Question

Max travels to the star proxima centauri 4.2ly away and returns immediately. He claims that the entire trip took just 8 years. How fast did he travel ?   ( special relativity)

Answer 1

Given that Max travels to the star proxima centauri 4.2ly away and returns immediately, that means, total distance traveled, d = 8.4ly and time taken, t = 8 years

Now, use and

This implies, and   

Now, use the formula

Therefore,

Now, as per the current knowledge we know that nothing can travel more than the speed of light. So, there must be some probem in the solution.

Now, the problem is we are considering distance as normal length but in relativity distance (or length) contracts and same for time (that is time dialation).

Now using special relativity

where, and

Substitute as calculated above.

The above equation will give us a quadratic equation,

or,

Now, solve this quadratic equation to get the speed.

Soluion of this equation is  

where, ; and

This implies,

So, either or

Since is not possible.

Therefore, Max (spaceship) speed is .