So? A measurement of location is not a measurement of speed. In
quantum theory, you are not allowed to speculate unless you make a
measurement. When you measure location, you are saying, "I don't
care what the speed is." When you decide that you care what the
speed is (i.e. make a measurement), you always find that it is the
same constant, within experimental error.
This is, in fact, a paradigm of the quantum view of nature: if
you are not making a measurement of some variable, then don't ask
about it. (In classical physics, we are free to speculate.)
> > From "QED" by Richard Feynman:
>
> "You found out in the last lecture that light doesn't only
> go in straight lines; now, you find out that it doesn't go
> only at the speed of light!"
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.
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 ;-)
Regardless, as I noted in an earlier post, I still find it
interesting that the collapse of the wavefunction appears to
take place everywhere instantaneously.
- JPSchneider
- jschneid@hanoverdirect.com
-------
Addendum: concerning the 'addition of arrows' that Feynman talks
about in the book "QED: The Strange Theory of Light and Matter".
He is talking about adding 'probability amplitudes', which are
complex numbers (that are hard to calculate, but in the end, just
complex numbers). Complex numbers have amplitudes and phases: we
usually see them written: z = a + bi where z is 'complex', a and b
are real, and i = sqrt(-1).
If we plot this on a graph where the x-axis is the 'real axis',
and the y-axis is the 'imaginary axis', then we can draw an
arrow from the origin to the point in 'complex space'. That
is the arrow that Feynman is talking about. All he is doing
by adding arrows, is adding complex numbers.
Another way to represent points on a graph is polar coordinates,
and similarly we can also write a complex number as z = Rexp(i*t),
where R is the amplitude (the length of the arrow, a real number),
and t (short for theta), is the phase angle: the angle between the
'real axis' and the arrow.
Also, since Euler's formula says: exp(i*t) = cos(t) + i*sin(t), we
then have: a + bi = R*cos(t) + i*R*sin(t); therefore, a = R*cos(t),
and b = R*sin(t), (as expected, for those familiar with polar
coordinates).
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.