L–Evolution of Terminology
By U.W. on 21 November 2025 — summarizing thoughts gathered during this week.
Physics terminology is not static. Terms coined for specific phenomena often grow beyond their original definitions, expanding to new contexts as our understanding deepens. This evolution can be seen in concepts like the Berry phase, Lamb shift, and Mpemba effect. Each began as a crisp, narrowly-defined idea but has since been broadened by scientists applying the concept in novel situations. Such generalization reflects intellectual creativity and unifying insights across fields. However, it also raises challenges: when a term strays far from its original meaning, there’s a risk of confusion or of glossing over important differences. This essay explores how these three terms have evolved, and how we can harness their broadening scope while remaining epistemically responsible in our language.
Berry Phase: From Quantal Phase to Geometric Phenomenon
When Sir Michael Berry described a “quantal phase factor accompanying adiabatic changes” in 1984¹, he likely didn’t anticipate how quickly the idea would generalize. The Berry phase originally referred to a subtle phase shift acquired by a quantum system’s wavefunction when the system’s parameters are changed slowly in a closed cycle¹. It was a precise quantum phenomenon in the context of adiabatic (slow) and cyclic evolution. Soon, however, physicists realized this phase was one example of a more universal behavior now known as the geometric phase. In fact, an earlier precursor existed: in 1956, S. Pancharatnam had discovered a similar phase shift in optics, arising when polarized light undergoes a cyclic change in polarization state². Pancharatnam’s work, largely overlooked at the time, was recognized and incorporated into the broader framework decades later by Berry and others, bringing it into the modern conversation.
The Berry phase concept quickly transcended its original bounds. In 1987, Aharonov and Anandan showed that a Berry-like phase can arise even without the adiabatic slow-change requirement³. This meant the geometric phase is a general feature of quantum (and even classical) systems undergoing cyclic evolution – it depends only on the path taken through state space, not on how long the journey takes. By 1990, the literature was rich enough that Zwanziger et al. published an extensive review of “Berry’s phase” covering myriad examples from molecular physics to condensed matter⁴. The term “Berry phase” itself came to be used colloquially for any such geometric phase, even in contexts far from Berry’s original single-valued quantum scenario. In classical mechanics, for instance, an analog called Hannay’s angle was identified as the classical counterpart to the Berry phase, and in optics one often speaks of Pancharatnam–Berry phases for polarization changes.
This expansion of meaning illustrates both the power and the pitfall of terminology evolution. On one hand, referring to a “Berry phase” in a new context immediately communicates that some cyclic geometric aspect is at play, invoking a rich theoretical framework. On the other hand, casual use of the term Berry phase outside its original scope can ignore important qualifiers. For example, calling a phase shift in a non-adiabatic optical system a “Berry phase” might inadvertently downplay Pancharatnam’s earlier contribution or the differences between quantum and classical phase acquisition. Best practice is to use “geometric phase” for the broad class of phenomena, reserving “Berry phase” for the prototypical quantum adiabatic case or when highlighting Berry’s 1984 discovery. This ensures clarity and proper credit: indeed, many authors now explicitly say “Pancharatnam–Berry phase” in optical contexts to acknowledge the term’s evolution. Ultimately, the Berry phase’s journey from a quaint quantum phase factor to a ubiquitous concept shows how a good idea gains traction – and why careful labeling matters as it does.
Lamb Shift: From Hydrogen’s Vacuum Quirk to a Universal Shift
The Lamb shift entered physics in the late 1940s as an experimental surprise with profound implications. In 1947, Willis Lamb Jr. and Robert Retherford measured a tiny difference in energy between two levels of the hydrogen atom that, according to then-current Dirac theory, should have been degenerate⁵. This fine-structure anomaly, now known as the Lamb shift, was eventually explained by quantum electrodynamics as the effect of the quantized electromagnetic vacuum on the atom’s electron⁵. In simple terms, the vacuum isn’t truly empty – transient “vacuum fluctuations” of the electromagnetic field perturb the atom’s energy levels, causing a slight shift. Lamb’s finding was a watershed moment for QED, and the term “Lamb shift” originally denoted this specific QED effect in hydrogen (and by extension similar shifts in hydrogen-like atoms).
