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The effect of rotation of earth on the OPERA neutrino experiment

October 12, 2011

Mohan, mdashf

Major UPDATE: 7 nov 2011


“There is a fundamental way to understand just about anything …” {just an epithet}

It seems there are 3 remaining nails that need to be removed to free the neutrino from it’s coffin: 1st two are experimental methods at OPERA

1. pulse of Proton at source and pulse of neutrino at target, has a “time” offset which gives us 60 ns early arrival, need to be re-checked as per OPERA internal proceedings.

2. Neutrino target timing (measured from 2ndary decay?) needs to be rechecked as per OPERA internal proceedings.

The 3rd is basic physics:

3. Earth’s rotation wrt “sidereal inertia” (=distant stars) gives a centrifugal motion and a corilolis motion to the neutrino. The instantaneous Lorentz transformations accorded to the neutrino from the relative rotation along CERN & Gran-Sasso, also need to be calculated.

Between when I wrote this article and today a lot of understanding has developed reg. the results of OPERA neutrino most of which from my blogsite can be summarized into two categories. (all articles that were written after this one, you may consider this one of the main article that marks my discomfort with Dr Elburg’s paper, my discomfort may have started a little early to this article, but I haven’t gone back and check it. My discomfort with Sheldon Glashow’s paper I showed with another article prior to this one, but it didn’t take me long to dwell on the latter since there were not anything that was technically wrong although Glashow’s analysis didn’t convince me as I had mentioned.)

a. The shear incorrectness of basic physics of Dr Elburg’s paper

b. the details of the problem of rotation and GPS system.

I had started this rotation problem as a classical motion problem (and will eventually try to link to the relativistic motion effects, have successfully pointed out though that these are beta^2 effects in both cases hence the classical effect is good approximation of the scenario.) I will try to bring a betrer review in teh near future but for now I am commuting to another town to welcome a newborn kid to our family system which is not really badly synchronized. My elder sister got another baby-daughter just yesterday. SO I will put the calculations (that I had done before writing this article  and I had promised that day that I would update this, but haven’t had a time since most of the debates concentrated around the paradigm created by Dr Elburg’s paper)

SO here is another development that is very crucial (from my blogsite)

c. The relativistic loss of photon energy is significant enough and may be causing the neutrinos to cruise past the photons. This has also been described with enough details and diagrams. (today I posted the latest diagram which perhaps needs more explanation from me why it is a wow thing to notice, but there is a limit to human elation and I disgracefully cut myself down for lack of focus)

Here are teh calculations of this article.


The 3rd reasoning (point 3 at top) comes from the basic precinct of Classical mechanics and Relativistic mechanics. These are formulated in terms of inertial frames of reference. And at any time if you encounter non-inertial frames of references you have to take care of these in a proper way before you can be confident that you are correct in your calculations.

All terrestrial (earth-bound) computations can be considered from an external frame which is bound to a distant fixed star so that from that view/F.O.R. the calculations and laws are correctly implementable. When there are other frames (F.O.R.) attached to bodies that are accelerating linearly or angularly (=rotating) these latter are not inertial F.O.R. hence additional care is necessary before we can obtain correct results from the calculations of the Laws. eg Our earth is spinning around itself, rotating around the sun in a perennial orbit and the Solar system including the sun is in motion wrt the Galaxy C.O.M and the Galaxy is drifting/expanding in the Universe.

For terrestrial measurements the earth spin and it’s sidereal motion (motion wrt the star because of orbiting around the sun) must be taken into account. For most classical processes on the earth that we can observe unaided by instruments (such as the motion of a football kicked in a stadium) this does not bring any significant deviation from actual result. But an airplane or a space-projectile like a rocket may be significantly affected by such non-inertial-ness of F.O.R.s attached to our planet earth.

BEGIN UPDATE: 7 nov 2011

(One of) These effects is maximum along the equator and minimum at the poles because of the size of the circumference at these places along which rotation takes place. (the other is reverse!) At any latitude the effects (such as angular and linear velocity) are reduced by the cosine of latitude. For a maximal effect one can consider the maximums at the equator and the maximum earth radii which is 12 kms above the average earth radii.

