# Converting energy to matter

According to Einstein, energy and matter are equivalent; E=mc[sup]2[/sup]. And matter has been converted to energy in nuclear reactors and bombs.

But I never heard of anyone trying the conversion in reverse - turning energy into matter. Has this been done, even if only to prove the point?

It happens all the time, spontaneously. A photon will sometimes turn into an electron-positron pair, for no particular reason.

Unless I’m mistaken particle accelerators - such as the soon to be activated LHC - do this in a fashion. Small particles are accelerated to nearly the speed of light, then collide, resulting in a spray of daughter particles which mass more than the original particles. Energy imparted by the accelerator coils gets turned into mass.

Also, I’m probably wrong, but don’t chemical reactions involve converting tiny amounts of energy into matter? I’m thinking of photosynthesis specifically.

Would you count the formation of chemical bonds to be converting energy to matter?

Strictly speaking, mass is one kind of energy, but mass is itself also conserved. You can, for instance, turn two photons travelling towards each other into an electron and a positron, and there’s certainly mass after that interaction, but there’s also mass before the interaction, in the two photons. Even though a single photon doesn’t have mass, a system of multiple photons can and usually does have mass.

Could somebody elaborate on this? Thanks.

Let’s see what I can do. First of all, the energy of a system depends on the frame of reference you’re measuring it in. For instance, if I’m in an airplane, and the flight attendant walks down the aisle next to me, I would measure a fairly small kinetic energy for em (perhaps 50 Joules or so, since the attendant probably masses about 50 kg, and is travelling at perhaps 1 meter per second relative to me). But if I’m standing on the ground and measure that same flight attendant, I’ll use a speed relative to me of several hundred meters per second, and therefore measure a much higher speed for that flight attendant. All the other forms of energy the flight attendant has don’t depend on frame of reference, so the total energy of the flight attendent is greater in the ground reference frame than in the airplane reference frame.

However, most systems will have some minimum amount of energy, such that, no matter what frame of reference you’re using, you’ll never measure less than that amount of energy. If you’re in a frame such that the system you’re looking at has no net momentum, this is the amount of energy you’ll measure. If, for instance, I’m sitting on the beverage cart, then relative to me, the flight attendent isn’t moving, so I won’t measure any kinetic energy. The only energy I’ll measure is from things like the binding energies of subatomic particles (which, incidentally, is far greater than the kinetic energy, for most objects you’ll encounter). It’s this minimum amount of energy, that you never lose no matter what reference frame you go to, that’s referred to as the mass of the system.

Now, not everything has a mass. If a photon is zipping past me, I’ll measure some energy for it, but if I start moving in the same direction as the photon, I’ll measure a lower energy. The faster I go in that direction, the lower the energy I’ll measure for the photon, and if I can go fast enough, I can make the photon’s energy as low as I want. Since a photon has no minimum energy, we say that an individual photon is massless.

However, suppose I have a system of two photons, going in different directions. I can move in the same direction as one photon, and that photon’s energy will then be less, but when I do that, I’ll also find that the other photon’s energy is greater than it was. I can’t make the total energy go arbitrarily low, since there will always be at least a certain amount of energy in one photon or the other. This system now does have a reference frame where the energy is as low as it can possibly be, and that amount of energy is the mass of the system.

Thanks Chronos. You are a good, patient explainer of things.

This seems to be a good place to ask this. I teach HS chemistry, and I was talking to my physics grad brother about the binding energy in molecules. I seem to remember a professor saying that all energy release was essentially extremely small amounts of mass being converted. (I know that something falling isn’t converting mass; I’m talking about the energy to get the thing up high in the first place.)

I have a disconnect with this idea, though, as some things seem to contradict it. If it’s binding energy you’re using to keep the atoms together, then isn’t that what you’re releasing in an exothermic reaction? And how is it that two protons together in a He nucleus are less energetic than the protons being separate? I thought there was binding energy there too, and how can that be lower than the 0 binding energy a bare proton would have?

I doan gettit.

First of all, binding energy is a negative (potential) energy; that is to say, the binding energy of a system is the quantity required to separate the components so that they no longer influence one another. In the case of electron binding energies found in electrochemical bonds, the binding energy is the energy required to break chemical bonds; once the bond is broken, the resultant electrons or ions shoot away with an equivalent kinetic energy with the balance as photons radiated. The total mass of the system doesn’t actually change; while their might be a tiny “mass deficit” in the original components due to the energy in the “massless” photon, this is mere bookkeeping. Once the photon interacts with (absorbed by) another electron the mass of the overall system is returned, hence why photons are considered “force carriers”. The invariant masses of the nucleons and electrons do not change because the particles themselves are unchanged.

A similar scenario exists with nuclear forces, with the residual strong force standing in for electromagnetic forces in chemical bonds. The binding energy that must be exceeded is then returned as kinetic energy of mass particles and the frequency of energetic massless particles. There is again a mass deficit based on the binding energy; however, it is also possible for composite particles to decay with resulting products of particles of different masses plus the equivalent amount of energy per Einstein’s famous equivalence. This isn’t just “binding energy” between nucleons but an actual change in the composition of nucleons. In beta decay, for instance (which occurs as a result of D-T fusion), a proton is converted into a neutron (which sticks to the nucleus) plus an electron and an antineutrino, which shoot away with additional kinetic energy. The overall invariant mass of the system is actually changed because of the identity conversion of the particle, so we can say that there is really a mass-energy conversion that is occurring. This can be reversed in other situations, for instance in electron capture (typically the result of some other nucleic decay event). So to answer the o.p., yes, energy can be bound back into mass, and not just in the ephemeral manner of creating a particle and it’s anti-particle.

Ultimately, mass is just a type of energy that is bound up into particles and acts in such a way to distort spacetime. This is obvious even to our primitive senses, although it took a series of spectacularly clever people to describe the relationship mathematically. Why does mass-energy have this property? Nobody really knows, although a lot of smart people have and continue to front theories that sound like complete gibberish to explain it in ways that segue with the Standard Model of particle physics.

Stranger