On Saturday, March 23, 2019 at 7:59:40 AM UTC-6, John Clark wrote:
>
> On Thu, Mar 21, 2019 at 7:46 PM Lawrence Crowell <goldenfield...@gmail.com
> <javascript:>> wrote:
>
>
>> *> The wave function for a plane wave e^{ikx} has the phase ikx for k =
>> 2πp/h, h = Planck's constant, is then real and the total phase ikx - iEt
>> then means time is imaginary valued as well. [...] The imaginary part is
>> not time we measure with clocks and so tunneling has no meaning with
>> respect to that definition of time.*
>
>
> The trouble is, to get some sort of intuitive physical understanding of
> Quantum Tunneling, as opposed to a purely mathematical understanding, it is
> necessary to make a connection between the thing we measure with a clock
> and the thing we wish to understand. This is how I think about it, I'm sure
> it's not exactly correct but let me know if it's at least approximately
> right or if you know of another way that is less wrong:
>
> If I want to send you a electron as a message (attack at dawn for example)
> and speed is important I can't use Quantum Tunneling to send it to you
> faster than light because only the successful attempts are instantaneous.
> If you're on the other side of an energy barrier and I don't have enough
> energy to get through it most of my attempts to send you an electron will
> be unsuccessful. And the probability of the electron getting through drops
> exponentially with the width of the barrier. Thus although my very rare
> successes will be instantaneous if you take into account all my failed
> attempts then the time between my desire to send you a message and the time
> you receive it will always be longer than if I forgot about Quantum
> Tunneling and just flashed a old fashioned low tech beam of light at you
> instead.
>
> John K Clark
>
The statistical set on the occurrence of the particle will have its average
or mean at the velocity of the wave. The appearance of the particle on the
other side of the barrier is no different than finding there is a
stochasticity to the appearance of the particle at points in free space.
The only difference is that the exponential decay of probability through
the tunneling barrier will mean it has less occurrences on the other side.
Where the particle occurs in space is the result of a statistical
distribution, and the reduction of the wave packet makes its occurrence at
some point evident.
LC
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