Doesn't $E=mc^2$ mean that mass can be converted to energy? But from what I have studied in high school nuclear physics, it seems that the only "$E=mc^2$" we can get is from binding energy between nucleons. This may sound really stupid but is it possible to actually convert matter into energy using a machine on earth? Like get 1 kilogram of dirt and convert it to $c^2$ joules? What would it take to make this happen?

  • $\begingroup$ There are some conservation rules, which should be respected. Assuming they are preserved, we can transform matter(read fermions such as electrons, protons, positrons, etc) to energy(read photons). $\endgroup$ – Ali Jul 14 '13 at 11:07
  • $\begingroup$ Related: physics.stackexchange.com/q/47417/2451 and links therein. $\endgroup$ – Qmechanic Sep 6 '14 at 6:46

Like get 1 kilogram of dirt and convert it to c2 joules? What would it take to make this happen?

To make something close to this happen you would need one kilogram of antimatter dirt. Then all the quantum number additions would be satisfied and a lot of radiation would come out, but not completely into kinetic or useful radiative energy. You will get pairs of weakly interacting neutrinos antineutrinos, and pairs of electrons and positrons that will have to meet each other to become pairs of photons.

The resources you would have to spend to create 1 kilogram of antidirt would make the whole process economically unfeasible, considering that we have only managed to make a bit of antihydrogen up to now.

  • $\begingroup$ Thank you. This pretty much answers my question :) Is there a way around the economical difficulties though? Will there be any way around it ever in the future? $\endgroup$ – please delete me Jul 14 '13 at 13:19
  • $\begingroup$ I do not think so. To create antimatter takes a lot of energy, even as individual antiprotons. To get the complexity of matter atoms molecules etc into antimatter is impossible with the tecnology we have. Fortunately there is no antimatter in our planetary and solar neighborhood so one cannot find it in nature either. Consider that an Abomb releases a tiny percent of the mass it contains and is extremely destructive. Multiply its effects by 100 and you see why I say fortunately no antimatter meteors in our neighborhood $\endgroup$ – anna v Jul 14 '13 at 13:44
  • $\begingroup$ But we can use that energy for useful purposes like colonising our solar system, strengthening the human race and then move on to colonising the galaxy and create a powerful human civilisation. i'm just dreaming hehe $\endgroup$ – please delete me Jul 14 '13 at 13:51
  • $\begingroup$ For the record, wouldn't you get $2 m c^2$ of energy from antimatter dirt? I acknowledge your points on the unrecoverable energy, such as neutrinos. That would make the recoverable energy lower, but to a coefficient possibly higher than 1. $\endgroup$ – Alan Rominger Jul 14 '13 at 16:16
  • $\begingroup$ @AlanSE Yes, if m is the mass of dirt/antidirt . The available energy is the total mass added, but it would depend how you would define the coefficient. $\endgroup$ – anna v Jul 14 '13 at 17:28

The laws of physics that makes it difficult to convert dirt into pure energy are the conservation of lepton and baryon number. Each proton or neutron has a baryon number of one and a lepton number of zero, while electrons have a lepton number of one and a baryon number of zero. To reduce matter to pure energy such as electromagnetic radiation you need to cancel out the baryon and lepton numbers using matter with negative numbers such as antiprotons and positrons, but these are not easily obtained naturally (there are samll amounts in cosmic rays but not enough) and to create them artificially you need to put more energy in than you will get back out.

The only way you can get round this is by finding a way to violate lepton and baryon number conversion to convert atoms to pure energy. According to some theories this happen naturally but only on ridiculously long timescales. There is only one method that stands any chance of being practical. That is to use a small black hole.

When matter falls into a black hole you lose track of its baryon and lepton numbers. This is a consequence of the no hair theorems which say that the only observable characteristics of a black hole are their mass, angular momentum and charge. This is a theoretical law not verified by experiment but let's assume that it is true. In that case if you had a black hole it would radiate Hawking radiation at a rate you could use to power a powerstation. Again this is pure theory but let's assume it is correct. You could then throw in dirt at the rate needed to balance the outgoing radiation and you would have a continuous powerplant fueled by dirt.

The rate that a black hole radiates Hawking radiation is given by the formula

$P = \frac{K_{ev}}{M^2}$


$K_{ev} = 3.562 \times 10^{32} W.Kg^2$

So if you wanted a powerstation of 1 GigaWatts you need a mass of 600 million tons, e.g. an asteroid about a kilometer across would be perfect.

Of course the hardest problem is to turn the asteroid into a black hole. Perhaps this is possible in some incredibly violent astrophysical event that we dont know about. Once you have your black hole all you need to do is feed in the dirt and use the radiation to generate usable power. Feeding matter in would also be difficult because you have to overcome the pressure of the outgoing radiation. This might be possible using many linear accelerators to form beams of protons and electrons but the size of the blackhole itself is as small as a nucleus making the task very difficult indeed.

A compromise would be to use a bigger black hole with a larger radius but then the power output is much less. In conclusion this is really just a theoretical possibility that would be virtually impossible to achieve in practice.


Yes of course, and this machine is called particle accelerator. We can convert mass to energy or energy to mass. Moreover, this conversion of matter to energy is what produce energy in nuclear reactors.

  • $\begingroup$ But particle accelerators are too inefficient :( $\endgroup$ – please delete me Jul 14 '13 at 11:19
  • $\begingroup$ @user2357 The goal of particle accelerators is to study particles not to produce large quantities and the goal of nuclear reactor is to produce energy and then they convert it to electricity. $\endgroup$ – user5402 Jul 14 '13 at 11:22
  • $\begingroup$ Is it physically possible in the future for reactors to convert 100% of fuel into energy without producing byproducts? $\endgroup$ – please delete me Jul 14 '13 at 11:30
  • 1
    $\begingroup$ Goodness gracious. Energy comes in the form of particles. There is no such thing as "pure" energy which is distinct from matter. Mass is one form of energy. Particles can also have a great deal of energy due to motion ("kinetic energy"), but something has to do the moving. You don't convert whatever to energy without "byproducts". The byproducts are the energy. Whether the energy comes out in a form that is practically useful is different question - an engineering question. $\endgroup$ – Michael Brown Jul 14 '13 at 12:03
  • 2
    $\begingroup$ Just want to make sure the OP has some idea about this. A great deal of popular lit. and tv shows a very confusing on this point, if not downright wrong. Anyway, what @user2357 wants is total matter-antimatter annihilation. This converts 100% of the rest mass into various forms which may or may not be useable (depending). But to get any antimatter you have to make it yourself, which costs exactly as much energy as you eventually get out. So it is more an energy storage/transportation idea than a production idea per se. Nuclear reactions are probably the best you can do on Earth. $\endgroup$ – Michael Brown Jul 14 '13 at 12:18

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.