The question of the certainty regarding infinitesimal probabilities, such as quantum tunnelling of macroscopic objects, is a philosophical and interpretational issue within the field of quantum mechanics. Different physicists may hold varying perspectives on this matter. Here are a few points to consider:
Empirical Success: Quantum mechanics, despite its probabilistic nature, has demonstrated remarkable empirical success in explaining and predicting a wide range of phenomena at microscopic scales. Its predictions have been verified through numerous experiments and observations. This empirical success lends support to the notion that the probabilistic nature of quantum mechanics reflects an inherent feature of the physical world.
Consistency and Mathematical Formalism: Quantum mechanics is a mathematically consistent and self-contained framework that provides a rigorous description of quantum phenomena. The mathematical formalism, including wave functions, operators, and probability amplitudes, has been extensively tested and found to be internally consistent. The use of infinitesimal probabilities arises naturally from the mathematical structure of the theory.
Experimental Confirmation: There have been experiments that directly confirm the existence of quantum tunnelling, even for macroscopic objects. For example, experiments with superconducting devices have demonstrated the phenomenon of macroscopic quantum tunnelling, where a macroscopic object can traverse an energy barrier that would be classically impossible to overcome.
Interpretational Perspectives: Interpretations of quantum mechanics offer different philosophical viewpoints on the nature of quantum probabilities. For example, the Copenhagen interpretation, which is one of the commonly discussed interpretations, treats probabilities as fundamental and intrinsically indeterministic. Other interpretations, such as the many-worlds interpretation or the pilot-wave theory, propose alternative explanations for the probabilistic behavior of quantum systems.
Limitations and Ongoing Research: It is important to acknowledge that our current understanding of quantum mechanics may have limitations, and there may be deeper underlying principles yet to be discovered. Ongoing research in areas such as quantum gravity and the quest for a theory of everything aims to provide a more complete and unified understanding of the fundamental nature of reality, including the nature of probabilities in quantum mechanics.
In summary, while there may be philosophical and interpretational debates surrounding infinitesimal probabilities in quantum mechanics, the empirical success, mathematical consistency, and experimental confirmation of quantum phenomena provide strong support for the existence and significance of these probabilities. However, the field of quantum mechanics remains an active area of research, and further exploration and investigation are necessary to deepen our understanding of the fundamental nature of quantum phenomena.