Accelerating to speed of light

[kannank]

When the an object is accelerated and when the velocity approaches the speed of light, its mass increases exponentially the force required to accelerate the object increases exponentially. So it cannot be done. Fine.

But what if I travel in a spaceship with A LOT of fuel and the spaceship is accelerated constantly by burning the fuel? When the velocity of spaceship approaches the speed of light, does increase mass in its own frame-of-reference?

This may be a silly question. I got confused somehow.

cheers!
KANNAN

 

[Dale]

When the velocity of spaceship approaches the speed of light, does increase mass in its own frame-of-reference?

No, rest mass is an invariant quantity, and an objects mass in its own frame is the invariant mass.

 

[kannank]

No, rest mass is an invariant quantity, and an objects mass in its own frame is the invariant mass.

Then what stops me from accelerating my spaceship to FTL? I still got fuel left in my spaceship.

 

[Integral]

The mass that is moving is not aware that its mass increases. So the answer to your question is no, no matter how much fuel you burn you still cannot reach the speed of light.
We can choose a reference point (e.g. some distant quasar) for the Earth which makes our velocity a significant fraction of the speed of light. Do you feel any heavier now? No matter how fast you are moving with respect to some outside reference point your flash light will still work the same.

 

[Integral]

Then what stops me from accelerating my spaceship to FTL? I still got fuel left in my spaceship.

The geometry of space time.

 

[DrGreg]

Suppose you have a spaceship which undergoes constant acceleration as measured by an on-board accelerometer, and that after 6 months' travel (as measured by an on-board clock) you have reached half the speed of light (0.5c) relative to your starting point. You might think that after another 6 months you would reach the speed of light. But you don't, because the rule for "adding" velocities is not$$u + v$$but$$\frac{u+v}{1+\frac{uv}{c^2}}.$$So , in fact your velocity would be$$\frac{0.5+0.5}{1+0.5^2}\,c = 0.8\,c.$$The formula always gives you an answer less than c, no matter how long you wait.

Another way of looking at this is that everyone measures the speed of light to be the same value relative to themselves (299792458 m/s). So at the start of your journey you reckon you are going 299792458 m/s slower than your target speed, but after 6 months you reckon are still going 299792458 m/s slower than your target speed: you've got no nearer to it.