In October of 1927, Born, Dirac, Heisenberg, Pauli, and Bohr came together and expounded as well as accepted "an" interpretation of the new quantum world that was reeling in the aftermath of Schrodinger's Wave Collapse experiments. They called it the Copenhagen Interpretation.
With the collapse of the wave wherein the countless possibilities and probabilities could be brought into physical reality, a Finite world was seen to be born out of Infinity! The foundational question was, therefore, posed to the scientists — how could Infinity give rise to the Finite? A question that was hitherto the headache of only the mystics.
Interpretations of the Quantum
The world of possibilities that were available to the particle, collapsed with its measurement, bringing down the calculated abstractions to a hard stop reality! How was the particle capable of being a wave and the particle at different point of its journey?
In Bohr's words, the wave and particle pictures, or the visual and causal representations, are "complementary" to each other. That is, they are mutually exclusive, yet jointly essential for a complete description of quantum events. Obviously in an experiment in the everyday world an object cannot be both a wave and a particle at the same time; it must be either one or the other, depending upon the situation. In later refinements of this interpretation the wave function of the unobserved object is a mixture of both the wave and particle pictures until the experimenter chooses what to observe in a given experiment.
By choosing either the wave or the particle picture, the experimenter disturbs untouched nature. Such favoritism unleashes a limitation in what one can learn about nature "as it really is." This limitation is expressed by Heisenberg's uncertainty relations, which, for Bohr, were related to what he was now calling "complementarity." Complementarity, uncertainty, and the statistical interpretation of Schrödinger's wave function were all related. Together they formed a logical interpretation of the physical meaning of quantum mechanics known as the "Copenhagen interpretation."
Now, the observer was not merely a witness — but creator of the reality as well. There were a few other interpretations of the Quantum Mechanics world, the next most prominent being the "Many-worlds Interpretation":
The Many-Worlds Interpretation (MWI) is an approach to quantum mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds which exist in parallel at the same space and time. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics.
Einstein came up with his interpretation — the "Hidden Variables" — since his God did not throw dice - basically saying that some hidden variables explain the probabilities of the wave function and determine "a" unique possibility so that it was not as indeterminate as the Copenhagen gang made it out to be. His hidden variables were never to be found however.