An interpretation is an explanation of why Quantum Mechanics is the way it is.
Not everyone believes in the need for interpretation. Feynman famously stated that "no-one understands Quantum Mechanics" and criticised those who felt that the Universe needed to be simple or beautiful. To Feynman, the Universe is the way it is. If a theory is in 100% harmony with observation, then the the theory should be accepted as it is. If it is logically consistent but does not appear to make sense, that's too bad.
There are some good reasons to search for interpretations. These include:
There is another problem with the interpretation of Quantum Mechanics. Quantum Mechanics is supposed to be, or lead to, the ultimate "Theory of Everything"
What would a theory of everything look like?
If theory A is the "Theory of Everything" but uses concept B, should we then pursue an explanation for concept B? When do we stop? What if B is something we are not comfortable with?
Should we accept a "Theory of Everything" which explains everything in terms of quarks and leptons and 3-dimensional space-time, or should we then seek to explain the quarks, leptons and space-time? If we explain quarks and leptons in terms of strings, should we then seek to explain the properties of strings?
Alternatively we can turn to philosophy. Kant for example, drew the distinction between the mind and the external world, and between information drawn from the senses and information resulting from the application of logic. Should we expect a "Theory of Everything" to reflect this philosophy? Arguably the Copenhagen Interpretation does; it is based on Positivism. Or is our belief in our common sense so strong that we should reject any theory that is not based on realism?
There are essentially 3 types of statements made when discussing interpretations of Quantum Mechanics.
A paradox is not an interpretation. It is a situation together with an analysis that shows up some feature of an interpretation or Quantum Mechanics as being incomplete or contradictory or inconsistent with common sense or some branches of physics. For example, Wigner's Friend (discussed later) posses problems for any of the "real waveform" interpretations of Quantum Mechanics because the two observers "see" the waveform doing different things.
Unfortunately the situation is not quite as clear cut as suggested above.
Firstly, "Interpretations" often contain subtle challenges or non-standard extensions to Quantum Mechanics. Any explanation of Quantum Mechanics necessarily inject new ideas and concepts into the discussion. Even when the interpretation attempts to be faithful to Quantum Mechanics, the logic of the interpretation may result in speculation about Quantum Mechanics.
For example, the Consciousness Causes Collapse interpretation pursues a chain of logic that suggest that Consciousness causes waveform collapse, yet Consciousness does not appear anywhere in the formulation of Quantum Mechanics.
Secondly, Quantum Mechanics is not "well defined"". The rules are sufficiently well known to allow calculations, but the assumption behind the mathematics are not.
Paradox Part 1: The Setting (a description of a situation): A cat is placed in a box with a radio-active isotope for a short time. There is a 50:50 chance that the isotope will emit radiation that will be detected by a Geiger counter. If the Geiger counter detects radiation, it will cause a poisonous gas to be released and kill the cat.
Paradox Part 2: The Analysis (any challenge must be viewed with great suspicion): The cat waveform is in a mixture of alive and dead states until the box is opened. When the box is open, the cat waveform instantaneously collapses to either a 100% alive cat waveform or 100% dead cat waveform.
Paradox Part 3: The Issue: What does it mean for a cat to have a waveform that is 50% alive and 50% dead?
Copenhagen Interpretation (should be consistent with QM): The waveform is not real and reflects our knowledge of the system. The paradox presents no problems.
State Vector Interpretation (should be consistent with QM): The waveform is real, and the cat is therefore really in a state which is "half dead and alive". But a number of questions arise: What does it mean to be half dead and half alive? How does opening the box cause the cat to come back from the half-dead to 100% alive or 100% dead?
The following comments about Schrodinger's Cat are speculative challenges to Quantum Mechanics:
There is no right way to choose the "best" interpretation (psychological factors play an unavoidable part), however the author suggests that the best interpretation require (1) the least speculation to resolve paradoxes and (2) raises the least unresolved questions. In the example above, the Copenhagen interpretation requires no speculation and does not raise any unresolved questions. The State Vector Interpretation (real waveform) raises a number of questions that cannot easily be answered. (E.g. What does it mean to be half alive and half dead?). The Copenhagen Interpretation should therefore be preferred to the State Vector Intrepretation.
Quantum Mechanics can be reduced to a small number of postulates built using rather sophisticated mathematics.The standard approach is due to John Von Neumann.
The set of axioms used to derive Quantum Mechanics is related to the choice of physical assumptions, which are in turn often related to different interpretations.top