2 ns spacing between the pulses implies that pulse shape and duration cannot explain the earlier OPERA result as a measurement error. Effectively one studies individual neutrinos. Pulse shape and size has provided for the main stream theorist a cheap and fast way to explain the observation out from his mindscape. Certainly this finding also kills large class of explanations for neutrino super-luminality. Of course, one must still keep mind open for some delicate measurement error. Lubos suggests that there is a systematic error in GPS system, other colleagues have not taken this option seriously.
Sooner or later colleagues might be forced to accept that there is no other alternative than admitting that special and general relativities are somehow wrong. I realized this already towards 1977;-) (and lost my job in Helsinki University within few weeks!). Sub-manifold gravity allows Poincare invariance of special relativity as an exact symmetry unlike general relativity and provides geometrization of known fundamental interactions in terms of sub-manifold geometry for H=M4×CP2.
Sub-manifold gravity also leads to the notion of many-sheeted space-time meaning a revolutionary vision about space-time topology in macroscopic and even astrophysical scales. Maximal signal velocity depends on space-time sheet, has an absolute upper bound, can depend on the distance scale and particle type but not on particle energy in continuous manner, and one can build an argument why it would be higher for neutrinos than for photons. This explanation is not anything tailored to explain OPERA result but is just one particular kinematical consequence of sub-manifold gravity. As a scientist I want to not lose professional skepticism as a basic attitude, but if you do not squeal to colleagues, I can just privately reveal that TGD is it;-)!
For the details of TGD based model of effectively super-luminal neutrinos see the article Are neutrinos super-luminal?.
8 comments:
The pions have the mean lifetime of 2.6 10^(-8) s that gives the wave packet "mean length" of 7.8 meters for neutrino. Does it have anything to do with the time uncertainty of the neutrino registration in Italy? Thanks.
You probably mean that pion decaying to muon and neutrino travels on the average 7.8 meters before decaying and this shortens the distance travelled by the neutrino.
This is true but does not explain the effective super-luminality. Since pion is on mass shell particle, it travels with a velocity of light at most (the velocity is very near to light velocity from the fact that the neutrino is very energetic).
It is enough to assume that what travels is first pion and then neutrino and that the travel begins at the reaction vertex creating the pion. If I remember correctly, the distance corresponding to the effective super-luminality was about 18 meters.
No, pion stays at rest and decays with a mean lifetime of 2.6 10^(-8) s. It is neutrino wave packet size which is estimated as 7.8 m. For a moving pion the time of decay is dilated, but the wave packet length is Lorentz contracted, no? So the neutrino position uncertainty is about 2*7.8 = 17 m.
What QM says about time uncertainty of registration of a very monochromatic wave packet?
Some comments.
a) Your observation about time scales is interesting. I understand that you are keen to understand whether this is a co-indicence or something deeper. Why pion lifetime at rest would define the width of neutrino wave packet? But even if you assume this, Lorentz boost to neutrino energy would make the wave packet much narrower.
b) Pion cannot be at rest. Neutrinos have energies much above pion rest mass so that pion must be relativistic. First a relativistic pion is created and decays to muon and neutrino. The collision time of protons beams defines the time interval at which the travel begins to Gran Sasso. This allows to get rid of unknown details of the event.
c) In Lorentz contraction one speaks about geometric size: wave packet size is not this kind of size and you should look what happens to wave packet in Lorentz boost. Particle lifetime is also time scale whose definition involves state function reduction and quantum statistical approach unlike time scale associated with the duration of wave packet.
I should refuse to say anything about time uncertainty in registration of a very monochromatic wave packet;-). The formalism of QFT uses momentum eigenstates and it is far from clear how a description in terms of plane waves are translated to the classical picture used to describe measurements.
I think that the key notion is finite measurement resolution for both momentum and for position. This is what wave packet description would correspond. What determines in particular case the width of the wave packet? I cannot answer this question. You propose pion lifetime.
I encounter this problem in TGD.
*Causal diamonds (intersections of future and past light-cones are basic objects) and this requires that measurement of particles with definite momenta involves also a localization at light-like boundaries of CD. Since measurement resolution is finite, one has wave packets both in x-space and momentum space and the conflict with uncertainty principle shoud be avoided.
*The localization inside CD suggest also problems with Poincare invariance. The proposal is that extension of Poincare algebra to Kac-Moody algebra allows to circumvent this conflict.
I applied the resting pion mean lifetime tau in order to estimate the wave packet length of a massless neutrino. You are right with saying that in a moving reference frame this length is shorter, but it is no Lorentz contracted, as a matter of fact. I first thought that time dilation would compensate the Lorentz contraction, but there is no Lorentz contraction. It can be explained in the following way: a moving pion has the mean lifetime dilated (Delta T = tau with the square root is in the denominator). The wave front moves with c and the pion moves with c - epsilon. The wave packet of the neutrino emitted in the direction of moving pion will be the dilated mean lifetime multiplied by the velocity difference (epsilon). It is shorter than the wave packet in the resting reference frame. It is even shorter than the Lorentz contracted length if the Lorentz contraction would be applicable here (by factor 1/2). I did not expect that there might me such a contraction. Thanks for conversations anyway!
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