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0 pointsmikeash9y ago0 comments

Not that much. Time dilation due to speed is sqrt(1 - v^2/c^2). At 0.2c, that's 98%, so 20 years would "feel like" 19.6 years.

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gus_massa9y ago

(I Agree.)

As a rule of thumb, you can approximate sqrt(1 - v^2/c^2) = 1 - 1/2 (v/c)^2. So if v/c = 2, then the correction is approximately 1 - 1/2 .2^2 = 98% as you said. This formula is easier for back of the envelope calculations and the important point is that it's quadratic. (I always forget the 1/2 :(. )

The GP comment used the wrong correction of 1 - v/c, that is not quadratic so the correction is much bigger.

mikeashOP9y ago

Cool trick. It starts to fall apart at higher speeds (at c, the approximation produces 1/2, when it should be 0), but it looks like up to 0.5 or 0.5 it's decent.

gus_massa9y ago

Yes, this is the first two terms of the Taylor series near 0, so it works only at "low" speed.

For speeds that are close to c, you have to use another "Taylor" series to get a good approximation. If v is close to c, then the approximation of the correction is sqrt(2(c-v)/c). So at 99%c you get 4.5%.

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gus_massa9y ago

(I Agree.)

The GP comment used the wrong correction of 1 - v/c, that is not quadratic so the correction is much bigger.

mikeashOP9y ago

Cool trick. It starts to fall apart at higher speeds (at c, the approximation produces 1/2, when it should be 0), but it looks like up to 0.5 or 0.5 it's decent.

gus_massa9y ago

Yes, this is the first two terms of the Taylor series near 0, so it works only at "low" speed.

j / k navigate · click thread line to collapse