Planck's constant (denoted by h) is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It has a fixed value in the current understanding of physics, approximately 6.62607015 x 10^(-34) joule-seconds. However, it is interesting to explore the consequences if Planck's constant were to become infinite or zero.
Planck's constant becoming infinite: If Planck's constant were to become infinitely large, it would imply that the energy levels in a quantum system become continuous rather than discrete. In other words, there would be no quantization of energy, and the wave-particle duality of matter and energy would cease to exist. This scenario would essentially resemble classical physics, where particles can possess any energy value rather than being restricted to specific levels.
Planck's constant becoming zero: If Planck's constant were to become zero, it would have significant implications. Planck's constant is a fundamental factor in the Heisenberg uncertainty principle, which states that the more precisely the position of a particle is known, the less precisely its momentum can be known, and vice versa. If Planck's constant were zero, the uncertainty principle would no longer hold. This would imply that both position and momentum could be measured with unlimited precision, which would violate the principles of quantum mechanics.
It is important to note that Planck's constant being infinite or zero is purely hypothetical and not supported by our current understanding of physics. Planck's constant is considered a fundamental constant of nature and has remained unchanged since its discovery.
Regarding the examples where such conditions might have occurred, it is highly speculative. Our current knowledge of the universe does not provide evidence for Planck's constant undergoing significant changes during the Big Bang or any other cosmic event. The laws of physics, as we understand them, are thought to have been consistent throughout the evolution of the universe. However, the earliest moments of the Big Bang involve extreme conditions that are not yet fully understood, and some theories attempt to describe these early stages. But even in these theories, Planck's constant remains a fundamental and unchanging constant.