Friday, November 18, 2011

Statistical Analysis of the OPERA experiment

This one (sticky) blogpost will serve for accumulating everything related to the statistical analysis of the OPERA experiment (that found faster-than-light neutrinos).

PS: There is a rumor that OPERA has repeated its experiment with very short pulses of protons and the faster-than-light result persists.  If the rumor is true, then everything under the fold is irrelevant to the issue of whether OPERA is right or wrong.

PPS: OPERA confirms its result! See Tommaso Dorigo for a discussion, waiting for the pre-print to show up.

PPPS: the updated pre-print is here.   Almost all the objections that had been raised about the original preprint have been addressed.  If there is an error, it is inaccessible to the remote observer.  The way forward is to repeat the experiment elsewhere.

Unstick-ing this post.

PPPPS: Further comments from Tommaso Dorigo.

{Last update: Nov 18, 1:07 PM}

A lot of commentators on the OPERA experiment explain the faster-than-light neutrinos in terms of exotic new physics.  Another set of commentators seek an explanation in neglected relativistic effects arising from the earth's motion, the gravitational field,  in the synchronization of clocks using satellites, and so on.  These set of authors I completely ignore.

The set of commentators of interest to me, whose papers I've tried to gather in the links below,  accept the veracity of the OPERA data, but challenge its statistical interpretation.   If I was a physicist, I'd belong to this school of thought.

  1. The OPERA experiment simply assumes that the neutrino detection rate is proportional to a time-delayed version of the proton rate.   Several authors have pointed out that even a small effect at the leading and trailing edges of the pulse can eliminate the superluminal effect.  Various proposals are made.  For instance, when turning up and turning down the proton current, the beam geometry varies slightly from the steady state configuration of the beam.  The graphite target that the proton beam hits has a lot of energy deposited and heats up considerably, possibly changing its density, and hence the collision rate.  And so on.  Various statistical tests of the fundamental assumption that OPERA makes are proposed, but I think without the actual data from the experiment, can be nothing but inconclusive.

External links that have a bearing on the statistical analysis:
  1. arxiv:1109.4897, Measurement of the neutrino velocity with the OPERA detector in the CNGS beam,The OPERA Collaboration
  2. Why OPERA’s claim for faster-than-light neutrinos is not wrong, John P. Costella.
  3. arXiv:1109.5727, A possible statistical mechanism of anomalous neutrino velocity in OPERA experiment?, Robert Alicki
  4. arXiv:1110.0239, A simple explanation of OPERA results without strange physics, Gilles Henri
  5. arXiv:1110.0595, Is there a neutrino speed anomaly?, Juergen Knobloch (also arXiv:1111.3284)
  6. arXiv:1110.3783, A potential issue for the OPERA neutrino velocity measurement, Antonio Palazzo
  7. arXiv:1110.4781, Narrowing of the neutrino light curve in the OPERA experiment, Maurice H.P.M. van Putten
  8. arXiv:1110.4805, Some light on "Measurement of the neutrino velocity with the OPERA detector in the CNGS beam", I. Area, X. Prado
  9. arXiv:1110.5275, About Statistical Questions Involved in the Data Analysis of the OPERA Experiment, H. Bergeron
  10. arXiv:1110.6291, Comment on OPERA neutrino velocity measurement, Pierluigi Frabetti, Leonid Chernenko  (also arXiv:1111.3116)
  11. arxiv:1110.6408, Possible Origin Of The Neutrino Speed Anomaly Reported By OPERA, Shlomo Dado, Arnon Dar
  12. arxiv:1111.0282, Statistical model uncertainty and OPERA-like time-of-flight measurements,Oliver Riordan, Alex Selby

My stuff:
Nov 6: Workbooks 3 & 4. These suggest that an excess of neutrinos at the edges of w[t] may invalidate the OPERA results; a deficit is not so important.
Nov 5: A simulation in Mathematica.
Nov 4: Workbook 1, with fewer events. The variance increases more than expected.
Nov 4: Workbook 2: A second idealized example.
Nov 3: (corrected, expanded) Workbook 1: The numbers from a simple idealized example (PDF)
Nov 3: A simple model (PDF)