# Can I tell that an electron is located at an exact location with 100% accuracy at an exact time through measurement?

Suppose I have no interest in the momentum of a particle, thus I want to measure the position of an electron with pinpoint precision. I know that before the measurement the electron didnt have any defined position or momentum, but right at the time of measurement can I tell the position of electron with 100% accuracy at the exact time of measurement ? I know that I wont have any idea about the momentum of the particle at the time of the measurement. Is this experiment possible hypothetically according to laws of nature?I'm concerned that such an experiment violates the HUP.

• Why do you think it would violate the HUP? May 9, 2021 at 16:58

Within Non-relativistic Quantum Mechanics, you can determine the position with arbitrary precision. There is no contradiction with the uncertainty relations because they just say that in such a case the statistical distribution of momenta gets a diverging variance. If you are not worried about the momentum, there is no problem.

Notice, however, that in real-world things become more complicated. As soon as the uncertainty in the electron position becomes smaller than its Compton wavelength, some electron-positron creation may occur, transforming the original two-body problem into a many-body problem. In particular, there are at least two indistinguishable electrons, and speaking about the position of one electron becomes quite difficult.

• Even within non-relativistic QM: a particle with a diverging average momentum has a diverging average kinetic energy as well. Therefore, when you consider the measurement as a physical process, only in the (unphysical) limit in which it can provide unbounded energy would the position measurement be arbitrarily precise. May 9, 2021 at 19:40
• Also, at a certain point the energy needed to measure the electron would become so much that it would create a black hole, so that is another potential limit (albeit one that is far beyond the pair-production energy mentioned above). May 9, 2021 at 19:42
• @Rococo As of today, there is no possibility of black holes, remaining within relativistic or non-relativistic QM. One needs a completely different theory (GR) or theories still to come. As far as the unphysical limit, it is just a limit. But remaining within NR QM one could get an arbitrary good precision in the measurement of position. May 9, 2021 at 20:32
• But contraction of the probability cloud of the electron to a single point in basically no time interval violates the laws of Relativity. Am I right? I know that you have mentioned non-relativistic QM May 10, 2021 at 14:37
• @TimCrosby Yes, within NR QM there is no Relativity that can be violated. On the other side, proper treatment of relativistic probability densities (and currents) is still underway (see for instance arxiv.org/pdf/quant-ph/0602024.pdf ). May 10, 2021 at 15:20

It is possible in principle to determine the position of an electron precisely, but its momentum thereafter could be anything. This means that if you then turned around and did the same position measurement in exactly the same place, the electron won't be there- it is now somewhere else, because you had to bump it to tell where it was in the first place.

In my way of looking at this, you know where the electron was but you now have no idea where it is, or where it will be.