Q: What happens to the wavefunction of an electron trapped inside a nonreflective sensor-container? Does it prove HUP is only an epistemological limit? Assume there is a spherical container of diameter of 1m, inside which at the center of which an electron is introduced at near zero velocity as limited by Heisenberg Uncertainty Principle(HUP) say at time 0s.
Now the inside of the container has a high potential of near infinity and outside the surface of the container the potential is zero. As the electron is introduced the wave function slowly expands over a period of time, the wave function, eventually collapses and falls outside the sphere and emits a photon of energy difference, this photon can be measured and thus this setup signals and detects the electron when the wave function collapses.
Note: The wave function only expands and is nowhere reflected.

What happens to this wave function of electron over a period of time as the container is non reflective? The wave spreads and spreads until the electron is eventually detected.
But here is the problem, during the period in between the electron is introduced and measured by the container, the uncertainty of space is fixed to a maximum of 1m as it can be anywhere inside the container and can't go outside.
But the uncertainty of velocity goes on decreasing as more and more time passes without the electron being detected.
For eg, let's say your friend calls you and says he's leaving his home and heading straight to your home which is 1 mile away. Now as more and more time passes without him reaching your home, the more slow he is coming towards you. Let us say its already been 30 mins, so your friend's possible speed ranges from 0 to 2 mile per hour. But after 1 hour the speed ranges from 0 to 1 mile per hour. As more and more time passes you become more and more certain about the velocity.
The same thing happens with electron as more and more time passes you become more and more certain of the velocity of electron. But the uncertainty in the position is limited to maximum 1 meter. After some time(Approx 12 minutes or 720 seconds) if the electron is still not detected wouldn't it prove that HUP is more of an epistemological limit rather than an ontological one?
Calculation:


A: You assume at the outset that the electron is in some kind of relatively localised state within the spherical detector. By relatively localised, I mean that the uncertainty in its position is around 1m. Given that, the uncertainty in its speed must be around 0.6 millimetres per second (you might want to check my maths as I worked that out in my head), which means that if the electron started somewhere near the centre of the sphere it would be likely to hit the container wall and be detected within 1000s (to the nearest order of magnitude).
Your question asked us to imagine a situation in which the electron is not detected for a long time (ie much more that 1000s) so you are describing an unreal situation that could only be the case if the HUP were untrue then asking if it would prove that the HUP was untrue. The answer then is yes, if that impossible unreal thing happened, it would prove that the HUP was untrue, just as a spaceship moving at 2c would prove that special relativity was untrue.
Addendum.
The HUP is not a conjecture, and it is not a measure of uncertainty in the sense of doubt or of lack of experimental prowess. It is a mathematical consequence of wave functions.
The position of a particle is determined in a probabilistic sense by the wave function. Roughly speaking, wherever the wave function is non-zero there is a chance of detecting the particle. It follows that the more narrowly a wave function is spread in space, the more localised is the volume in which an electron may be found.
The speed of a particle is determined in a probabilistic sense by the frequency of the wave function. If you have a wave function with some arbitrary form, it does not have a single frequency- however, you can represent it as a sum over plane wave components that do individually have a well defined frequency.
It is a property of waves that the more tightly a wave function is localised in space, the more broad is the spectrum of frequencies in the expansion of that wave function in momentum space. Put non-mathematically, a more tightly confined wave function will be one that corresponds to an expansion which includes greater contributions from plane waves of higher frequency (ie corresponding to higher speeds).
So it follows mathematically, not as a matter of conjecture or ignorance, that a wave function that is constrained in space to within 1m must have frequency components that correspond to relatively high speeds.
You therefore cannot accommodate the wave function of an extremely slow electron within a sphere of 1m.
If you did have a very tight confined electron initially within your sphere somewhere, then its speed would be very high and it would quickly collide with the wall of the sphere and be detected.