As with the Berry phase, the Lamb shift concept proved to have legs well beyond its initial definition. Over time, physicists drew analogies between Lamb’s vacuum-induced level shift and other instances where a system’s environment alters its energy. The phrase “Lamb shift” thus started appearing in diverse settings: any persistent energy level shift due to interaction with a background field or reservoir might earn the “Lamb” label. For example, in 2016, Rentrop et al. reported observing a *“phononic Lamb shift”*⁶. In their ultracold-atom experiment, an impurity atom coupled to a Bose–Einstein condensate experienced an energy shift due to phonon-like quantum vibrations – effectively a synthetic “vacuum” made of sound waves. The use of the term Lamb shift here was metaphorical yet apt: it signaled that an environment (the condensate’s phononic field) was renormalizing the impurity’s energy, much like the electromagnetic vacuum did for hydrogen⁶.
The Lamb shift idea has since been generalized further. Researchers now discuss Lamb-like shifts in systems ranging from superconducting qubits to trapped ions. Just this year, Colla, Hasse et al. (2025) observed a time-dependent Lamb shift in a single trapped ion strongly coupled to an engineered environment⁷. By monitoring the ion’s transition frequency in real-time, they observed its energy levels renormalizing as the interaction with a finite environment progressed – essentially a Lamb shift that unfolds dynamically⁷. Calling it a “generalized Lamb shift” situates this result within a familiar narrative: vacuum-induced energy shifts. Yet clearly an ion coupled to a designed reservoir is not the same as an electron in true vacuum. As terminology broadens, scientists must be explicit about such differences. The Lamb shift’s extension to “analog quantum vacuums” (phonons, quantized motion, etc.) is illuminating – it underscores a unity in physics where vacuum fluctuations, whether of electromagnetic fields or other bosonic fields, cause observable shifts. But to stay true to the term’s origin, it’s wise to qualify the context. For instance, one might say “phononic Lamb shift” or “Lamb shift analog” rather than implying the exact same mechanism as the atomic Lamb shift. By doing so, we honor both the legacy of the term and the nuances of the new system. In summary, the Lamb shift has evolved from a quirky hydrogen spectroscopic detail to a broad concept of environment-induced energy shifts – a testament to how a good idea in quantum physics can propagate widely, as long as we handle the terminology with care.
Mpemba Effect: From Freezing Water to Faster Relaxation
The Mpemba effect is perhaps the most playful of our three terms, originating in an everyday puzzle: Can hot water freeze faster than cold water? In 1969, Tanzanian student Erasto Mpemba and his mentor Denis Osborne published a short article titled “Cool?” describing exactly that phenomenon⁸. They reported that under certain conditions, a container of hot water could reach the freezing point sooner than an identical container of initially cooler water⁸. This counterintuitive result – a hotter system overtaking a colder one – captured the imagination of both scientists and the public. (In fact, Mpemba’s observation wasn’t entirely new; anecdotal reports go back to Aristotle’s time, and in the same year as Mpemba’s paper, physicist George Kell independently investigated hot versus cold water freezing, noting similar behavior⁹. But Mpemba’s name became firmly attached to the effect.)
