OK - time to get technical: the uncertainty principle is written
in terms of position and momentum (not speed), and these are both
vectors. 100% uncertainty just means that we have no idea where
it's going, or what its energy (momentum) is, even though its
speed is 'c'.
Even in one dimension, such a measurement, in order to measure
location *exactly*, would impart a totally unknown energy to the
photon, so that it could end up traveling either forward with a
totally unknown momentum, or backwards with an totally unknown
momentum: 100% uncertainty in momentum, and we still assume its
speed is 'c'.
> [clip]
> Why would we calculate something if it _always_ came out to zero?
> That's like saying "Let's add zero to all our numbers at every
> step of our calculation." What's the point? (Actually, there
> _is_ a point to this if you have Cohesive Math and a religion
> named Zero, but I don't think Feynman is my "John the Baptist".)
The point is that they are in the equations whether we want them
there or not. We do not need to use Feynman's techniques to do
calculations in quantum electrodynamics. But, since it's a LOT
easier to do it his way, that's the way it's done. Each term in
an equation will relate to a Feynman diagram, and each factor in
the term can be related to a piece of the diagram.
[Note, his Nobel prize was shared with two others (Schwinger and
Tomanaga (sp?)) They had solved all the equations on their own,
mathematically, something Feynman had never done. He solved the
main problem using his diagrams (the 'main problem' being this:
quantize electrodynamics, one way or the other.) Later on,
Freeman Dyson showed that Feynman's technique was equivalent
to the other one. If you like reading about Feynman, this is
talked about in the biography 'Genius', by James Gleick.]
> "It may surprise you that there is an amplitude for a photon to
> go at speeds faster or slower than the conventional speed, c.
> The amplitudes for these possibilities are very small compared
> to the contribution from c; in fact, they cancel out when light
> travels over long distances. However, when the distances are
> short - as in many of the diagrams I will be drawing - these
> other possibilities become vitally important and must be
> compared." - Richard Feynman, QED
The Feynman rules say: draw any topologically conceivable picture
of the interaction (draw a 'Feynman diagram'), then write down
factors for each external line, each internal line, and each vertex.
Multiply it all out, take an integral, and you have your probability
amplitude for that diagram. Does that mean that, since the n'th
diagram looked like it had a virtual particle (an internal line)
in it that looked like it was going faster than light, that we can
ever make things go faster than light in an experiment? No, it
doesn't. It's just a diagram - a useful device in making the
equation easier to write down and solve.
> Feynman then goes on to show examples when photons _do_ go
> faster than the speed of light (and therefore backwards in
> time!), and discusses why these examples are not only possible,
> but important to understanding nature. See Figure 6.1, page 96.
Really? As measured by experiments? I'll check the reference
when I get home, and I'll try to bring a few ref's of my own
tomorrow....
Feynman also said: "I think it's safe to say that nobody under-
stands quantum mechanics." If he's using quantum mechanics to
"understand nature," when he doesn't understand QM to begin with,
something is definitely amiss.
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| ... towards a crisper definition of |
| that which remains undefined ... |
| JPSchneider |
| jschneid@hanoverdirect.com |
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