Why are relativistic effects very small in our daily lives
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Why don't we generally notice the effects of special relativity in our daily lives? Be specific.
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Solution Summary
We show that relativistic effects are generically of order (v/c)^2. We also point out that there are relativistic effects that are not small in our daily lives. We conclude by explaining the classical limit c --> infinity.
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The short answer is that relativistic effects are generically of order (v/c)^2, where v is some typical speed of the system you are looking at and c is the speed of light. In our daily lives the typical speeds are much lower than the speed of light (which is about 3*10^8 m/s), so relativistic effects are very small.
Put differently and slightly more rigorously, suppose you do an experiment e.g. you measure the period of a pendulum. If you calculate theoretically what you should find using special relativity and using classical mechanics, then the fractional difference of the two predictions is:
[Prediction of Relativity - Prediction of Classical Mechanics]/Prediction of Classical Mechanics =
some constant times (v/c)^2
for v a typical velocity of the system. So, for a pendulum swinging at an average velocity of 1 m/s, you would expect the fractional difference to be of order 10^(-17) and even for very fast moving objects, say 1 km/s, the relativistic correction is only of order 10^(-11).
But why are relativistic effects only of order (v/c)^2 and not of order v/c? This is because relativity does not merely say that the speed of light is some finite large number but also ...
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