Classical mechanics 
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    A perplexing aspect of quantum mechanics is that it defies an intuitive 
    understanding. It is so different from classical physics as built by Newton, 
    Maxwell, and Einstein. Laws of classical physics are deterministic in the 
    sense  that  given,  say,  Newton’s  laws  of  motion,  and  initial  conditions 
    (position and momentum) at some instant t = 0 for a system and a time 
    history of the force(s) acting on the system, we can, in principle, accurately 
    predict the state of that system at any time in the past or the future. In 
    principle, at least, we can measure the state of the system (position and 
    momentum) without disturbing it.
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    Quantum mechanics 
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    In quantum mechanics, the situation is completely different. The counter-
    part of Newton’s laws of motion for a quantum system is the Schrödinger’s 
    equation, and the state of the system is described by something called the 
    “wave function”,, which no one understands intuitively. It is so abstract 
    that we understand it only in a mathematical sense. 
    It has not been possible for physicists (or anyone else for that matter) to 
    understand the wave function in any other way. If we try to measure the 
    state of a quantum system, hell breaks loose; we have no way of deter-
    ministically  predicting  what  the  result  of  a  measurement  will  be! And  , 
    even  in  principle,  there  is  no  way  we  can  measure  a  quantum  system 
    without  disturbing  it.  That  is  why  physics  is  divided  into  two  parts: 
    classical physics, and quantum physics. 
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    Quantum measurement is a mystery 
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    No one knows what transitory changes a quantum system undergoes when 
    it  is  measured.  We  do  know,  however,  that  while  we  cannot  make  a 
    deterministic prediction of the result of a measurement, we can make an 
    amazingly accurate probabilistic prediction of it. I and a former student of 
    mine, Vikram Menon, have come up with a hypothesis to explain this very 
    unusual aspect of quantum systems. You can look up our paper at arXiv: 
    Bera,  R.K.,  and  Menon, V., A  new  interpretation  of  superposition,  entanglement,  and  measurement  in 
    quantum mechanics, arXiv:0908.0957v1 [quant-ph], 07 August 2009, at http://arxiv.org/abs/0908.0957.
    The  probabilistic  aspect  of  quantum  mechanics  is  intriguing  because 
    Schrödinger’s equation has no built in probabilities; indeed it produces only 
    deterministic results! So where did the probabilities come in? 
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        Measurement is probabilistic 
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          The probabilities came in because a bunch of physicists, sometime in the 1920s, 
          said  so!  (This  became  known  as  the  Copenhagen  interpretation  of  quantum 
          mechanics.) They looked at available experimental data, and they found that the 
          results  of  measurements  carried  out  on  quantum  systems  follow  an  unusual 
          probabilistic pattern. 
          Just as Isaac Newton observed that material things are gravitationally attracted to 
          each other  (but  only  “God”  knows  why)  and  stated  it  as  a  fundamental  law  of 
          nature, so did Max Born* state this probabilistic aspect of quantum systems as a law 
          of quantum mechanics.
          It is extremely important to note that laws of nature are like the man-made axioms 
          in mathematics. We do not know (and can never know) why the laws are as they 
          are. Only “God” can enlighten you. We can only marvel at the intellectual genius of 
          those physicists who are able to read the mind of “God”. 
          *Born shared the Nobel Prize in Physics, 1954 (with Walther Bothe) “for his fundamental research in 
          quantum mechanics, especially for his statistical interpretation of the wavefunction”. 
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       Axioms of quantum mechanics  
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        Here are the laws (or postulates or axioms) of quantum mechanics stated informally. 
           
             Quantum mechanics describes a physical system through a mathematical 
           object called the state vector (or the wave-function) |. | is complex (i.e., it 
           has real and imaginary parts) and a vector of unit length.
           
             | evolves in a deterministic manner according to the linear Schrödinger 
           equation:
                                       2                     
                                             2
                                          Vi
                                       2m                      t
                                                                                2
               where    is the wave function,  is the reduced Planck's constant,   is the 
               Laplacian operator that describes how the wave function changes from one place 
               to another, V describes the forces acting on the particle, m is the mass of the particle 
               being described, and  t describes how the wave function changes its shape with time. 
             | remains a unit vector during its evolution, only its orientation changes.
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