On 20 Nov 2014, at 19:27, John Clark wrote:
On Thu, Nov 20, 2014 Bruno Marchal <[email protected]> wrote:
> The "mutiverse" is only the quantum configuration space taken
seriously. The SWE describe all quantum evolution as a rotation (a
unitary transformation) of a state vector in the Hilbert space. I
can hardly imagine something more reversible.
Yes the Schrodinger Wave Equation is easily reversible (and it's
continuous and deterministic too), but with regard to the
reversibility of time that's a irrelevant fact because the SWE is a
unobservable abstraction.
To be sure I was reasoning assuming the usual non relativistic SWE.
Then it is reversible in the same unitary sense that quantum computer
gates are reversible, which includes the usual notion of time.
To get something real that you can actually see
I am a platonist. If I see something, I very much doubt it is real ...
you must square the amplitude of the SWE of a particle at a point
and that will give you the probability you will observe the particle
at that point, and probability, unlike the SWE, is something that
you can observe and measure.
Only from a first person perspective. It is psychologically real, but
that does not exist at the ontological level (that is the spirit of
both computationalism and Everett's QM).
And Schrodinger's equation has complex values, that means it has a
"i" (the square root of -1) in it, and that means very different
quantum wave functions can give the exact same probability when you
square it; and if X and Y both produce Z then things are not
reversible, if you're in state Z there is no way to know if the
previous state was X or Y.
There are equivalent up to a global phase factor.
You get all sorts of strange stuff with i, like i^2=i^6 =-1 and
i^4=i^100=1. And in the macroscopic non quantum world if the
probability of me flipping a coin and getting heads is 1/2 and the
probability of you flipping a coin and getting heads is 1/2 then the
probability of both you and me getting heads is 1/4, but in Quantum
Mechanics that's not necessarily true because now you must deal with
i and complex numbers. I think you could say that mathematically
it's the existence of that damn i in the SWE that makes Quantum
Mechanics so weird.
I am not so sure. I am actually teaching quantum computation, mainly
to illustrate quantum weirdness and the many-worlds, and I can manage
to do that without using complex numbers. (the audience is not all
well versed in mathematics). The real Pauli matrices (sigma_x and
sigma_z) are enough. That is not new, David Albert does the same in
his little book "QM and experience".
I am forced to consider the wave as real (ontologically), because it
interferes even when I don't look at it (especially if I don't look at
it actually), so that when I want to "measure" the probability (by
taking the square of the amplitudes) I get the correct numbers.
Bruno
John K Clark
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