Date: Thu, 24 Oct 96 12:14:13 -0500 (CDT)
From: cutter@pkmfgvm4
To: External Network Bboard 
Subject: Heisenberg Uncertainty Principle

     In a discussion with a colleague the HUP came up.  I agreed that
its usual interpretation was based on the rationale that one could
not measure something without disturbing it.
     However, I seem to recall having read somewhere that there was
a deeper cause/rationale for HUP, to the effect that HUP would
still apply even if one could make accurate simultaneous measurements
of complementary properties (like position and momentum).
     Can someone correct my understanding and/or point me to a source.
     It's possible I may be confusing the no-measurement-without-
disturbance argument with the particle-wave-duality argument, which I
would consider to be a deeper conceptual basis.

Larry Cutter
===================================================================
Date: Thu, 24 Oct 96 17:21:18 -0500 (CDT)
From: czar@owgvm3
To: External Network Bboard 
Subject: Heisenberg Uncertainty Principle

Ref:     Append at 17:14:13 on 96/10/24 GMT (by CUTTER at PKMFGVM4)

The "deep" uncertainty principle asserts that there must at least a
minimum amount of spread associated with complementary
characteristics.  The quantum-mechanical classic is position and
velocity.  This spread has come to be known as "uncertainty", but this
is in a technical sense, not in the sense of uncertainty due to error.
The "spread" principle asserts that a particle cannot be both point-
like (and thereby have single position) and move with single velocity--
we can't measure position and velocity simultaneously with arbitrary
position simply because nature doesn't allow particles to behave
in such a way that they have both an exact postion and velocity!

There are analogies in the classical, macroscopic world.  For example
the duration and bandwidth of a signal obey an uncertainty principle;
they are measures from complementary domains (time and frequency) and
the product of a signal's duration and its bandwidth must be greater
than a minimum value that may be established from first princtiples.
For example, short pulses have large bandwidth, and narrow bandwidth
implies long pulses (fast rise and fall times have lots of high
frequency content; if you have energy at low frequencies only, then
the thing can't change very quickly).  The signal duration defines an
aperture that bounds a time interval for when the signal arrives.  The
bandwith defines an aperture that bounds the range of frequencies at
which the signal exists.

Note that this has nothing to do with measurement errors; a signal
simply doesn't *have* both a sigle, discrete time of arrival and
single frequency.  In general, the signal is smeared out somewhat in
both domains.  For example, consider the pathological cases of a delta
function and a sine wave.  A delta function has zero duration, but
infinite bandwidth.  A sine wave has zero bandwidth, but infinite
duration.

Now let's relate this to measurement of time and frequency:  the
implication is that to measure time of arrival of a signal accurately,
on must have a very large frequency aperture.  Conversely, to measure
the signal frequency accurately, one must have a very large time
aperture.  The uncertainty principle does not allow us to have
simultaneously large time and frequency apertures, and we cannot
measure time and frequency simultaneously with arbitrary accuracy.
If we wanted to measure the time of arrival of a delta function, the
measurement uncertainty would be proportional to the reciprocal of the
device's bandwidth.  Similarly, if we want to measure the frequency of
a sine wave, the frequency accuracy would be proportional to the
reciprocal of the observation time.  These limitation are are due to
practical limitations of our measurement approach, not fundamental
limits of nature.  It's easy to think from this argument that the
uncertainty principle is a limitation on measurement ability.  The
reality is twofold:  first, the measurement limitation arises as
consequence of the deeper time-frequency uncertainty principle; but
secondly, even setting this measurement limitation aside, uncertainty
principle inists that signals simply don't *have* both exact time of
arrivals and exact frequencies.

Back to quantum physics.  Effectively, the position-velocity
uncertainty principle fundamentally says that no particle can
simultaneously be both point-like and moving with single velocity;
instead, the particle must be smeared out in position as well as in
velocity, at least to some minimal amount so that the product of its
size and velocity spread is larger than some nonzero minimum, with
that minimum defined by the unit systems and definitions of "size" and
"velocity spread".  And secondly, the uncertainty principle says that
as a consequence our ability to simultaneously measure position and
velocity will be limited by the contradictory need to have small time
aperture for position measurement ("where is it *now*") and large time
aperture for velocity measurement ("watch it for a while and see where
it's going")

Steve Czarnecki

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