What is the most simple/basic way to measure the position of a quantum particle? How does this experiment work exactly?
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1$\begingroup$ "When we try to measure the position of a quantum particle, we can never get infinite precision. That would violate the Heisenberg uncertainty principle." This is a strange statement. The Heisenberg uncertainty principle is about the standard deviation of repeated measurements on identically prepared states, not about "precision". (If you don't adhere to an interpretation where the values of all observables exist at all times, what does "precision" even mean?) $\endgroup$– ACuriousMind ♦Jan 14 at 23:23
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$\begingroup$ @ACuriousMind I'm not the asker, but maybe precision means "how narrow the position-based wavefunction is". A Dirac delta function would be "infinitely precise". But such state could only be achieved by using an infinitely dense detection screen. $\endgroup$– Juan PerezJan 14 at 23:41
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$\begingroup$ You're asking for an example of an experiment and how it works. That's a good question. I have asked similar questions before and have yet to find how quantum measurements are actually made. There are many videos and discussions about measurements in QM, but so far I have only found the timelapse double slit experiment. There must be many more. I hope your question generates some good answers. $\endgroup$– LambdaJan 15 at 1:19
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2 Answers
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The double slit experiment is typically described as passing a photon or electron through a double slit and letting it hit a screen. A cathode ray tube is an example of this type of screen. The inside of a glass tube is coated with phosphor. An electron hits an atom on the screen, which gives off light. You can see the position of the light.
On electron gives on flash. But if you repeat this experiment many times, the flashes add up to an interference pattern.
You can measure any electron and get a precise measure of its position, to the size of an atom.
The uncertainty principal prevents you from predicting which atom an electron will hit. You can predict the position as precisely as the interference pattern.
In a real old-fashioned television you do not put a double slit in the CRT. The electron is emitted from a small hot wire and given as low a transverse velocity as possible. The uncertainty in the position and momentum as it leaves the wire is not necessarily as small as the uncertainty principal would permit. It might be larger because of the size of the wire, imperfectly controlled voltages, and so on. Never the less, it is sufficiently precise that it can be steered to hit a small spot on the screen.
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The simplest setups that come to my mind:
- Any photomultiplier tube (PMT) in a dark box with a dim light diode (LED). When you see a signal of the right size, you know a photon has hit its photocathode.
- A Geiger tube. When it clicks, you know a particle was in it.
