# Mass energy question

1. Sep 25, 2006

### QuantumKing

I have a hard time understanding the concepts of total energy, rest energy and kinetic energy.

I know that when a mass is at rest, it is moving at c through spacetime. Motion through time can be diverted into motion through space, resulting in a "slower" time, relative to another inertial system...Anyways, my question is, why is the total energy of a system equal to its rest energy + its kinetic energy? Wouldnt its energy at rest be converted into kinetic energy, which is the energy of motion?..I know that a body in motion gains mass, and with e=mc^2 that would mean the total energy would increase, but im thinking that c would decrease to conserve the energy of the body previoulsy at rest. Since motion through time is diminished when motion through space is taking place, how come this isnt the case??

Some help with this would be greatly appreciated:P thanks

Eric

2. Sep 25, 2006

### pmb_phy

That is a comment that people love to say and for which it has no meaning. The term "speed" as in "speed of light c" means that an object has moved a certain about of "space" during a certain amount of "time". Since this cannot be applied to the term "speed" as applied to "moving through spacetime" it is a nonsense phrase to be avoided like the plauge.
The answer is available through calculation. But the total energy is the sum of the rest energy, kinetic energy and potential energy. For a derivation please see

http://www.geocities.com/physics_world/sr/relativistic_energy.htm

No. Why would you think so?? Kinetic energy is energy of motion, potential energy is energy of position. Rest energy is energy of rest mass.

Best wishes

Pete

3. Sep 26, 2006

### actionintegral

Rest energy is not "converted into" kinetic energy. It is retained by the object. The kinetic energy is then added to that.

4. Sep 26, 2006

### lightarrow

This can happen, sometimes and for a little percentage of the rest mass. Examples:
-chemical reactions releasing energy (Very little percentage of rest mass transformed into energy, a part of which can be transformed into kinetic energy).
matter-antimatter annichilation (all the rest mass becomes energy, a part of which...).

5. Sep 26, 2006

### masudr

Yes indeed. What they really mean is that the 4-velocity vector has only a non-zero time component when the object is at rest. If it has a velocity v (or we are in a ref. frame moving at -v), then the 4-velocity vector starts pointing in these other directions: the component in the time direction gives us the Lorentz contraction of time.

Of course, the real reason for this is that 4-velocity is a spacetime vector, as is 4-position, and not the notions of speed through spacetime, as you have explained. I blame Brian Greene for this section in his book The Elegant Universe which expounds this description.

6. Sep 26, 2006

### actionintegral

Can you tell me how this happens? I need to know "which" rest mass gets converted into energy

7. Sep 26, 2006

### lightarrow

I think you are talking about potential energy, isnt'it?
If this is the case, I agree with the fact that what is rest mass for molecules is, partially, potential energy of atoms, nuclei and electrons.
However, the rest mass of a nucleus is, partially, potential energy of nucleons...and so on. Maybe everything is potential energy.

In chemistry, we start from the standard state of reagents to arrive to the product's standard states. Example: molecular hydrogen + molecular oxygen--> molecular water. The difference in mass from products and reagents has gone away as energy.

So, it's (part of) the rest mass of molecules which gets converted into energy.

Last edited: Sep 26, 2006
8. Sep 26, 2006

### actionintegral

I think I see. Let me ask this question then: Suppose I have two identical objects. One object is at rest, floating in space, and the other is at rest, but at the end of a spring that I stretched out (so it has potential energy).

Please compare the relativistic masses of the two objects.

9. Sep 26, 2006

### pervect

Staff Emeritus
The stretched out object will have a higher "relativistic mass". It will also have a higher "invariant mass".

I generally prefer to deal with invariant mass, because it is the only sort of mass that is a property of the system and independent of the observer, as long as the system is isolated. Non-isolated systems have several tricky aspects to them. Unfortunately, your example is a non-isolated system, unless you let the mass on the end oscillate naturally. If you hold it in a "stretched out" position, you do not have an isolated system.

Invariant mass is, in geometric units, E^2 - p^2, where E is the energy of the system, and p is its momentum.

When you stretch out the spring, you increase E, but you do not change p, which remains at zero. Ergo, you increase the invariant mass.

Relativistic mass is almost universally understood as being equivalent to energy, so when you increase the energy E, you also increase the relativistic mass.

Note that, except for gravitational radiation (negligible), if your mass-spring system is isolated, the mass stays constant. The spring converts potential energy into kinetic energy, and vica-versa, but the total energy of the system stays constant. This means the relativistic mass stays constant, and because the momentum stays constant (and zero), the invariant mass is also constant.

You might try the wiki articles:

http://en.wikipedia.org/wiki/Rest_mass
http://en.wikipedia.org/wiki/Mass_in_General_Relativity

10. Sep 26, 2006

### actionintegral

Hi Pervect,

I read your answer carefully, but I am confused. You refer to an attribute of the object called "invariant mass", but then you say that it increases.