For decades, the Mpemba effect was discussed mostly in the context of water and freezing, with debates over its causes (evaporation, convection, supercooling differences, and so on). In recent years, however, the term “Mpemba effect” has leapt from the kitchen freezer to the realm of theoretical and experimental physics at large. Scientists asked: could an analogous effect happen in other systems – not necessarily involving ice? The answer has been a resounding yes. The essence of the Mpemba effect is about nonlinear relaxation: sometimes, an object further from equilibrium can relax to equilibrium faster than a closer-to-equilibrium object. This general idea has now been explored in magnetic systems, colloids, and even quantum systems. For example, researchers have identified Mpemba-like behavior in magnetic alloys and in the thermal relaxation of nanomechanical oscillators⁸. In the quantum domain, multiple studies in the early 2020s (both theoretical and experimental) reported “quantum Mpemba effects.” These include scenarios like a quantum spin or qubit ensemble prepared in a “hotter” state that returns to its ground state faster than an ensemble prepared in a slightly cooler state. Such findings prompted commentary in the literature: in 2024, a Physics magazine Viewpoint titled “Exploring Quantum Mpemba Effects,” highlighted how a classical curiosity had evolved into a broad inquiry across statistical physics¹⁰.
This rapid broadening of the Mpemba effect’s meaning is exciting – it suggests a unifying principle of thermodynamics and kinetics that transcends specific materials or temperature ranges. But it also exemplifies the risks of terminology creep. Unlike the Berry phase or Lamb shift (which have relatively straightforward theoretical definitions in their original contexts), the Mpemba effect’s definition has always been a bit fuzzy. What exactly does it mean to “freeze faster” or “equilibrate faster”? Different studies have used different metrics and criteria (for water, is it the time until first ice forms, or until fully frozen? In other systems, are we measuring time to reach 50% of equilibrium, or a specific threshold?) – which makes comparisons difficult. As the Wikipedia entry dryly notes, “the definition of the Mpemba effect used in theoretical studies varies,” and this lack of a universal definition complicates matters for experiments as well. In broadening the term to quantum and other realms, scientists must therefore take extra care to define their usage. Often the term is used with qualifiers – for instance, “quantum Mpemba effect” or “inverse Mpemba effect” (for cases where a colder system heats faster, the opposite scenario) – and accompanied by a clear operational definition of what “faster relaxation” means in that context. This is essential to maintain scientific clarity: without it, Mpemba effect could devolve into a catchy but meaningless label pasted onto any surprising relaxation curve.
In summary, the Mpemba effect’s journey from a peculiar ice manufacturing incident to a general label for anomalous relaxation shows how ideas in physics can gain metaphorical power. A term originating from one specific observation now spurs research across disciplines, linking themes in water supercooling, statistical mechanics, and quantum information. Embracing this metaphor has value – it helps communicate the core idea (fastest cooling from a hotter state) to a broad audience. Yet, as with Berry phase and Lamb shift, context is paramount. We must clarify what we mean by “Mpemba effect” each time we invoke it, lest the term become too dilute. In practice, this means specifying the system (water, spin system, etc.), the conditions, and the measure of “faster” being used. By doing so, we let the Mpemba effect enrich our cross-disciplinary dialogue without sowing confusion.
Special thanks to all my past, current, and future environments.
Terminology Evolution Table
To crystallize the discussion, the table below compares the original usage, the generalized modern usage, and a suggested labeling practice for each of the three terms:
Term
Original Specific Meaning
Generalized Usage Today
Suggested Modern Labeling
Berry phase
A quantum-mechanical phase acquired by a system undergoing a slow, cyclic adiabatic change (Berry’s 1984 discovery¹).
Any geometric phase arising from cyclic evolution of a system’s parameters, even if non-adiabatic or in classical waves (often called “geometric phase” in general).
Use “geometric phase” for the broad phenomenon; reserve “Berry phase” for the original quantum adiabatic context or when referring historically to Berry’s work. In optics, say “Pancharatnam–Berry phase” to acknowledge the optical precursor².
Lamb shift
The specific QED effect of vacuum electromagnetic fluctuations shifting the 2S level of hydrogen (measured by Lamb in 1947⁵).
Any persistent energy level shift of a system due to interaction with a surrounding field or reservoir (e.g., shifts induced by phononic fields⁶, circuit modes, etc., analogous to the original Lamb shift).
Qualify the term when used generally: e.g. “phononic Lamb shift”, “Lamb-like level shift”, or “environment-induced level renormalization”. Make clear whether it’s an analog system or the original atomic effect.
