What is the main problem with simultaneous measurements in quantum mechanics

4 upvotes

3 years and 9 months later

GPT-3.5

January 1, 2023

In quantum mechanics, the concept of simultaneous measurement refers to the idea of measuring two or more properties (also known as observables) of a quantum system at the same time. However, it is generally not possible to make simultaneous measurements of certain pairs of observables with perfect accuracy. This is known as the uncertainty principle. The uncertainty principle states that the more accurately you measure one observable of a quantum system, the less accurately you can measure another observable that does not commute with the first. This is because the act of measurement disturbs the quantum system, causing the values of the observables to become uncertain. In other words, the main problem with simultaneous measurements in quantum mechanics is that it is not possible to measure certain pairs of observables with perfect accuracy at the same time. This is a fundamental feature of quantum mechanics and cannot be overcome.

GPT-6 Astra

October 19, 2026

The main limitation is that some pairs of quantum properties cannot both have perfectly definite values at the same time, so they cannot be measured simultaneously with arbitrary precision.

For example, position and momentum obey the Heisenberg uncertainty relation:

\Delta x\,\Delta p \geq \frac{\hbar}{2}.

The more sharply defined a particle’s position is, the less sharply defined its momentum can be.

This is not merely a flaw in measuring instruments or a result of disturbing the particle—it is built into quantum mechanics. Mathematically, such properties are represented by noncommuting operators. By contrast, properties whose operators commute are compatible and can, in principle, be measured simultaneously with exact outcomes.

What changed

The real difference is in the why. GPT-3.5 gets the headline right, that certain pairs of observables can’t be measured together with perfect accuracy, and it even mentions that such pairs “do not commute.” But it then explains this as happening “because the act of measurement disturbs the quantum system.” That is the classic textbook misconception. Astra goes straight at it, insisting the limit is “not merely a flaw in measuring instruments or a result of disturbing the particle” but something built into the theory: the properties themselves cannot both have sharp values at once. The word “merely” is well chosen, since measurement disturbance is real but isn’t the root cause.

Astra also adds what GPT-3.5 left out. It names position and momentum as the standard example, gives Heisenberg’s inequality, and notes that commuting properties can be measured together exactly. GPT-3.5, meanwhile, spends its final paragraph restating its first. Astra’s answer is shorter and teaches more.

Analysis by Claude Opus 5.5, comparing the two answers above.