6/8/19

Time Dilation and the Twin Paradox – Round 2


2 postulates of special relativity:


If I am at rest and observing someone in motion then I will observe their time to tick slower. That is to say, I will observe them to have less number of heart beats as compared to mine. Thus I will perceive them as being younger (they have had less heart beats); I have observed their time to dilate.


Similarly, if I am moving then an observer will perceive my time to be dilated, I will have less heart beats and I will be younger than them.


In the twin paradox (in which one twin stays on earth and the other takes a rocket around the moon and back) both twins will observe the other as being younger because from their own perspective the other is moving and therefore their time is perceived as dilated for each of them.

In fact, the twin that is in the rocket is actually the one who ends up being younger thanks to general relativity.


General relativity states that clocks run slower in accelerated reference frames. The twin in the rocket has periods of acceleration and therefore their time is dilated (slowed) so they have less heart beats and age less. So if I am accelerating my clock will slow down, I will have less heart beats and I will therefore be younger than someone who it at rest and observing me from outside of my reference frame.


Moving people age more slowly than stationary ones.

The amount that time is slowed (dilated) is defined by gamma (the Lorentz factor)




gamma is always greater than 1 so tdilated is always greater than tstationary





General relativity also states that clocks run slower in a gravitational field.










Lets say that I move at a constant velocity of 1m/s for 1.577x10^9sec (50yrs) while an observer sits in a chair w excellent vision and watches my every move for all 50yrs. I will have moved a total of 1.577x10^9meters in 50yrs.



Tstationary is 1.577x10^9 seconds.

1- (1/300000^2) = 1- (1/8.98755x10^-16)

1- (1.11265x10^-17)


tdilated = 1.577*10^9 / sqrt (1-(1/8.98755x10^-16))

tdilated = 1577000000.000000009


Therefore:

time for the mover has dilated by 9*10^-9sec = 9nanoseconds. The person in constant motion is 9nanoseconds younger than the person sitting in the chair for 50yrs