

Comparing Ease of Conversion: Mass and Energy
Name: Yasine
Status: student
Grade: 912
Country: United Kingdom
Date: Fall 2012
Question:
Hi there,
At the moment we are learning about particle physics in school: fundamental particles, particle accelerators and some of the maths that go with it all. But what I want to ask is specifically about the famous equation E=mc^2, and about the fact that mass is simply a manifestation of energy. Matter IS, in a way energy, and can be created and destroyed. And matter is being created or converted into energy all the time right? The Sun undergoes nuclear fusion which converts mass to energy, and nuclear power plants use fission which does the same, mass to energy.
But the BIG question I have tried to ask, and have received a variety of responses from teachers is this simple one: Is matter easier to convert into energy, or is energy easier to convert into matter? What I am trying to say is: is mass 'more stable' than maybe kinetic energy for example? Does my question even mean anything? When you think of the equation E=mc^2 you think more of how mass > energy rather than the other way round because it seems to me to happen to a bigger degree in nature and in our lives... and if mass is 'more ordered' than 'energy' and entropy is increasing all the time according to the second law of thermodynamics, then it makes sense that the "ordered" mass is becoming "more disordered" when it turns to energy. But conversely, if that is indeed the case, and the universe started from a singularity of energy which induced the big bang, why did the big bang create mass after all?? Would not there have been a massive decrease in entropy with the begging of the universe when so much matter was created?
Replies:
So far it looks like the conversion of energy to mass is far more difficult. That definitely has to do with entropy.
Hope this helps.
Bob Avakian
Oklahoma
You are making the problem more subtle and difficult than is necessary. Look at the coefficient in the equation: E = mc^2. It is (c^2). That is a BIG number, so a SMALL amount of mass converts into a LARGE amount of energy. That is why atomic and hydrogen weapons are so powerful. It only takes a small amount of mass loss to produce a large amount of energy.
You have made the problem way too complicated by invoking entropy effects. A ?backortheenvelope? calculation shows that entropy effects are way too small compared to the energy effects. In addition, your exposure to entropy is limited. You have been taught and/or read that entropy is a measure of ?order? / ?disorder?. A correct explanation is much more subtle. The correct definition of entropy, S, is: S = k x ln[n] where k is Boltzmann?s constant, and [n] is the number (that is, density) of quantum mechanical states (the is, wave functions) consistent with the energy of the system. If that sounds obscure, that is because it is!! In any case it is small compared to the energy changes in this case.
Another place where you have to be careful is ?explaining? mechanisms that occur under the conditions of the formation of the Universe with our ?low density? of matter in our ?Universe?. The conditions of the ?Big Bang? are so different than anything we experience, extrapolating back in time to the beginning? is a treacherous path, fraught with possibilities of errors in the analysis.
Vince Calder
Hi Yasine,
Thanks for the question. Yes, matter and energy are inter convertible. One can convert energy (specifically kinetic energy) into matter by colliding two particles together. The actual experimental details of how this occurs are very complicated.
Jeff Grell
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