I'm a high school junior. I assumed there would be an incredibly huge number of atoms in the universe if not infinite. Recently, I've come across a few articles which claim that scientists believe there are 1083 atoms in the universe. I'm not sure if I should believe in this, to me, this seems like a small number. In average, a human alone has 1027 atoms, so, it's kind of unconvincing to me that there's only 1083 atoms in the whole universe.
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10$\begingroup$ Imagine this: for every atom in human ($10^{27}$), there exist $10^{27}$ atoms, but for every such atom, there exist $10^{27}$ atoms, but for every such atom, there exist 100 atoms. Huge, right? $\endgroup$– User123Jun 26, 2021 at 15:10
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10$\begingroup$ I think you really must not understand exponential notation. 10^83 is 10^27 * 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 (if I counted right), which is a rather large number :-) $\endgroup$– jamesqfJun 26, 2021 at 16:14
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11$\begingroup$ "only 10^83"... Surely that a least deserves an upper-case "Only"? This is the most mindbogglingly huge usage of "only" that one is likely to every encounter in the real universe outside of abstract mathematics, a number so large that calling it "infinity" might be more accurate than "only" $\endgroup$– PcManJun 26, 2021 at 19:08
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13$\begingroup$ I'm curious: what number of atoms would have sounded about right? $\endgroup$– RobertJun 26, 2021 at 20:23
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1$\begingroup$ Get yourself one million small ball bearings. They can be arranged in a square of 1000 by 1000 – that doesn't sound impossible, does it? – do that. Now imagine doing that a thousand times. And then a thousand times more. $\endgroup$– Andrew MortonJun 26, 2021 at 20:56
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5 Answers
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This is a reasonable estimate for the number of atoms in the observable universe.
It might seem like a small number, compared with the number of atoms in a human only as a result of our brain's inability to have an intuition about very large numbers and exponential scales.
There is a very very big difference between $10^{27}$ and $10^{83}$. How big is the difference? Well $10^{83}- 10^{27}= 9.9999999999999999999999999999999999999999999999999999999\times10^{82}$
A human is only a very small part of the universe.
Note two things, firstly this is for the observable universe, the Universe may be isotropic, open and unbounded and if so the total number of atoms in the universe is infinite. Secondly most of the estimates of the number of atoms in the universe that I've seen put the value at about $10^{80}$
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17$\begingroup$ I think saying that 10^83-10^27 is more than 10^82 would be more helpful than spelling the number out with all of its nines (I didn't count them). $\endgroup$– NobodyJun 26, 2021 at 15:33
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4$\begingroup$ @nobody actually saying that "10^83-10^27 is more than 10^82" is about as useful as saying "there is more than one grain of sand on Earth". True, but utterly useless in estimating how much sand is on Earth. $\endgroup$– PcManJun 26, 2021 at 19:14
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3$\begingroup$ Yet another way to see how much larger 10^83 is than 10^27 is to divide both numbers by 10^27: 10^27/10^83 is 0.000000000000000000000000000000000000000000000000000000000000000001, which is pretty tiny :) $\endgroup$– fishJun 26, 2021 at 19:53
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1$\begingroup$ @fish HA! You just estimated how much percentage a single human is part of the universe :) $\endgroup$ Jun 26, 2021 at 22:09
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1$\begingroup$ @Nobody: 10^83 - 10^27 is not just "more than 10^82", it's basically still 10^83. It's like the old joke : "What's the difference between a dollar and a ruble? ................. a dollar." $\endgroup$ Jun 27, 2021 at 12:54
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I similarly thought that the difference in mass between a proton and an electron was minuscule. I think the proton is like 3x10^(-27) kg and electron is 3x10^(-31) kg.
But the way you think about it is that the proton is 10,000 times bigger (10x^-27/10^(-31) = 10^4 = 10,000).
So in your case, the universe has 10^56 times more atoms than a human. So if my networth is 1 cent, Apple's networth is 1 trillion dollars which is 10^14 times more than mine.
I guess that's a poor analogy but the idea is that if something is 10^56 times more than something else, there is a inconceivably big difference between the amounts.
