There are many different types of "transmutation" in the real world. The most general idea of transmutation is a chemical change or a change on the elemental level. This idea is basically all about chemistry the change of one type of energy to another type of energy...
However the idea of changing base metal into gold is a bit of a misnomer.
Nuclear Transmutation: In 1901 two scientists Frederik Soddy and Ernest Rutherford discovered that the element thorium was converting itself into radium. The two scientists realized they had discovered transmutation...however back in 1901 they would be persecuted and probably hung for their use of alchemy. Later in 1917 Ernest Rutherford was able to accomplish transmutation of nitrogen into oxygen, using alpha particles directed at nitrogen 14N + α → 17O + p
Later in the twentieth century the transmutation of elements within stars was elaborated, accounting for the relative abundance of elements in the universe...they called this idea nucleosynthesis.
Nucleosynthesis is a scientific term used to describe the idea that during the first moments of the universe there was just a collection of tiny particles and they combined into the lighter elements....it seems however that humans cannot trigger this change without vast amounts of energy, currently this sort of change only occurs with the use of a particle accelerator or a nuclear reactor. So if this can be done without machinery where does the energy come from?
I digress....there is evidence of transmutation...it is a natural occurrence in the real world...but what triggers the change to occur?
|Magic Circle Called "Grace"|
|Reverse Transmutation Circle or Counter Circle|
|Another Sort of Magic Circle|