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What is an interpretation?

An interpretation is an explanation of why Quantum Mechanics is the way it is.

Why do we need interpretations?

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:

1. Humans need to find an explanation that they personally feel comfortable with. Manipulating equations is just not satisfying enough. There is There is a psychological need for interpretation. Psychology however has proven to be a poor guide in the interpretation of Quantum Mechanics.
2. It's hard for humans to apply abstract rules - solving problems without intuition is hard. A little intuition goes a long way. There is a pragmatic need for interpretation to guide us in the solution to problems.
3. Quantum Mechanics is unfinished business - there are still unresolved problems. Interpretations should increase our "understanding" of physics and point the way forward towards new and better theories. Despite Feynman's comments, philosophy and a sense of beauty has had a profound effect on the development of physics, and the writings of all great scientists, including Feynman, show a deep appreciation of such things.

The Halting Problem

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?

Understanding interpretations

There are essentially 3 types of statements made when discussing interpretations of Quantum Mechanics.

1. Predictions of Quantum Mechanics. These cannot be challenged by an interpretation. Our current formulation of Quantum Mechanics may well be an approximation to some other grander theory, but interpretations accept the current theory as it is and try to make sense of it.
2. Pure Interpretation. By definition, these are (1) an explanation, or part explanation, of some part of Quantum Mechanics and (2) must be consistent with the predictions of Quantum Mechanics.
   
   If, for example, the standard treatment of Quantum Mechanics indicates that a system should be regarded as being in a superimposition of two states, the interpretation must also regard the system as being in a superimposition of two states.
3. Challenges to Quantum Mechanics. Statements regarding conditions under which Quantum Mechanics fail are always speculation. There is currently no experimental evidence that Quantum Mechanics fails under ANY conditions, so the issue of conflict between Quantum Theory and observation does not arise.

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.

The Golden Rule

• It is important when analysing statements to determine whether the statement is a prediction of Quantum Mechanics, or part of an interpretation or a challenge to standard Quantum Mechanics.
• When attempting to understand Quantum Mechanics, challenges to standard Quantum Mechanics must be treated with great suspicion.

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.

An Example: Schrodinger's Cat

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:

1. The waveform collapses after some short time period for an unspecified reason. Comment: This is challenge to Quantum Mechanics so is therefore speculation.
   
   
2. The waveform collapses because common sense dictates that it is so. Comment: This is challenge to Quantum Mechanics so is therefore speculation. This comment indicates a complete failure to understand the so-called "scientific method". Common sense does not trump an experimentally established scientific theory.
   
   
3. The cat is not really in a superimposition of two states because QM might not work for cats because they are too big. After all, no-one has every seen a cat diffracted through a grating so it might not be described by a waveform. Comment: This is challenge to Quantum Mechanics so is therefore speculation.

Evaluating interpretations

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.

Postulates of Quantum Mechanics

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.

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