Was Heisenberg Too Uncertain?

Econintersect:  A fundamental concept of the statistical probability model for the structure of elementary matter is that it is impossible to know at exactly the same instant in time both the precise energy and position in space for any elementary particle.  Heisenberg postulated an uncertainty principle:  the product of the uncertainty for energy (more exactly Heisenberg used momentum, not energy) multiplied by the uncertainty of spatial position could never be smaller than a factor related to a specific amount, called the quantum of action, or Planck’s constant.  The idea of an uncertainty related to Planck’s constant is a very logical extension of the idea that constant represents the minimum packet of energy that can exist.

New research has raised questions about whether the Heisenberg principle may not have universal applicability.  A corollary to the principle is that it is impossible to measure a property of an elementary particle without disturbing it.  If you measure its energy you must necessarily disturb its position; if you measure its position the energy will be perturbed.  The research questions that corollary, and thus the Heisenberg Principle itself.

Ph.D. students at the University of Toronto found a way to measure properties of a photon by a “weak measurement technique” that barely disturbs the particle.  Each measurement yields an imprecise value for the property but making very many repeated measurements of photons going through an identical process allows the precision to be refined to a very small uncertainty.

The students then sent many photons through the exact same traditional measurement process with the weak measurements applied both before and after the traditional process.  Because uncertainty is decreased by averaging repeated measurements of the same thing, a precise measurement result is obtained from a large volume of repeated imprecise weak measurements.

The students found that the disturbance of a photon by a traditional measurement process was less than predicted by the Heisenberg Uncertainty Principle.   The implication is that some fundamental concepts, such as the indivisable quantum of action, may be open for further definition.

If a quantum is no longer a quantum, what is next?  The speed of light is not a universal constant?  The flow of time is not only one direction?  E does not equal mc² and the laws of thermodynamics are only occasionally obeyed?

Would only that Robert A. Heinlein could return to write a science fiction novel to explain it all to us.

The lead author of a research note in Physical Review Letters publishing the results is Lee Rozema, a Ph.D. candidate in Professor Aephraim Steinberg’s quantum optics research group at University of Toronto.

Here is the abstract of the paper from the American Physical Society:

Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements

Lee A. Rozema, Ardavan Darabi, Dylan H. Mahler, Alex Hayat, Yasaman Soudagar, and Aephraim M. Steinberg

Phys. Rev. Lett. 109, 100404 (2012) Published September 6, 2012

When first taking quantum mechanics courses, students learn about Heisenberg’s uncertainty principle, which is often presented as a statement about the intrinsic uncertainty that a quantum system must possess. Yet Heisenberg originally formulated his principle in terms of the “observer effect”: a relationship between the precision of a measurement and the disturbance it creates, as when a photon measures an electron’s position. Although the former version is rigorously proven, the latter is less general and—as recently shown—mathematically incorrect. In a paper in Physical Review Letters, Lee Rozema and colleagues at the University of Toronto, Canada, experimentally demonstrate that a measurement can in fact violate Heisenberg’s original precision-disturbance relationship.

If the observer affects the observed, how can one even make such a measurement of the disturbance of a measurement? Rozema et al. use a procedure called “weak” quantum measurement: if one can probe a quantum system by means of a vanishingly small interaction, information about the initial state can be squeezed out with little or no disturbance. The authors use this approach to characterize the precision and disturbance of a measurement of the polarizations of entangled photons. By comparing the initial and final states, they find that the disturbance induced by the measurement is less than Heisenberg’s precision-disturbance relation would require.

While the measurements by Rozema et al. leave untouched Heisenberg‘s principle regarding inherent quantum uncertainty, they expose the pitfalls of its application to measurements’ precision. These results not only provide a demonstration of the degree of precision achievable in weak-measurement techniques, but they also help explore the very foundations of quantum mechanics. – David Voss

Editor’s note: A story that was told to me in my student days was that Heisenberg’s thesis defense was rejected by his faculty committee because they would not accept the postulate he made therein which was later to be called the Heisenberg Uncertainty Principle.  Once the thesis was rejected a revision could not be submitted for six months.  After the required interval Heisenberg resubmitted the same thesis with the citation of the uncertainty principle removed to a footnote.  The committee accepted the thesis.  I have not found these details documented in what I have reviewed currently in Heisenberg references.

Heisenberg’s Ph.D. was awarded in 1923 (at the age of 21).  Two years later he published his theory of quantum mechanics which addressed the probabilistic nature of atomic structural properties (and thus was incorporating the concepts of the uncertainty principle), for which he was awarded the Nobel Prize in physics for 1932.  Even in that case Heisenberg had to wait.  The Nobel committee in 1932 found that no work was qualified for the award and the 1932 prize was actually awarded in 1933 after another year of deliberative gestation had been endured.

So, it might be said, in real life Heisenberg actually lived his own uncertainty principle.

John Lounsbury

Sources:

• Scientists cast doubt on the uncertainty principle (R&D Magazine, 10 September 2012)

• U of T scientists cast doubt on the uncertainty principle (Sean Bettam, University of Toronto News, 07 September 2012)

• The Nobel Prize in Physics 1932 (Official Nobel Prize website)