onsdag 3 juni 2015

The Copenhagen Interpretation vs Leibniz' Sufficient Reason

The article Inconsistency of the Copenhagen Interpretation in Foundations of Physics, Vol. 21, No. 5, 1991, by  C. I. J. M. Stuart, argues that:
  • The Bohr-Heisenberg scheme, which forms the basis of any current version of the standard or Copenhagen interpretation of quantum mechanics, is shown to be internally inconsistent.
with the following introduction:
  • The predictive success of quantum mechanics has always been accompanied by vigorous debate concerning the theory's physical content as specified by the Copenhagen interpretation, i.e., the Bohr-Heisenberg scheme. 
  • Einstein at first thought the scheme inconsistent, but later concluded that it made quantum mechanics consistent but incomplete.
  • Since then, the question of completeness has persisted in connection with "hidden variable" theories; but Einstein's opinion as to the scheme's consistency has been generally accep- ted and perhaps overshadowed by concern with the completeness issue, though a widely held modern view is that the scheme is incoherent and perhaps incomplete. 
  • The main objective in this paper is to show that incoherence is not the problem but, much more seriously, the scheme is internally inconsistent. 
The article starts out by identifying the following basic postulates of the Copenhagen Interpretation:
  1. The completeness postulate requires that the quantum mechanical wave function gives a complete specification of what can be known concerning quantum states. 
  2. The superposition principle requires that a quantum state represented by a linear superposition of allowable quantum states is itself an allowable quantum state. 
  3. The Heisenberg uncertainty principle requires that observables represented by noncommuting operators cannot simultaneously be measured with equal exactness, the exactness of the one being inversely proportional to the exactness of the other. 
  4. The probability interpretation requires that the wave function does not correspond to a material wave; instead, its amplitude corresponds to a probability amplitude and its absolute square corresponds to a probability density. 
  5. The principle of inseparability requires that, in quantum mechanics, a physical system consists of the object-system under investigation inseparably from the experimental apparatus used to make measurements; and, moreover, the interaction between object and apparatus forms an inseparable part of quantum phenomena. 
  6. Bohr's principle of complementarity requires that complementary experimental arrangements wilt yield complementary quantum phenomena. 
  7. Bohr's correspondence principle requires that quantum mechanics must converge to classical mechanics in the limit where quantum effects can be disregarded.
This is important information, since the Copenhagen Interpretation seldom is described in precise terms, which makes critical evaluation difficult. Let us subject postulates 1-7 to Leibniz' test of sufficient reason:
  1. What is the reason to believe that the wave function gives a complete specification of what can be known of  the physics of atoms?
  2. What is the reason to believe that the physics of atoms is linear? 
  3. What is the reason that position and velocity cannot be measured simultaneously? 
  4. What is the reason to believe that the wave function cannot correspond to a material wave? What is the reason to believe that it instead corresponds to probability amplitude?
  5. What is the reason to believe that a physical system consists of the object-system inseparably connected to experimental apparatus?
  6. What is reason for complementarity?
  7. What is the reason for requiring that quantum mechanics must converge to classical mechanics if quantum mechanics effects can be discarded?
Let us thus seek the sufficient reason for each postulate and see what we can come up with:
  1. No reason found.
  2. No reason found.
  3. With matter as wave the answer is trivial. With matter as particle, no reason is found.
  4. The reason is the spatial multi-dimensionality of the wave function.
  5. No reason that a physical system must be connected to experimental apparatus.
  6. No reason.
  7. No reason to explicitly require something self-evident: quantum mechanics without quantum effects must be classical mechanics.
We conclude that only one reason has been found: the spatial multi-dimensionality of the wave function makes direct physical interpretation impossible, since physics as we know it takes place in three space dimensions. No other reason has been identified. 

After this evaluation showing that the sole reason for the Copenhagen Interpretation is an ad hoc assumption about mathematical formalism, it is natural to ask if there is a quantum mechanics with wave functions depending on a common three-dimensional space variable plus time?  

In a sequence of posts the category "physical quantum mechanis" I seek to give a positive answer to this question.  The reason for this form of quantum mechanics is the same as for classical mechanics, which may well be sufficient.

We have not found any sufficient reason for the Copenhagen Interpretation which fits with Stuart's observation that the Copenhagen Interpretation is internally inconsistent: Of course, there can never be a sufficient reason for the validity of a scientific model which is internally inconsistent. Of course, there can never be a sufficient reason to view a scientific contradiction as a scientific truth. Only in the Copenhagen Interpretation is this possible, but that means that whatever it is,  it is not science.

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