How fast can we arrive at a certain place, in theory?
Hi there,
In theory, we cannot travel faster than light.
Therefore, is the answer to this question "The speed of light" ?
Definitely NO.
According to Enstain's Special Theory of Relativity,
if someone travels in a inertial reference frame which moves at a speed that near the speed of light, then the time in the frame flows slower.
As the velocity approaches the speed of light, the ratio of time between the outside world and the inside world goes to infinity.
That is to say, if we travel in a speed that very close to light, then when we arrive at the destination, it may be hundreds of thousands of years later. It is not FAST at all.
So we should redefine "fast": Make the ETA(estimated time of arrival) as short as possible.
In this sense, we can formulate the question:
Assume a reference frame moves at constant speed V, and the speed of light is V_light. The distance is D.
T_i is the time that people in the inside world feel, which is
D/V .
T_o is the time that people in the outside world feel, which should be (D/V)*(V_light/sqrt(V_light^2  V^2)) by applying Lorentz transformation.
Then, Find the MIN(T_o), which is a function of V.
By simple calculas, V should be V_light/sqrt(2).
What do you think about the deduction above?
Any reply would be appreciate.
