While physicalism requires only that a conscious state depends entirely on an underlying physical state, it is often assumed that consciousness is algorithmic and that conscious states can be copied, such as by copying or digitizing the human brain. In an effort to further elucidate the physical nature of consciousness, I challenge these assumptions and attempt to prove the Single Stream of Consciousness Theorem (SSCT): that a conscious entity cannot experience more than one stream of consciousness from a given conscious state. Assuming only that consciousness is a purely physical phenomenon, it is shown that both Special Relativity and Multiverse theory independently imply SSCT and that the Many Worlds Interpretation of quantum mechanics is inadequate to counter it. Then, SSCT is shown to be incompatible with Strong Artificial Intelligence, implying that consciousness cannot be created or simulated by a computer. Finally, SSCT is shown to imply that a conscious state cannot be physically reset to an earlier conscious state nor can it be duplicated by any physical means. The profound but counterintuitive implications of these conclusions are briefly discussed.