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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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