# Electron position uncertainty

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1. Jul 20, 2015

### Shailesh Pincha

What are some of the failed experiments to determine electron's position? One could be by electromagnetic radiation of suitable wavelength (here X rays) but that tears apart the atom.

I want to know the different views tried to determine electron position.

2. Jul 20, 2015

### bhobba

There is no problem in determining an electrons position - why do you think there was?

The issue is determining both position and momentum - QM says you cant have an observation that measures both to a high degree of accuracy at the same time.

Is your question about experiments that have attempted to do that? I am not aware of any - but I am not that into experimental stuff.

Thanks
Bill

3. Jul 20, 2015

### Shailesh Pincha

Ya that's, precisely, my question and I want to know the possible methods to measure position and momentum.

4. Jul 20, 2015

### Staff: Mentor

Just about all methods involve bouncing something off the electron (or bouncing the electron off of something, which is the same thing if you choose a frame in which the electron is at rest). That covers scattering, cloud chamber trails, spots on a photographic film, detector clicks, and pretty much everything else.

In some experimental setups you can get a very good idea of the momentum of the electron by passing it through a magnetic field of the way to the detector; the Lorentz force deflects the electron in a velocity-dependent way so that you can arrange that only electrons with a specific momentum make it to the detector.

However, I have this nagging suspicion that you're thinking about the Heisenberg uncertainty principle, and imagining that it says that a measurement of position has to change the momentum and vice versa. That's a 1920s-vintage misunderstanding that was abandoned as more was discovered about the mathematical basis of QM - but by then it had entered the popular imagination, and it's proven impossible to uproot it from there.

The uncertainty principle in the modern understanding says something different. If I prepare a system so that the electron is in a precisely known position I can still, if I am clever enough, devise a way of measuring its momentum to whatever degree of precision I wish. However, if I perform this experiment many times with the electron in the exact same position every time, I will get different values on the momentum on each run - and the spread of the momentum values will be given by the uncertainty principle.

5. Jul 21, 2015

### Shailesh Pincha

I was just thinking about the ways tried to understand electron and maybe made a mistake their. Thus I wanted to know the possible mistakes in observing electron. But you made me a lot of things clear. Thanks

6. Dec 3, 2016

### jeremyfiennes

But this would mean that by taking the mean of a large number of momentum measurements, I can get a definite value for the momentum, i.e. one that I can repeat by taking the mean of another large number of momentum measurements, averaging out the uncertainty.

7. Dec 3, 2016

### Staff: Mentor

That's not giving you a definite value for the momentum of any one particle, it's giving you the expectation value (loosely speaking, the mean) if you prepare a particle in a particular way, measure its momentum, then prepare another particle in the exact same way, measure its momentum, and repeat a large number of times so that you can get an average. Do remember that measuring the momentum changes the momentum, so if you perform repeated measurements on the same particle you're measuring something different every time. The only way of measuring the same thing every time so that you can calculate the mean is to set up an ensemble of identically prepared particles so that you can make one momentum measurement, unaffected by all the other measurements, on each member of the ensemble.

The uncertainty principle, stated properly (and after the past few threads you're likely realizing that a lot of what you've heard about quantum mechanics was not stated properly), is a statement about the likely difference between any one measurement on one particle and the average value of that measurement across an ensemble of identically prepared particles.

An analogy may help here. In my neighborhood, there are one hundred households. Fifty of them have three children and fifty of them have two children. Now, if I measure the number of children in a random sample of these households and take the mean, I'll get 2.5. But if I measure the number of children in any particular household, I can be absolutely morally certain that the result I get will not be 2.5; it will be either two or three. The uncertainty principle is saying that the difference between any particular measurement and the 2.5 value that I expect as an average will be .5.

Last edited: Dec 4, 2016
8. Dec 4, 2016

### jeremyfiennes

Thanks. That seems to have cleared it up.