Grandfather’s
Walk – and why is it a surprise photons can be a particle and a wave at the
same time.
October 8, 2015
Revision
History
October 9, 2015 – Added note on the use of time for
observations and waves
Grandfather
So, grandfather likes to walk. It turns out, he’s on
an old 200 acre farm and in retirement, he likes to putter here and there. One
day, he’s out somewhere, and grandmother asks me where he is. I say I don’t
know. I could have said there’s some probability he’d be at the lake, or say
working on the pump, or at one of the cottages.
Probability can be used to describe where he is. Most
likely (high probability), he’s down by the lake and much less likely he’s up
in the woods (low probability). But we can be sure if we sum the probabilities
up, they’d equal one.
So, I go to find him, and at the instance I do find
him (a physicist would say observe), he exists in only one place. Again, a
physicist would say, from my frame of reference, I know exactly where he is,
which I do.
But, since grandmother doesn’t yet know where he is,
she would describe his location as a wave / probability function only knowing
if she sums them up, it equals one.
I turn my back for a second. Now, I don’t know exactly
where grandfather is, as he is puttering around. However, my wave/probability
function is different from grandmothers, as I’m sure he’s pretty close to where
I last saw him.
So, grandfather is both a wave and a particle, and
both at the same time, depending on the frame of reference of the observer.
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So, why is it that physicists have so much trouble
understanding that an electron or photon (or anything for that matter) can be
both a particle and a wave at the same time?
We can also infer from this example for all this to
work, that grandfather has to be moving, and somewhat faster than some
reasonable time frame for the observer. Otherwise, if say, grandfather were a
snail, and we waited five minutes, he wouldn’t have moved much.
Also, multiple observers only agree on where
grandfather is at only one time, which is pretty difficult to calculate from
spatially separated observation points.
Further, probability distribution functions vary,
based on the frame of reference of the observer and last observation.
Note: The observation of the particle did not involve
time, whereas if you use the wave function, time must be involved, as the
probability distribution function is a function of time (and other parameters).