On 21 Nov 2014, at 17:36, John Clark wrote:
On Fri, Nov 21, 2014 Bruno Marchal <[email protected]> wrote:
>> 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.
That is incorrect because computer gates are observable
They are unitary transformation. Some like the Pauli one are hermitian
too.
but the SWE, both relativistic and non relativistic, are
unobservable, only the square of the wave is observable and then
only as a probability. So the SWE may be reversible but it's square
is not; if 4 is the product of two integers there is no way to know
if they were 2 or -2, so you can't reverse things and find the
previous probability, much less get back into the actual previous
state with 100% certainty.
Locally you are right, but globally, the universal wave is reversible.
This means that locally it will look like quantum amnesia or erasing.
Bruno
John K Clark
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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