THE CIRCULAR STATE OF PI

“Mimicking Matter with Light,” by Charles D. Brown II, discusses a phase of matter called a Bose-Einstein condensate (BEC) acquiring a geometric phase, “a term in the mathematical description of its quantum phase that determines how it evolves.” The article mentions the BEC picking up a geometric phase of pi (π) in one experiment, and it shows a full circle in an accompanying graphic. Later it depicts a phase of 2π with two full circles.

I understand that a geometric phase has no physical interpretation, which the article also mentions. But I am still confused because a single full circle is usually associated with 2π, as I remember from my telecommunications engineering studies, which had a lot of math as their base. Can you clear up this seeming contradiction?

ULRICH MESSERLE STUTTGART, GERMANY

BROWN REPLIES: As described in my article, the BEC's quantum state acquired a geometric phase of π when it was moved around a Dirac point—a position where two energy bands take on the same value—and a phase of 2π when it was moved around another type of singularity called a quadratic band touching point (QBTP). In both the Dirac point and singular QBTP experiments, we measured the quantum state of the BEC along the same circular path: it went around either point exactly once. We observed, however, that in the Dirac case, the BEC's quantum state rotated once, whereas in the singular QBTP experiment, it rotated twice.

I don't make the claim that π is enough to complete a full circle. Rather, after completing a circle in momentum space, the BEC picked up a geometric phase of π. While 2π is associated with completing a circle in mathematics, our measurements are about the geometric phase accumulated by the BEC's wave function after it completes a circle around either the Dirac or singular QBTP.

PRIMAL POLITICS

In “Divided Mindset” [Mind Matters], Jer Clifton discusses his research finding that liberals and conservatives have fundamentally different beliefs about whether the world is inherently hierarchal. The article resonated with my own effort to understand the growing, and destructive, divide among free people. I would add that one especially significant dividing line that liberals see as blurry and conservatives see as well defined is the boundary between “us” and “them.”

Like many of the “primal world beliefs,” or “primals,” that Clifton describes, the definition of us is context-sensitive. During a World War, all Americans and the country's allies are part of us. When their baseball teams compete in the World Series, New York City and Boston are clearly on opposite sides of a divide. The primal bias that keeps the definition of us smaller is more conservative, and making the definition larger is more liberal. This applies to race, religion, income level, national origin, profession, and so on. We need to understand why the distinction matters and how to soften the boundaries that divide us. If we learn to see our world with a broad enough perspective, we might be able to share the understanding that everything alive, on this small planet we share, is one of us.

ARI BERMAN LEXINGTON, MASS.

PINPOINTING PAIN

“Origins of Pain,” by Haider Warraich [Forum], mentions the shortcomings of magnetic resonance imaging as an indicator for spinal pain. If one looks only at mechanical and anatomical explanations of pain, this surely is true. Especially in the previous century, spinal imaging focused on findings associated with degenerative spinal changes, including disk degeneration and disk herniation. Although a disk herniation definitely can be a possible cause of pain irradiating in the leg, it is only rarely a cause of local back pain. In general, computed tomography and MRI are reliable indicators of these changes. So they do very well in identifying the cause of radicular pain, or pain originating from a nerve that is pinched by a herniated disk or a narrowing of the spinal canal and its outlets (a phenomenon called spinal stenosis).

But recently the interest of spine radiologists has shifted to finding the pain generator in local low back pain, which can be classified as somatic pain. By using newer MRI techniques, we are now able to reliably detect small inflammatory changes in the spine, mainly in the vertebrae. In many people, these inflammatory changes are believed to be associated with local pain, and as such, they can pinpoint the pain generator. This can be highly beneficial to a patient, for example, in the case of an inflamed facet joint, not an unusual finding in low back or neck pain. These small joints can be precisely targeted by interventional radiologists or pain physicians either with injections using local painkillers and anti-inflammatory drugs or, in patients with more persistent pain, by neurolysis, a procedure where the pain fibers are locally disrupted by thermal or chemical intervention.

Many radiologists need to be updated on these developments because they still believe that spinal imaging is all about spine degeneration. This can lead to unnecessary treatments because degenerative changes that are normal for age can be identified as abnormal and suspected to be the cause of a patient's complaints. Failing to identify the pain generator and consequently treating something else without any beneficial result leads to disappointment and disbelief in spinal imaging's relevance, even among some radiologists.

Luckily, a new generation of radiologists is very active in research on spinal imaging in low back pain. Not only are we able to find the pain generator in a significant percentage of patients with low back and neck pain, but research is also focusing on chronic and neuropathic pain caused by a lesion or disease of the pain system itself. Although the approach is still in its infancy, researchers are starting to visualize the workings of the pain system in people with chronic pain in the hope of finding out what is going wrong and treating it effectively.

JOHAN VAN GOETHEM EDITOR IN CHIEF, NEURORADIOLOGY, DEPARTMENT OF MEDICAL AND MOLECULAR IMAGING, VITAZ, BELGIUM, AND PROFESSOR OF NEUROIMAGING AND BIOMEDICAL IMAGING TECHNIQUES, UNIVERSITY OF ANTWERP

PUBLIC HEALTH PRIORITIES

“Pandemic Reckoning,” by the Editors [Science Agenda; May], calls for Congress and the Biden administration to support a COVID Commission to investigate why the U.S. didn't do a better job of responding to the recent pandemic and to prevent future catastrophes.

If politicians have a choice of funding a bridge that will reduce rush-hour delays in a town or building a warehouse in the same town to stock with supplies and equipment to prepare for the next pandemic, they will choose the bridge. The bridge will provide immediate traffic relief, which translates into votes in the next election. The warehouse full of pandemic supplies and equipment may never be of benefit to the residents of the town or people elsewhere, which isn't a vote getter.

A bipartisan COVID Commission could give us a better understanding of what went wrong, but I doubt that Congress would do much about it.

STEVE WRIGHT VIA E-MAIL