Regardless of any other arguments against this idea, I think that the key implied proposition is false; that there are other brains 'similar enough' to your own

Regardless of any other arguments against this idea, I think that the key implied proposition is false; that there are other brains 'similar enough' to your own to share the same physical processes is extremely unlikely. There are more possible configurations of the neurons in your brain than there are atoms in the universe. Even worse, the future excited state of your brain depends on the current excited state of your brain. In order for the decision you make to be correlated to the decision of someone else's brain you almost certainly need to work at quite a few abstractions above the physical one. This comment is getting longer than I meant, but an interesting counter point to my previous statement would be that many brains will react in similar ways to the same stimulus, and this may be put down to a 'physical process'. An example might be reactions to attractive people.