So, you two are ganging up on me, huh? Ok, starting with John:
; > David Leeper wrote:
; > [clip]
; > > > Measuring the speed of a photon (light) is subject to the
; > > > Uncertainty Principle.
; > >
; > > That's not quite how it works: the uncertainty principle relates
; > > pairs of observables. Even though knowledge of both speed and
; > > location is subject to the uncertainty principle, it is still
; > > the case that the speed of a photon may be determined with
; > > arbitrarily small uncertainty (in theory).
; >
; > The photon receives no special treatment in QM. If we know
; > its location with 100% certainty, we are 100% uncertain of it's
; > speed, like every other particle.
;
; So?
So if light always traveled at the speed "c", we'd be 100%
certain of it's speed, not 100% uncertain.
; What we really find is that if we add up the probability amplitudes
; of everything, then the amplitudes for all those other non-straight
; and/or variable speed paths always seem to add up to zero - and what
; that means is that the probability that they will actually happen
; when we run experiments is zero: light travelling faster than 'c'
; does not happen in experiments. And the quantum point of view is
; that we only care what happens in experiments - we don't care that
; the calculation included consideration of strange occurances.
Um, it _does_ happen, read on...
; In fact, you could almost say that Feynman 'proves' that, even
; though we need not assume that light travels at constant speed
; in straight lines, it always does anyway: the 'proof' is done
; by calculating all the other probability amplitudes and showing
; that they all add up to zero. (QED ;-)
What! You're using my own references against me?!? That's not
legal! Judges, can we get a ruling on this? WHAT!! Its OK!?!?
I can't believe it... (That'll teach me to provide references.)
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".)
"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 possiblities 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
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.
; Anyway, Feynman's 'addition of arrows' analogy is meant for those
; who get confused by the notion of complex numbers. For those who
; have no trouble with them (which I suspect is the case for most of
; us on this list), the 'addition of arrows' analogy is not very
; useful at all - it makes it sound like he's simplifying something
; way over our heads. He isn't.
I'll go along with this, but I doubt Feynman wrote QED for the
Virus list.
And now Jason:
; There is a difference between the speed of light being variable
; and being uncertain. I have yet to speak to someone about this
; issue but my gut reaction is this. The speed of light can be a
; constant and still suffer from Heisenburg's uncertainty
; principle.
As I've shown above, I think it's illogical to say, on the one
hand, that photons always travel at the speed "c", and on the
other, that we are 100% uncertain of the speed of some given
photon.
My "gut reaction" is that, at the Quantum Level, things aren't
hard and fast, it's difficult to say "This always works this
way" and "That never works that way." I'd be interested in your
opinions on this.
-- David Leeper dleeper@gte.net Homo Deus http://home1.gte.net/dleeper/index.htm 1 + 1 != 2 http://home1.gte.net/dleeper/CMath.html