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There may be a serious conceptual error in the Hawking Gibbons paper of 1977

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  • JACK SARFATTI
    Unruh effect is T(r) = hg(r)/ckB for the black body photon temperature seen by the accelerating detector that is not seen by the unaccelerating detector. It
    Message 1 of 2 , Feb 1, 2011
      Unruh effect is 

      T(r) = hg(r)/ckB

      for the black body photon temperature seen by the accelerating detector that is not seen by the unaccelerating detector.

      It may well be that the Hawking radiation never makes it to the far field. 

      The only counter-evidence that it does is the Pioneer Anomaly.

      The basic rule for static LNIFs is

      covariant acceleration = (Newton's g-acceleration)(gravity time dilation)

      For example in de Sitter (dS) space the CLASSICAL calculation is

      g(r) ~ c^2/\r(1 - /\r^2)^-1/2

      for the observer at r = 0

      note that g(0) = 0 which contradicts Hawking & Gibbons that it should be c^2/\^1/2

      this is for Unruh-Hawking radiation from the past dS horizon - of course we don't have on in our real universe.

      The only way to get their result is to put in their term ad-hoc as a zero point type of correction not seen in the classical calculation.

      Similarly for the simplest black hole

      g(r) ~ (c^2rs/r^2)(1 - rs/r)^-1/2

      with the observer at r ---> infinity 

      again   g(infinity) = 0

      so we do not see the Unruh-Hawking radiation at infinity in the far field - unless we stick in the term ad-hoc again.


      On Feb 1, 2011, at 10:45 AM, JACK SARFATTI wrote:

      PS - the coordinates one uses don't matter in any physics theory obviously.
      The physics of local gauge invariance in GR is that

      1) the instantaneous relative velocity mapping between two un-accelerating inertial geodesic non-rotating coincident detectors measuring the same events is a redundant gauge transformation, i.e. Lorentz group SO1,3  LIF <--> LIF'

      2) the instantaneous mapping between two accelerating non-inertial off-geodesic, possibly rotating coincident detectors measuring the same event is a redundant gauge transformation, i.e., T4(x) LNIF <--> LNIF'

      so the above are 10 gauge transformations.

      3) the instantaneous map between a LIF and a coincident LNIF , i.e. tetrad mapping  eI^u etc.

      On Feb 1, 2011, at 10:35 AM, JACK SARFATTI wrote:


      On Feb 1, 2011, at 2:26 AM, Paul Zielinski wrote:

      Bottom line here is that even in the tetrad formalism frame invariance under LNIF' -> LNIF''  transformations means
      covariance wrt general coordinate transformations. So frame invariance still presents itself as coordinate covariance
      even in the tetrad formulation of the GTR. The (non-orthonormal) LNIF basis vectors change in lockstep with the
      coordinates to which they are aligned.

      What difference does it make to the physics?
      What mathematical distinctions do you mean?
      Show the equations.
      If you can't show the equations then the above words have no importance.
      A local frame is basically a material detector
      The arbitrary coordinates one uses don't matter.
      The acceleration g-force does matter.
      the relative velocity between coincident detectors does matter.
      The invariants constructed in each frame for the same measured events by different coincident detectors are the objective reality of the theory.

      So this brings us back to my original question: Can the interaction between accelerating detectors and the physical
      vacuum that supposedly produces Unruh radiation, or particle pair production in the Gibbons-Hawking model for cosmological
      event horizons, be given a generally covariant formulation in the GTR?


       "the reality of the membrane can not be an invariant which all observers agree upon."

      "
      An experiment of one kind will detect a quantum membrane, while
      an experiment of another kind will not. However, no possibility exists for any observer to
      know the results of both. Information involving the results of these two kinds of experiments
      should be viewed as complementary in the sense of Bohr."


      June 1993
      hep-th/9306069

      The Stretched Horizon and Black Hole Complementarity
      Leonard Susskind, L´arus Thorlacius,† and John Uglum

      “stretched horizon” or membrane description of the black hole, appropriate to a distant observer

      the dissipative properties of the stretched horizon arise from a course graining of microphysical degrees of freedom that the horizon must possess.



    • JACK SARFATTI
      Z sent Is there Unruh radiation? G. W. Ford Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120 R. F. O’Connell Department of
      Message 2 of 2 , Feb 1, 2011
        Z  sent

        Is there Unruh radiation?
        G. W. Ford
        Department of Physics,
        University of Michigan,
        Ann Arbor, Michigan 48109-1120
        R. F. O’Connell
        Department of Physics and Astronomy, Louisiana State University,
        Baton Rouge, Louisiana 70803-4001
        (Dated: February 1, 2008)

        "we consider the case of a point mass moving under a constant force (hyperbolic
        motion). There we make use of the convenient parametric representation of the motion
        sometimes called Rindler coordinates [10]. We find that the zero-temperature correlation of
        the field evaluated at a space-time point moving along the hyperbolic path is identical with
        the correlation evaluated at a point fixed in space, but with the field at the elevated Unruh
        temperature.

