I have read about the uncertainty principle. As it applies to electrons, how is it that we can get exact tracks of electrons in cloud chambers? That is to say that how is it that the position is fixed?


2 Answers 2


In this article electrons seen in a bubble chamber are shown.

electron in bc

The spiral is an electron knocked off from an atom of hydrogen, a bubble chamber is filled with supercooled liquid hydrogen in this case. The accuracy of measuring the tracks is of an order of microns. The momentum of the electron can be found if one knows the magnetic field and the curvature.

The little dots on the straight tracks are electrons that have just managed to be kicked off from the hydrogen, this would give them a minimum momentum of a few keV.

The total system, picture and measurements give a space resolution of 10 to 50 microns.

$$\Delta x \sim 10^{-5}\, {\rm m}$$ $$\Delta p \sim 1\, {\rm keV}/c = 5.344286×10^{-25}\, {\rm kg\cdot m/s}$$ $$\Delta x \cdot \Delta p > \hbar/2$$ with $\hbar=1.054571726(47)\times10^{−34}\, {\rm kg\cdot m^2/s}$ is satisfied macroscopically since the value is $10^{-30}$, four orders of magnitude larger than $\hbar$.

With nanotechnology, one is getting into dimensions commensurate with the size of $\hbar$, but not with bubble chambers or cloud chambers or most particle detectors up to now.

  • 1
    $\begingroup$ This was an answer which is actually a comment by @fredMcfreddy :*Isn't the process of leaving a trace "an observation" therefore it changes the behavior of the electron. Why doesn't the energy of creating the bubble absorb the energy of the electron. Are we sure it is a single electron? * $\endgroup$
    – anna v
    Commented Nov 11, 2018 at 4:57
  • $\begingroup$ The behavior of the electron changes, it loses a small part of its energy with each micro-scatter and thus the spiral.observable in the chamber. The track seen is the footprint is of a single electron, carrying ~MeV, and loosing it to other electrons, the small dots which take order of eV of energy., the bound electrons in hydrogen are of ~13eV .. $\endgroup$
    – anna v
    Commented Nov 11, 2018 at 4:59

The idea that an individual particle cannot have both a well-defined position and a well-defined momentum is a common misunderstanding of the Heisenberg Uncertainty Principle (HUP). If one subscribes to the notoriously opaque Copenhagen Interpretation, one must eschew all such ontological statements. If one subscribes to the much more illuminating Bohmian Mechanics, then individual particles have well-defined trajectories, as evidenced in a cloud chamber.

The HUP constrains state preparation, and refers to the properties of an ensemble of particles: one cannot create a state where the spread of position and the spread of momenta are simultaneously more constrained than the HUP limit. The HUP has nothing to say about the position or momentum of a single particle.

The track left by a particle passing through a cloud chamber is much wider than the diameter of an atom - sufficiently wide to be seen with the naked eye. The cloud chamber track is therefore not an accurate measurement. However the accuracy a cloud chamber has nothing to do with the HUP, and there is no reason in principle why a particle's position and momentum could not be determined as accurately as one likes.

Useful videos:

A clear introduction to Bohmian mechanics

Heisenberg and trajectories

  • 2
    $\begingroup$ Hi @jcsubmit and user132890, to merge accounts go here. $\endgroup$
    – Qmechanic
    Commented Oct 13, 2016 at 20:43
  • $\begingroup$ I rejected your edit because I cannot be sure that you are the same person as user132890. If you are the same person, please do merge your account as @Qmechanic suggested. $\endgroup$
    – Gonenc
    Commented Oct 14, 2016 at 13:55

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