Answer to Question #217838 in Mechanics | Relativity for James

Question

I don't know if this is accurate, but I've been told based on relativity, if one were in a space ship and attempted to travel close to the speed of light, energy would turn to mass making the space ship heavier. Thus, one would need more and more energy to go faster and faster. Where does this mass appear on the space ship?

Answer 1

Firstly, the physical consequence of traveling at the speed of light is that your mass becomes infinite and you slow down. According to relativity, the faster you move, the more mass you have. The same works on Earth when you’re driving down the freeway. You weigh a tiny bit more driving around than you do when you’re completely at rest.

So, traveling at the speed of light in the conventional way is impossible. Fortunately, nature offers us a few ways of cheating. These methods include wormholes and traveling at warp speed, among others.

To Further Explain:

As far as I know, time dilation (which is what your question is centered around) doesn’t apply in any of these cases (or, at least at a much less-noticeable for things like warp where you are still in ‘normal’ and ‘non-relativistic‘ space – again, as far as I’m aware). So, I’m going to skip these and talk about traveling really fast using ‘conventional’ means.

Time dilation is “an actual difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses”. This is why astronauts returning from the International Space Station have ‘traveled’ 0.007 seconds into the future after spending 6 months in orbit. Of course, they haven’t really traveled forward in time; they just aged slower relative to everyone on Earth. So, how about I use Alpha Centauri as an example. Lets assume you are able to instantly accelerate to 99.9% the speed of light, as well as instantly decelerate, without killing yourself or destroying your ship (which would probably result in your death).

Relatively mass

$M=\frac{M_0}{\sqrt{(1-\frac{V^2}{c^2}})}$

Space shiass is high

And travel at light velocity

$$V\approx C$$

$M=M_0$

Space ship energy

$E^2=\sqrt{P^2C^2+M_0^2C^4}$

This is relatively energy