The neutrino speed excess as a function of energy.

This article was majorly updated on 31-01-2012, Some of the contents in this article are hypothetical and/or phenomenological in nature, for a sound theoretical basis review my paper:  Opera Anomaly Analysis — many equations might have disappeared, word-press issue, these are gradually getting fixed by me.

“If you are not willing to commit a mistake in learning you are not learning, when you are not learning you are committing a bigger mistake than that, as far as I know there is no substitute to learning ..”

2 points of OPERA experiment raised:

1. accuracy of GPS,

2. ref. index of material in the path/base-line

**also they are mentioning rotation of earth, HolyS, should they also mention budget-time and tax-dollars?**

these two are not adding any uncertainty of significant ignorance, why?

1. GPS is keeping an eye on both baseline of photon and neutrino, {Updated, 31-01-2012: the baseline of photon being a hypothetical one} it will add the same effect to both, if you found it affecting only one of the beams you have possibly found a syst. effect, in-case both of them are affected and it was not accounted for, you still have a syst. effect but in that case you deserve a champagne treatment from the experiment folks, if not thanks for being a netizen {Updated, 31-01-2012: I have also done plenty of analysis in this blog-site which shows why GPS contribution is merely insignificant, a ps scale effect to a ns scale measurements in the OPERA tof of 2.43 ms}.

2. ref. index: the two baselines **actual path covered by neutrino and photon** is known to 20 cm accuracy. That is, this is the only source of error. It adds negligibly to neutrino baseline. For photon even if you consider a high refractive index **eg IRON:  n=3** and assuming this unknown path has iron throughout, the light has an optical path of 20 x 3 = 60 cm, a 40 cm excess: again negligible for a ~731 km photon-baseline.

optical path: the maximum distance traveled by light in a given time. [Fermat thought “in the smallest time”]

Fermat’s principle: in any media of any combination and degree of refractive index light takes that path which is closest to it’s optical path. **Snell’s law of reflection and refraction is derivable from Fermat’s principle**

The above two definitions I gave, I am proud of them, I did review a lot of basic physics before I made my mind for these definitions. Welcome to venture to find inconsistencies.

Fermat’s principle is responsible why we see ourselves in the mirror in the first place. **nothing  about why we seek ourselves in the mirror** Vampires not only violate parity, they also violate Fermat’s principle. **Joke; Once Fermat called his wife a vampire: you vampire you do not obey my principles … **

There is also an explanation for that joke **if you need message me** well here it is: Fermat stood in front of his mirror and could saw himself, thought of the reflection and derived his famous principle, his wife didn’t know of the mirror thing and didn’t believe the community would take Fermat’s conclusions seriously hence said “this is not true” what else Fermat could have come up with?

Here is a biography of Fermat, since I am using his principle: he was an accomplished mathematician who is called the father of number theory or “modern theory” and he calculated probabilities based on this theory. He had given the law of reflection **deducible from Fermat’s principle**. He was a counselor of legalities and ethical conduct and general scholar and linguist. In short a polymath …

Here is the plot of the data from the 4 experiments above **and don’t say they do not tell you anything, they say a plenty of things, read after the plot**

NOTE: The speed excess in ppm, I have plotted here, can be directly seen as average of (mean-error) and (mean+error) or the upper limits, at their mean energy. In case of MINOS I have taken only the highest energy and the highest speed-excess ppm. ppm: parts per million, error = syst. and stat. in quadrature, we take quadrature because that is “up-to the 2nd order blowing of the errors”?

Here is the conclusion/observation: the neutrinos have been found to be consistently traveling faster than photons in vacuum, in 4 independent experiments. **I will try to include two more experiments all independent from each other**, their speed increased beyond photon speed, with increase in their energy,

1. there is no speed limit in nature if this curve goes above and above and above.

2. there is a speed limit **for neutrinos** if this curve saturates at a point.

3. particles other than neutrino, in principle, can show this kind of energy dependence in breaking the speed limit of each other.

4. The photon energy dependence is the horizontal axis since it has a zero rest-mass …

5. in string-theory like understanding (STU): photon does not have a zero mass: it’s mass lies in range

hence the photon curve may have a similar increase in speed with energy, at the level of it’s precision in the STU, if that were so, this would be a validity of string-theory like structures, a correspondence we had been looking for in nature …We don’t see it cos we do not have the capability at present to see it, given the precision required to do this.

6. most likely emerging situation: every particle has their speed limit, a function of their energy, that is there are as many theory of relativity as there are “energy sectors” which do not run into each other … {Updated: 31-01-2012, I am Happily wrong, situations like this reminds me Hawking’s wit in losing bets where he is on the side of the underdogs but when he is wrong it only goes towards the side of those who are correct, I call it Hawking like Wisdom HLW, at-least for now there is no multiple theory of Relativity }

7. we should make this test on other suitable particles that have a required energy scale.

NOW a little more I think that can be done to this study: the emerging experimental situation reg. neutrino is this: (eg) in Belle/Belle-II there are plenty of neutrinos to study **has been studied from other angles**, there are also a vast amount of neutrino. One can study a “pure” neutrino energy Vs speed. This will give the energy dependence of the neutrino wrt to their measured speed distribution. This is important, what is not important is the bias wrt speed of the neutrino sample, if any. **a baseline measurement such as OPERA and MINOS take care of this bias**. One can match the nature of energy dependence of all neutrino (wrt speed) available to experimentalists and give a suitable hypothetical bias, if it can be assigned, if needed and see that indeed “there is more to Relativity than we have been prepared to accept”.

Updated, 31-01-2012, wrt the above paragraph; read our newest analysis which restores the validity of Relativity, of OPERA neutrinos; {OPERA anomaly analysis by M. Dash and M. Franzen }. Then we can study such energy-speed distributions but aso be cautious about the uncertainties on energy and speed.

Now something I just feel like sharing with you:

People in the Physics community knew that the neutrinos are doing something funny with the photons much before I was borne, so they did not approach this problem directly but through particle physics, they knew that if they could come up with a large spectrum of energy they could possibly tackle the “holier than Einstein”, Lord’s slaves, much efficiently than if they deal with the question of speed-limit directly. You will see how many results will actually pour in. 1st will come the Lord’s slave mania, they will cram you with all their silly notions. {Updated: 31-01-2012, The Lord’s slave mania often serves many people to go with pride “see didn’t we say OPERA was incorrect?” That’s the biggest folly of science today, we have become smarter with what to say and not to say, but not to study science as such..}

Even if they do so I just hope we see what is reason and what makes sense Physics wise in the best traditions of science and work on those to propel the caravan of science.