The word "observables" is spelled with four syllables: /əbˈzɜːrvəblz/. The first syllable, "ob," is pronounced like the word "ahb." The second syllable, "serv," is pronounced with a soft "e" sound like "sərv." The third syllable, "a," is pronounced like the letter "a." The fourth syllable, "bles," is pronounced with a hard "e" sound like "bleez." In essence, the spelling of "observables" follows the standard English principle of matching letters to their corresponding sounds.
Observables are entities or properties in the physical world that can be measured or observed. They are fundamental concepts in the field of physics and play a crucial role in describing and understanding the behavior of systems.
In quantum mechanics, observables are represented by mathematical operators that correspond to physical quantities such as position, momentum, energy, or spin. These operators act on quantum states, allowing the calculation of the corresponding values of the observables when measured in an experiment. The results of measurements are obtained as eigenvalues of the operators, providing a specific value for the observed quantity at that instant.
Observables are often characterized by their associated eigenstates, which represent the possible states that can be measured for that observable. These eigenstates form a set of mutually exclusive outcomes that define the discrete or continuous spectrum of possible measurement results. The probabilities of obtaining each eigenstate are typically described by the wave function, which evolves according to the Schrödinger equation.
In classical physics, observables are also properties of physical systems that can be measured or observed directly, such as the temperature, velocity, or position of an object. They are typically represented by real numbers and can be measured repeatedly to provide consistent results. Observables in classical physics are governed by deterministic laws, where the behavior of the system can be accurately predicted given its initial conditions and the governing equations of motion.
The term "observables" is derived from the English word "observe", which comes from the Latin word "observare". In Latin, "observare" means to watch, keep, or pay attention to something. By adding the suffix "-ables" to the word "observe", we create the noun form "observables", which refers to things that can be observed or measured.