Last night, just as I was going to sleep after watching a science program, something occurred to me. What is the chance of our universe to exist with as much matter as it currently holds? So I did a little research on some of the characteristics of our universe. Apparently, shortly after the Big Bang, matter and antimatter were created from energy. However, there is a clear asymmetry between the matter that was created and the antimatter. This asymmetry may seem small if I say that there was only one surplus proton or neutron for every 10 billion antiprotons and antineutrons, but the fact is that there is so much matter in the universe that the likelihood of this asymmetry to happen by random is extremely small.There is estimated that there are 10^{80} atoms (of matter, of course) in our universe, most of which are hydrogen atoms. That means that there are even more subatomic particles, such as protons and neutrons, but I’ll use the number of atoms as a reference. Now, the probability of just one surplus particle in 10 billion, or more, antiparticles to be created by chance alone is (10^{10}-1)/(2∙10^{10}), which is just below 50%. However, because it’s not important whether a universe is made of matter or antimatter [1], the chance of either one of them having this surplus is double of that, meaning it is 1-1/10^{10}, which is equivalent to 1-10^{-10}. This probability is quite close to 100%, being exactly 99.9999999%. However, because this surplus is repeated for so many particles [2], the probability drops drastically to show the probability of one surplus particle in every 10 billion, or more, antiparticles to be created by chance. That probability is just smaller than 10^{-1070}, which is 10^{-10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000}, which is 1/1000...0000, with a number of zeros equal to the number from the exponent of the previous form of this number, i.e. 10^{70} zeros. This means that there would have to be more than 10^{1070} universes [3], in which the laws of physics are in such a way that matter and antimatter exist and are created randomly, so that a universe with as much matter/antimatter, or more, as ours to exist. In fact, it’s most likely that a universe with as much energy as ours, in which particles and antiparticles were created randomly, would have only between 100 million particles (protons and neutron), with a probability of approx. 90%, and 1 billion particles, with a probability of approx. 37%. This amount of matter is not enough to create one human being, let alone a vast universe.
However, according to physicists, baryogenesis is the generic term for hypothetical physical processes that produced an asymmetry between baryons and antibaryons in the very early universe, resulting in the substantial amounts of residual matter that make up the universe today. This process would render my calculations obsolete. But I still think it’s fun to think about what if there is no baryogenesis, or any other process that would account for the asymmetry found in the creation of matter? That would mean that there could be 10^{1070} universes out there, similar to our universe. The number could be immensely higher for the universes that are quite different than ours.
P.S. I wasn’t trying to prove anything with these calculations. I just thought it would be fun to see what would happen IF particles and antiparticles were created randomly (with equal probabilities). I’m not saying this is the case. Quite the contrary, if physicists say that whatever process could be responsible for this asymmetry, then that’s probably the case.
[1]Matter is anti-antimatter. If we were in a universe filled with what we now call antimatter, everything would be the same, except that we would call matter antimatter, and antimatter matter.
[2]It’s like the probability of flipping a coin ten times and getting 6 heads, or more, and 4 tails, or less, or 6 tails, or more, and 4 heads, or less; essentially not getting exactly 5 with 5. It’s a pretty big chance, being approximately 64%. However, the chance of getting 60 heads, or more, and 40 tails, or less, (and its counterpart) is significantly lower. That’s because it’s the probability of getting 6 heads, or more, and 4 tails, or less, (on average) 10 times in a row. After a million tosses, for example, the chances of getting 600,000 heads, or more, and 400,000 tails, or less, is almost 0. The same applies for the number of particles and antiparticles, even if it’s just 1 in 10 billion. If we multiply with 10^{80}, so that we can account for all the particles we estimate to exist, then the probability drops very much, just like in the case of the coin tosses. Therefore, the probability of having 10^{90}+10^{80}particles and just 10^{90}
antiparticles, is incredibly small.
[3]That number is bigger than we can imagine. Just as I’ve mentioned before, the total number of atoms in the universe is estimated to be 10^{80}, which is such a tiny fraction of this number. In fact, if every single human that ever existed would use all his spare time to write down zeros for this number, I don’t think we would even be close to writing it. In fact, I made a computer application to see how much time it would take to write the number. My application (using a single core), wrote 10^{106} in its “normal” form (1 followed by a million zeros) in 233 seconds. That means that it would write that huge number in 7.4∙10^{58} years. To give you some perspective, the file in which I wrote the number 10 to the power 1 million is 953 MB in size, almost 1 GB, meaning that 10^{1070} would occupy a little less than 10^{61} TerraBytes.
Tags: antimatter, big bang, matter, universe
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