Hitoshi Kitada (hitoshi@kitada.com)
Wed, 3 Nov 1999 19:17:59 +0900
Dear Stephen,
As Todd Desiato misunderstands in his response to you (see below), many seem to
misunderstand time as the one like the number of jumps from one eigenstate to
another. (This misunderstanding appears also in some of the papers in
http://xxx.lanl.gov/abs/gr-qc/ .) I have to remark that the change occurs only
*between* the initial and final eigenstates, the process of which is called
scattering process, but does not occur when the state is in an eigenstate. Time
is related with this scattering process.
Time in my context is defined as a parameter which describes the extent to that
the scattering process has processed. This extent is described by t in
exp(-itH_L), which is my definition of time. This might correspond to
"individual" time in Matsuno's word, but there might be some difference between
the two.
Observation usually done is thought to be about the comparison between two
eigenstates: the initial eigenstate and the final one after a jump, as in the
case of the observation of emission of light from an atom. But what we actually
observe in this case is the light emitted from the atom by some stimulation from
the outside like irradiating the atom by another photon. The energy of light (or
photon) emitted is thought as the difference between the energies of the two
eigenstates of the atom, and one tends to think one observes the two eigenstates
as though "directly." But what is measured directly is the energy of the emitted
light, and it is measured by some plate by which the energy of photon is
detected, but the two eigenstates are NOT measured DIRECTLY. What is actually
observed in this case is the scattering process of one atom (with a nucleus and
electrons around) and one photon. The photon targets the atom and the photon
with another energy is emitted with the atom's inner structure changed. This is
usually thought as a measurement of transition of the atom's state from one
eigenstate to another, but this is, in actuality, an observation of that
scattering process and this process can be traced only by describing it by using
unitary propagator exp(-itH_L). Many physicists misunderstand this point and
confuses it with a quantum jump. But the "jump" has an inner structure that is
described by unitary propagator. Physicists seem to make a naive
misunderstanding on this point. Actually there are works that suggest this
misunderstanding of usual physicists, but physicists are not aware of the
importance of those works. Physicists remain still in a primitive image that
they observe the jump "directly," which leads to a misinterpretation of what
they are treating.
Best wishes,
Hitoshi
> Hello Stephen,
>
> > Have you worked out the implications of your model with regards to the
> > phase shifting of neutrons as discussed in: R. Collela, A. W. Overhauser
> > and S. A. Werner, Observation of gravitationally induced quantum
> > mechanics, Phys. Rev. Lett. 34 (1975), 1472-1474.
>
> I've heard tell of it, but I have not looked it up. It appears to me to be
> an obvious expectation, even for GR. The action of gravitation induces a
> phase shift in any time dependent wave function, just as would be predicted
> for a uniformly accelerating reference frame.
>
> > BTW, your paper is very interesting! I would be interested in your
> > critique of Prof. Hitoshi Kitada's Local Systems Theory:
> > http://www.kitada.com/
>
> I read it last night. While I would agree that time should be defined
> locally for one system relative to another, I find there is no understanding
> of Relativistic QED or GR. In essense it seems to be a simple critic, and
> some common sense.
>
> I'm pretty certain that this statement,
>
> "If a local state is not an eigenfunction, it varies, and thus
> using the change of the wave function, one can define a
> local clock of the local system."
>
> is a complete misunderstanding of QM. In the first place if a state is not
> an eigenfunction, then it is not a solution of the equation, and does not
> exist. Only solutions that are eigenfunctions are physically real. Second
> you could not measure this sort of "change" to use it as a clock.
>
> A Quantum mechanical clock of this type is made by considering two different
> states, which **are solutions** of the wave equation. Then determine the
> transition probability distribution to go from one state to the other. These
> sort of transitions are observable.
>
> He seems to imply that QM is not relativistic, which has been wrong since
> Dirac's equation. QED is definitely a relativistic theory. I hope you will
> agree.
>
> Regards,
> Todd Desiato
>
Note 0:
> A Quantum mechanical clock of this type is made by considering two different
> states, which **are solutions** of the wave equation. Then determine the
> transition probability distribution to go from one state to the other. These
> sort of transitions are observable.
As I wrote above, transitions are not observable in any direct sense.
Note 1: Todd seems to think wave equation as H_L psi = a psi. Wave equation in
my context is
-i d/dt psi = H_L psi.
Note 2:
> Second
> you could not measure this sort of "change" to use it as a clock.
Matsuno's paper that Stephen found:
http://bio.nagaokaut.ac.jp/~matsuno/preprints/HELSIN98.html
will be a help to understand how this sort of "change" can be used to define a
clock.
Note 3:
> He seems to imply that QM is not relativistic, which has been wrong since
> Dirac's equation. QED is definitely a relativistic theory.
I do not imply QM is not relativistic. I imply I adopt non-relativistic QM as a
basic QM framework.
Hitoshi Kitada
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