# Why doesn't DEceleration add mass as well?

1. Sep 27, 2007

### Meatbot

If I accelerate to .9c I am gaining mass, but if I reverse thrust and decelerate why aren't I still adding mass since I'm still putting energy into the system? I thought it wasn't about speed but about changing speed. It takes energy to slow down as well. Or does deceleration lower mass? Or does the decrease in kinetic energy from the lower speed make up for it? I'm sure I just don't understand it properly.

I mean, one observer might think you're accelerating and another might think you're decelerating. Isn't it irrelevant whether you are slowing down or speeding up? How do you know which one you are really doing? What if you and a planet are both moving at the same speed in the same direction but you are in front? For me to get to the planet I'd need to reduce speed, but from my perspective I'd be increasing speed.

Thanks!

Last edited: Sep 27, 2007
2. Sep 27, 2007

### OOO

The fact that you need energy for slowing down is a consequence of using dissipative processes (burning fuel) for that. If you imagine you didn't have a rocket engine in your space ship but a contracted spring connected to a large mass then releasing the spring accelerates you but as you pass the equilibrium length of the spring you start to decelerate without requiring energy. That's an example of a conservative propulsion.

3. Sep 27, 2007

### JesseM

The gain in relativistic mass at higher speeds can be understood in terms of kinetic energy contributing to the relativistic mass along with the object's rest mass. So, the only way in which it makes sense to say that relativistic mass increases because you're "putting energy into the system" is if by "putting energy into the system" you just mean "increasing its kinetic energy". And under this definition, decreasing speed is clearly not putting energy into the system, since the kinetic energy is decreasing.

4. Sep 27, 2007

### Meatbot

But how do you know whether kinetic energy is increasing or decreasing since you may not have been aware of any previous increases/decreases? What if you are already moving at .9c and have been since birth. You think you are stationary and accelerate opposite the direction of motion. Are you gaining or losing kinetic energy? How do you know?

5. Sep 27, 2007

### JesseM

Kinetic energy is just a function of present speed in your frame, it doesn't depend on past history. In classical mechanics kinetic energy is (1/2)*mv^2, where m is mass and v is speed, while in relativity it's given by $$(\gamma - 1)mc^2$$, where m is rest mass, c is the speed of light, and $$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$
You can only talk about gaining or losing kinetic energy relative to a particular inertial frame, it's not an absolute concept. In any frame where the acceleration increased your speed, you've gained kinetic energy, while in any frame where the acceleration decreased your speed, you've lost kinetic energy.

Last edited: Sep 27, 2007
6. Sep 27, 2007

### Meatbot

So an observer in your frame would see you gain mass while an observer in an outside frame would see you lose mass, right? So anyone who would see you as decelerating would also see you as losing mass, even if in your frame you were gaining mass. I was mixing frames I guess.

7. Sep 27, 2007

### JesseM

If you're actually in the process of accelerating, you don't have a single inertial rest frame--"inertial" just means non-accelerating. The usual equations of SR, such as the time dilation equation or the equation I gave for kinetic energy, can only be used in inertial frames.

8. Sep 27, 2007

### Meatbot

What about an observer that remains in the frame of your starting location before you accelerated. He would see you gain mass, but an observer who was able to see that you and the planet were moving fast relative to him would see you lose mass.

9. Sep 27, 2007

### JesseM

Yes, that's right (assuming that you were losing speed relative to the second observer).

10. Sep 27, 2007

### Staff: Mentor

In your own reference frame you are always stationary. You can't observe your own "relativistic mass."

11. Sep 27, 2007

### alvaros

I think this is a problem of misunderstanding "what is an Inertial Reference Frame ( IFR )".

You dont define system.

This is not true. How do you define acceleration ? Respect to a IFR.

Kinetic energy ( and relativistic mass, I suppose ) is relative to a IFR.
How much energy can you get stopping this body that is moving ? This is kinetic energy.
And how could you stop this body ? Exerting a force between this body and and your IFR.

And the only way you can exert a force from your IFR is that your IFR have a mass, but this belongs to another thread.

12. Sep 27, 2007

### pervect

Staff Emeritus
When you say that someone gains or loses mass, you undoubtedly mean "relativistic mass".

Relativistic mass is not a property of an object alone, but just like energy in Newtonian mechanics, depends on the observer.

Thus, if we consider one object, it has one value for relativistic mass when viewed from a frame that's "moving along" (co-moving) with the object in question, but has a different value for relativistic mass when viewed from a frame that's moving at a different velocity.

There is a sort of mass that is a property of an object (at least if the object is isolated), but this sort of mass is not relativistic mass. It's called invariant mass.

I get the impression that you are viewing "relativistic mass" as a property only of the object, and that this is what is confusing you. Relativistic mass is not a property of the object alone, but depends both on the object and the frame from which it is viewed, i.e. relativistic mass is observer dependent.

13. Sep 27, 2007

### alvaros

.
And it doesnt depend on acceleration, just on relative velocity. True ?

14. Sep 27, 2007

### pervect

Staff Emeritus
Correct, the relativistic mass of a (small) body that is accelerating depends only on its rest mass (aka its invariant mass), and its velocity.

This is similar to the way that the energy of a body in newtonian mechanics, .5 m v^2, is a function only of m and v, and is not a function of the acceleration.

Of course a body that is accelerating cannot be an isolated system.

15. Sep 27, 2007

### Staff: Mentor

First, "relativistic mass" is not really considered a very useful concept, so I would not recommend using it.

Having said that, consider two inertial reference frames here. Frame A where you are initially at rest and then accelerate to .9c, and frame B where you are initially at -.9c and accelerate to rest. In A you gain relativistic mass and in B you lose it. If you then reverse thrust you will undo any change in "relativistic" mass.

-Regards
Dale

Last edited: Sep 27, 2007