Although metaphysics and quantum physics deal with the scholarly examination of the surrounding world, the two approach the subject from two different disciplines, namely philosophy for metaphysics and hard science for quantum physics.
Origin of Metaphysics
The term “metaphysics” (“meta-” meaning “beyond”) refers to the title given to a compilation of Aristotle’s works on the subject. Because they follow Aristotle’s “Physics,” the work took the name “Metaphysics.”
Origin of Quantum Physics
The beginning of quantum physics is far more recent, with major contributions being Max Planck's 1900s proposal that energy is made up of smaller units called quanta and Albert Einstein’s 1905 study of the photoelectric effect.
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Metaphysics in Philosophy
Metaphysics is the philosophical study of the notion of existence as well as concepts such as space, time, free will and the individual.
Quantum physics, on the other hand, is the study of quanta -- small units that make up energy. These quanta are problematic because they are unpredictable in behavior and movement as they have qualities akin to both particles and waves.
The Two Approaches
The importance of metaphysics is that it is the basis for all ensuing philosophy. Quantum physics, however, is a way of attempting to scientifically understand how the universe works by studying its smallest parts.