⚛️ quantum physics

Where should we look for the deviation from quantum mechanics?

This paper argues that measuring the lifetime and decay law of metastable helium offers a promising avenue for detecting deviations from standard quantum mechanics, as even small quartic deformations can produce significant, observable changes in mean lifetime and non-exponential decay patterns within the Wigner–Weisskopf approximation.

Original authors: Jerome Nicolas, Albert Schwarz

Published 2026-10-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jerome Nicolas, Albert Schwarz

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For nearly a century, the rules of quantum mechanics have governed our understanding of the subatomic world with astonishing precision. This framework describes how particles behave, how they interact, and how they change over time, predicting outcomes that have been confirmed in countless experiments. Yet, physicists have long suspected that these rules might not be the final word. Just as Newton's laws of motion work perfectly for everyday objects but break down at the speed of light or the scale of an atom, the current laws of quantum mechanics might eventually reveal cracks when tested under extreme conditions or with enough sensitivity. The question is not whether these rules are wrong, but where and how they might need adjustment. To find such a deviation, scientists often look at the energy levels of atoms or how particles scatter off one another. However, if the deviation is tiny, these standard tests might miss it entirely. A more promising approach lies in watching how long a particle or atom survives before it decays. Because the lifetime of a particle is the inverse of its decay rate, even a minuscule change in the underlying physics can accumulate over time, leading to a noticeable difference in how long the particle lasts.

This is the specific territory explored by Jérôme Nicolas and Albert Schwarz in their recent work. They focused their attention on a very particular atom: helium in a metastable state. This is a version of the helium atom that is excited and unstable, yet it manages to hang on for a surprisingly long time—about two hours—before it finally releases its energy and drops to a lower state. The researchers chose this atom because its lifetime is not only long enough to be measured with high precision, but it is also short enough that scientists can calculate exactly how long it should last using standard quantum mechanics. This creates a perfect setup for a test: if the measured lifetime matches the calculation, the rules hold; if it differs, the rules might need rewriting. The authors investigated what would happen if the standard laws of quantum mechanics were slightly altered. They did not propose a completely new theory but rather a small, specific deformation of the existing one, adding a subtle term that changes how the atom's energy depends on its state.

The core of their investigation was to see how this tiny modification would affect the atom's decay. In standard quantum mechanics, an unstable atom typically decays in a predictable, exponential pattern, meaning the chance of it surviving drops by a fixed percentage over equal intervals of time. The researchers calculated what would happen if the modified laws were true. They found that even if the change to the fundamental laws is incredibly small, the effect on the atom's total lifetime could be surprisingly large. Because the atom lives for so long, the small error accumulates, shifting the average survival time by a measurable amount. Their calculations showed that the absolute change in the lifetime could be significant enough to be detected by future experiments, even if the underlying modification to the physics is minute.

Beyond just the total time the atom survives, the study also looked at the shape of the decay curve itself. In the standard view, the decay is smooth and exponential. However, under the modified laws, the researchers found that the decay would not follow this simple pattern. Instead, the rate at which the atom decays would change as the atom itself changes. As the atom loses its energy and moves toward its ground state, the speed of its decay would shift, causing the survival curve to bend away from the straight line expected by standard theory. This deviation from the exponential law would be visible on the same time scale as the atom's lifetime. The authors emphasize that this is a distinct signature of the modified physics, separate from the simple shift in the total time.

The significance of this work lies in its proposal for a concrete experimental path. The researchers argue that by measuring the lifetime of metastable helium with greater precision than has been done before, scientists could either confirm the current laws of quantum mechanics to a new degree of accuracy or uncover the first evidence of their breakdown. They note that while the current measurements of helium's lifetime have some uncertainty, a more precise experiment could either close that gap or reveal a discrepancy. If a deviation is found, it would not just be a correction to a number; it would suggest that the fundamental way we understand the universe's building blocks is incomplete. The study concludes that metastable helium is an ideal candidate for this search because its behavior can be calculated from first principles, providing a clear target against which to test the limits of our current understanding.

Technical Summary: Deviation from Quantum Mechanics via Metastable Helium Decay

Problem Statement
The paper addresses the challenge of detecting potential deviations from standard Quantum Mechanics (QM). The authors argue that while energy level shifts and scattering modifications in elementary particles or atoms are likely to be negligible for small deviations, the decay of metastable states offers a more sensitive probe. Specifically, the relative change in the decay width ( $|\delta\Gamma|/\Gamma$ ) corresponds to the relative change in lifetime ( $|\delta\tau|/\tau$ ). For long-lived particles, even a minute relative change in the decay rate can result in a significant absolute change in the mean lifetime. The authors propose metastable helium as the ideal candidate for such a test due to its exceptionally long lifetime (approximately two hours) and the ability to calculate its theoretical lifetime precisely from first principles.

