I received a good question today on how Special Relativity theory allows effectively faster than light travel, especially since the assumption of the speed of light as a maximum speed is so intrinsic to Special Relativity theory. This is a good question that deserves more than just a reply to a comment, so I’ll provide a quick answer here.
According to Special Relativity theory, neither an Earth-based observer nor a traveling observer can ever measure that the traveler travels faster than light speed. This is the headline that is generally known. However, if you look at the whole trip to a another star something interesting happens. Assuming that trip distance is measured at both ends of the trip, the distance will be measured in approximately the Sun’s reference frame so that the Lorentz contraction factor is approximately 1 and length contraction is insignificant. If the traveler considers his or her own experience, then the traveler’s time measurement is the important one and assuming relativistic speeds are reached the Lorentz contraction factor varies from 1 and time dilation is significant. It is in this mixed-reference frame perspective that Special Relativity theory allows travel at effectively faster than light speed.
This is where economics becomes important. If investors (and other stakeholders) back on Earth are important, their perspective is important and to them the traveler never travels faster than light speed. However, if all investors and other important stakeholders are themselves travelers, then the traveler’s perspective — where effectively faster than light speed travel occurs — is the important one. Even better for the travelers, using the constant acceleration approach the effective speeds reached are far higher than would occur under simple Newtonian approach.
I intend to post an article on the mathematics of constant acceleration in Special Relativity theory, including the calculus involved, but that must wait for a later date.
As always, I value your perspective. Please leave your questions and comments in the comment area below.
Good question. A traveler’s speed relative to himself or herself must be zero. However, a traveler can measure his or her speed relative to the Sun, and that in general will be non-zero but must be less than the speed of light. However, at relativistic speeds the traveler observes length contraction in the direction of motion. From the traveler’s perspective the distance between the origin and destination becomes noticeably shorter. From this perspective, the change in distance allows the traveler to make the trip at effectively faster than light speed without ever measuring a speed faster than light speed.
The speed of light is always c in every reference frame. The trick is to consider the perspective of different reference frames. That’s what is so often missed.
im confused, wouldnt from the travelers frame, the speed be 0? since thats how we define reference frames? this snippet has left me quite confused yet enticed. you win, i guess ill have to come back
Ooh I thought the speed of light could never be measured as anything other than c from any reference frame.