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$\begingroup$ The proton/electron mass ratio is more like 1836. But your point stands. 10^56 is an inconceivable number. $\endgroup$ Jun 27, 2021 at 18:39
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Yes, the number is reasonable for our observable universe. The problem with imagining the decimal notations of numbers is that every added digit can represent approximately 10 times numbers more.
Most of the other answers just say that this number is huge and give representations with abstract numbers. But I would like to give some physical meaning. If you don't understand the following, just skip to the end.
The neutron is not a fundamental particle. It is made of the three quarks, which have their own bounding sphere. It's radius is $r_n=8.5\cdot 10^{-14}m$. Its volume is equal to $$V_n=4\pi r^3/3=2.57\cdot10^{-45}m^3$$ If we just add the volume of such neutrons, we get $$V'=10^{83}\cdot 2.57\cdot10^{-45}m^3=2.57\cdot10^{38}m^3$$ But this is only valid if we could "melt" the neutrons, which we can't. Therefore, we need to use the densest sphere packing possible: $$V=V'/0.74048=3.47\cdot10^{38}m^3$$ Using that volume and the formula for volume of sphere, we can find a radius for such neutron packing $$R=4.36\cdot10^{12}m=29.1 AU$$ For comparison, $10^{27}$ neutrons densely packed give a radius of about $0.85\mu m$.
Physical meaning: The radius we got is the approximate distance between the Sun and the Neptune. The neutron is very small. And imagine bunch of them stacked into the sphere with the radius of the Neptune's orbit.
Wow.
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$\begingroup$ While its true that the number of volumes you added have the large volume you have calculated of is not true that the neutrons can be stacked that way. Al particles are point like and all particles can be stacked in a planck size volume. So this doesnt make the distinction very clear. The distance to Saturn aint that big. $\endgroup$ Jun 27, 2021 at 18:43
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$\begingroup$ @DescheleSchilder Neutrons are composed from the fundamental particle, and between them there is a measurable distance. Therefore, we can approximate the neutron by the bounding sphere. And we are here looking just the volume for the approximation. I might also know where does the downvote come from and why, but I am not mad at you :) $\endgroup$– User123Jun 27, 2021 at 21:12
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$\begingroup$ It came from me. Because of the reason I gave. Your answer gived a good feeling for the amount of small volumes you can put in the big volume but I think it would have been better to put it the other way round. So to start at the volume of the universe and look how big the volume would be if you divide it by 10exp83 Like that you have an idea how much volume each particle has and at the same time how big the number 10exp83 is. The number 10exp27 isnt mentioned at all. The number of neutrons is not 10exp83. The total of quarks and leptons and photons is the total number. $\endgroup$ Jun 27, 2021 at 21:30
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$\begingroup$ @DescheleSchilder First, we don't know the volume of our universe. Second, I wanted to go away from 10^27 because why would I include it? The other answers tell enough about it and OP just used it as a reference for his misunderstanding. Maybe I want clear enough when I said that I want the physical representation, but I can include it if you want. $\endgroup$– User123Jun 27, 2021 at 21:44
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$\begingroup$ Im not saying its a bad answer. But it could have been better. I meant the observable universe. And the number of neutrons is not 10exp83. $\endgroup$ Jun 27, 2021 at 21:48
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Compare
1 000 000 000 000 000 000 000 000 000 (10^27)
1 00 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 (10^83)
For reference, a thousand and a million
1 000
1 000 000
You probably are aware that a million is quite much more than a thousand but the visual difference between them, if you compare to the first example, is quite small.
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2$\begingroup$ It would be more appropriate if this were a comment. $\endgroup$– User123Jun 27, 2021 at 15:06
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Another way of looking at it. The number with 27 zeros can be laid $10^{56}$ times behind each other. I guess you'll arrive somewhere on Pluto). First guess though and it of course depends on how big you write the one and 27 zeros.If you write 1mm numbers the row of numbers 0 and 1 would even be bigger than the observable universe...(thanks to @User123)
So 27 and 83 seem pretty close to one another but the exponentials are. absolutely not.
There simply could not have been another number. If it was bigger or smaller(relatively spoken) the universe would not be our universe anymore. Every elementary particle(so not atom, as the question poses), every one of the $10^{83}$, has the optimum amount of space at it's disposal for life to come about.
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$\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$– Connor Garcia ♦Jun 27, 2021 at 17:29