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Why can observers moving at constant speed not use mechanical experiments to determine which one is at rest?

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Brian Greene sits in a living room, holding a pen, with handwritten equations m = E/c^2 and E = mc^2 on a whiteboard beside him, highlighting c^2 as the speed of light. — relativity Brian Greene kicking off his *Your Daily Equation* video series with Albert Einstein's famous equation E = mc².

Observers moving at a constant speed cannot use mechanical experiments to determine which one is at rest because of the principle of relativity. This fundamental law of physics states that the laws of nature are the same in all inertial frames of reference—systems that move with constant velocity relative to one another without rotation.12

Because the laws of mechanics take the same form in every inertial frame, any mechanical experiment performed in one frame will yield the same results as the same experiment performed in another. For example, playing a game of table tennis on a train moving at a constant velocity is physically indistinguishable from playing it while the train is at rest.21

Historically, this concept was recognized in Galilean relativity and remains a cornerstone of special relativity. Since there is no mechanical way to distinguish between these states of motion, the concepts of "rest" and "uniform motion" are physically equivalent within these frames.132