Furthermore, the object is still at rest, regardless of whether it is attached to a spring or not.

I am trying to see if potential energy can be considered as relativistic mass. From where I stand, it doesn't seem like it.

11. Sep 26, 2006

### QuantumKing

so, back to my first question, apparently brian greene is a dueshbag? lol, so, what he said about motion through time being diverted into motion through space is just a load of crap? Although it made sense to me, explaining the time dilation phenomena..so what did einstein base his equation of rest energy on? why does he use the constant c?

12. Sep 26, 2006

### actionintegral

I am familiar with that idea. The concept was not "motion through time" per se but rather a trade-off between velocity and proper-time.

The concept of rest energy is based on the relativistic definition of work.

13. Sep 26, 2006

### actionintegral

QUOTE:
Originally Posted by lightarrow
Examples:
-chemical reactions releasing energy (Very little percentage of rest mass transformed into energy, a part of which can be transformed into kinetic energy).
QUOTE

Please check the following for correctness:

An object of mass m0 is at rest and attached to a spring.

We move the object and stretch the spring.

Then we stop the object, and the spring remains stretched.

At this time, the mass of the object is still m0.

Therefore, it is incorrect to refer to the potential energy of the loaded spring as mass. Perhaps you could call it "potential mass".

14. Sep 26, 2006

### Staff: Mentor

"Invariant" in this context means "invariant between inertial reference frames." That is, the invariant mass of an object (in a given state) is the same when measured by different observers moving at constant velocity with respect to each other. It does not mean "invariant between its stretched and unstretched conditions."

15. Sep 26, 2006

### actionintegral

Understood. What started the thread was the suggestion that chemical reactions convert matter to energy. I don't get that.

16. Sep 26, 2006

### Staff: Mentor

Let's first look at nuclear reactions rather than chemical reactions. If a nucleus can spontaneously decay into another one plus some other particles, releasing energy in the process, then the sum of the invariant masses of the final nucleus and the other particles is less than the invariant mass of the original nucleus, and the difference corresponds the the energy released, via $E = mc^2$. We know this is true, because we can measure nuclear and particle masses with enough precision to verify it.

We assume that the same sort of thing is true for chemical reactions. That is, we expect that in an exothermic reaction (one that generates heat), the sum of the invariant masses of the product molecules is less than the sum of the invariant masses of the reactant molecules, with the difference corresponding to the heat relased. I don't think this has been experimentally verified (although I'd be delighted to find out that it has), simply because the mass difference is exceedingly tiny.

Does this mean that matter is converted to energy? It depends on whether you consider "matter" to be equivalent to "invariant mass". The invariant mass of a composite system such as a molecule, atom or nucleus, is the sum of the invariant masses of its components, plus the mass-equivalent of the potential energy associated with binding the system together, plus the kinetic energy of the "internal motion" of the components (more precisely, the kinetic energy of the components in a reference frame where the system as a whole is at rest, i.e. the total momentum is zero).

Do you consider the part of a molecule's invariant mass that is due to potential energy or internal kinetic energy of its atoms, to be "matter"? If yes, then you can consider an exothermic chemical reaction as converting matter into energy. Otherwise... well, you can fill that in for yourself.

17. Sep 26, 2006

### pervect

Staff Emeritus
Please read the wiki links I quoted for some more of the background information if you are not familar with invariant mass.

I'll repeat the most important link
http://en.wikipedia.org/wiki/Rest_mass

You might also try
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

I thought my answer was reasonably clear - "relativistic mass" is another name for energy, and when you stretch a spring, you increase the energy of the spring, therfore you increase its relativistic mass.

Relativistic mass depends on the observer, as I commented before. Invariant mass does not. If you read the wiki articles I mentioned, they go into a lot more detail, including the defintions, which can be summarized as

m_r = E/c^2
m_i = sqrt(E^2 - (pc)^2)/c^2

where E is the energy of a system and p is its momentum. You can see that if p=0, the two defintiosn are equivelant, i.e. relativistic mass equals invariant mass in the "rest frame" of a system, the frame in which the momentum of a system is zero.

I would suggest reading the links I quoted for more of the background information on the defintions of "relativistic mass" and "invariant mass" if these terms aren't familiar.

18. Sep 27, 2006

### actionintegral

I would agree with you if you replace the word "energy" with "kinetic energy" in the above phrase.

19. Sep 27, 2006

### Garth

Actually it should be "total energy" - that due to rest mass or the energy-momentum of the object, plus "kinetic energy".

Garth

20. Sep 27, 2006

### actionintegral

Hi Garth,

The reason I have focused on this point is I am trying to understand why
some people refer to potential energy as mass. What is confusing me is that potential energy is a mathematical fiction (what would happen IF I let go...) whereas kinetic energy is quite measurable.