How many protons does it take to fill a known universe?
I'm reading a number theory book (a topic I disliked greatly in college, but am trying to decide if I can deal with it now), and the author claims that the known universe would only be able to hold about 10E123 proton-sized objects. While that is indeed a large number, it doesn't seem like it is large enough. Comments?
Note: book published 1977. Has our concept of "known universe" expanded since then?
well, I looked it up, and a proton is 1E-16 cm (femtometers!) radius. The known universe is said to have a radius of 46 billion light years. Each light year is about 10E15 kilometers, so on each ray leaving earth approaching the boundary of the known radius (assuming it's spherical) will contain about 1E43 protons (if lined up single file). ....
Assuming that's correct, if there are at least 1E80 such rays leaving the earth, the claim is valid. The question for me is how are these rays spaced? If they are spaced such that there is a single layer of protons on the surface of our spherical earth (using their circular footprint).... Let's see, earth radius mean=6,371 km, giving earth surface area 5E8, so 1.6E40 such rays can originate on earth and head toward the outer boundary, giving me 1.6E83 protons on rays originating from earth.... but that will still leave a LOT of empty space between the rays as the distance from the surface of earth increases.
oooooh...now I can see the calculus being added to the problem. To find the angle between the rays, we'd need to know the normal slopes of two "adjacent" protons... I still think the claim is low.
Note: book published 1977. Has our concept of "known universe" expanded since then?
well, I looked it up, and a proton is 1E-16 cm (femtometers!) radius. The known universe is said to have a radius of 46 billion light years. Each light year is about 10E15 kilometers, so on each ray leaving earth approaching the boundary of the known radius (assuming it's spherical) will contain about 1E43 protons (if lined up single file). ....
Assuming that's correct, if there are at least 1E80 such rays leaving the earth, the claim is valid. The question for me is how are these rays spaced? If they are spaced such that there is a single layer of protons on the surface of our spherical earth (using their circular footprint).... Let's see, earth radius mean=6,371 km, giving earth surface area 5E8, so 1.6E40 such rays can originate on earth and head toward the outer boundary, giving me 1.6E83 protons on rays originating from earth.... but that will still leave a LOT of empty space between the rays as the distance from the surface of earth increases.
oooooh...now I can see the calculus being added to the problem. To find the angle between the rays, we'd need to know the normal slopes of two "adjacent" protons... I still think the claim is low.