Re: [asa] Re: Cosmos in the Light of the Cross

The language of "stronger" & "weaker" is my own & may or may not be helpful.

The uncertainty principle usually is discussed in connection with particular ways of trying to measure position & momentum - e.g., Heisenberg's gamma ray microscope. Clearly one can't present such arguments as a proof of the principle - there is no strict induction from N failed attempts to beat Heisenberg to the N + 1st.

A formal proof of the principle - dpdq = or > h/4*pi*i with p = momentum and q = position - follows from the basic commutation relations between the operators p and q, pq - qp = h/2*pi*i . dp and dq are defined as RMS deviations from the mean & thus the proof presupposes the standard QM ideas about the statistical distributions defined by wave functions. Details are in any QM text.

But without going into details, the point is that the uncertainty relation follows from the fact that p & q are noncommuting operators. They simply aren't the kinds of things which can simultaneously have unique numerical values. An operator A has the value a in a state F if AF = aF. In order for p & q to have unique values p' & q' in the same state F we would have to have pF = p'F and qF = q'F. & it's not hard to show that this would require pq - qp = 0.

Some may complain that this is just an orgy of math rather than physics. But (as will not surprise those who've been on the list for awhile), I think the mathematical pattern underlying the world has an objective existence.

Shalom
George
http://web.raex.com/~gmurphy/
  ----- Original Message -----
  From: Jim Armstrong
  Cc: asa@calvin.edu
  Sent: Tuesday, June 05, 2007 10:48 AM
  Subject: Re: [asa] Re: Cosmos in the Light of the Cross

  George - I've been away from the formalism of physics for a long time, so I ask this out of relative ignorance.
  When I first encountered the uncertainty principle, it was in the context of measurement. If one made a measurement of one of the two interrelated values (e.g., position and momentum), the very measurement act disturbed the state of the measured entity such that the second of the values could no longer be determined accurately at a scale where quantum effects are measurable. And, of course, one can calculate the best one can do in such a measurement.

  This calculation seems to have arisen naturally out of efforts to quantify the accuracy of experimental measurement.
  To my mind, this is a pretty simple concept, and therefore I would think it would be characterized as the stronger model. The parameters are real enough, but the measurement process interferes with the ability to accurately determine both of these linked parameters because the measurement process itself "touches" the measured entity, altering the state of the measured entity.

  The other language and concepts, particularly that of the entities existing in some sort of quasi-state, seem to flow out of the mathematical representations.

  To get to the point, my simple question is, is your characterization of "stronger" and "weaker" your take, or is it the language now residing in the formal realm of physics where you reside (and I admittedly don't).
  JimA

  George Murphy wrote:
    Merv -

    There are, of course, different interpretations of QM & the uncertainty principle. I think there is good reason to take the strong view that position & momentum really do not and cannot have precise values simultaneously, & not just the weaker view that they do have such values but that we can't know them. This is seen clearly in the mathematical formalism in which position & momentum (& other dynamical variables) can represented by matrices - whole arrays of numbers - rather than single numerical values. (In older language, q numbers rather than c numbers.) That being the case, the initial data required for Laplacian determinism don't exist.
    The connection between this microscopic indeterminism and the macroscopic variety with chaos theory is a little tricky but I think that the QM variety rules out the absolutely precise initial data which chaos theory says would be necessary for long range forecasting in principle.

    This indeterminism is not required to allow God to act in a hidden way in the world. A strictly Laplacian view does not rule out ongoing divine action. But with such a view one would have to say that God's ordinary action in the world is completely predictable (because the physical processes with which God cooperated were completely deterministic), and that any positive responses to prayers for rain, e.g., when the mechanistic laws of physics didn't predict rain would have to be strictly miraculous interventions. What the breakdown of detrminism allows is not divine action itself but divine action which has some freedom and is still in accord with the laws of physics, & is thus still in a sense hidden.

    Shalom
    George
    http://web.raex.com/~gmurphy/
      ----- Original Message -----
      From: Merv
      To: George Murphy ; asa@calvin.edu
      Sent: Monday, June 04, 2007 9:54 PM
      Subject: [asa] Re: Cosmos in the Light of the Cross

      This is addressed to George since I've been corresponding with him about his book "Cosmos in the Light of the Cross", but I'm running this particular question of mine on the list because I covet any insights which any scientifically minded folks can enlighten me with. --Merv

      A long-standing physics inquiry of mine summarized by your statement from p. 52: "This uncertainty principle cuts down Laplace's determinism at the roots."
      On p. 65 you exactly nail my hang-up with this when you state: "We may argue that an electron really has a precise position and momentum even if we cannot know them, ..." and you go on to answer that objection, in part, concluding that "Quantum mechanics does not say that there is no external reality at all, but that that reality is not strictly separated from our consciousness."

      I have nearly despaired of grasping these conclusions and how they deal the supposed "death blow" to Laplace's demon. While I can appreciate (without even understanding) that scientific verification exists for the proposition that our mere observation affects reality (and apparently in a far deeper way than its merely being altered by the presence of our physical measurement tools - which is easily understood and conceptually dealt with), I still cannot see the definitive conclusion that you and all modern physicists so easily adopt. It looks to me like just a more sophisticated and impenetrable "God of the gaps" wall than ever. Only this could be called "science of the gaps". We can't find something out, and our consciousness is even inextricably intertwined in it. Therefore we declare it to not have any objective reality at all (even in principle). Chaos theory pulls a similar trick for mathematics. Since error amplification makes sensitivity to initial conditions virtually infinite, and we can't be infinitely precise in describing an initial state: we can solidly conclude there can never be an exact weather prediction - a well-founded conclusion. But then comes the maddening next (and IMO totally unfounded) additional conclusion: "...so a future state of weather can't have been exactly determined by a prior state, even in principle. Chaos and QM teamed up. It may be true, but there is a scent of arrogance in declaring it true, when it actually seems unknowable whether or not determinism is really correct behind those locked doors.

      Here is one scenario easy to imagine: People for years tend to give God praise more easily when the complexity of something reaches beyond their horizons or capacity to understand. We easily said "God is great - look how far beyond us He is!" Then science enters the world making huge conquests. Formerly unreachable horizons are now suddenly "conquered territory", and the "God of the gaps" inclination is now revealed as a dangerous way to do theology.

      So we Christians seem to have had two responses:
      1. backup and declare that God is present in all processes whether we understand them or not (which was always correct and is very Biblical anyway).

      Or 2. Let's find an apparently "unscalable" wall (QM with its inherent uncertainty in nature, and Chaos theory with its corresponding defeat of mathematics) and erect our new flag there in confidence that NOW - finally science and math have reached their limits. And we can rest up against that last refuge glorying in the many ways which God can now work such mischief as free-will, consciousness, miracles... etc. safely beyond the reach of empirical science.

      The main thrust of your writing is to show that a "hidden" God in nature is not inconsistent with a God who is willing to die as a forsaken "nobody" on the cross. Shouldn't this "hiddenness" be just as applicable to a Laplacian 'billiard ball' universe as the QM 'mischief behind locked doors' universe? I can understand our religious preference for the second and our universal aversion for the first, but that doesn't mean the Laplacian understanding couldn't be true. Why & how are scientists so sure they have defeated this demon?

      --Merv

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Received on Tue Jun 5 13:47:33 2007