This was one of two really embarrassing posts I made--my only excuse, lack of sleep. Apologies to anyone I offended, I can’t say what I was thinking and obviously didn’t know what I was doing. r
Errr.... the median of two numbers is their mean and the mean of a huge number and a little number is about half the big one and the Earth is not half the radius of the visible universe. You have used a different formula to the one in your title.
Hi rusty, and welcome to Sciforums! The radius of the observable Universe is much bigger than your figure, which is only about as far as the Orion nebula - not even close to out of the galaxy. The radius of Earth is about 6400km. Your size for a carbon atom is about right... but we can't see carbon atoms. They're too small. And what kind of average is that? The only thing I can think of that would be remotely close is a geometric mean, but that's not it.
The universe is 13.7 billion light years but we can see about 46 billion light years due to space-time expansion. 46 billion light years = \(4.35 \times 10^{26}\) metres. Earth radius = 6400km = \(6.4 \times 10^{6}\) metres Radius of atoms ~ \(10^{-10}\) metres. Since the radius of the universe is so much larger than that of an atom the mean is almost exactly half the radius of the universe, \(2.18 \times 10^{26}\) metres. The geometric mean of N quantities is \(\left( \Product_{n=1}^{N}R_{n} \right)^{\frac{1}{N}}\) and that is approximately (going by powers of 10) \(10^{8}\) for the universe and atom. Which is still more than an order of magnitude out from the Earth. In a very arm waving way we are 'in the middle' of scales, in that we're around as small to the universe as an atom is to us but, as just demonstrated, this is only a very rough relationship. It does serve to illustrate that the physics of the cosmological and the physic of the atom are just as alien to our every day lives as each other. People who don't know much physics all too often say "I refuse to accept that's how atoms behave" because results sound so odd to us. But just as the universe is a very very different place over billions of light years compared to our lives, our lives are a very very different place compared to the scale of atoms. We really shouldn't be too surprised when it turns out the very very big or the very very small aren't working the same way as the very very average.
Sorry about the presentation however, in EXCEL the medium(0,10) is 5... still half way (or /2). But how embarrassing!! My spread sheet has a huge error in it regarding the radius of the visible universe! So Sorry.
How embarrassing!! My spread sheet has a huge error in it regarding the radius of the visible universe! So Sorry. Good for me though (this didn't turn out the way I remember it turning out). We can 'see' carbon atoms (I think): http://en.dogeno.us/2009/09/first-captured-image-of-electron-clouds-inside-one-atom/ Rusty
Hi Alphanumeric, How embarrassing!! You are right! My spread sheet has a huge error in it regarding the radius of the visible universe! So Sorry (God I hate it when that happens). I afraid I can't follow your notation. According to your calculations what is the midway point between the two extremes? We can 'see' carbon atoms (I think) (in case you doubted this like almost everyone else): http://en.dogeno.us/2009/09/first-captured-image-of-electron-clouds-inside-one-atom/ Rusty
It depends how you define 'middle'. You can work by addition, in that the mean is \(\frac{A+B}{2}\) or by multiplication, \(\sqrt{AB}\). If you use the former method you get just half the visible universe radius and if you use the latter you get a number about \(10^{8}\), which is still too big. There's something which Dirac noticed which follows a similar line of reasoning. I can't remember what its called but he noticed certain quantities are in much the same ratio, including something to do with the size of the universe. I'm sure Google can help. if you're interested.
Do I have my figures in line now? light years km meters Radius Visible Universe 46,500,000,000 450,482,142,182,407,000,000,000,000 atom 1E-10 0.000000000100000000000000000000 nucleus 1E-14 0.000000000000010000000000000000 proton 1E-15 0.000000000000001000000000000000 quark/electron 1E-18 0.000000000000000001000000000000 Planck/string? 1E-33 0.000000000000000000000000000000 It seems EXCEL can't display 'Planck/string?' as a real. Edit: my formating went to hell and my upload of images fails for some reason. Not to worry, I'll confirm all after I get some sleep! Rusty
This is the observation that the age of the universe \(\frac{tm_ec^3}{e^2}\sim 10^{39}\) in terms of a natural time unit, and the nondimensionalized gravitational constant \(\frac{e^2}{Gm_em_p}\sim10^{39}\) are of the same order of magnitude. Dirac reasoned that it cannot be coincidence. Since the age of the universe is not a constant, he was led to imply that the gravitational constant is decreasing with time \(G\sim t^{-1}\) which would be a nice explanation of why the gravitational constant is so small (it is simply because the universe is very old). Varying gravitational constant would imply that the Moon must be receding from the Earth at certain rate and it was refuted by accurately measuring the distance to the Moon for a long time (involving laser beam and the mirror an Apollo team left there). He also found another big number, which is the mass of the universe expressed in proton's mass \(\frac{M}{m_p}\sim10^{78}\) which is surprisingly of the order of \(t^2\). So he hypothesized \(M\sim t^2\) that is, new matter must spontaneously come into existence. I don't know about the fate of the later hypothesis.
