I think prior to my Physics analyses in the last 3 months = 12 weeks, I was enamored with learning a little more Japanese than I already knew more than 4 years ago, which is still a very little. In general I was doing some language analysis and wrote a few articles reg. this.

One fine day there was news that there has been a particle physics experiment that now finds neutrinos that move beyond the light, to make sense they are faster than the photons which as per Physical laws as we understand them now is a great shock. Nothing moves faster than light as nothing has a mass which is less than photon which is the lightest particle we know since ages. It is for this reason every elementary particle process is described in terms of speed of light which is conveniently taken to be beta = c = 1. So anything that has mass corresponds to 0 <= beta <= 1.

Neutrino is one funny elementary particle which we have discovered since 8 deacdes but know not pretty much about it. It eludes us in many ways mainly because their detection is a very rare process. If we do not catch them in large number in a short period of time we can not study all the detailed behavior as soon as we would like to. We understand every other old particles a great deal.

Neutrino is atmost as massive as 2 eV, as per our latest investigations which are based upon the fact that neutrinos occur in 3 types and they constantly convert into each other. No other particle has this property. It’s like a showman in a movie which can come in various attires and fool you until you realize it’s the same person. When I was a kid this kind of Bollywood movies were a favorite making, where I was often confused and lose my interest. But every one else would enjoy the movie. So in a way it was written that I would become a scientist because I would not catch these simple tricks. But to tell you the truth I was only ever partially interested about movies. If I thought hard I would lose interest from the mundane nature of entertainment and if I do not I would not follow the story. Later it has so happened that I would understand and enjoy the movies actually but would not spell it out. Gradually I fell out of any need to watch movies in crowds because it interferes with my imagination. That led me to watch movies that are not often talked about. I hated people who watched such untalkable movies in crowds. You can’t do a thing.

These neutrinos therefore were not supposed to move past the photons since they have some mass. Nothing does if it has some mass. I had wrotten 1 or 2 articles explaining why this is so prior to the OPERA experiment’s announcement of it’s results.

But in the last 3 months 70% of my effort was towards understanding this shocking “revelation”.

I started studying every detail and made few articles every day or alternative day. Based on my own analysis I was thinking consciously OPERA could be right. I am not one who tricks in serious investigations unless I tricked myself and realized that I did this on purpose to see something more interesting than I was ready to.

So I started studying special theory of Relativity and General theory of Relativity, the latter perhaps for the 1st time.

In the mean time I came across other fundamental problems of Physics and studied the motion of satelites from a Relativity perspective. They all pointed to lack of any explanation towards why one must see superluminal neutrino. By employing basic principles of Quantum Mechanics I had immediately seen that the much talked about Glashow and Cohen effect was actually not sufficiently convincing and infact the basic laws rather than a complicated, onesided and arbitrarily chosen constants must not have explained sufficiently the observed anomaly. Infact the conclusions drawn were hasty and they did not correspond to what was being observed notwithstanding what conclusions OPERA team was making of it’s observations. This I had described in two articles one of which was based on (special )Relativity only and the other on Relativity as well as Quantum Mechanics.

In the mean time I had reviewed some General Relativity from Weinberg’s text which I had coincidentially purchased from a book store, as I wanted to learn more clearly the ideas. There I came across the interesting equation which gives the causality violations for particles that have mass, in terms of the violation to the propertime.

Then I was involved a lot with studying the flyby anomaly where I had to work out on pen and paper about 50 pages or more and I saw very accurately why the flyby Galielo-1 is not actually an anomaly but expected with Theory of Relativity (general). When I thought more about it, it was clear that one need to have done all these calculations because one could readily see that teh Schwarzschild radi of the earth is only 9 mm, which is in teh order of the anomaly, all the satelites, not just Galileo-1. This naturally extends to Pioneer as well, and turns out that it is so. But till today I haven’t done any further analysis of Pioneer or other satelites. When I summarize my results in a paper or otherwise, it will be clear why all these data fits in their. That will be a test of my results as well.

Before this I had written one article which was based on the equation of Weinberg constraining the causality violation of Relativity by mass-have particles. I had made a small error and the constraint vanished, so I thought there is no constraint.

But now that my analysis with the satelites was over and again based on the handy calculations of Weinberg’s another equation I saw the exact time offset of GPS satelites, if any predicted by Relativity, special Relativity was my effort but general Relativity I immediately interpreted Weinberg’s equation and made some adjustments and saw that the GPS would only actuate very very small uncertainties for the OPERA time of flight of 2.43 ms, I think this number was prominently used by me as I had done a plenty of pen and paper calculations that I had obtained this number, I was also the first in all the blogs I had read to obtain the numbers 0.0025% or ~25 ppm as these were not directly quoted by OPERA. When things are like this, I like calculations, it is a pleasure of sorts because one need to think clearly and get good values before one can publish them in one’s blog.

So I turned my interest back to focus on OPERA again. Now I saw that I had made a few unscrupolous advent as to why uncertainty relationship itself might explain what OPERA sees as normal. I had done by this time a binomial analysis which was a diversion of sorts if you think, but not really, because it was needed in the satelite motion and relativistic time dilations etc that I had calculated.