Thus the spinning of earth gives rise to two pseudo forces that need to be subtracted from the regular force to get the effective inertial forces in the problem at hand. One of them is the centrifugal force or inside the rotating earth the centripetal force, which comes because of the rotational non-inertial-ness of the earth along the axis through the two poles. The earth spins at ~500m/s =0.5 km/s at the equator (>1000 miles/hr). This corresponds to a pseudo acceleration (centripetal acc.) of about 3.38 cm/ss, or 3.38 aua. (this is with sidereal or distant star correction) This is usually balanced by the attraction of the sun. (Did not check the last statement but it is true, read from various sources such as Weinberg’s text on Gravity)

One aua is 1 cm/ss. I have defined this unit as this fits perfectly for the atomic phenomena. AUA = aua = atomic unit of acceleration = 1 cm/ss = 10 x 10^-6 x femto-meter/(ns)(ns), in this unit, g = acceleration due to gravity = 9.8 m/ss = 980 aua (atomic units of acceleration) If a particle is accelerated across the “diameter of a proton” in one nanosecond at a change in speed of “1o0 ppm of the proton-diameter in one nanosecond” WE call it atomic unit of acceleration.

Note that 1cm/ss is actually 1 AUA/aua.

So the centripetal acceleration from Earth-spinning is about 3.38 aua or a very small fraction of acceleration due to gravity which is 980 aua. (0.345% of g) [|a_cfg|max=wv]

The other pseudo-acceleration is called Coriolis Effect. It becomes active only when an object has a relative motion wrt the non-inertial F.O.R., all objects at rest in this frame experience only the centripetal effect. This effect is zero at the equator and goes down with latitude in both hemispheres with opposite direction respectively, in the northern hemisphere such a deflection is always to the right of the original motion of the particle and opposite for the southern hemisphere. At the equator since the angular vel. is horizontal this effect is zero. At the equator the speed is 0.5 km/s. This acceleration is never larger than 2wv ~= 1.5 x 10^-4 v, [SO |a_crs|max=2wv] (~0.69% of g) that is, this is nearly double the maximum centripetal acceleration.

The detailed values for our situation of OPERA time of flight is available in the scanned pages above.

The 3rd effect is associated with relativistic transformations, where the changing speed of a particle makes the F.O.R. of the particle non-inertial wrt the Lab frame and infinitesimal inertial F.O.R.s are considered for Lorentz Transformation. This gives rise to secondary boosts and rotations. The rotation is called a Thomas precession. This angle or frequency depends on the various velocities associated. But for our purpose since the neutrino and photon travel essentially at the same speed (the speed excess is only 25 parts per million parts hence any non-inertial effects are only minuscule)

NOTE: I have posted today, 7 nov 2011, the general relativistic contributions to the time-relay of the GPS satelite, a few weeks earlier I had shown the special relativistic shift or time dilation towards the time-relay (this latter is actually Transverse Doppler shift) SO we do not need any Thomas precession frequency analysis any more. I will post another article with longitudinal Doppler considerations. If I could, I will think about how Sagnac effect fits into the whole situation. The effect of solar radiation is considered in a GPS satelite system. One can also integrate the potential energy of the Sun and other perturbing masses in the Solar system by having a good functional trajectory of the satelite in a convenient coordinate system. Also I have noted in the article posted today, 7 nov 2011, one can have a general relativistic treatment to the Centrifugal and coriolis effects described above by converting their forces into potential energy terms and invoking the gravitational time-shift as treated in Weinbergs text. The 2nd of this will only lead to an effect consistent with the 0.3% or 0.6% of acceleration due to earth’s gravity effects on the satelite. The perturbation of Sun and other planetary masses will cause a very very negligible effect as is obvious.

END UPDATE: 7 nov 2011

I will attach the calculations I have made, once there is internet and power, so I can scan the papers and post. Here is the result. (NOW the scanned pages are attached above)

Classical mechanics gives maximum centripetal deflection of 0.55 cm for the neutrino and maximum coriolis deflection of 1.136 cm for the neutrino for the entire 733 kms (with sidereal inertia correction). Relativistic deflection will be far less since neutrinos and photons have essentially same speed. Assuming these deflections are zero for the photon one does not make any special privilege for the neutrino. WILL upload the calculations later … (Relativistic deflection is Thomas precession frequency)

Maximum comes from maximum earth radii (12 km more than average) equatorial spin of earth (at any latitude it goes down because of cosine)

any zero contribution because of direction issues is not given priority, hence maximum is over-ruling as it comes from maximal deflection.

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