Real Quantum Theory Avoids Falsification by Untestable Assumptions

A new analysis reveals that real quantum theory reproduces all Bell correlations observed in conventional quantum theory, challenging the idea that the two frameworks are fundamentally distinguishable through experimentation. Timothée Hoffreumon and Mischa P. Woods at the Mathematical Institute, Slovak Academy of Sciences, identify a key flaw in previous arguments proposing a method to falsify real quantum theory, originating from an untestable assumption concerning source independence. Establishing equivalence between quantum theory and real quantum theory under operational independence, the analysis proves that no finite network correlation can differentiate between the two, effectively restoring their empirical indistinguishability and highlighting differing interpretations of quantum correlations. Demonstrating equivalence via correlation-based source independence Operational independence, a key technique in this work, redefined how assessment of whether the source of particles in an experiment secretly influenced results occurred. Traditionally, investigations into source independence relied on mathematically constraining the source states, demanding they be uncorrelated with the measurement settings. This approach, known as product-state independence, often involved assumptions about the preparation of the quantum states that were difficult, if not impossible, to verify experimentally. The new analysis shifts the focus entirely to a demonstrable lack of correlation between different sources, mirroring the principle of a truly random process like a fair coin toss. This means independence is established not by what the source is, but by what we observe about its behaviour. Specifically, if different sources produce outcomes that are statistically uncorrelated when measured, then the assumption of source independence is satisfied, regardless of the underlying physical mechanism. This shift from product-state independence, which focuses on the mathematical form of the source, allowed equivalence between real quantum theory and standard quantum theory in a way previous approaches hadn’t. The approach assesses independence through demonstrable observation, distinguishing it from previous methods. Consequently, any quantum correlation achievable within standard quantum theory, given a specific measurement structure, is also achievable within real quantum theory. This equivalence extends to complex protocols involving quantum channels, which can transmit quantum information, and measurements, demonstrating that real quantum theory cannot be experimentally falsified if standard quantum theory remains unviolated. The significance lies in addressing a decades-old question regarding the necessity of complex numbers in the foundations of quantum mechanics.

Operational Source Independence Resolves Equivalence of Quantum Theories A finite network correlation achievable in standard quantum theory is also achievable in real quantum theory. Previous research, attempting to distinguish between the two, suggested a discernible difference existed, predicated on the assumption of product-state independence. However, equivalence is established once source independence is defined operationally, focusing on measurable outcomes rather than mathematical constraints. This operational definition allows for a rigorous comparison of the predictive power of both theories without relying on unverified assumptions about the source. The researchers consider a scenario involving multiple parties, each performing measurements on particles originating from a common source. They demonstrate that any correlation pattern observed by these parties can be replicated using real quantum theory, provided the source is operationally independent. This is achieved by constructing a real-valued quantum state that mimics the behaviour of the complex-valued state in standard quantum theory. This approach is key, as it bypasses the previously untestable assumption that constrained real quantum theory and allowed for the restoration of empirical indistinguishability between the two frameworks. This equivalence extends to complex, multipartite protocols involving multiple channels and measurements, all while maintaining a defined locality structure, meaning that influences cannot travel faster than light. As long as no violation of standard quantum theory is detected experimentally, real quantum theory cannot be definitively ruled out through observation. The implications of this finding are substantial, suggesting that the complex numbers in standard quantum theory may not be strictly necessary for describing the observed correlations, prompting further investigation into the fundamental nature of quantum reality. Demonstrating experimental indistinguishability does not guarantee theoretical equivalence or Despite resolving a long-standing debate about the necessity of complex numbers, this work doesn’t deliver a final verdict on real quantum theory’s usefulness. Real quantum theory cannot be falsified by experiment, given current assumptions about standard quantum theory’s validity; however, proving something cannot be disproven is distinct from proving it’s a superior or even equally valid framework. A key tension arises from the fact that while both theories yield identical correlations, they do so with fundamentally different mathematical structures, potentially impacting computational efficiency. Standard quantum theory relies on Hilbert spaces with complex numbers, while real quantum theory operates within Hilbert spaces with only real numbers. This difference, while not affecting the observable outcomes, can have significant consequences for the computational resources required to simulate or analyse quantum systems. Acknowledging the computational differences between real and standard quantum theory remains important. Exploring these alternative mathematical structures could unlock more efficient algorithms or simulations, even if the ultimate experimental outcomes are identical to those predicted by the established framework. For instance, representing quantum states with real numbers might reduce the memory requirements for certain quantum computations. Both frameworks predict identical results, but utilise distinct mathematical structures which may affect computational demands. Establishing empirical indistinguishability between standard quantum theory and its real counterpart clarifies a fundamental aspect of quantum mechanics. By redefining ‘source independence’ to focus on measurable outcomes rather than mathematical assumptions, real quantum theory cannot be experimentally ruled out, provided standard quantum theory remains unchallenged. Shifting from constraints on source states to a demonstrable lack of correlation proved equivalence in predicting network correlations, restoring the theories’ empirical similarity. The work highlights that while two theories can be empirically indistinguishable, they may still differ in their internal structure and computational properties, opening avenues for further research into the foundations of quantum mechanics and the potential for alternative quantum frameworks. The research demonstrated that real quantum theory could not be experimentally distinguished from standard quantum theory, given current methods. This matters because it suggests that the complex numbers traditionally used in quantum mechanics may not be fundamentally necessary to explain observed phenomena, potentially simplifying calculations. By focusing on observable correlations rather than mathematical assumptions about the sources of quantum particles, researchers proved equivalence in predicting outcomes across networks. This finding encourages continued investigation into alternative mathematical frameworks for quantum mechanics, potentially leading to more efficient quantum algorithms and simulations utilising real numbers instead of complex ones. 👉 More information🗞 Quantum theory based on real numbers cannot be experimentally falsified🧠 ArXiv: https://arxiv.org/abs/2603.19208 Tags: