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I'm reading this post:

Definition of Fine-Tuning

and John Rennie's answer that we can calculate the probability that the cosmological constant has its observed value (the answer being around 1 in $10^{120}$.

I'm not a physicist. I'd like to understand what this probability means. When I think of probability, I think of a space of possibilities... for example a dice with 6 sides. The probability of getting a 3 is 1/6.

So what does it mean to say the probability of the cosmological constant being what it is, is 1 in $10^{120}$? My naive way to make sense of it is to say that there are multiple universes and around every 1 in $10^{120}$ of them has our particular cosmological constant. But I get the feeling this is the wrong way to think about probability in this situation.

Ameet Sharma
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As John mentions on his comments, we should take this 'probability' with a grain of salt. We obviously can't seriously talk about probabilities when we have no other universes to compare to. (It's more like rolling a dice and getting '4' but not knowing how many sides the dice has, whether it's a fair dice/roll, etc). Calculating a probability in this case then necessarily relies on our assumptions about how the cosmological constant takes the value it does, as well as it's allowed values, and a whole bunch of other physics on the edge of our understanding (e.g. whether mechanisms do/don't exist that drive the CC to its observed value).

The probability mentioned here, the $1$ in $10^{120}$, is more akin to assuming the CC can randomly take any value, looking at its value and saying 'ah, the chance of having this value is 1 in whatever'. If I remember correctly, the $10^{120}$ figure is usually contrived by comparing the observed value of $\Lambda$ with the naive QFT vacuum prediction of $\Lambda$, which differ by around $10^{120}$ orders of magnitude. This is why I don't think there's any benefit to giving a probability to something like this. It also belittles the more serious theoretical problems with the cosmological constant, namely, it's radiative instability.

Eletie
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1x10 raised to 120 means you multiply 10 a hundred and 20 times. So the chance of one in that ginormous number means that the chances of that one event of happening is exponentially impossible. Our entire universe has 1x10 raised to the 90 particles, that is, subatomic particles.

Gerard Espiritu
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