10$^{70}$ or 10$^{80}$.  How do scientists determine this number?   And how accurate is it (how strong is the supporting evidences for it)?  Is it more likely (logically >50% chance) that the numbers are right, or is it more likely that the numbers are wrong?
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So i was reading about  on Wiki and I found a interesting thing written there .    It says that the S. radius of the universe is as big as the size of the universe?   How is this possible?  Since most the universe is empty space shouldn't the S. radius of our universe be significantly smaller then 13.7 light years?
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I've always wondered why the number of protons in the Universe exactly matches the number of electrons. They are such different particles with totally different cross sections. So, first of all, is this true? And, secondly, how could it be that they have been produced in the same amount after the Big-Bang?
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Infinity, is clearly not . But there is some dissent on whether or not zero is finite. I have seen authors use "finite" to indicate the value of $0$ is excluded as well as infinity.  Is there any rule about this?
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All of the force-particles in the standard model are bosons, now my question is pretty short, namely:     Why are all force particles bosons?   This can't be a coincidence.
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I have a really hard time learning math when I can't find any justifications for the existence of infinity (in this case actual infinity).  Are there any justifications for the Axiom of Infinity?   Thank you very much.
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-I'm not a religious person so this is not a denial. I'm just trying to understand the most fundamental topic about Universe.  -I know the Big Bang cosmological model is not a law but it's a theory.  -I'm a non-Native English speaker so please let me know if the question is not clear for you.  -This question came to my mind after watching
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I was reading about countably infinite sets and the definition goes as, "A set is countably infinite if its elements can be put in one-to-one correspondence with the set of natural numbers"(Source: Google). Well yes, this make sense. As the set $\mathbb{N}$ is countably infinite and set which can it can create a bijection with, would end up having the same number of elements and thus they too would be countably infinite. But this would be true iff $\mathbb{N}$ is countably infinite. How would you prove that? Or is the idea of countably infinite base on some assumption that $\mathbb{N}$ is countably infinite?
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What will be the wavelength of a particle whose velocity is zero?   According to de Broglie's hypothesis, then the wavelength would become infinite as the momentum is zero. But, I think for a stand still particle, its particle nature should be more dominant, as at that moment it is highly localized.
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(I was requested to edit the question to explain why it is different that a proposed duplicate question. This seems counterproductive to do here, inside the question it self, but that is what I have been asked by the site and moderators. There is no way for me to vote against their votes. So, here I go: Please stop voting this as a duplicate so quickly, which will eventually lead to this question being closed off. Yes, the other question linked to asks the same math, but any newcomer to the problem who was exposed to it via physics, as I was, will prefer this question instead of the one that is purely mathematically. I beg the moderators to not be pedantic on this one. This question spills into physics, which is why I did the cross post to the physics forum as well.)  How does the sum of the series “1 + 2 + 3 + 4 + 5 + 6…” to infinity = “-1/12”, in the context of physics?  I heard Lawrence Krauss say this once during a debate with Hamza Tzortzis (). I found a transcript of another debate between Krauss and William Lane Craig which has the same sum. Here is the paragraph in full:     Let’s go to some of the things Dr. Craig talked about. In fact, the   existence of infinity, which he talked about which is   self-contradictory, is not self-contradictory at all. Mathematicians   know precisely how to deal with infinity; so do physicists. We rely on   infinities. In fact, there’s a field of mathematics called “Complex   Variables” which is the basis of much of modern physics, from   electro-magnetism to quantum mechanics and beyond, where in fact we   learn to deal with infinity; without the infinities we couldn’t do the   physics. We know how to sum infinite series because we can do complex   analysis. Mathematicians have taught us how. It’s strange and very   unappetizing, and in fact you can sum things that look ridiculous. For   example, if you sum the series, “1 + 2 + 3 + 4 + 5 + 6…” to infinity,   what’s the answer? “-1/12.” You don’t like it? Too bad! The   mathematics is consistent if we assign that. The world is the way it   is whether we like it or not.   -- Lawrence Krauss, debating William Lane Craig, March 30, 2011  Source:   CROSS POST: I'm not sure if I should post this in mathematics or physics, so I posted it in both. Cross post:   EDIT: I did not mean to begin a debate on why Krauss said this. I only wished to understand this interesting math. He was likely trying to showcase Craig's lack of understanding of mathematics or logic or physics or something. Whatever his purpose can be determined from the context of the full script that I linked to above. Anyone who is interested, please do. Please do not judge him out of context. Since I have watched one of these debates, I understand the context and do not hold the lack of a full breakdown as being ignorant. Keep in mind the debate I heard this in was different from the debate above.
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I'm sorry if this was asked before but with all the stars and dark matter and all the other stuff, curently in the Universe, what's the avarage temperature of the Universe? Is it like extremely high or extremely low?
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Just watched the 'How Big is the Universe?' TV program and it indicated that the universe is believed to be infinite in size. They used an approach involving measuring the internal angles of triangles. Or something like that anyway.  But hang on, the Universe has a known starting time and size followed by a finite time expanding at a finite speed. So surely, by definition, it cannot be infinite? I can accept it is honking big but by definition it cannot be infinite. Are they misleading me?
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This is part of a bigger problem I'm trying to prove, but my argument relies of the validity of the following idea. Note that when I say countable, I don't mean finite -- I mean countable infinity.   Consider the set of natural numbers, $\mathbb{N}$. Now take a countable subset of them, call it $\mathsf{S}_1$. Then take a countable subset of $\mathbb{N}\setminus{\mathsf{S}_1}$ and call it $\mathsf{S}_2$. Then take a countable subset of $\mathbb{N}\setminus\{{\mathsf{S}_1}\cup{\mathsf{S}_2}\}$ and call it $\mathsf{S}_3$. Continue in this manner to construct $\mathsf{S}_i$'s such that ${\mathsf{S}_i}\cap{\mathsf{S}_j}=\emptyset$ for $i≠j$.  My question is this: is it necessarily the case that eventually there will be finitely many $\mathsf{S}_i$'s with $\mathbb{N}\setminus\bigcup_{i}{\mathsf{S}_i}={P}$ where $P$ is either empty or finite? My guess is yes, but I'm not how to prove it or how to find a counterexample.
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I just finished the book of Lawrence Krauss "Universe from nothing" and he said that virtual particle can pop to existance from nothing by quantum fluctuations of the field from the vacuum and in the same way our universe can pop to existence, but my question is..  How this quantum fluctuations works? If the space-time began to exist with universe how can this quantum fluctuations generate universe? Doesn t them requer space-time in the first place?? The book doesn t answer that..  I dont get a answer also on Yahoo
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I am reading the book of Lawrence Krauss "A universe out of nothing", where he explained that the vacuum is not empty. It is a boiling brew of virtual particles that come out of their existence. And they can create a universe, even space.  But virtual particles are inner lines in a feynman-diagram. They converge in a vertex and so on. They are off-Shell.  I am a layman and I cannot grasp clearly about this stuff.  My question are:    Is the vacuum empty or is it not?  Are there particles in the vacuum and can they create a universe? But when virtual particles are just a mathemacical "trick" to calculate something, what does Lawrence Krauss mean? What is the matter about the vacuum?
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Why that exact number of electrons in one coulomb? who decided it? there is nothing wrong with the number, it just seems slightly messy. Why didn't the scientific community just settle on an easier number, such as $1\times10^{-19}$ for example?
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So I've been reading a bit and watching some videos about the double slit experiment, and therefore the wave particle duality; I've also read this "implies" that a particle can be in two places at the same time. Can you clarify this, and how could that be possible?