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Question: Tom leaves on 1st Jan 2024, travels at 80% the speed of light, and returns to earth on 31st Dec 2024. How many earth years will he have aged?
The time dilation effect of Special Relativity dictates that time passes slower for an object moving at relativistic speeds compared to a stationary observer. Einstein's theory of relativity provides us with a formula to calculate this. Here are the things we know: - Speed of light (c) = 100% = 1 (in natural units) - Tom's speed (v) = 80% of the speed of light = 0.8 The formula for time dilation is given by: T = To / sqrt(1 - (v^2 / c^2)) where: - T is the dilated time observed by Tom. - To is the time observed by an Earth observer, which is from Jan 1 to Dec 31, 2024, equals 1 year. Plug the values into the formula: T = 1 / sqrt(1 - (0.8^2)) Solve the equation: T ≈ 1 / sqrt(1 - 0.64) = 1 / sqrt(0.36) = 1 / 0.6 ≈ 1.67 years So approximately, Tom would have aged 1.67 Earth years during his journey. Please note that this is a rough approximation as it does not take into account acceleration/deceleration periods and assumes that Tom moves at a constant speed.
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