X-Message-Number: 15037 From: Date: Mon, 27 Nov 2000 18:20:27 EST Subject: discreteness and uploading Lee Corbin (#15032) questions whether quantum mechanics requires discrete states, noting that the Schroedinger equation shows time as a continuous variable. Well, I am far from an expert in this area, but in Schroedinger's (one-dimensional free particle) equation, time and space and mass are all shown as continuous variables, and yet we know that mass and energy are quantized. We also know e.g. that the uncertainty principle can be applied to energy vs. time as well as to space vs. momentum. We also know that q.m. makes no allowance e.g. for anything happening "between" jumps in the energy states of an atom. All this certainly suggests that time, like everything else physical, occurs only in discrete packages. We can even make a speculative philosophical or metaphysical case for discreteness. Any continuous variable, to be expressed as a physical condition, requires INFINITE accuracy at a given moment or a given point, and we could well postulate that infinite accuracy is unattainable, even for Nature. We also know that most physicists seem to agree on the validity of the Bekenstein Bound, which places a finite upper limit on the number of possible quantum states of a system of given mass and volume, such as a human brain. This arises from applying the uncertainty principle to the phase space of a system, so a "point" in phase space has a non-zero volume. (This also implies that, unless the brain can grow without limit, eventually it can no longer have new experiences.) Yet in some interpretations, we have to be careful about the very notion of the "state" of a quantum system. Bohm, several decades ago in his classic text, wrote that the wave function contains all possible information about the system, yet is not in one-to-one correspondence with the actual behavior of matter, having only a probabilistic interpretation, because the wave function describes potentialities rather than actualities, the latter only being realized in interactions or observations. Two systems with the same wave function can behave or evolve differently. As frequently noted, all this (interpretation) is STILL very far from understood or agreed. Now the uploaders have painted themselves into another corner. When a computer describes or calculates the "quantum state" of a physical system, my understanding is that this means it states or calculates the value of each coordinate in the phase space of the system, as precisely as the uncertainty principle or the Bekenstein Bound allows. For a particle in a one-dimensional flat well this means it specifies x and p (position and momentum) at time t. x1 includes a short space interval, p1 includes a small momentum dispersion, and t1 includes a short time interval. The computer then goes on to calculate the "next" (t2) values of x and p, etc. But this is not quantum reality! It is just selecting, out of the infinite possibilities, the one "most probable" succeeding state. For the computer to reflect quantum reality (as presently understood by most physicists) or to reflect Many Worlds, it would have to calculate ALL the possible successive "states" and would therefore effectively grind to a halt immediately. Note carefully that the Turing Machine ITSELF is CLASSICAL, even though it can calculate quantum mechanics. So--once more--what do we have? The Turing Machine does not and CANNOT emulate a person, because a real person does not always evolve into the next most probable configuration. Sometimes his next configuration is less probable. Therefore the emulation is guaranteed to be different from what real life would be. (At least "the" real life, as opposed to "a" real life.) Robert Ettinger Cryonics Institute Immortalist Society http://www.cryonics.org ----------------------------------------------- Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=15037