        We find the net energy flux at any point in the field is identically zero, the result of a detailed balance
        of a flux of field energy emitted by the oscillator and a flux of field energy supplied to the
        oscillator. This is entirely what one should expect, since the mean energy of the oscillator
        in equilibrium is constant. The point of this exercise is seen in the next two sections, where
        we find the for an oscillator in hyperbolic motion through a zero temperature field the net
        flux vanishes in the same way and for the same reasons as for an oscillator at rest.

        we present our conclusion that, whereas one can speak of an Unruh temperature
        there is no corresponding radiation to be detected. In this
        context, we also analyze Unruh’s counterclaim [5] and argue that it is not valid."


        On Feb 1, 2011, at 12:18 PM, JACK SARFATTI wrote:

        Unruh effect is 

        T(r) = hg(r)/ckB

        for the black body photon temperature seen by the accelerating detector that is not seen by the unaccelerating detector.

        It may well be that the Hawking radiation never makes it to the far field. 

        The only counter-evidence that it does is the Pioneer Anomaly.

        The basic rule for static LNIFs is

        covariant acceleration = (Newton's g-acceleration)(gravity time dilation)

        For example in de Sitter (dS) space the CLASSICAL calculation is

        g(r) ~ c^2/\r(1 - /\r^2)^-1/2

        for the observer at r = 0

        note that g(0) = 0 which contradicts Hawking & Gibbons that it should be c^2/\^1/2

        this is for Unruh-Hawking radiation from the past dS horizon - of course we don't have on in our real universe.

        The only way to get their result is to put in their term ad-hoc as a zero point type of correction not seen in the classical calculation.

        Similarly for the simplest black hole

        g(r) ~ (c^2rs/r^2)(1 - rs/r)^-1/2

        with the observer at r ---> infinity 

        again   g(infinity) = 0

        so we do not see the Unruh-Hawking radiation at infinity in the far field - unless we stick in the term ad-hoc again.


        On Feb 1, 2011, at 10:45 AM, JACK SARFATTI wrote:

        PS - the coordinates one uses don't matter in any physics theory obviously.
        The physics of local gauge invariance in GR is that

        1) the instantaneous relative velocity mapping between two un-accelerating inertial geodesic non-rotating coincident detectors measuring the same events is a redundant gauge transformation, i.e. Lorentz group SO1,3  LIF <--> LIF'

        2) the instantaneous mapping between two accelerating non-inertial off-geodesic, possibly rotating coincident detectors measuring the same event is a redundant gauge transformation, i.e., T4(x) LNIF <--> LNIF'

        so the above are 10 gauge transformations.

        3) the instantaneous map between a LIF and a coincident LNIF , i.e. tetrad mapping  eI^u etc.

        On Feb 1, 2011, at 10:35 AM, JACK SARFATTI wrote:


        On Feb 1, 2011, at 2:26 AM, Paul Zielinski wrote:

        Bottom line here is that even in the tetrad formalism frame invariance under LNIF' -> LNIF''  transformations means
        covariance wrt general coordinate transformations. So frame invariance still presents itself as coordinate covariance
        even in the tetrad formulation of the GTR. The (non-orthonormal) LNIF basis vectors change in lockstep with the
        coordinates to which they are aligned.

        What difference does it make to the physics?
        What mathematical distinctions do you mean?
        Show the equations.
        If you can't show the equations then the above words have no importance.
        A local frame is basically a material detector
        The arbitrary coordinates one uses don't matter.
        The acceleration g-force does matter.
        the relative velocity between coincident detectors does matter.
        The invariants constructed in each frame for the same measured events by different coincident detectors are the objective reality of the theory.

        So this brings us back to my original question: Can the interaction between accelerating detectors and the physical
        vacuum that supposedly produces Unruh radiation, or particle pair production in the Gibbons-Hawking model for cosmological
        event horizons, be given a generally covariant formulation in the GTR?



        June 1993
        hep-th/9306069

        The Stretched Horizon and Black Hole Complementarity
        Leonard Susskind, L´arus Thorlacius,† and John Uglum

        “stretched horizon” or membrane description of the black hole, appropriate to a distant observer

        the dissipative properties of the stretched horizon arise from a course graining of microphysical degrees of freedom that the horizon must possess.




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