Re: [Vo]:The faster than light neutrino speed should be determined in a non rotating frame

[Horace Heffner]

On Sep 30, 2011, at 11:16 AM, David Jonsson wrote: I made a calculation in an inertial system and found that the CERN-OPERA neutrino speed was by some percent due to the rotation of the Earth around its own axis. Do you agree that the calculation should be made in a non rotating system? By the time CERN sends and OPERA receives the Earth rotation makes OPERA to come a bit closer. How many of you agree or disagree with this?   Silvertooth, Bryan G. Wallace, GPS and laser gyroscopes also supports this view. It is not suitable to apply the principle of relativity in a non inertial rotating frame.   David David Jonsson, Sweden, phone callto:+46703000370 The OPERA experiment neutrino beam is directed from CERN, 46°14'N   6° 3'E,  to  Gran Sasso LNGS lab,  42°25'N  13°31'E.  The geometry of this is shown in Fig.1, in OPERA.jpg, attached. Point C is CERN, the neutrino origin.  Point S is San Sasso at the time of neutrino departure.  Since San Sasso is east of CERN, the earth rotates away, eastward,  from CERN during the time of flight of the neutrino.  This makes the distance longer than would be estimated by distance between geodetic coordinates.  The neutrino arrives at the new San Sasso location S', which is eastward from S by distance d.  Only the neutrinos initially aimed at point S' arrive there.   Assume the distance C to S is 730 km stated in the Adam et al. OPERA article.  Assume point B to be 730 km from point C on the line from C to S'.  The neutrino thus has to travel the additional distance x from B to S' due to the eastward motion of the earth during its time of flight.  Let point A be the point due south of CERN and due wet of San Sasso, i.e. at 42°25'N, 6°3' E.  The distance C to A s then about 404 km, and A to S 608 km.  The angle of the direction of CERN from due wast as seen from San Sasso is thus roughly ATAN(404/608) = 33.6°.   The earth's radius if 6371 km.  San Sasso is located at latitude 42.42°N.  Its radius of rotations is thus cos(42.4)*(6371 km) = 4720 km. Its speed of rotation is thus 2*Pi*(4720 km)/(24 hr) = 343 m/s. The speed of CERN due to earth's rotation is 2*Pi*cos(46.2°)* (6371 km)/(24 hr) = 321 m/s.  The 22 m/s speed difference between CERN and San Sasso is not enough to relativistically affect the measurements, especially given the extreme effort put into clock synchronization and geodetic coordinate location.  The relative motion however,  is enough.  A non-rotating linear motion approximation is sufficient to approximate the expected effect.  Light travels 730 km in (730 km)/(3x10^8 m/s) = 2.435x10^-3 s.  In that time San Sasso moves d = (2.435x10^-3 s) * (343 m/s) = 0.835 m eastward. The distance x added to the travel can thus be approximated as x = cos(33.6°) * d = 0.833 * (0.853 m)  = 0.71 m.  The travel time of the neutrinos should be increased by (0.71 m)/(3x10^8 m/s) = 2.36x10^-9 s = 2.36 ns. The neutrinos were observed arriving 60.7 ns early.  This extra 0.71 m, 2.36 ns, had it not been taken into account, would have made the neutrino arrival time 60.7 ns + 2.4 ns = 63.1 ns early vs speed of light.   Failure to account for earth's rotation thus provides approximately a 2.4/60.7 = 4 % error.  However, this error is in a direction which makes the anomaly even greater.  Best regards, Horace Heffner http://www.mtaonline.net/~hheffner/