Readers will recall in my previous blog to do with the claimed CERN detection of superluminal or faster-than the speed of light neutrinos, I showed that if this were so then it would require the enhanced mass (i.e. over the rest mass) to be imaginary, as well as the associated kinetic energy. See, e.g. the very end of:
http://brane-space.blogspot.com/2011/09/faster-than-light-neutrinos-not-so-fast.html
But much more plausible than that the CERN team actually created imaginary mass neutrinos, is that they made assorted systematic or other errors they didn't detect. One can almost call this a variant of David Hume's "miracle" principle:
"No testimony is sufficient to establish a miracle, unless the testimony be of such a kind that its falsehood would be more miraculous than the fact which it endeavors to establish."
In this case we need only substitute the words "fantastic claim" for "miracle". Then by the Hume test one would ask whether the prosaic claim of an experimental error is more or less fantastic than the discovery of superluminal neutrinos violating a centuries old postulate that holds up most of modern physics? The answer, of course, is that the experimental error would be less fantastic and hence the more probable explanation.
Now, to be sure, the researchers insist they left no stone uncovered in their desire to eliminate any errors: using the GPS or global positioning system they measured the distance accurately to within 8 inches, they factored in the rotation of the Earth, and even stopped traffic in a tunnel through the Gran Sasso mountain in order to calibrate their instruments.
They made it certainly sound like they dealt with all conceivable errors, but have they? Consider first that small perturbative glitches could have transpired due to anomalous differences in the Earth's crust over the time the experiment was conducted. Thus, a tiny deviation in the actual shape of the Earth itself (based on a science called Geodesy) could have incepted the 60 ns difference in speeds.
In geodetic refinements of shape (which also have a bearing on the value of g, the acceleration of gravity) a first correction is made relative to the initiating station. (E.g. see Spherical And Practical Astronomy Applied to Geodesy, 1968, p.
471). In other words, a first correction will be made such that (ibid.):
delta φ = φ - φ(T) = -H/g' (@g'/@x) cosec (1")
where H is the orthometric height of the observation station, and g' and @g'/@x (a partial derivative) are the gravity and the north component of its horizontal gradient, respectively at the initializing station.
A secondary correction is then made to the eccentricity of the station. The correction is to be applied when the latitude is observed off the reference station, and thus reduced the observed latitude to that of the reference station. For example, in the lower diagram, let P be the reference station and P' the eccentric station where the latitude φ(T) is observed. If the distance PP' is d, and the azimuth of the line is A, the identity for the length of the applicable meridian arc is:
R (delta φ) sin (1") = d cos (A)
and hence the correction:
delta φ = φ - φ(T) = d/ (R sin (1") x [cos (A)]
where R is the mean radius of the Earth.
http://brane-space.blogspot.com/2011/09/faster-than-light-neutrinos-not-so-fast.html
But much more plausible than that the CERN team actually created imaginary mass neutrinos, is that they made assorted systematic or other errors they didn't detect. One can almost call this a variant of David Hume's "miracle" principle:
"No testimony is sufficient to establish a miracle, unless the testimony be of such a kind that its falsehood would be more miraculous than the fact which it endeavors to establish."
In this case we need only substitute the words "fantastic claim" for "miracle". Then by the Hume test one would ask whether the prosaic claim of an experimental error is more or less fantastic than the discovery of superluminal neutrinos violating a centuries old postulate that holds up most of modern physics? The answer, of course, is that the experimental error would be less fantastic and hence the more probable explanation.
Now, to be sure, the researchers insist they left no stone uncovered in their desire to eliminate any errors: using the GPS or global positioning system they measured the distance accurately to within 8 inches, they factored in the rotation of the Earth, and even stopped traffic in a tunnel through the Gran Sasso mountain in order to calibrate their instruments.
They made it certainly sound like they dealt with all conceivable errors, but have they? Consider first that small perturbative glitches could have transpired due to anomalous differences in the Earth's crust over the time the experiment was conducted. Thus, a tiny deviation in the actual shape of the Earth itself (based on a science called Geodesy) could have incepted the 60 ns difference in speeds.
In geodetic refinements of shape (which also have a bearing on the value of g, the acceleration of gravity) a first correction is made relative to the initiating station. (E.g. see Spherical And Practical Astronomy Applied to Geodesy, 1968, p.
471). In other words, a first correction will be made such that (ibid.):
delta φ = φ - φ(T) = -H/g' (@g'/@x) cosec (1")
where H is the orthometric height of the observation station, and g' and @g'/@x (a partial derivative) are the gravity and the north component of its horizontal gradient, respectively at the initializing station.
A secondary correction is then made to the eccentricity of the station. The correction is to be applied when the latitude is observed off the reference station, and thus reduced the observed latitude to that of the reference station. For example, in the lower diagram, let P be the reference station and P' the eccentric station where the latitude φ(T) is observed. If the distance PP' is d, and the azimuth of the line is A, the identity for the length of the applicable meridian arc is:
R (delta φ) sin (1") = d cos (A)
and hence the correction:
delta φ = φ - φ(T) = d/ (R sin (1") x [cos (A)]
where R is the mean radius of the Earth.
If these corrections aren't factored in, then the timing error could amount to as much as d{e(t)} ~ 6 x 10^-8 s or a factor of ten in excess of the 60 nanoseconds of difference in the speed of the neutrinos. In that case, the CERN team's results would be found insignificant.
Stay tuned!
Stay tuned!
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