On Wednesday, December 23, 2020 at 8:43:05 AM UTC-6 johnk...@gmail.com
wrote:
> On Tue, Dec 22, 2020 at 4:52 PM Bruce Kellett <bhkel...@gmail.com> wrote:
>
> > *There are many 1p views*
>>
>
> Yes.
>
> > *and for each the probability of that particular observation is one*
>>
>
> Yes, AFTER Bruce Kellett has observed that the electron went left rather
> than right then the probability the electron had gone left rather than
> right is exactly precisely 1. And that proves that making accurate
> predictions is very very easy if one is permitted to make the predictions
> AFTER the events in question have happened.
>
> > contradicting the Born rule calculation of the probability in every
>> case.
>>
>
> No, the Born rule Is about making a prediction BEFORE the event has
> happened not AFTER.
>
>
>> > *The Born rule cannot be deduced from the Schrodinger equation*
>>
>
> That is true. The Schrodinger equation just says for every particle there
> is a wave that is associated with it, the equation says nothing about what
> is waving, it doesn't even say if that wave has any observable
> consequences; for that you need a quantum interpretation. The Born Rule is
> a quantum interpretation. Max Born advanced the idea because from
> experiments it was shown to have worked and for no other reason. Max Born
> noticed that if Max Born took the square of the absolute value of the wave
> function at a point it would provide the probability that Max Born would be
> able to observe that particle at that point.
>
> For example, Max Born noticed that if Max Born assumed that the square of
> the absolute value of the wave function at a point was a probability and if
> it said the electron was 60% likely to go left and 40% likely to go right
> under the specified experimental conditions and the experiment was repeated
> many times with the same conditions then Max Born would observe the
> electron go left about 60% of the time and right about 40% of the time, and
> the more times the experiment was repeated the closer it would get to that
> 60/40 ratio.
>
> > *they are incompatible.*
>>
>
> If there is one thing that we know for certain about Quantum Mechanics
> it's that the Born Rule WORKS, so if the Schrodinger Equation was
> incompatible with the Born Rule then the Schrodinger equation would be a
> useless piece of garbage. It's not.
>
> John K Clark
>
There is a correspondence between the geodesic deviation equation and the
Schrodinger equation. A unitary operator U(t) acts on a wave function so
that U(t)ψ(0) = ψ(t) and U obeys the Schrödinger equation
iU_t = HU.
This Schrodinger equation may be re-expressed as iU_tU^{-1} = H or iU_tU^†
= H. We can take an overall time derivative to get
iU_{tt} = H_tU + HU_t
or
iU_{tt} = i∂_t(U_tU^†) + iU_tU^†U_t.
The term ∂_t(U_tU^†) or ∂_tH is equal to the commutator [H, H] = 0 and so
we have the elementary equation
U_{tt} = U_tU^\dagger U_t.
This equation is analogous to
d^2x^α/ds^2} = R^α_{μβν}U^μx^βU^ν.
which is like the unitary evolution equation. The curvature terms may be
absorbed into the U^μ where the geodesic equation this is a real valued
analogue of unitary evolution.
LC
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