Quantum tunneling is a phenomenon predicted by the mathematical framework of quantum mechanics, and it has been extensively observed and verified at the microscopic scale. The concept of quantum tunneling arises from the wave-particle duality inherent in quantum mechanics.
While quantum tunneling is primarily associated with the behavior of particles at the atomic and subatomic scale, the theory of quantum mechanics does not impose any fundamental limitation on the size of objects that can exhibit this phenomenon. Theoretically, macroscopic objects can also exhibit quantum tunneling, albeit with extremely low probabilities.
The reason we haven't observed macroscopic objects tunneling on a large scale is due to the exponential decrease in the probability of tunneling as the size and complexity of the system increase. The probabilities involved become so small that the occurrence of such tunneling events becomes extremely rare and difficult to observe in practice.
The understanding that quantum tunneling can, in principle, apply to macroscopic objects is derived from the mathematical consistency of quantum mechanics, which has been extensively tested and validated in numerous experiments. Quantum mechanics has proven to be an incredibly successful and accurate framework for describing the behavior of particles and systems at the microscopic level.
In the case of macroscopic objects, the probabilistic nature of quantum mechanics suggests that while the likelihood of observing tunneling events becomes astronomically small, it is still non-zero. The probabilistic nature of quantum mechanics does not invalidate the possibility of macroscopic tunneling, but rather indicates that such events are highly improbable and challenging to observe directly.
Additionally, theoretical models and calculations based on quantum mechanics provide insights into the behavior of macroscopic objects and suggest that quantum effects, including tunneling, can still play a role, albeit with diminishing significance, as systems increase in size and complexity.
It is important to note that the observation or experimental verification of macroscopic quantum tunneling is an ongoing area of research. Scientists are actively exploring ways to design and perform experiments that can probe and detect quantum phenomena at larger scales, pushing the boundaries of our understanding and potentially uncovering new insights into the quantum nature of macroscopic objects.