I have read this question:
Where pglpm says:
So the answer to your question is that in a single measurement instance we actually can (and do!) measure position and momentum simultaneously and with arbitrary precision.
and where mmesser314 says:
The electron doesn't have a precise position.
As far as I understand, the electron is defined as a point particle in the SM, with no spatial extension or size. One of the answers says we can measure position with arbitrary precision. The other one says the electron does not have such a precise position, just a probability distribution. But that is not what I am asking about. Just to clarify, I am not asking about the HUP or any kind of simultaneous measurement of observables. What I am asking about is when they both talk about arbitrary precise position for a point particle.
The electron is a point particle, that is, defined as the smallest thing we know of. Smaller then any measuring device. And spacetime is currently known to be continuous, any distance (for position measurement) can be divided into yet smaller and smaller pieces.
For a point particle, that does not have spatial extension, what do we mean when we say arbitrary precise measurement of position? Can this be farther improved with new technology or not?
As far as I understand, the precision is limited by cross sections. This is the limit of precision, because to measure the observable of a QM particle, we need to interact with it, with another QM particle. These have a cross section, and as I understand that limits the precision. Can this then be farther improved somehow?
Is this limit set by the QM nature of QM particles, and their cross section, or can this be improved using better technologies?
So basically, is the limit theoretical, or technological?
Question:
- Is there a theoretical or technological limit for arbitrary precise measurement of the position of a point particle in QM?