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The double-slit experiment is a classic experiment in quantum physics that demonstrates the wave-particle duality and the indeterminacy or randomness inherent in quantum systems. Here's a simplified explanation of the experiment and its implications:

In the double-slit experiment, a beam of particles, such as electrons or photons, is directed toward a barrier with two closely spaced slits. Beyond the barrier, a screen is placed to detect the particles' positions.

When particles are sent through the double-slit apparatus one by one, something remarkable happens. Instead of observing a pattern of two distinct bands on the screen corresponding to the slits, as one might expect from classical particles, an interference pattern emerges. This pattern consists of alternating light and dark bands, indicating the presence of constructive and destructive interference.

The interference pattern arises because the particles exhibit wave-like behavior. As they pass through the slits, they interfere with themselves, resulting in regions of reinforcement (constructive interference) and cancellation (destructive interference) on the screen. This behavior is characteristic of waves.

However, when particles are detected individually, the interference pattern disappears, and instead, they behave as if they passed through one of the two slits, creating two distinct bands on the screen. This observation suggests that the particles behave as discrete particles (particles) when their positions are measured or observed.

The key insight of the double-slit experiment is that the behavior of individual particles cannot be precisely predicted beforehand. Even when particles are sent through the slits one by one, the outcome of each particle's detection on the screen appears random. The experiment shows that at the fundamental level of individual particles, their behavior is not deterministic but rather probabilistic. The particles exhibit a wave-like nature that interferes with itself, yet when measured, they manifest as discrete entities at specific locations on the screen.

This indeterminacy or randomness is a fundamental aspect of quantum mechanics. It arises from the probabilistic nature of wave-particle duality, where the behavior of quantum entities, such as electrons or photons, cannot be precisely predicted but only described by probability distributions. The double-slit experiment vividly illustrates this fundamental characteristic of quantum systems and challenges classical notions of determinism.

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