# Going the speed of light in a vacuum?

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1. Nov 21, 2014

### DaveDem

If an object is in a vacuum and it is constantly increasing its velocity, since it would need to use energy to do so it would create a waste. Since it is the largest mass in the vacuum would the waste created be pulled towards the mass causing it never to reach the speed of light?

2. Nov 21, 2014

### Staff: Mentor

What do you mean with "create a waste"? Rocket exhaust?
What does that mean?
Well, gravity is always there... but usually negligible.
No, this limit is much more fundamental and independent of the acceleration mechanism.

3. Nov 21, 2014

### DaveDem

Well unless you have an unlimited amount of energy then yes i mean some sort of waste

4. Nov 21, 2014

### DaveDem

would you not need to loose mass in order to achieve the speed of light?

5. Nov 21, 2014

### pervect

Staff Emeritus
While a rocket in a vacuum would indeed have an exhaust that would interact gravitationally with the rocket, slowing it down very slightly, there is something much more fundamental that prevents an object that constantly increases it's velocity (i.e. an object that accelerates) from reaching the speed of light.

This is the fact that velocities don't add the same way in special relativity that they do in classical mechanics. By "velocity addition, I mean that if we have three observers, A, B, and C, and that the relative velocity between A and B (as measured by either A or B) is $v_1$, and the relative velocity between B and C (as measured by either B or C) is $v_2$, and the velocity between A and C (as measured by either A or C) is $v_3$, $v_3$ is not equal to, and is in fact less than , $v_1 + v_2$. The exact formula when the velocities are all parallel is $v_3 = (v_1 + v_2) / (1 + v_1 \, v_2 / c^2)$. I'll suggest that the mathematically inclined reader try to show that with this formula, no matter how many times one adds together a chain of velocities less than c, the result will always be less than c.

So while one can always add that extra meter/second to A's velocity in A's frame (creating an observer which we call B in the above formula), from the non-accelerating frame C, the change in A's velocity is much less than 1 meter/second and A's velocity will never reach the speed of light.

6. Nov 21, 2014

### DaveDem

how would i write an equation adding the speed decrease with the waste product?

7. Nov 21, 2014

### Staff: Mentor

You cannot achieve the speed of light.
There is no need for rocket exhaust to accelerate. You could have a large mirror and reflect light (coming froms somewhere else) back. Or the rocket could get attracted by something in front of the rocket.

The gravitational interaction? With the usual formula for the force between two masses: $F=\frac{GMm}{r^2}$ with the masses M and m, the gravitational constant G and the distance r. Note that this equation can be used in the perspective of the rocket only, not in a frame where the rocket is very fast.
And to repeat that: you can ignore it. It does not appear at all or it is completely negligible.

8. Nov 21, 2014

### DaveDem

Well not even for going the speed of light (as I knew was impossible) but how would i combine both of the equations listed?

9. Nov 21, 2014

### Staff: Mentor

Which equations do you want to combine in which way?

10. Nov 21, 2014

### DaveDem

and

11. Nov 21, 2014

### Staff: Mentor

Those two formulas have a completely different meaning. You cannot "combine" them.

If you want to calculate the velocity change of a rocket, you can do that in the frame of the rocket (with the rocket equation - ignore gravity) and then use relativistic velocity addition (the formula pervect posted) to relate it to a velocity change in the frame of another observer.
If you want to calculate something else, please give more context what exactly you want to do.

12. Nov 21, 2014

### Staff: Mentor

You may want to read up on the relativistic rocket equation.

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]

Last edited by a moderator: May 7, 2017