# E=mc^2, wikipedia says mass can't be turned into energy?

1. Oct 30, 2012

### Albertgauss

Hi all,

Recently, I was surprised to find that Wikipedia asserts that “rest mass” cannot be turned into energy via E=mc^2 (webpage link at bottom). If Wikipedia is correct,

A) why don’t people conserve “rest mass” in high-energy reactions?
B) How do I know when I have mass that can’t be changed/turned/converted into energy and when I have matter that can?

Is this something subtle particular to only what experts know? The article distinguishes between “mass” and “rest mass”, but it seems that “rest mass” is not conserved. Usually, Wikipedia is pretty accurate, but I am skeptical of this article.

Here is how the Wikipedia article opens up:

Mass–energy equivalence does not imply that energy may be "converted" to matter, but it allows for matter to be converted to energy. Through all such conversions, mass remains conserved, since it is a property of matter and any type of energy. In physics, mass must be differentiated from matter. Matter, when seen as certain types of particles, can be created and destroyed (as in particle annihilation or creation), but the system….as a whole, retain both the original mass and energy, with each of these...remaining unchanged (conserved) throughout the process.

Why would matter be allowed to be converted to energy, but not the other way around? Wouldn’t this be a reversible process?

Then, the article seems to contradict itself latter on:

The concept of mass–energy equivalence connects...conservation of mass and energy which continue to hold separately in any isolated system (one that is closed to loss of any type of energy, including energy associated with loss of matter). The theory of relativity allows particles which have rest mass to be converted to other forms of mass which require motion, such as kinetic energy, heat, or light. However, the system mass remains. Kinetic energy or light can also be converted to other types of particles which have rest mass, but again the energy remains…

1. Pair Production

]If “rest mass” really is conserved, how would I account for it in such a reaction like (pair production)

hf = 2 x moc^2 + KEe- + KEe+ = 2mc^2

In such equations, I have never seen “rest mass” conserved, as the article implies. At threshold, the two photons are just barely able to produce the e-,e+. The 0.5 MeV rest mass imparted to either e- or e+ clearly came from the energy of the incident photons, sure proof that “rest mass” is not conserved.

I do know that pair-production needs a nucleus to conserve momentum. Could some of the “true mass” be buried in a small correction or be thought of as some kind of nuclear binding energy?

2. Pion Production

Wikipedia says:

If the photons are formed by the disintegration of a single particle with a well-defined rest mass, like the neutral pion, the invariant mass of the photons is equal to rest mass of the pion.

This reaction also seems clearly to say to me that “rest mass” can be converted to energy and is, thus, not conserved. The pion has rest mass, the photons, do not. The pion and its rest mass disappear before the reaction; the photons--all energy and no rest mass--appear after the reaction.

I understand that pions and other exotic particles may not be true particles, but short-lived bound states, or maybe even fields, but then why don’t people talk about pions as such states, and, even among scientists, refer to them as real/tangible/definate particles?

There is further info about how 3) rest mass is conserved in nuclear reactions and 4) neutron absorption produces gamma rays, but I omitted these examples for brevity, as these Wiki examples have the same kinds of contradictions and subtleties as the two examples above.

Is this wikipedia article correct that rest mass is conserved, and that “rest mass” can’t be turned into energy or vice versa? If so, how does one conserve “rest mass” for the above examples? How would it be written in the above reactions? Why is the lore so common about E=mc^2 being the basis for “rest mass” converted to energy and vice versa? Even if one takes the position that the “mass” terminology refers to both rest mass and kinetic energy, the appearance or disappearance of real particle like pions or pair-production would seem to contradict this. Here is the link:

http://en.wikipedia.org/wiki/Mass–energy_equivalence

2. Oct 30, 2012

### The_Duck

The rest mass of particles can be converted to energy. The cleanest example of this is that an electron and a positron, each with nonzero rest mass, can come together and annihilate into photons, with zero rest mass. So the quantity given by the sum of the rest masses of all the particles in a system is not conserved.

When Wikipedia talks about mass always remaining unchanged, it is talking about the "invariant mass" of a system of particles. See http://en.wikipedia.org/wiki/Invariant_mass . As the name suggests, the invariant mass of a (closed) system never changes. For example, we can define an invariant mass for the above electron-positron system that remains unchanged (and nonzero) when the electron and positron annihilate into photons. Crucially, the invariant mass is not the sum of the rest masses of the particles in the system: rather, it is proportional to the total energy of the system.

3. Oct 30, 2012

### Staff: Mentor

...in the reference frame in which the total momentum of the system is zero (the "center of mass" a.k.a. "center of momentum" a.k.a. "zero-momentum" frame).

4. Nov 5, 2012

### Albertgauss

Hi all,

Thanks for helping me out with this. I understand now.

Albertgauss