I have seen this addressed here Is it possible to use bitcoin as interplanetary money/store of value?
I am not sure however that the solution provided there is actually correct, so I want to share my thoughts with the question being wether or not these assumptions are correct or not.
The essence of the problem, as far as I understand it, is that finding new blocks is probabilistic and linked to time.
As mentioned in the solution of the above post:
Following the laws of relativity, it is fundamentally impossible to communicate between them in less than 22 minutes in that case. A propagation time of 22 minutes would utterly destroy any ability to mine on both sides.
But isn’t this also the solution to the problem? Any blockchain from planet A will probably be shorter than the one on planet B, since when the information from planet A of 22 minutes ago reaches planet B, planet B will already on average have found two more blocks, effectively rejecting the chain from planet A. To planet A this doesn’t matter though, because the inverse applies as well, essentially leading to two different blockchains, both of which are weirdly true due to the relativistic nature of the universe.
The catch might be that the time it takes to mine blocks is dependent on the hashing power of the entire network, so one planet might be at a disadvantage.
Mathematically speaking what would the exact equation here be? How much percentage of the hashing power would a planet need to compensate, for a time delay of, let’s say the minimum distance to mars: 3:02 minutes? Is it fair that you would need 182/600, so ~30 percent of the hashing power to pull this off, meaning reaching a state where each planet has their own Bitcoin?
Wouldn’t this also lead to a "decrease" in the hash rate of the entire network, since effectively the 30 percent would now become the 100% of the blockchain of the specific planet?
Or am I missing something obvious here/are these assumptions false?