# How precisely can particle position be measured in a laboratory?

If we have any given particle, such as a photon or an electron (it doesn't really matter what for the sake of the question), how precisely can modern physics devices measure their position? Specifically, assuming that the wave function collapse is a real, physical process (which is of course not certain yet), how 'tight' can we make the wave function (from end-to-end of the biggest 'spike'). Given the existence of the Heisenberg Uncertainty Principle, can we measure the position of a particle precisely enough (make the wave packet 'tight' enough) to invoke an increase in the 'spread' of possible position values using current technology? Given how incredibly small the values in the formula for the Heisenberg Uncertainty Principle are, measuring a particle to the point where the uncertainty in position is low enough to warrant an increase in uncertainty in momentum must be incredibly small. Can modern measurement devices decrease the uncertainty in position to such an amount?

## 1 Answer

There is a basic misunderstanding in this question:

how 'tight' can we make the wave function (from end-to-end of the biggest 'spike').

The wave function controls the probability of interaction, probabilities are about the accumulation of data for many particles in the same boundary conditions and cannot constrain a track/footprint of a particle, except probabilistically.

Look at this double slit experiment one photon at a time, to understand the difference between particle and wave function describing a particle. This is the de facto solution of a "scattering a photon on double slits, a given width, a given distance apart"

. Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.

The dimensions of the footprint of the individual photon have to do with the accuracy of the screen in microns, the wavefunction describing the system appears in the interference pattern. The same is true for single electrons.

Can modern measurement devices decrease the uncertainty in position to such an amount?

Modern devices have not reached that precision yet for individual particles, as Plancks constant is very small, $$4.135667696×10^{−15}$$ eVs.

In bubble chambers the accuracy is in microns and the momenta too low . The detectors in the high energy labs are not much better, so the detector measurements obey the HUP .

Given the existence of the Heisenberg Uncertainty Principle, can we measure the position of a particle precisely enough

Yes, because with our detectors up to now the HUP holds.

(make the wave packet 'tight' enough)

The wavepacket representation of free particles comes again quantum mechanically, we cannot make it "tight". It will depend on its momentum and the particular detector, we can only affect the momentum, the space depends on the detector choice and as a said above, at present the HUP holds

• While the wave function of a system does work in probabilities as you described up until measurement, I was under the impression that each individual particle has its own wave function that describes where it is likely to be measured. Once the measurement is made, if the particle is measured again, the same particle will almost certainly be measured in approximately the same place. I interpret this as meaning that the wave packet is now 'tighter' as the position will now be measured to be in a smaller variety of places for an individual particle. Commented Feb 3, 2021 at 23:04
• Furthermore, I find your wording in the section describing measurement devices in bubble chambers and such unclear. Can such measurement devices measure the position of these particles to a point where its position is known to a small enough range of locations to invoke the HUP? Finally, why does it matter if their momentum is small? 1) The HUP deals with UNCERTAINTY in momentum, to the difference between minimum and maximum momentum would be similar regardless of their values relative to the origin, and 2) momentum, being a function of velocity, is relative anyway, and not objectively 'low'. Commented Feb 3, 2021 at 23:08
• @Sciencemaster "if the particle is measured again, the same particle will almost certainly be measured in approximately the same place. " The same particle cannot be measured again, measurement is interaction, and new wave functions are obeyed. If the measurement is a spot on a screen, as above, for example. Same boundary condition particles will show the probability of interaction. The HUP of uncertainty in momentum, means that the larger the momentum the smaller the position can be defined [dp,dx]>h Commented Feb 4, 2021 at 5:05
• .the momenta we can reach and the location of position in detectors is such that the HUP is always obeyed Commented Feb 4, 2021 at 5:05
• Okay, it took me a moment to realize what you meant by 'the wave function is destroyed'. You and I think of the wave function post-collapse differently. I imagine it as the same wave function instantly having its properties changed to have a smaller standard deviation and such, because it can be measured again, and when that happens, it will be seen in approximately the same location if enough time has not passed for it to spread back out. However, you seem to view observation as the initial particle being destroyed and a new particle with a new wave function replacing the old one. Commented Feb 9, 2021 at 21:11