X-Message-Number: 15037
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 

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 

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

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