What is the relationship between mass and energy according to E=mc^2?

[quicksilver123]

so... just learned about mass energy equivilance.

10kg object.

e=mc^2
e=9*10^17which is insane. my mind is blown.

wiki says this:

Mass–energy equivalence does not imply that mass may be "converted" to energy, but it allows for matter to be converted to energy. Mass remains conserved (i.e., the quantity of mass remains constant), since it is a property of matter and also any type of energy. Energy is also conserved. 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 a closed system of precursors and products of such reactions, as a whole, retain both the original mass and energy throughout the reaction.

I guess this implies some stoichiometry. Could someone give me an example of mass being conserved in a reaction like this?

 

[quicksilver123]

i think i may be misunderstanding the concept as it applies to real life.

to clarify...
if you converted mass to energy (i'm thinking nuclear reaction)
matter would be conserved (particles are merely split into smaller components, not annihilated)
yet shouldn't the sum of these components equal the mass of the whole? in other words, shouldn't energy remain stable without a loss of mass?

 

[Nugatory]

if you converted mass to energy (i'm thinking nuclear reaction)
matter would be conserved (particles are merely split into smaller components, not annihilated)
yet shouldn't the sum of these components equal the mass of the whole? in other words, shouldn't energy remain stable without a loss of mass?

In a nuclear fission reaction, a heavy nucleus (for example uranium or plutonium) splits into two mid-sized nuclei and a few stray neutrons. The total mass of all these pieces is less than the mass of the heavy nucleus we started with; the difference shows up as energy according to E=mc².

In a fusion reaction, multiple light nuclei (often hydrogen) combine to form a single heaver nucleus (often helium). In these reactions the mass of the pieces we start with is greater than the mass of the single nucleus we end up with; again, the difference shows up as energy according to E=mc².

In this context, we would say that the particles and nuclei are "matter", so the amount of "matter" is reduced in the reaction; we started with a certain mass of "matter" and ended up with less. The total energy is conserved; energy stored in the mass of the "matter" has turned into light energy and heat energy.

And you are right that c² is a huge number, so a very little mass yields up a lot of energy. In round numbers, the atom bomb that wrecked Hiroshima in 1945 released about 10¹⁴ joules of energy; it contained about 50 kg of uranium and only a tiny fraction of that mass was converted into energy.

 

[quicksilver123]

Thanks, that really helped.

I think we've all been told, since we were kids, that Einstein was a genius. When I was introduced to general and special relativity a few years ago, I had no trouble agreeing with that position.

Now that I'm formally learning Gen/Spec. Relativity though, I can appreciate his work at a different level.

 

[mathman]

The only reaction that results in a complete matter to energy is a matter-antimatter annihilation. Example: electron - positron ending up as two gamma rays (or more stuff, if the particles are going fast enough).

 

[Graniar]

Problem with antimatter is that it requires same energy to produce it.
There is only known way to turn most of the matter to energy is by lowering it to a black hole.

 

[DrZoidberg]

The term "mass" usually refers to the rest mass.
The rest mass of an object is simply the energy content that object possesses at rest. It doesn't matter what unit you use to measure the rest mass - kg, Joule, eV. It's the same thing. c^2 is simply a conversion factor to convert from one unit to another.
So, saying you convert mass to energy is like saying you convert rest energy to energy. It's incorrect terminology.
You could however say you convert matter to another form of energy.
Every particle is a form of energy. Not just photons. And energy bends space which is the reason for gravity. So matter has gravity because it is a form of energy and energy bends space.
The binding energy between the protons and neutrons in the nucleus is of course also bending space and is part of the mass of an object. About 99% of the mass of an object comes from the binding energy between the quarks and gluons that are inside of protons and neutrons. So you could say, when you are lifting a heavy object you are really lifting binding energy.

 

[jtbell]

saying you convert mass to energy is like saying you convert rest energy to energy.

More precisely, it's converting rest energy to kinetic energy. Consider a neutron at rest. It has 939.565 MeV of rest energy and no kinetic energy. It decays to a proton, electron, and antineutrino. Ignoring the tiny mass and rest energy of the antineutrino, we end up with

938.272 MeV = rest energy of proton
  0.511 MeV = rest energy of electron
  0.782 MeV = total kinetic energy of the three outgoing particles
-----------------
939.565 MeV = total energy

The total energy is the same before and after the decay, but 0.782 MeV is converted from rest energy to kinetic energy.

 

[catbuckle]

Please give an example of energy being turned back into mass. Please keep it simple.

 

[ZapperZ]

Please give an example of energy being turned back into mass. Please keep it simple.

Pair production. Look it up.

Zz.

 

[jtbell]

For something related to my other example, consider an antineutrino with 5000 MeV of energy interacting with a proton at rest to produce a neutron and an electron: ##\bar \nu + p \rightarrow n + e##. Again we ignore the mass (rest energy) of the neutrino because it's tiny.

Before:
5000.000 MeV = (kinetic) energy of neutrino
 938.272 MeV = rest energy of proton
----------------
5938.272 MeV = total energy

After:
 939.565 MeV = rest energy of neutron
   0.511 MeV = rest energy of electron
4998.196 MeV = total kinetic energy of neutron and electron
-----------------
5938.272 MeV = total energy

1.804 MeV of the kinetic energy of the incoming neutrino has been converted to the rest energy of the electron (0.511 MeV), and the additional rest energy of a neutron versus a proton (1.293 MeV).