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The concept that the flow of time changes with speed is a fundamental aspect of the theory of relativity, specifically the theory of special relativity proposed by Albert Einstein in 1905. According to this theory, the passage of time is not absolute but is relative to the observer's motion and the gravitational field they are in.

The key idea behind time dilation, which is the term used to describe the change in the flow of time with speed, is that the speed of light is constant for all observers, regardless of their relative motion. This means that the perception of time can vary depending on the relative velocities of different observers.

According to special relativity, when an object or observer moves at a high velocity relative to another object, time appears to pass more slowly for that moving object from the perspective of the stationary observer. This effect is known as time dilation. It means that as an object's velocity approaches the speed of light, time dilation becomes more significant.

The reason for this phenomenon is that as an object accelerates, it gains energy, and this increase in energy affects the passage of time. The faster an object moves, the more energy it possesses, and the more time slows down for that object.

This concept has been experimentally verified through numerous experiments, such as particle accelerators and measurements involving high-speed particles. The effects of time dilation have practical implications for technologies like GPS systems, where precise timekeeping is crucial for accurate positioning calculations.

In summary, the flow of time changes with speed due to the fundamental principles of special relativity, where the perception of time is relative and depends on the relative velocities of observers.

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