One example that illustrates how a quantum object is affected by probability is the famous double-slit experiment. In this experiment, a beam of particles (such as electrons or photons) is directed towards a barrier with two slits. When the particles pass through the slits and hit a screen behind the barrier, they create an interference pattern, as if they were behaving as waves.
The interesting aspect of this experiment is that when the particles are sent through the slits one at a time, they still create an interference pattern over time. This suggests that each particle behaves as a wave that passes through both slits simultaneously and interferes with itself. However, when a measurement is made to determine which slit the particle actually goes through, the interference pattern disappears, and the particles behave more like classical particles, going through one slit or the other.
The interpretation of this phenomenon is a subject of debate in quantum mechanics. One interpretation is the Copenhagen interpretation, which states that until a measurement is made, the particle exists in a superposition of states, simultaneously going through both slits. The act of measurement "collapses" the wavefunction, forcing the particle to be in one definite state (going through one slit or the other) and destroys the interference pattern.
Another interpretation is the Many-Worlds interpretation, which suggests that the particle exists in multiple parallel universes, each corresponding to a different outcome of the measurement. In this interpretation, the interference pattern is still present, but our observation leads us to perceive only one outcome.
These interpretations highlight the probabilistic nature of quantum mechanics. Prior to measurement, we can only assign probabilities to the different possible outcomes of an experiment. The measurement itself introduces randomness, and the outcome is determined probabilistically. The meaning of this probabilistic behavior is still a topic of ongoing research and philosophical discussion in the field of quantum mechanics.