In any physically possible case, in which the computer’s speed can be arbitrarily close to c, things develop completely normally in the computer’s own reference frame.
For the right right value of ‘arbitrary’ the computer never performs a single operation. The entire box is obliterated by collision with a stray electron before the processor can tick. The collision releases arbitrarily large amounts of energy and from there things just start getting messy.
In a thought experiment, you can assume anything, however unrealistic, as long as it’s logically consistent with the theory on which you’re basing it. Assuming away stray electrons is therefore OK in this particular thought experiment, since the assumption of a universe that would provide an endless completely obstacle-free path would still be consistent with special relativity. In fact, among the standard conventions for discussing thought experiments is not to bring up objections about such things, since it’s presumed that the author is intentionally assuming them away to make a more essential point about something else.
In contrast, introducing objects that move at exactly the speed c into a thought experiment based on special relativity results in a logical inconsistency. It’s the same mistake as if you assumed that Peano axioms hold and then started talking about a natural number such that zero is its successor. Since the very definition of such an object involves a logical contradiction, nothing useful can ever come out of such a discussion.
Could someone please explain why this was downvoted? (I don’t care about losing score, but I am concerned about the possibility that I wrote something stupid that I’m unaware of.)
Assuming away stray electrons is therefore OK in this particular thought experiment, since the assumption of a universe that would provide an endless completely obstacle-free path would still be consistent with special relativity.
Of course it is OK. But since it was unspecified it was a whole lot more interesting to imagine the effects of a cataclysmic collision with arbitrarily large energy. (Because any discussion of a question of consciousness that goes for more than 3 paragraphs before dissolving the question or finding an interesting tangent is at least two and a half paragraphs too long!)
Now I’m wondering whether such a collision would release enough light to obliterate Earth from an arbitrarily large (but within light cone) distance away. I’m thinking it would.
For the right right value of ‘arbitrary’ the computer never performs a single operation. The entire box is obliterated by collision with a stray electron before the processor can tick. The collision releases arbitrarily large amounts of energy and from there things just start getting messy.
In a thought experiment, you can assume anything, however unrealistic, as long as it’s logically consistent with the theory on which you’re basing it. Assuming away stray electrons is therefore OK in this particular thought experiment, since the assumption of a universe that would provide an endless completely obstacle-free path would still be consistent with special relativity. In fact, among the standard conventions for discussing thought experiments is not to bring up objections about such things, since it’s presumed that the author is intentionally assuming them away to make a more essential point about something else.
In contrast, introducing objects that move at exactly the speed c into a thought experiment based on special relativity results in a logical inconsistency. It’s the same mistake as if you assumed that Peano axioms hold and then started talking about a natural number such that zero is its successor. Since the very definition of such an object involves a logical contradiction, nothing useful can ever come out of such a discussion.
Could someone please explain why this was downvoted? (I don’t care about losing score, but I am concerned about the possibility that I wrote something stupid that I’m unaware of.)
Of course it is OK. But since it was unspecified it was a whole lot more interesting to imagine the effects of a cataclysmic collision with arbitrarily large energy. (Because any discussion of a question of consciousness that goes for more than 3 paragraphs before dissolving the question or finding an interesting tangent is at least two and a half paragraphs too long!)
Now I’m wondering whether such a collision would release enough light to obliterate Earth from an arbitrarily large (but within light cone) distance away. I’m thinking it would.