Question about the Planck spaces and observable universe, .

megahmad
Messages
2
Reaction score
0
From Wikipedia:
http://en.wikipedia.org/wiki/Googolplex

A Planck space has a volume of a Planck length cubed, which is the smallest measurable volume, at approximately 4.222×10^-105 cubic meters = 4.222×10^-99 cubic cm. Thus 2.5 cubic cm contain about a googol Planck spaces. There are only about 3×10^80 cubic metres in the observable universe, giving about 7.1×10^184 Planck spaces in the entire observable universe, so a googolplex is far larger than even the number of the smallest measurable spaces in the observable universe.

If the entire volume of the observable universe (taken to be 3 × 10^80 cubic meters) were packed solid with fine dust particles about 1.5 micrometres in size, then the number of different ways of ordering these particles (that is, assigning the number 1 to one particle, then the number 2 to another particle, and so on until all particles are numbered) would be approximately one googolplex.


---------
So if the observable universe doesn't have enough space to contain a Googolplex of Planck spaces how come a Googolplex of 1.5 micrometres fine dust particles woud fit inside it?

Thanks in advance and sorry if I've made any mistakes, this is my first post here :)
 
Last edited:
Mathematics news on Phys.org
It doesn't say a googolplex dust particles fit in the universe, it says that if n is the number of dust particles, then a googolplex is approximately n factorial (the number of ways of ordering the dust particles)
 
Office_Shredder said:
It doesn't say a googolplex dust particles fit in the universe, it says that if n is the number of dust particles, then a googolplex is approximately n factorial (the number of ways of ordering the dust particles)

Awww, I feel like a noob :o I get it now! Thank you really!

And BTW this is really a great forum, thanks for the quick answer! :P
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
Back
Top