The question of whether quantum tunnelling can occur for macroscopic objects is a topic of ongoing scientific investigation. While quantum tunnelling has been observed and well-documented for subatomic particles, extending its applicability to macroscopic objects poses several challenges.
One key challenge is related to the concept of decoherence. Macroscopic objects, such as everyday objects, consist of a large number of particles interacting with their environment. These interactions lead to the phenomenon known as decoherence, where quantum superpositions, which are crucial for tunnelling, break down and the system behaves classically. Decoherence tends to suppress quantum effects on macroscopic scales, making it difficult for tunnelling to occur.
However, theoretical proposals and experiments are exploring the possibility of observing quantum effects in macroscopic systems by reducing or mitigating the effects of decoherence. For instance, in certain experimental setups, researchers have been able to maintain quantum superpositions in relatively large systems for longer durations, which could potentially enable the observation of quantum tunnelling on a macroscopic scale.
Regarding the question of whether the non-zero probability for quantum tunnelling of macroscopic objects is an unfalsifiable claim based merely on the mathematical framework of the theory, it's important to note that scientific theories are typically based on mathematical models that describe physical phenomena. The mathematical framework provides a language for making predictions and testing them against experimental observations.
In the case of quantum mechanics, the mathematical formalism has been highly successful in describing and predicting the behavior of subatomic particles. However, when it comes to macroscopic objects, the challenges of decoherence and the lack of definitive experimental evidence make it difficult to firmly establish whether macroscopic tunnelling is possible.
Scientific theories are typically considered falsifiable if they make specific predictions that can be tested experimentally. In the case of macroscopic tunnelling, while there are theoretical proposals and ongoing research to explore this possibility, the lack of empirical evidence makes it challenging to definitively confirm or refute the claim at this point. Therefore, the question of macroscopic tunnelling remains an open and active area of scientific investigation.