It takes time to check your calculation. I can confirm one thing and that is that the eastern location of OPERA relative CERN makes the beam to travel longer, not shorter, than the distance measured on earth. I was wrong in my first calculation
David David Jonsson, Sweden, phone callto:+46703000370 On Sat, Oct 1, 2011 at 7:47 PM, Horace Heffner <hheff...@mtaonline.net>wrote: > Hopefully this one is correct. Sorry for the multiple posts on this. I am > surprised and happy to see the archives now save and show jpgs. > > 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/ > > > > > >
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