Reply to post: Re: Faster than light not needed?

Re: Faster than light not needed?

"The problem is that at any point, to get 1g acceleration relative to your destination, you have to accelerate not the rest mass but the relativistic mass. As the time dilation scales with the relativistic mass factor, to get a large time dilation requires a lot of energy."

As far as I'm aware, that's a popular misconception that comes from the way that special relativity is sometimes explained to undergraduates.

If you (the observer) see a ship flying past at a relativistic velocity, it intuitively appears that it is getting heavier and heavier as its velocity approaches c, because its acceleration reduces despite it firing its engines at full power, while its momentum increases. This is what is sometimes described as relativistic mass.

Which doesn't actually exist, it's just a useful way of getting a concept across.

The ship's momentum = mass x velocity is only true when the observer and the ship have the same relative velocity - the actual value is gamma x m x v (where γ is derived from the difference in velocity between the observer and the ship and equals 1 at non-relativistic speeds), so as the ship's velocity approaches c relative to the observer, the value of γ rises exponentially above 1, and the ship's momentum (energy) can increase without its mass increasing. The γ value explains how (to the static observer) acceleration can be falling while energy input (force) is constant.

I think even Einstein used the phrase relativistic mass in trying to explain special relativity, so it's easy to see why people use it even though it causes confusion.

If a ship starts its journey with a mass of 50 tonnes (sometimes called its rest mass, though its really just its mass), the mass will still be 50 tonnes at 99.99999% of c, so to the crew onboard the acceleration will be Newtonian i.e. the ship's engines are generating a constant force and mass remains constant so they will experience constant acceleration. The crew won't experience the falling acceleration seen by the static observer due to the time dilation they are also experiencing.

So astronomical amounts of energy are not required - all you need is a propulsion system which can provide approximately 10N of force per Kg of ship's mass, and enough fuel to keep it going for a few decades.

That's all you need he said...