On Thu, Mar 21, 2019 at 7:46 PM Lawrence Crowell <
goldenfieldquaterni...@gmail.com> 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
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