What is a ghost? It is a memory without a body, a memory made of nothing. In our universe, living matter forms a memory. Dead matter doesn't do anything. A rock, for example, only moves when the wind moves it, rolls when water pressures it.
There is no such thing as living matter and dead matter. There is only matter.
There are living systems; there is no living 'matter.' No substance, no single molecule, extracted and isolated from a living being possess, of its own, the aforementioned paradoxical properties. They are present in living systems only; that is to say, nowhere below the level of the cell.
Because the expression "living matter" borders on vitalism, on mysticism, it can lead only to bad thinking. If the history of science has taught us anything, it is this: Nothing is too wonderful to be true.