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A question in my revision guide:

"Explain why the mass of a tree cannot be converted directly into energy."

The answer explains that the tree contains particles but not their corresponding anti-particles, so the particles cannot annihilate to create energy.

The question arises: Do you always need matter and antimatter to create energy, or can energy be created from matter alone?

Note: If you are going to use equations I would highly appreciate an intuitive explanation alongside them because I'm only in AP physics and don't understand all the "higher physics" stuff yet.

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    $\begingroup$ You don't "create energy" (or "convert mass into energy") if you annihilate matter and antimatter, you convert the energy bound in the particles into other energy bound in particles, mostly photons of light. The question must implicitly mean why you cannot "directly" convert the mass of a tree into photons (which is because of conservation laws), but it's an imprecise and not very well posed question. $\endgroup$ – ACuriousMind♦ May 7 '15 at 18:07
  • $\begingroup$ @ACuriousMind: "You don't "create energy" (or "convert mass into energy") if you annihilate matter and antimatter" But in the book it says that mass can be converted to energy and you can work out the energy using $E=mc^2$. Why doesn't this equation apply here? Thanks! $\endgroup$ – user45220 May 7 '15 at 18:11
  • $\begingroup$ To amplify @ACuriousMind's comment, mass isn't a thing distinct from energy, it is a kind of energy just as kinetic and potential energy. But that is a finally drawn distinction that introductory books often ignore or handle badly. For the purposes of class you need to know what the expected answer is. $\endgroup$ – dmckee --- ex-moderator kitten May 7 '15 at 18:12
  • $\begingroup$ @dmckee: Thanks, I think I'm starting to understand it. So $E=mc^2$ is just saying this in an equation? $\endgroup$ – user45220 May 7 '15 at 18:17
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    $\begingroup$ The issue is that you cannot convert all mass energy into massless energy (as @ACuriousMind clearly explained). So the poorly phrased question is open to interpretation... $\endgroup$ – Floris May 7 '15 at 18:38
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Energy is never created nor destroyed, and to say "X is converted into energy" is just meaningless. We don't convert things distinct from energy into energy, all we ever do is convert one form of energy into another.

The badly posed question from your book probably intends to ask why we cannot convert the mass energy that any chunk of matter contains as per $E=mc^2$ into other forms of energy without needing antimatter.

The answer is that we would have to carry out a process at the end of which massless particles are produced, so that there is no (or at least less) mass energy left. Massless particles means photons, basically, and to get a photon from an electron you need to supply a positron - the conservation laws for charge, spin, and so on mean that you need something that cancels all the conserved quantities of the electron exactly out (since a photon is neutral with respect to most conservation laws).

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  • $\begingroup$ Thank you I think I understand now. I have a related question: Would all the photons created at the end be gamma photons? (Sorry if this is a bad posed question) $\endgroup$ – user45220 May 7 '15 at 18:34
  • $\begingroup$ @user45220 - "gamma" photon is a term sometimes used to describe a photon that was created as a direct result of a nuclear interaction. They are not actually in any way distinguishable from "any other" photon. In fact, when we talk about annihilation of a positron and electron, people tend to say the resulting 511 keV photons are not gamma rays, but just "annihilation photons". $\endgroup$ – Floris May 7 '15 at 18:51
  • $\begingroup$ @Floris: Thanks! Regarding the last part, would it still be correct to call them gamma rays? $\endgroup$ – user45220 May 7 '15 at 18:54
  • $\begingroup$ If the definition of "gamma ray" is penetrating electromagnetic radiation of a kind arising from the radioactive decay of atomic nuclei (Google), then no - because annihilation is not the same thing as radioactive decay of a nucleus. But if you take the 3rd definition at dictionary.reference.com, "electromagnetic radiation with wavelengths shorter than approximately one tenth of a nanometer." the answer is "yes". $\endgroup$ – Floris May 7 '15 at 18:55
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When a radioactive element decays, part of its mass is converted to energy - no obvious need for antimatter anywhere. Instead, the energy is released because the binding energy of the sum of the fragments might be higher than that of the parent nucleus.

However, to fully convert matter to energy you do need the antiparticle. Otherwise, you run into conservation laws that tell you that the baryon number can't change, for example. Similarly, if you started with a charged particle you could not get rid of its mass without also getting rid of its charge.

I will let the particle physicists on this site chime in and give a more authoritative answer now...

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Explain why the mass of a tree cannot be converted directly into energy.

That's a tricky one, because it could turn out that it is possible to turn matter alone into energy. Floris hinted at this with radioactive decay, but there are potentially other methods such as melting hadrons in a quark-gluon plasma (QGP), see for example this report. The interesting thing about that, is that the quark-gluon plasma is something like pea soup. And there aren't any peas in pea soup. See Wikipedia where you can read that the gluons in ordinary hadrons are virtual. There aren't any real gluons in a QGP. It's arguably the same for the quarks. Only then it gets squiffy, because the QGP is allegedly a perfect superfluid akin to a BEC, which features the rather enigmatic Bosenova. Poof! Gone! This might turn out to be a "cheat" which tramples all over the conservation laws. Another possible cheat involves dropping your tree into a black hole, wherein Friedwardt Winterberg's firewall means it turns into a gamma-ray burst. This may involve orthogonal photons and/or neutrinos, but I can't give any references on that. All in all, yes there are laws, but laws do get broken. Where there's a will there's a way, and scientific progress rewrites the law.

Do you always need matter and antimatter to create energy, or can energy be created from matter alone?

Like ACuriousMind said, energy is neither created nor destroyed. That's the law. I know of no way to break this the law of conservation of energy. It's just about the most important law there is. But as to whether the Big Bang was illegal, I just don't know.

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