# Mass and energy, time and and space, the misconceptions

Quanta Magazine, a web service which often brings interesting articles, published shortly an interesting article where relativity, quantum physics and black holes played an important role. However, in reading it I did hit upon a very common misconception, about which I like to comment here.

Quote from: Einstein, Symmetry and the Future of Physics | Quanta Magazine

Solar energy arrives on Earth and becomes mass in the form of green leaves, creating food we can eat and use as fuel for thought.

The misconception is that mass and energy are different things and that energy is somehow mysteriously converted into mass and vice versa. However, that’s not the message of E=mc2. Energy and mass are, in the opinion of almost all physicists, more like the two sides of the same coin. They are identical. This can be understood by considering what happens when an object is accelerated up to the speed of light.

According to the special relativity, all the energy that you spend into that acceleration is converted into inertial mass. It will cost you more and more energy to keep accelerating it. That is why we can never reach the speed of light itself in this way, the inertial mass would become infinite. This effect has been convincingly demonstrated when accelerating protons in the Large Hadron Collider at CERN. The faster they go, the more mass they get and the stronger the magnetic fields must be to keep them neatly in their circulair loop.

In general relativity, the central basic assumption is that inertial mass and heavy mass are identical or that the acceleration force due to gravity is identical to the acceleration force that you encounter in, for example, a merry-go-round. The implication therefore is that inertial mass, heavy mass and energy are really all the same fundamental thing. This means for instance that a charged battery must also be slightly heavier than when discharged. However, the energy released by nuclear fusion is often explained in popular terms as follows:

The mass of the two fused atomic nuclei is smaller than that of the original fused nuclei together. That mass deficit has become energy and that mass is gone.

Thus it seems as if mass alone is not conserved, mass plus energy should be the conserved property. However, Wikipedia says otherwise: “Mass and energy can be seen as two names (and two measurement units) for the same underlying, conserved physical quantity. Thus, the laws of conservation of energy and conservation of (total) mass are equivalent and both hold true”.

Ponder this. The fused atomic nucleus has received an enormous amount of kinetic energy during the fusion, and that is speed. That kinetic energy is exactly having the same mass as the ‘disappeared’ mass. So, that mass has not disappeared at all. Due to the speed with which the fused core now moves, which means kinetic energy, it also has more mass. That is the message of special relativity. If you could have this fusion taking place in a thermally completely sealed box balanced on a pair of scales, you would find zero difference in weight – and therefore in mass.

Another but related topic. That every observer always observes the same speed of light is a physical observation but goes against our so-called common sense which tells us how adding up speeds normally works. Elsewhere on this website I say something about that in ‘What is light‘.
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