Because quantum mechanics is universal, the Uncertainty Principle always holds for any system, regardless of its energy scale. For instance, in a particle‐in‐a‐box model at large n (the classical limit), we still have Δx Δp≥ℏ2. However, at high energy, measuring the particle’s position need not significantly disturb its momentum. In practical terms, this means we can effectively measure both position and momentum simultaneously without seeing a noticeable “quantum kick,” even though the Uncertainty Principle is still valid in a strict, mathematical sense.
Hence, the usual phrase “we can’t know position and momentum at the same time” doesn’t strictly apply in this case, so it's better to say that the principle is only a statistical statement about the wavefunction’s position‐space and momentum‐space spreads, rather than a literal prohibition on simultaneously measuring both observables.
This leads us to reconsider the meaning of this principle even at low energies, particularly since the very concept of velocity is unclear in the quantum realm. Consequently, it seems we can only describe the principle as it is—a purely statistical law—while its interpretation at the individual (single‐particle) level remains unresolved.
You’re absolutely right to say that the common phrase “we can’t know position and momentum at the same time” oversimplifies the actual meaning of the uncertainty principle. In quantum mechanics, the principle reflects a deep feature of how the theory is structured — it’s not just a limitation of our measuring tools.
Different interpretations of quantum theory understand this in different ways. For example, in the Copenhagen interpretation, the uncertainty is tied to the way measurement is defined. In Bohmian mechanics, particles have exact positions and momenta, but we don’t know them exactly. In many-worlds, all possibilities evolve in different branches. And in QBism or relational interpretations, it’s more about what an observer can know or expect.
If you’re interested in exploring this further, I recommend my recent review paper which brings together all these perspectives in detail. It’s called:
“The Quantum Measurement Problem: Foundations, Interpretations, and Recent Developments”
You can find it on ResearchGate here:
https://www.researchgate.net/publication/390671023
It might be useful for anyone wanting to write about or study the deeper structure of quantum theory, including topics like the uncertainty principle, measurement, and the collapse problem.
Thanks for raising such an important point with clarity and curiosity!
- Badges
- Science topic
- Similar topics
- Entomology
- Resistance