Mpemba effect
Hot water freezing faster than cold water under certain conditions (Mpemba’s 1969 observation⁸).
Any situation where a system initially further from equilibrium reaches the target state faster than a system closer to equilibrium. Found in various contexts: water and other liquids, colloids, magnetic systems, quantum states, etc.
Always define the effect explicitly for the system in question (what “faster” means, and under what conditions). Use qualifiers like “quantum Mpemba effect” or “thermal Mpemba effect” as needed, and avoid assuming a single mechanism.
Best Practices: Using Broad Terms Responsibly
Define the term in context: When using a broadened term, clearly state what it means in your specific case. For example, if you mention observing a “Mpemba effect” in a polymer, explain how you’re measuring “freezing” or relaxation in that system. This guards against ambiguity stemming from different definitions.
Acknowledge the analogy: If a term is borrowed from another domain (like calling a phonon-induced energy shift a “Lamb shift”), signal the analogy. Use phrases like “analogous to the Lamb shift” or include the field (e.g., “phononic Lamb shift”⁶) so readers understand it’s a metaphorical extension, not the original phenomenon one-to-one.
Credit original context: Scientific terms carry history. Mentioning Berry’s 1984 paper¹ when discussing geometric phases, or Mpemba’s experiment⁸ when talking about non-equilibrium relaxation, pays homage to the origins and helps readers appreciate how the concept evolved. It also distinguishes the original narrow meaning from the newer broad usage.
Avoid over-stretching a term: Not every loose similarity warrants using the same name. If the connection is tenuous, consider coining a new term or at least using “-like” language. (For instance, a minor energy shift in a classical oscillator might be better described as a “frequency shift” rather than immediately dubbed a “Lamb shift” if the quantum vacuum aspect is absent.) Overusing famous terms for superficial similarities can dilute their meaning.
Communicate mechanism, not just name: Whenever possible, accompany the term with a brief description of why the effect occurs in the new context. Saying “quantum Mpemba effect” is stronger when followed by “…where a higher-energy spin state thermalizes faster due to XYZ mechanism.” This educates the audience and reminds us that the terminology is an entry point to understanding, not a complete explanation.
By following these practices, physicists can enjoy the intellectual cross-pollination that comes from reusing and generalizing terms, without sacrificing clarity or rigor. Good terminology should enlighten rather than obscure – even as it evolves.
Disclosure: The author of this essay was involved in two of the works cited (Colla, Hasse et al. 2025 and Warring 2024), and thus has a direct perspective on the broadening usage of the term “Lamb shift” in trapped-ion systems and the discussion of Mpemba effects in quantum contexts. Every effort has been made to present these topics objectively and with appropriate context.
References
Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A 392, 45–57 (1984).
Pancharatnam, S. Generalized theory of interference, and its applications. Proc. Indian Acad. Sci. A 44, 247–262 (1956).
Aharonov, Y. & Anandan, J. Phase change during a cyclic quantum evolution. Phys. Rev. Lett. 58, 1593–1596 (1987).
Zwanziger, J. W., Koenig, M. & Pines, A. Berry’s phase. Annu. Rev. Phys. Chem. 41, 601–646 (1990).
Lamb, W. E. Jr. & Retherford, R. C. Fine structure of the hydrogen atom by a microwave method. Phys. Rev. 72, 241–243 (1947).
Rentrop, T. et al. Observation of the phononic Lamb shift with a synthetic vacuum. Phys. Rev. X 6, 041041 (2016).
Colla, A., Hasse, F. et al. Observing time-dependent energy level renormalisation in an ultrastrongly coupled open system. Nat. Commun. 16, 2502 (2025).
Mpemba, E. B. & Osborne, D. G. Cool? Phys. Educ. 4, 172–175 (1969).
Kell, G. S. The freezing of hot and cold water. Am. J. Phys. 37, 564–565 (1969).
Warring, U. Exploring quantum Mpemba effects. Physics 17, 105 (2024).
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