måndag 21 oktober 2013

Quantum Contradictions 24: Against Measurement

John Bell questions in Against Measurement Bohr's and Born's Copenhagen Interpretation of quantum mechanics (allowing physicists to speak only about what can be be measured and not what "is", and then in statistical terms): 
  • Surely, after 62 years, we should have an exact formulation of some serious part of quantum mechanics?
  • It would seem that the theory is exclusively concerned about "results of measurement", and has nothing to say about anything else.
  • What exactly qualifies some physical systems to play the role of 'measurer'? 
  • Was the wavefunction of the world waiting to jump for thousands of millions of years until a single-celled living creature appeared? Or did it have to wait a little longer, for some better qualified system . . . with a PhD? 
  • If the theory is to apply to anything but highly idealised laboratory operations, are we not obliged to admit that more or less "measurement-like" processes are going on more or less all the time, more or less everywhere? Do we not have jumping then all the time?
This is the same as asking if there is no sound in the desert if there is nobody there to listen? To claim that we are not allowed to speak about (and mathematically model) sound as an air vibration unless there is a physicists ear drum reacting to the vibration, would seem absurd.

Bell gives the reason driving modern physics into this form of absurdity:  
  • In the beginning, Schrödinger tried to interpret his wavefunction as giving somehow the density of the stuff of which the world is made. 
  • He tried to think of an electron as represented by a wavepacket - a wavefunction appreciably different from zero only over a small region in space. The extension of that region he thought of as the actual size of the electron - his electron was a bit fuzzy. 
  • At first he thought that small wavepackets, evolving according to the Schrodinger equation, would remain small. But that was wrong. Wavepackets diffuse, and with the passage of time become indefinitely extended, according to the Schrodinger equation. 
  • But however far the wavefunction has extended, the reaction of a detector to an electron remains spotty. 
  • So Schrödinger's "realistic" interpretation of his wavefunction did not survive. 
Bell here expresses the idea that we have to give up reality because we are supposed to believe that a pointlike blip on a screen cannot be generated by an electron wave extended in space. We are thus only allowed to speak about (and mathematically model) the blip effect and not the cause of the blip.
But an extended sound in the desert can give rise to a pointlike "oh" from the listener, and thus the logic  of requiring a pointlike input for pointlike output is missing.

Anyway, this missing logic is behind the Copenhagen Interpretation, which Bell cannot embrace:  
  • Then came the Born interpretation. The wavefunction gives not the density of stuff, but gives rather (on squaring its modulus) the density of probability. 
  • Probability of what, exactly? Not of the electron being there, but of the electron being found there, if its position is 'measured'. 
  • Why this aversion to 'being' and insistence on 'finding'? 
  • The founding fathers were unable to form a clear picture of things on the remote atomic scale.
  • They became very aware of the intervening apparatus, and of the need for a 'classical' base from which to intervene on the quantum system. And so the shifty split.
Bell tells us: 
  • We do not yet have an exact formulation of some serious part of quantum mechanics. 
Bell thus gives modern physics a bad grade. Bell supports his insistence to ask for an exact formulation (physically meaningful understandable formulation) with a quotation by Feynman:
  • We do not know where we are stupid until we stick our necks out. 
Bell did that but nobody wanted to listen to his questions as if the desert was empty.

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