Is there a correct interpretation of quantum mechanics? The short answer is 'No'. Perhaps a better answer is 'Not Yet', but actually it is not clear at this point that there can be a single 'correct' interpretation of quantum mechanics. The most important notion is that there is nothing 'magic' about quantum mechanics - it is simply a description of how our universe works. Probably incomplete, probably blind to some possibilities, but those who treat it as license to justify any existential notion they might bring in from philosophical grounds are sadly mistaken. We invent quantum mechanics to explain reality - but reality is the ultimate touchstone.
Here is a sampling of opinions of outstanding scientists past and present:
"The more success the quantum theory has the sillier it looks." Albert Einstein, 1921 Nobel Prize for Physics
"Anyone who is not shocked by quantum mechanics cannot possibly have understood it." Niels Bohr, 1922 Nobel Prize for Physics
"I think I can safely say that nobody understands quantum mechanics. 'But how can it be like that?' Nobody knows how it can be like that." Richard Feynman, 1965 Nobel Prize for Physics
"I never met an interpretation of quantum mechanics that I didn't dislike." N. David Mermin, Horace White Professor of Physics Emeritus, Cornell University
These are not simple concepts. Even if quantum mechanics descirbes reality, it is not clear why it does. This is perhaps the most significant question in natural philosophy today - not that the theory works, but why?
But let's go back a step. Why does quantum mechanics need an interpretation? After all, if we "shut up and calculate" (advice given to most graduate students of quantum mechanics), the result of our calculations is shockingly accurate when compared to experimental data. Why do we need anything in addition to the mathematical formalism?
To most physicists, simply being able to make predictions about events in the Universe does not mean that one understands those events. Traditionally, physics (or earlier, natural philosophy) has been more concerned with why events occur rather than what happens. (Creating a comforting myth which does not accurately describe what happens is not the practice of physics.) Stories about why quantum mechanical events occur are inextricably tied up with one's interpretation of quantum mechanics.
Classical physics is remarkably successful at predicting the behavior of macroscopic bodies, such as billiard balls on a pool table. The equations describe the paths taken by objects as they interact with each other - a picture very similar to how our senses perceive classical objects moving through our three-dimensional space. As the picture of reality suggested by classical physics is largely compatible with our common sense about how the world works, there is little need for specialized interpretation. Although when such interpretation is seriously undertaken by philosophers and physicists, the result is a remarkably deep understanding of a rather successful model of the universe.
Quantum mechanics, however, is a different story. It was discovered during attempts to explain how atoms can be stable, why atoms only radiate certain colors of light, why the photoelectric effect occurs, and many other phenomena which could not be understood or described within the rules of classical physics. Debate and conjecture among at least half a dozen major physicists over a period of 25 years led in the mid-1920s to a version of quantum mechanics which is exquisitely accurate - it has never made a prediction in conflict with experiment.
Unfortunately, the mathematical structure of quantum mechanics is couched in the language and concepts of the theory of linear operators in Hilbert space. As a result, it does not have an intuitively satisfying correspondence with our everyday view of reality. Physicists have long sought some interpretation of quantum mechanics which satisfies the desire to understand why it works so well. We need words and images that assign meaning to the mathematics. Sadly, intense efforts of the physics and philosophical communities over the past 80 years have not shown any real sign of converging on a generally accepted interpretation.
The most widely held interpretation of quantum mechanics is also the original, developed as a nearly mature child in 1927. Called the Copenhagen interpretation, it is mainly the product of debates between two remarkable minds, Niels Bohr and Werner Heisenberg, both of whom were separately awarded the Nobel Prize for Physics for their work in the development of quantum mechanics.
The Copenhagen interpretation requires that an additional postulate be added to the basic formalism of quantum mechanics. Before a measurement is carried out on a quantum system, the quantum mechanical model for the measurement simultaneously describes and assigns probabilities to all possible outcomes of the measurement. This is called a superposition of states.
The Copenhagen postulate requires that after the measurement, the quantum mechanical description of the system collapses so that it reflects only one version of reality - that giving the measured result. This must be added as a postulate because the collapse process fundamentally cannot be described using the mathematical structure of quantum mechanics - it is not a unitary process. Note that adding this postulate does not change any of the predictions of quantum mechanics. In a sense, it appears only to be a self-consistency condition. But what happened to the other potential results, which were a part of quantum mechanical reality prior to the measurement?
Among the more compelling examples of the oddness of quantum superpositions is the case of Schrodinger's cat. Briefly, a cat is put into a box also containing a bottle of poison gas, a radioactive material, and a radiation detector which, when radiation from the radioactive material is detected, triggers a hammer to fall and smash the bottle, an event followed shortly by the death of the cat. Before we look into the box and determine what actually happened, the quantum mechanical description of the system considers both outcomes (cat is dead, cat is alive) as having equal and superimposed levels of reality. That is, the cat is predicted to be both alive and dead until we complete the experiment by opening the box and examining the cat. This seemingly absurd viewpoint is required for quantum mechanics to work.
Intuitively, should this rather grisly experiment be carried out, we expect that the experimentalist will not experience two conflicting realities. Rather, either a dead cat or a live cat will be found, but not both. But until a quantum mechanical experimentalist opens the box, the theory suggests that they exist in a superposition of quantum states (cat is dead, cat is alive), even if the hammer has fallen and the cat is already dead.
As we do not experience living in such superpositions of states, this does not seem a reasonable option. The problem can be avoided if experimentalists are classical systems, which do not experience superimposed states. However, as quantum mechanics produces essentially perfect physical predictions, it seems inconceivable that it does not apply to an experimentalist! We are faced with two unacceptable positions - either we live in quantum superpositions without knowing it, or people are classical systems. Or the Copenhagen interpretation is not acceptable. Although most physicists simply ignore these problems, it is not surprising that the Copenhagen interpretation is not seen as 'correct' by most physicists, no matter how useful a metaphor it provides for thinking about quantum mechanics.
The unsettling features of the Copenhagen interpretation have led physicists and philosophers to develop a large number of alternate interpretations. While the details of these alternate interpretations lie outside the scope of this article, some of the more widely known versions include the statistical or ensemble interpretation, the Everitt-Wheeler many-worlds interpretation, Bohm's 'pilot-wave' interpretation, and the newer consistent histories and transactional interpretations.
At this point in time no one interpretation has gathered sufficient allegiance to be considered dominant, to say nothing of 'correct'. Time may tell if the existential oddness of quantum mechanics is intrinsic, if it will succumb to further study and research, or if it is an indication that quantum mechanics is an approximation to a deeper, but perhaps simpler, description of our Universe.