Speed of the CERN Neutrinos released on 22.9.2011 - Was stated superluminality due to neglecting General Relativity?
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Speed of the CERN Neutrinos released on 22.9.2011
Was stated superluminality due to neglecting General Relativity?
Wolfgang Kundt
Received: date / Accepted: date
Abstract
During the years 2009 to 2011, neutrino beams were fired repeatedly fromCERN towards a detector in Italy’s Gran Sasso tunnel, some 4 deg south and 7 degeast of CERN, at a distance of 730.5 km, in the shape of short bunches of particles.Their time of flight (2.5 msec) was measured at high accuracy (nsec) with caesiumclocks [3]. Remarkably, the CNGS team found a deficit of 61 nsec compared withpropagation at the speed of light, and concluded at superluminal speeds, of order10 − . . In this communication, I will argue that this is the first experiment to test Ein-stein’s theory for the (weak) gravity field of Earth, with the result that the neutrinospropagated (just) luminally. Keywords
Superluminal Neutrinos · General Relativity · Tachyons
Newtonian physics loses its applicability when speeds approach the speed of light,like for neutrinos; we should pass at least to Special Relativity (SR). In SR, the worldlines of CERN and of the Gran Sasso neutrino detector form two almost straighttimelike lines of spatial separation 0 . · km, with a relative velocity v given bycorotation with our home planet Earth at the respective latitudes { ◦ , 42 ◦ } and lon-gitudes { ◦ , 13 ◦ } . The magnitude of v is some 12% of the corotation speed withEarth at CERN’s (northern) latitude, seen redshifted when viewed from CERN. Con-sequently, the Gran Sasso clock moves redshifted w.r.t. the CERN clock, hence runsmore slowly than the CERN clock by a redshift of z = v/c ≈ − . . If SR were theproper spacetime geometry for this experiment, the neutrino travel time would thusbe found shortened by some 10 − . . W. KundtArgelander-Institut f¨ur Astronomie, Auf dem H¨ugel 71, 53121 Bonn, GermanyTel.: +49-228-731771Fax: +49-228-733672E-mail: [email protected]
But as is well-known, gravity at the surface of Earth modifies clock rates morestrongly than do typical kinematic redshifts (given by b := v/c). The general-relativistic(GR) counterpart to b in Robertson ’s line element – which describes a generalised
Schwarzschild geometry – is 2m/R: (cid:18) d t dt (cid:19) = − − (cid:18) d x cdt (cid:19) − x · J cdt (1)in application to Earth in which the three PPN parameters b , g , and d have been setequal to unity, t is proper time (measured, e.g., by caesium clocks), m := GM/c =10 . cm is the gravitational length of Earth, corresponding to its mass M = . g,r := radial coordinate, and J := − R d x cdt dmr is the vector potential for the spin motionof Earth; J is understood as the retarded volume integral over Earth; it describes the Lense-Thirring effect . In our application, m/r is & − (for r ≈ R), and b := dx/cdt & − holds for our comoving clocks, so that J is negligibly small ( ≈ − ), andthe line element simplifies to: (d t /dt) = (1 - 2m/r - b ), [2][4].We now see that for the curved GR geometry of Earth described approximately bythe truncated Robertson line element, all we have to do is replace the kinematic po-tential b of the SR approach by the full gravitational potential 2m/r + b ( & b ( & − ) by the much larger gravitational redshift p / R ≈ − . inRobertson’s line element, a shift which is just slightly larger than the relative timedeficit (10 − . ) measured recently by the two clocks. This estimate leads me to theconclusion that the caesium clocks have measured a coordinate effect, not an excessof the neutrinos’ speed over luminal. Note that one nsec in a day means a clock uncer-tainty of smallness 10 − ! General Relativity must no longer be ignored in terrestrialhigh-time-resolution measurements. When the terrestrial Loran (Long-range-navigation) system was improved from atiming accuracy of m sec to nsec, we entered the era of general-relativistic kinematicson Earth. This experiment is the first to have shown it. Acknowledgements
I am indebted to Ole Marggraf for support, encouragement, and help with the elec-tronics.