Could there exist a machine, consistent with the laws of physics, that “non-invasively cloned” all the information in a particular human brain that was relevant to behavior—so that the human could emerge from the machine unharmed, but would thereafter be fully probabilistically predictable given his or her future sense-inputs, in much the same sense that a radioactive atom is probabilistically predictable?
The answers are not obvious and certainly not amenable to a “simple proof”.
Consider reading Scott Aaronson’s The God in the Quantum Turing Machine, it goes in considerable depth stating and answering the questions such as
The answers are not obvious and certainly not amenable to a “simple proof”.