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Wave-particle duality is a fundamental concept in quantum mechanics that suggests that all subatomic particles, such as electrons, protons, and photons, can exhibit both wave-like and particle-like behavior under certain conditions. The reason for this phenomenon lies in the mathematical framework and principles of quantum mechanics.

In classical physics, particles are typically described as localized entities with definite positions and velocities. However, in the microscopic realm of subatomic particles, the laws of classical physics break down, and the wave-particle duality becomes apparent.

According to quantum mechanics, particles are described by wavefunctions, which are mathematical functions that represent the probability distribution of a particle's properties, such as position or momentum. These wavefunctions can exhibit wave-like properties, such as interference and diffraction, which are characteristic of waves.

When a particle is not observed or measured, its wavefunction evolves according to the Schrödinger equation, which describes the time evolution of quantum systems. This evolution can lead to interference effects, where the wavefunctions from different paths can overlap and interfere constructively or destructively, resulting in characteristic wave-like patterns.

However, when a measurement or observation is made to determine a specific property of the particle, the wavefunction "collapses" to a particular state corresponding to the measured value. This collapse is a probabilistic process, with the outcome determined by the probabilities encoded in the wavefunction.

The exact nature of wave-particle duality is still subject to ongoing scientific investigation and interpretation. Various interpretations, such as the Copenhagen interpretation, the many-worlds interpretation, and the pilot-wave theory, offer different perspectives on the underlying reality and the relationship between particles and waves.

It is worth noting that while wave-particle duality is a fundamental concept in quantum mechanics, it does not mean that particles are literally waves or particles at different times. Instead, it highlights the inherent dual nature of particles, where their behavior can exhibit both wave-like and particle-like characteristics depending on the experimental setup and the nature of the observation or measurement.

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