Quantum Mechanics - Interpretations
1. Interpretations
This section is intended to assist readers who are new to Quantum Interpretations. Theses readers should satisfy themselves that they understand the points raised on this page.
1.1 What is an interpretation?
Interpretations are explanations of why Quantum Mechanics is the way it is.
1.2 Why Interpretation?
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.
The Stopping Problem
There is another problem with interpretations: When do we stop? If theory A is the "Theory of Everything" but uses concept B, should we then pursue an explanation for concept B? What if B is something we are not comfortable with?
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?
If interpretations are so problematic, why do we invest so much time in them? Some reasons include:
- Humans need to find an explanation that they personally feel comfortable with.
Manipulating equations is just not satisfying enough.
I.e. there is a psychological need for interpretation. Psychology
however has proven to be a poor guide in the interpretation of Quantum Mechanics.
- It's hard for humans to apply abstract rules - solving problems without
intuition is hard. A little intuition goes a long way. I.e. There is a pragmatic
need for interpretation.
- Quantum Mechanics is unfinished business - there are still unresolved problems. Interpretations hopefully 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 Feynman's own writing show a deep appreciation of such things.
1.2 Understanding Interpretations
There are essentially 3 types of statements made when discussing interpretations of Quantum Mechanics.
- Predictions of Quantum Mechanics - these cannot be challenged by an
interpretation. 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.
- Interpretations, or parts of an interpretation - by definition, these (1) must be consistent with the predictions of Quantum Mechanics,
and (2) be an explanation, or part of an explanation, of some
part 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. Furthermore, it is not acceptable to challenge the validity of Quantum Mechanics to escape the unpleasant consequences of an interpretation.
- Speculation - statements which are not any of the above. Speculation is inconsistent with the predictions of Quantum Mechanics, or
does not form part of an explanation of some part of 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) The statement that there exists an objective reality underpinning existing Quantum Mechanics, on its own, is speculation. If the statement forms part of an argument that does not challenge the predictions of Quantum Mechanics and explains some aspect of Quantum Mechanics, then it can represent part of an interpretation.
A paradox is not an interpretation. It is a situation which, when analysed, 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 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 pure speculation
- When attempting to understand Quantum Mechanics, speculation is a bad thing.
Mixing speculation into an argument only results in more speculation. An interpretation mixed with speculation is speculation, not interpretation. Unfortunately authors often skip between prediction, interpretation and speculation, making it very difficult to clearly ascertain the final status of assertions.
An Example: Schrodinger's Cat
The paradox ( 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.
Quantum Mechanics ( cannot be challenged ): The cat is in a mixture of alive and dead states until the box is opened.
Copenhagen Interpretation ( must be consistent with QM ): The waveform is not real and reflects our knowledge of the system. The paradox presents no problems.
State Vector Interpretation ( must 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? Can the cat's status be objectively established? 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 speculation:
- The waveform collapses after some short time period for an unspecified
reason. Comment: This is challenge to Quantum
Mechanics so in not part of any interpretation; it is therefore speculation.
- The waveform collapses because common sense dictates that it
is so. Comment: This is challenge to Quantum
Mechanics so in not part of any interpretatio; it 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.
- 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 in not part of any interpretation, it is therefore speculation.
1.3 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 resolved. (E.g. What does it mean to be half alive and half dead?). The Copenhagen Interpretation should therefore be preferred to the SVI.
1.4 Two types of interpretation?
The classification of statements into Quantum Mechanics, interpretation and speculation is extremely helpful in preventing discussions and arguments degenerating into speculative nonsense. The classification however does not entirely reflect real world usage.
Consciousness Causes Collapse (CCC), for example, speculates that the waveform collapses when it interacts with consciousness. Arguably that contradicts standard Quantum Mechanics (e.g. Schrodinger's Cat - CCC so the cat causes waveform collapse; the system is not in a superimposed state of half alive and half dead). It would therefore be reasonable to claim CCC is not an interpretation and is pure speculation. CCC however is regarded as a well established interpretation. Why? Probably because (1) historically it is associated with John Von Neumann, (2) it is arises from a plausible line of reasoning, and (3) the postulate (speculation) that Consciousness causes collapse is a central tenant of the interpretation and not invoked in an arbitrary way.
It therefore makes sense to classify "interpretations" into 2 categories:
- True interpretations - No part of the intrepretation is inconsistent with
Quantum Mechanics. Copenhagen and Many Worlds are true interpretations.
- Speculative interpretations - A central tenant of the interpretation is strictly in conflict with the predictions of Quantum Mechanics. Consciousness Causes Collapse is a speculative interpretation for the reasons stated above. Many authors treat speculative interpretations on the same basis as true interpretations (although this author believes this is granting them a status they do not deserve)
The same disciplined approach should be taken when analysing speculative interpretations - the introduction of additional ad-hoc speculation should be regarded as departing from the original interpretation and producing speculation.
1.5 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 the rest of Quantum Mechanics is related to the choice of physical assumptions (interpretation). Different interpretations therefore are associated with different axiomatic treatments of QM. This approach is not taken here because it is very involved and not really suitable for presentation in HTML.
If you have any comments about this page, please email me at sokane@bowmain.com.
Copyright (c) Shaun O'Kane, 2005. You are free to redistribute this work provided you give due credit to it's author.
since 4 April 2005 (SOMETIMES BROKEN).