I always hear about matter converting to 'energy' - fusion, fission.

When does it go the other way around? What conditions lead to it? Are there reproducible experiments on this topic?

  • $\begingroup$ I was going to write an answer about how endothermic nuclear reactions (in which energy turns into matter) are common in both fusion and fission reactors. But other people beat me to the punch. Suffice it to say they are, although they can't be the majority in a net-power reactor, obviously. $\endgroup$ – Alan Rominger Nov 10 '11 at 5:01

It is annoying to talk about mass-energy conversion, because it is too often misinterpreted to mean that energy doesn't weigh on a scale before it "turns into matter". So I will preface the answer by saying that if you heat up a gas, the heat weighs on a scale, if you burn some paper and let the heat escape, the escaping heat makes the combustion products weigh less than if they stayed hot, and if you seal up a nuclear bomb, let it explode, and keep all the products and heat inside the box, the box has the same total mass before and after the explosion.

The conversion of energy, kinetic or electromagnetic, to particles with rest mass is experimentally observed only when the energy comes in big enough clumps to create a massive particle, when the energy is low, this is going to be the lightest charged particle, the electron. Electrons can only be created along with a positively charged particle, to conserve charge, and this is almost always a positron (in rare weak interactions you can make an electron, a proton, an antineutron and an electron-antineutrino). The production of electron positron pairs only happens for very hard X-rays, or particles moving with a comparable kinetic energy, and you don't have this much energy in a single particle even in an atomic explosion. You need to accelerate particles specially.

Because of this gap between the energy of particles and the energy of the lightest charged particle, you don't usually see conversion of energy to mass in day-to-day life.

  • $\begingroup$ I would like to add here that specifically the e+e- colliders create out of energetic electrons Psis, if the invariant mass (IM) of the electrons is at the mass of Psi and a lot of other mesons, Z bosons if the their IM is on the Z . see page five in pdg.lbl.gov/2013/reviews/rpp2013-rev-cross-section-plots.pdf . $\endgroup$ – anna v Apr 14 '14 at 14:04

All the particle accelerator in the world are continuously (when they are operating) converting kinetic energy into matter. For example, when two protons collide at the LHC the kinetic energy of the protons is converted in to tens to hundreds of particles (matter) which the experimenters then try to characterize with their detectors. Most of these particles are very short-lived and either decay into multiple less massive particles or they may interact with the detector material and create even more particles. However there will always be a significant number of electrons, protons, positrons and antiprotons (that are all stable) as the eventual result of the collision. The positrons and antiprotons will eventually annihilate with electrons and protons but in principle if they could be kept separate from ordinary matter they would all last forever. So the original two protons can create multiple protons and electrons (and their antiparticles) and this additional matter is made from the kinetic energy of the original protons.

High energy cosmic rays that strike the earth from outer space do the same thing - the kinetic energy of the cosmic ray will be converted into additional electrons, protons and their antiparticles.

On a much smaller scale, any chemical reaction that requires energy to run will convert the energy required by the reaction into a very slight additional mass. For example, photosynthesis which takes $$6\space CO_2 + 6\space H_2O + \text{sunlight} \rightarrow C_6H_{12}O_6 + 6\space O_2$$ will convert the energy of the sunlight into a very very slight additional total mass of the product chemicals when compared to the total mass of reactant chemicals. There was a question on this topic recently but I cannot find it right now.

  • $\begingroup$ I wouldn't call pair production as an example of matter/mass creation from energy, because its only temporal. The pairs will disintegrate soon after, no additional particles remain. There is some asymmetry in disintegration, which is blamed for the creation (shortly after BB) of the mass we see in universe, but was that asymmetry ever seen in experiments? $\endgroup$ – Georg Nov 10 '11 at 11:33

A photon is emitted when an electron jumps from a higher energy state to a lower energy state in an atom.


In a process called pair production, a photon can turn into an electron and a positron.


These processes have been understood for about 50-100 years and are perfectly reproducible and measurable in a physics laboratory.


Depends on what you refer to as energy. I presume you are speaking about radiation. The standard model is made out of fermions and bosons and all energy is distributed among them (ignoring dark energy in the universe or dark matter) at it already includes special relativity (including the realtion $E=mc^2$). So within such framework there are allowed processes, technically speaking, that produce fermions out of photons see Breit-Wheeler process.


If there was no sunlight keeping photosyntesis and the rest of the biosphere going in a state of matter carried by a flow of energy, biomass would not exist. As the earth absorbs solar energy in the troposphere it flows through matter continously towars the final destination in vacuum of space. Biomass is continously created from solar energy by all lifeforms on the surface, and all that biomass would not exist without solar energy being transformed to mass in realtime by an inflow of energy at the speed of light multiplied with an outflow at the same speed. So, a lifeform is mass sustained by continous transformation of energy into mass and an equal transformation into energy. The mass itself must contain an equal amount of energy stored as the amount flowing through it, to keep it´s form.

The same is true for all matter on earth that has a temperature, solar energy flows through all matter at constant speed and density, as long as irradiation doesn´t change. Maybe someone has the motivation to calculate what mass earth would have if we turned off the sun. Subtracting 1.4kW/m^2 worth of energy flowing into half the surface area of earth, from the energy present in mass as it is heated by the sun, must reduce mass alot.

Energy is transformed into mass at the speed of light wherever there is a particle heated by radiation, similar to a standing wave shaped to a form containing the same amount of energy as what is coming in, otherwise it could not conserve energy as it is going out.

It helps if one accepts that there is no difference between energy and matter other than it´s geometrical distribution in space, energy being one dimensional and matter exists in continous expansion into dimensions relating to surrounding space and matter.

It also helps to accept that energy as matter has to have the speed of light squared, to exist in spacetime. Without the increase in energy coming from mass travelling at a speed much higher than light, there is no need for expansion from zero dimensions of static energy E, into spacetime as the geometric form we call mass. Energy interacting with spacetime expands into spacetime when energy exceeds what can be contained in the size of a lightquanta. Expansion in all directions cause the speed to increase to c^2 in relation the speed in one dimension, mass extend into three dimensions compared to the photon acting more like a point of energy.

By it´s geometry mass is energy flowing at the squared speed of light in all directions relative to the photons single direction in one dimension.

To transform matter into energy, a nuclear reactor is a good example of how to use collisions to slow the speed of matter, extracting energy in the same way as a car crash into a massive wall. The opposing force must change acceleration to a level where the geometry collapses releasing it´s content or some part of it.

The resistance from energy expanding in spacetime is an opposing force balancing the potential to zero shaped as wells of potential energy storage. Expansion is ongoing but deflation is equal. Only an increasing intensity of the source can expand further, with less expansion per unit energy as volume increase.

Matter is explained easy as just a container of energy, a shape created by local expansion in spacetime sustained by equal energy inside the shape as the amount flowing in, and flowing out into space.

E=mc^2 is very clear about matter being a form of energy accelerated into a higher state. If taken literally, it explains how the energy in matter that is obviosly very large, is unavailable for extraction under normal circumstances. If we travel at the same speed as mass with energy, being mass with energy ourselves, side by side, there is no way to make use of the energy in matter because the energy is shared between all matter travelling together.

Deceleration to extract energy from matter is more intuitive as a description of transformation into energy. We are familiar with the concept of kinetic energy extracted from potential energy difference in relative motion.


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