Methodology
The study employs a theoretical framework where QM is viewed as a limiting case of classical mechanics near equilibrium, specifically utilizing a deformation of the Hamiltonian.

Model Construction: The authors adopt the framework from reference [4], interpreting QM as classical mechanics on complex projective space where only quadratic observables are measurable. To introduce a deviation, they add a small, gauge-invariant, quartic term to the standard quadratic Hamiltonian.
System Definition: The system is modeled as a two-level atom (metastable helium) interacting with a quantized electromagnetic field. The ground state is $|0\rangle = |1\,^1S_0\rangle$ and the metastable excited state is the triplet $|1\,^3S_1\rangle$ .
Hamiltonian Deformation: The standard interaction Hamiltonian ( $H_2$ ) is modified by adding a quartic term $H_4 = A_1 n_1^2$ , where $n_1$ is the population of the excited state and $A_1$ is a small real constant. This deformation affects only the metastable level, leaving the photon sector and the magnetic moment unmodified.
Dynamics: The evolution is analyzed using the Rotating Wave Approximation (RWA). The authors derive a non-linear memory equation for the probability amplitude. Unlike standard QM, the phase evolution in the modified theory depends on the instantaneous population of the excited state, introducing a nonlinearity.
Approximation: The analysis utilizes a "Nonlinear Wigner–Weisskopf approximation." In this regime, the population is assumed to change slowly relative to the field's memory time, allowing the decay rate to be treated as a function of the instantaneous population, $\Gamma(x)$ .

Key Contributions and Results

Non-Exponential Decay Law: The primary theoretical finding is that in the modified theory, the decay law is generically non-exponential on the time scale of the lifetime. While standard QM predicts an exponential decay (except for very short and very long time intervals), the quartic deformation causes the decay rate to vary as the population decreases.
Population-Dependent Rate: The decay rate $\Gamma(x)$ becomes dependent on the survival probability $x$ . For a specific cubic spectral density model, the rate is given by $\Gamma(x) \approx \Gamma_0 (1 + 6A_1 x / \Delta E)$ , where $\Delta E$ is the energy gap.
Mean Lifetime Correction: The authors calculate the mean survival time $\tau_{red}$ for the deformed theory. They find that the absolute change in the mean lifetime is significant even for small deformations. Specifically, to first order in the deformation parameter:
$\tau_{red} - \tau_0 \approx -3\tau_0 \frac{A_1}{\Delta E}$
Given that $\tau_0 \approx 7870$ seconds (two hours), a small relative deformation $A_1/\Delta E$ results in a measurable absolute shift in the lifetime.
Shape of the Decay Curve: The paper demonstrates that the decay curve deviates from a pure exponential. The logarithmic decay rate $r(t)$ varies from an initial value $\Gamma(1)$ to a late value $\Gamma(0) = \Gamma_0$ . The relationship between the initial and late rates and the mean lifetime is derived, showing that the curve's shape itself serves as a signature of the deformation.
Robustness of the Signal: The authors note that while the fractional change in the mean lifetime is small ( $3|A_1|/\Delta E$ ), the absolute change is large due to the long $\tau_0$ . Furthermore, if the theoretical lifetime cannot be calculated precisely for a specific atom, the observation of a non-exponential decay law itself serves as an indicator of QM violation.

Significance and Claims
The paper claims that the experimental measurement of the lifetime and decay law of metastable helium constitutes a promising method for finding deviations from quantum mechanics.

Sensitivity: The study concludes that the absolute change in the mean lifetime can be appreciable even if the modification to QM is small, making long-lived metastable helium a highly sensitive probe.
Experimental Feasibility: The authors highlight that the theoretical lifetime of metastable helium is calculable from first principles with high precision. This allows for a direct comparison between theory and experiment. A more precise experiment could either confirm QM within tighter bounds or reveal a deviation.
Generalizability: The authors state that their calculations can be generalized to other decay models with specified deformations. They emphasize that for systems where precise theoretical lifetime calculations are difficult, the detection of a deviation from the exponential law remains a viable strategy to test the fundamental laws of QM.

The paper does not propose a new experimental apparatus but rather identifies a specific physical system (metastable helium) and a specific observable (deviation from exponential decay and shift in mean lifetime) where existing or improved experimental precision could test the limits of quantum mechanics.

Technical Summary: Deviation from Quantum Mechanics via Metastable Helium Decay

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