

Influence of Measurement
Name: Matthew F.
Status: other
Age: 20s
Location: N/A
Country: N/A
Date: Sunday, September 15, 2002
Question:
A question in your archives was inquiring about the proper use of the
Heisenberg Uncertainty Principle (HUP). Your response was that the general
notion that the act of measurement can influence the result is *not*
proper use of the HUP.
As a side question, is there a term or type of error that is
defined as the error potentially induced by the act of measurement?
For example, the name for the error in the "soup temperature" measurement
caused by the heat transferred into the thermometer/measuring device.
Replies:
You raise a question that remains a point of contention among
physicists. It all started with Young's classic "double slit" experiment
which you can do a search to find the details. The results are not seriously
in question, but the "explanation" can initiate a lively discussion about
their "explanation" or "interpretation". Briefly, suppose you have a source
of light (does not have to be visible light, it can even be electrons or
other "particles" but the experimental setup gets more complicated), and two
slits separated by a distance great enough so that the time it takes the
light from one slit to the other is longer than the time it takes the light
to travel from the source to the plane of the slits. Now you decrease the
intensity of the light source so that light (photons) are emitted "one at a
time". Just how this is done need not concern us here, but everyone agrees
that it is possible to do so. On the other side of the slits is a detector
of some type (again, just how this is done experimentally need not concern
us here. (Every one agrees that this is possible using photographic film,
Geiger counter, etc., or some other type of detector.).
First one slit is covered. What is observed is that the photons that
pass through the other open slit strike the detector at a single spot behind
the slit (Actually its a narrow Gaussion distribution, but that too is not
relevant.).
Second the opened and closed slits are exchanged, i.e. the one covered
in the first experiment is opened and the other slit is closed. The same
result is observed  the photons pass through the open slit and strike the
detector at a single spot defined by extending a line from the source to the
slit back to the plane of the detector.
Conclusion: "Clearly" light is behaving like a stream of particles 
photon bullets that start at the source, travel through the respective slits
and strike the detector in the "line of sight" from the source to the slit.
Case Closed: Light is a particle (photons), and electrons are also particles
because you get the same result with electrons.
Well not quite: Open both slits. What is observed is an interference
pattern on the detector screen!!!
That is, a pattern of light and dark lines where the light (or electrons)
constructively and destructively interfere. If light were behaving like
particles (bullets) what you would expect is just two lines on the detector
at points in line with the source and slits.
Conclusion: "Clearly" light is behaving light waves. Case Closed!! Or is
it? Remember the distance between the slits is far enough that light from
the source gets to the slits before a photon could travel from one slit to
the other!!
The paradox is this: "How does a photon traveling from the source to
slit A know whether or not slit B is opened or closed, since the photon from
the source arrives at the slit before the photon could "send a signal from A
to B to "tell" a photon traveling from the source to slit B.
This paradox has led to a lot of contentious argument for many years. I
do not think it is resolved to everyone's satisfaction even today. Some argue
that it is the act of observation that causes the result. That before the
observation the photons do not know. This interpretation led A. Einstein to
ask: You mean if I do not see the moon on a particular day, that it does not
exist?
Results like this is what lead Richard Feynman to say that anyone who
says they understand quantum mechanics, does not understand the problem!!!
Vince Calder
Matthew,
The HUP is based on the "statistical" nature of quantum physics. It is not
the process of placing a ruler to an electron that causes the momentum to be
uncertain. It is the knowing. One cannot know the position AND momentum of
a particle perfectly at the same time. At the center of quantum physics is
a wave function. If quantum physics is correct, every object in the
universe has a wave function. Within this is a mathematical definition of
that one individual object. This function stores the "state" of the object,
determining in what ways it may respond to interactions. This wave function
usually allows a variety of responses. When a measurement is taken, one of
the responses is randomly picked. The state of the object is now 100% what
was ever chosen. All others are eliminated by the measurement. This
changes the wave function.
Some quantities are linked through this wave function. Position and
momentum are such a pair. Energy and time as well. To find the probability
distribution of momentum, take the first derivative of the wave function
with respect to position. To find the position probability distribution,
take the first derivative with respect to momentum. These linked quantities
are the means to working each other out of the wave function. This results
in a link between uncertainties. The more narrow you trim the position
wave function, the more the momentum wave function spreads out. The more
narrow the momentum wave function, the more the position function spreads
out.
A narrow wave function corresponds to a very small uncertainty: the next
measured value can only fall within a narrow range. A wide wave function
corresponds to the next measurement having very little restriction.
Measuring position precisely makes the next possible momentum measurement
have a wide range of possibilities, and vice versa. In order not to limit
each other's reliability, these "incompatible" measurements must both be
allowed some uncertainty. If you make a position and momentum measurement
with uncertainties that don't break the HUP, then the measurements can be
made without messing up each other. It is due to statistical properties of
quantum mechanics. We do not know for a fact it is true, but so far what
quantum physics tells us does match what we observe at the level of
individual particles.
Dr. Ken Mellendorf
Physics Instructor
Illinois Central College
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Update: June 2012

