Thursday, June 28, 2018

special relativity - If traveling at the speed of lights stops time, why does it take light 8 minutes to reach Earth?



I just learned that, according to Einstein's relativity theory, time reaches zero for an observer (light) when traveling at the speed of light, so everything is supposed to be at the same place in the universe for light. But why does it take 8 minutes for light to travel from the Sun to Earth? Is it because we are observing it from earth? At 300.000 km/s distances in the universe are hardly zero? I can't seem to grasp this.



Answer



Light travels at the speed $c$ this speed is finite and with out using any relativity we can calculate the time it takes for something travelling at this speed to reach us: $\text{time} = \frac{\text{Distance}}{\text{speed}}$ or $ t= \frac{d}{c} = \text{8 minutes}$ in this case.


For a person travelling very close to the speed of light with velocity $v$ from the sun towards the earth time does slows down, and he goes past the earth in a matter of seconds. But for us time doesn't slow we see the person with almost the speed of light and the time it takes to reach us is again $ t= \frac{d}{v}$ which will be almost 8 minutes but slightly longer.


Now for light you say time freezes completely this is not really accurate, but for arguments sake I will accept it: Then the same logic applies as before. For light it seems that zero time has passed but for us it is still 8 minutes.


This might seem like a paradox, but time is relative in Einstein's theory of relativiy.


Note that your argumentation is backwards, "time reaches zero for light, because everything is at the same place". While the more "correct" way to say it would be that the photon does not experience time and therefore everything seems to be at the same place.


Hope this helps


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