Fuel per unit distance decreasing?

RobinSky

I was reading a link i found here on physicsforums called "The relativistic rocket".
There was lots of calculations of the required fuel for certain distances and such.

However, I understand that time→0 when our velocity v→c.
And that will mean we travel a larger distance for a shorter amount of time in our (he/she who travels) frame of reference, right?
During that time though, we are using fuel, so my question is, or maybe I should call this a statement, however. Doesn't this mean that the fuel required to travel a distance d also goes to zero?
Fuel required→0 when v→c because t→0.
I mean, the engine "stops" in it's frame of reference (as time is felt for the engine) when v is c, right? Let's now say it's possible to reach the velocity c.
Let's say v is now (9999999999999/10000000000000)*c. If statement above is true, this velocity will give a very large distance traveled for a minimal used up fuel.
Or is all this nonsense?

Very thanks in advance.
/Robin Andersson

Naty1

no, not in the frame of the rocket ship.

no, not in the frame of the rocket ship.

RobinSky

Could you care to explain how this could not be the case? I mean time stops for me because I move at a velocity close to c, so is the rocket ship, why wouldn't time decrease for the ship?

harrylin

"Time for you" is called "proper time". Your proper time rate has not slowed down if you go fast relative to something else. Instead, it's the time rate of clocks that move fast relative to you that you interpret as being slowed down, if you presume that you are in rest.

someGorilla

No, the engine keeps working at the same rate always, in its own reference frame. It's slower only relative to someone else (say, someone staying on Earth).

You don't need fuel to travel. You only need fuel to accelerate. So "the fuel required to travel a distance d" doesn't make much sense.

RobinSky

Sorry for not beting clear, I ment that this distance d was not enough to accelerate to the speed of light. In my concept I'm trying to accelerate to the speed of light, and I was thinking how the engine would behave as time slows down as I reach the speed of light.
But now I'm just more confused since I thought everything slowed down, since you age much slower and such at such velocities relative a person, let's say, a person on earth...

harrylin

No distance is enough to accelerate to the speed of light. In other words, you need d=∞.
And we both already explained the error you made for v<c.

The simplest explanation that may help to end your confusion is based on common sense: if you compare your watch with a reference clock on board, and if they were running at the same pace before take-off and they are not sensitive to acceleration, then they should still run in pace (that's what is meant with "proper time"). So, that kind of "time for you" must remain the same - it can't be any different.

DaleSpam

Note that this fuel/distance effect is not specifically a relativistic effect. Under Newtonian physics the fuel per unit distance is monotonically decreasing also for constant thrust.

RobinSky

Ah yeah now I understand! This was actuall an answer to another question that I had in mind, thanks a lot for the help I appreciate it a lot. I remember a friend to me asking this sort of question while I explained the basics of relativity for him, how time slows down and such.
The question was if I will feel any difference in time, we both thought about it and came to a no actually, interesting though that I didn't apply this to the engine.

Thanks a lot! This is interesting!