From: *Brent Meeker* <[email protected] <mailto:[email protected]>
On 6/17/2018 10:41 PM, Bruce Kellett wrote:
But the lens doesn't send one color to one photoreceptor and another
color to a different photorecptor. It focuses a spot of light on
several photorecptors and the one with the right pigment fires its
neuron. So it is energy detection.
But if you use a different position basis the lens will no longer
focus point objects to points on the retina.
I don't know enough about the physics of calorimeters as used in
HEP to comment here. But if temperature changes are measured by
bimetals or strain gauges, position comes into it in an essential way.
Most work by measuring a voltage. But you miss the point. Those
position measurements are not essential in the QM sense. They are
just changing one classical value into another. Temperature is the
first classical level.
Fair enough. I suppose I am just very conscious of the fact that in a
different position basis all of this physics will be very different.
The classical universe will not look the same at all.
I guess I don't understand your idea of "position basis". My
understanding of linear algebra is that any basis that spans the space
can be used to represent any relation between structures. Why should
choosing a different basis make any difference to the physics aside
from the simplicity of its representation. It's just a coordinate
basis in Hilbert space. Or are you thinking of bases different from
position, e.g. momentum, energy, live/dead,...
Yes, there does seem to be a degree of miscommunication. I am not think
of different variables such as energy, momentum, or the like. These are
not different bases, they are different variables and they inhabit
different Hilbert spaces. So a change of base in one Hilbert space does
not take you to another space.
No, what I am considering is the possibility of different bases in a
single space, such as position space. If you assume an eignevector
interpretation of a set of basis vectors, then a different basis will
correspond to the eigenvalues of some different operator. It still acts
in the same, position, space, so it must be regarded as a position
operator, but it will have quite different physical properties from the
usual position operator that we use from classical mechanics, where the
eigenvectors are delta functions along the real line.
Because this will be a different operator, it will correspond to
different physics. For instance, if the position eigenvalues are
superpositions of delta functions, corresponding to superpositions of
different points, the point interactions of particles that we assume in
constructing the interaction Hamiltonian will be replaced by some set of
interactions between superpositions of points. This why I suggest that
the physics will be different. If the physics is the same under this
basis change, why is there any question about the preferred basis? The
point is that a change of basis does not mean that we simply go to
measure some other variable. I think Schlosshauer makes this mistake, if
I remember correctly; he seems to suggest that the basis choice is
between position or energy in most cases. That is just wrong.
Bruce
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