Contrary to what most people learned in high school physics, conversion between mass and energy IS possible, albeit in strictly limited circumstances.
If one asked a 19th century physicist about conversion between mass and energy, that physicists' response would without hesitation be to scoff and say, "Mass-energy conversion-no such thing!" Given the state of the evidence until the early 20th century, this view would be perfectly correct. In all physical phenomena observed to that point, mass and energy were completely separate quantities without any apparent relationship between the two. Whenever Newtonian physics applies, meaning either at speeds much less than that of light or when the gravitational field is relatively weak, mass and energy ARE completely separate quantities.
The state of the evidence started to change when technologies developed which allowed physicists to view the sub-atomic world. For example, a neutron will sometimes decay radioactively into a proton, an electron and an anti-neutrino, but although the total mass or total energy of a proton, electron and anti-neutrino is almost the same as the mass of the original neutron, it is not quite the same. The difference can be accounted for exactly if one uses Einstein's famous equation E=mc^2 as follows: the increase in energy, i.e., E,- usually associated with the anti-neutrino- is exactly equivalent to the decrease in mass, i.e., m, times a proportionality constant c^2 which is the speed of light in vacuum c times itself. Therefore, the total of a combined quantity mass-energy is conserved, i.e., remains constant, when a neutron decays but mass and energy separately is not conserved. For many people, this is one of the hardest concepts from 20th century science to grasp because something most people were taught in high school as a fundamental principle is not quite correct.
The question that then immediately presents itself is: WHEN can mass and energy not be treated separately? Decay of a neutron does not at first glance appear to involve relativity but in fact it does because the electron is emitted at a speed nearly that of light. [The anti-neutrino is massless and so travels exactly at the speed of light as well.] Yet, the equation E=mc^2 is not always about ACTUAL conversion of mass to energy or vice-versa; this is one of the consequences of general relativity. For example, Newton's law of gravitation does not correctly predict the orbit of the planet Mercury, but general relativity- an improved theory of gravity- does because it includes a small correction to the effective mass of the sun due to the sun's energy. Namely, the orbit of Mercury is only correctly predicted when one calculates that orbit treating the effective mass of the sun as the sun's actual mass plus an amount equal to the sun's energy divided by a factor c^2. Because division by the factor c^2 makes the correction to the actual mass relatively small, of all the planets in the solar system, the correction term only really matters when calculating the orbit of the planet Mercury because that planet is so close to the sun. For all the other planets, such a correction makes no significant difference in the orbit calculated. The effect of the sun's gravitation field on Mercury is much stronger than on any other planet, too strong for a Newtonian description of gravity to yield the correct result in a calculation.
The deeper question is what physically the equation E=mc^2 and the phenomena it describes mean. If one can even in principle convert between mass and energy and both produce a gravitational field, as has been experimentally verified that they do, then the inescapable conclusion is that mass and energy are two forms of the same thing, termed mass-energy. The usual comparison is to ordinary water and ice, which are different forms of the same thing, although that analogy is rough at best. Yet, rough as the analogy may be, it serves to get across the idea; just as physicists once thought electricity and magnetism completely separate phenomena but now speak of electromagnetism, so also we used to think mass and energy entirely separate phenomena but now speak of mass-energy.