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In what ways can energy transform into matter and vice versa? Annihilation is one way to tranform matter to energy. Fission is another (when splitting and atom, what happens to its two parts?)

Are quantum fluctuations one way to transform energy to matter?

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There's nothing special about nuclear reactions. Chemical reactions also result in a change in mass due to the energy released. It's just that the energy scale for chemical reactions is about $10^6$ times smaller. –  Ben Crowell May 29 '13 at 14:59
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2 Answers 2

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In what ways can energy transform into matter and vice versa?

Energy and matter are connected according to special relativity and this has been experimentally demonstrated . It is the famous formula:

$E=mc^2$ , where $m$ is the relativistic mass and $c$ the velocity of light. or

$E^2=m_0^2c^4 +p^2c^2$ , for a particle with rest mass $m_0$ moving with momentum $p$.

The rules of transformation follow Quantum Mechanical solutions of kinematic and potential problem equations .

Annihilation is one way to transform matter to energy.

Yes

Fission is another (when splitting and atom, what happens to its two parts?)

In the quantum mechanical description of nuclei they are represented by potential wells with energy levels, some filled. The number of baryons ( protons and neutrons) bound in this potential well characterize the nucleus. Nucleus A that is struck by a neutron ( for example) becomes a nucleus B higher up in baryons by absorbing it into an energy level of this potential well. In fission this higher up nucleus is unstable and falls into a lower energy state, giving up part of its mass in energy according to the relativistic formulae, and breaking into smaller nuclei and free neutrons which go on to sustain the fission on another original nucleus. Generally a form of fission happens if a nucleus is unstable.

There is also fusion, two deuterium nuclei adhering at a lower energy level and giving up energy. The binding energy curve shows whether nucleons can fuse or fission and give up as energy a part of their mass.

Are quantum fluctuations one way to transform energy to matter?

No, quantum fluctuations are virtual . If you mean tunneling, yes.

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Thank you for your answer! I was thinking about splitting up things, is it teoretically possible to split a neutron, electron and other particles smaller than an atom? What would happen? Even more energy? –  Rox Apr 2 '12 at 7:43
    
At the moment one cannot split elementary particles, and I think this will always be true. A neutron is not elementary, and it decays into a proton an electron and an electron_anti_neutrino, giving up the difference it has in mass with the proton also as energy . A proton, though not elementary because it composed of quarks, might decay in some theories, but cannot be split in the sense of separating the quarks because quarks are bound strongly, the further their distance from the center of mass of the proton, the stronger.I know no main stream theory that allows electrons to be composite. –  anna v Apr 2 '12 at 7:50
    
@Rox you can 'accept' an answer that you're satisfied with by clicking the green tick next to it. You don't have to if you feel that the answers are incomplete, though. Oh, and don't accept my answer above, it only addresses half the question. –  Manishearth Apr 2 '12 at 16:44
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Related note:

Fission isn't exactly turning matter into energy. It just releases the binding energy of the nucleus. This binding energy is part of the measured mass pf the nucleus, but if you want to separate "matter" and "energy" (not really possible), then it counts as energy. $\newcommand{\a}[3]{\mathrm{^{#1}_{#2}#3}}$ $$\a{235}{92}{U}+\a10n\to\a{236}{92}{U}^*\to\a{144}{56}{Ba}+\a{89}{36}{Kr}+3\a10n+|\Delta H|\approx177\:\rm{MeV}$$

Note that initially, we have 93 protons and 142 neutrons; and in the end this number does not change. From this POV, where particles count as "mass", we can say that no mass was created or destroyed, and the nuclear binding energy was released.

Why do we call this a conversion from mass to energy if its just a converseion of types of energy? Well, that's because mass is energy.

The fact is, if you "weighed" $\a{235}{92}{U}+\a10n$, it would weigh more than $\a{144}{56}{Ba}+\a{89}{36}{Kr}+3\a10n$. Actually, $\a{235}{92}{U}$ weighs less than $92\a11p+141\a10n$. That's because the binding energy of the nucleus is "negative" energy, and thus "annihilates" some mass (since mass is energy). It turns out that due to this, the fission products are lighter than the reactants, even if the number of nucleons is the same. And this loss of "mass" is converted into energy.

So really, there's a bit of fuzziness on the border of "energy" and "mass". Anything with an energy density will have extra mass, and you won't be able to tell the difference between a body with mass $m$ and a body with mass $m-\frac{U}{c^2}$ and internal energy $U$.

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