The phenomenon of quantum tunneling, where particles can penetrate through energy barriers that would be classically forbidden, is indeed a fascinating aspect of quantum mechanics. However, it is important to understand that the probability of macroscopic objects tunneling through substantial barriers is incredibly small.
While quantum tunneling is possible at the microscopic level, it becomes increasingly unlikely for larger objects due to the exponential decrease in probability. The probability of a macroscopic object tunneling through a barrier is extremely small because it depends on the mass, size, and energy involved, as well as the thickness and height of the barrier. For macroscopic objects like everyday items, the quantum effects are negligible and classical physics provides an accurate description.
Regarding the concept of an infinite number of tunneling events with infinitesimal probabilities, it is crucial to consider the statistical nature of quantum mechanics. In quantum mechanics, probabilities are calculated as the square of the wave function, and these probabilities add up when considering an ensemble of identical events. However, this does not mean that rare events will necessarily occur in a specific system.
The probabilities associated with quantum tunneling are related to the wave function amplitudes, which describe the quantum state of a system. The superposition principle allows for interference effects between different possible paths, including tunneling paths. These interference effects give rise to the probability distribution for finding a particle on the other side of the barrier.
The reason the big and small numbers do not cancel each other out is because the probabilities associated with macroscopic tunneling events are incredibly tiny. While there may be an enormous number of potential tunneling events occurring in the universe, the probabilities associated with each individual event are so minuscule that their cumulative effect is negligible. It is essential to distinguish between the possibility of an event occurring and the actual probability of it happening.
In summary, while quantum tunneling is a fascinating phenomenon that can occur even for macroscopic objects, the probabilities of such events are extraordinarily small. The vast number of potential events does not lead to their cancellation because each individual event has an extremely low probability, making the cumulative effect of these events negligible in practice.