Final answer:
Henri Poincaré's quote implies that endless time allows for endless discovery through observation, a concept reflected in physics theories on the perception of time near event horizons and weightlessness in a falling frame. Time may have a granular nature, and the concept of infinity within the universe is an ongoing challenge in physics.
Step-by-step explanation:
The quote 'If the scientist had an infinity of time at his disposal, it would be sufficient to say to him, Look, and look carefully' by Henri Poincaré suggests that with unlimited time, a scientist could uncover all truths by simply observing. This idea is reflected in physics concepts such as the event horizon of a black hole, where an astronaut's signals become increasingly redshifted, appearing to freeze in time. Einstein's theory of general relativity also touches on this concept, as illustrated by the idea of a weightless astronomer in a freely falling laboratory, where the perception of gravity is relative to the observer's reference frame. These examples demonstrate that the nature of time and observation is central to understanding physical phenomena in the universe.
Furthermore, discussions of finite time in quantum gravity suggest that time may be granular with a lower limit beyond which it cannot be subdivided. This contrasts with the concept of infinity in the universe, which Einstein addressed through the introduction of the cosmological constant to balance gravitational forces in a hypothetically static universe. These topics highlight the challenges faced by scientists and the importance of observation and theoretical considerations in exploring the vast complexities of space and time.
In essence, Poincaré's statement emphasizes the importance of careful observation over time as a means to understand the fundamental truths of our universe, a principle that is deeply entrenched in physics.