When I returned my focus I was playing on my newly installed gnuplot to play with various functions and uncertainty relationship. I wanted to check if there is any energy excess I see if I extrapolate my binomial analysis functions. In other words {I haven’t summarized ll these results very well, but this can be redone, once my priority is available} I fitted the uncertainty equation of energy-time to extract the speed or Lorentz factor beta. I obtained various values as I was not sure exactly what I needed, but this was an intermittent step. When I calculated by solving a quadratic equation of beta which was a quadratic of quadratic of quadratic of beta or so, I saw that I am getting interesting energy excess or uncertainty and I saw that this value is potentially significant that this may explain the OPERA anomaly. So I took this calculations and I saw that there are some use of my earlier binomial analysis again, not just in flyby anomaly that I had reported in this blogsite.

I continued to obtain various values so I sat doing a more rigorous calculation, in about a hour or two I was seeing something very concise or elegant you chose the word since you are trying to decide so many things for me, what I should like, what I should say and what I should not, if only world were this strict when I was 5. well it was, but it did not change much in me. 😉

In those couple hours a major thing started coming up. I was up to my blogsite here to report all these, which is when I wrote the blogs: Light again {Not the same title: click on the link} and the succeeding blogs.

I had some oversights and variations in the beginning which I fixed in the latter blogs. But I have now a very basic relation between speed uncertainty and time uncertainty in terms compton wavelength of neutrino, assuming the nominal mass used by OPERA. This gives a very stringent criteria for what OPERA must confirm in order to win it’s claim of superluminal neutrinos. This is very unlikely that OPERA could, not just because nothing wins against Einstein’s theory, but because we simply do not have the kind of precision for energy that could have made the claims correct. The precision if comes to the level of these stringent criteria still might push the observed value in a desired way so as not to see any excess. In other words we have found the exact reason why OPERA anomaly is not one.

The summary of all the Physics analysis I did in the last 3 months …

When I looked back, like incase of my flyby anomaly, there was a simpler connection between the causality violation of propetime of a mass-have particle and the mass of the particle {which is essentially what Weinberg had given in his book, but was not explicit about this} Lo and behold the compton wavelength is somewhat “equivalent” to the mass of the particle since there is only a constant “action” h-cross and a constant speed c=1, or any value. This is quite remarkable since “we had seen” that it is the Schwarzschild radius which is equivalent to the mass of the gravitational source. In other words in all the anomalies, the anomaly is a precise function of the mass of the gravitational source or the mass of the participating particle.

But I also found a way to derive the “relation of speed-time uncertainty” I had obtained from energy-time uncertainty from “the propertime violation or uncertainty due to a mass” and both are therefore in terms of the mass or compton wavelength equivalent to that mass.

This ends up as a beautiful pleasure of the mind where one sees an unified behavior enscribed into the laws of nature as we understand today. The mass whether it is that of the earth or the neutrino, in the latter case given to any additional uncertainty on energy is what explains all these 3 anomalies if one is sufficiently careful.

Help me out here, but I thought the faster an object traveled the more mass it would have to have thus infinitely never being able to exceed the speed of light.

Are you saying that causality is the exception that can violate this law?

Hi Dimitri,

thanks for reading this. Actually this is a summary of many analysis I had done over the past 6-8 weeks. So I just wrote from mind what I had done.

Basically as you pointed out causality is the condition that nothing moves faster than light. The OPERA experiment claimed/observed or rather wanted a review from the world Physics community that it’s results are in shocking violation of that causality.

Now nothing moves faster than light since light particles are the lightest. I have another article which gives a mundane explanation of why nothing with a mass can go past the photons, this was written before the OPERA anomaly had come to light.

When I started my analysis contrary to any of my internal beliefs I saw no sign of causality violation of OPERA being explained by any Physics I knew or any Physics the world was explaining it with. In-fact as you may be aware there have been more than 80 papers some refuting it but none explaining it exactly why OPERA is seeing this anomaly. I had to go through pain staking analysis, I checked Quantum Mechanics, special Relativity, General Relativity and all my experimental knowledge but everything gave a zero excess when OPERA was seeing a big deviation from causality. I even came across an equation by Weinberg that gives a limit on causality violation, by Quantum Mechanics.

That equation initially made me joyous that it does put a larger constraint on what is a violation and what is within that allowed violation. Quantum Mechanics being probabilistic in nature imposes a condition that causality is violated to some extent given by what is teh mass of teh particle violating the causality. This mass when becomes much bigger the violation becomes much much smaller. So for neutrinos this violation I found to be something like 3.28% above or below speed of light. The OPERA was seeing 0.0025% above speed of light. So naturally I thought that OPERA anomaly has vanished. But I had committed a small mistake, a very small one which again brought that constraint to zero instead of 3.28%.

I involved in other interesting studies and solved another daunting anomaly from teh world of Physics. All these studies were motivated by OPERA anomaly. I returned to OPERA now.

One evening/afternoon just in 3 hrs I saw what exactly OPERA is doing is an oversight. And that oversight completely explains why it is seeing that anomaly. I returned to Weinberg’s equation and see that teh equation I derived is what Weinberg had given in another form. But these were two entirely different methods or equations. They become equivalent only when you have seen all the details or thought about the Physics behind these equations which doess not take one just an hour or a week. I had been thinking and calculating these since 6 weeks now. SO I could readily see it. I hardly even knew any General Relativity before. WHich is why I solved the other anomaly quickly, in about 2 weeks. It was a rigorous calculations spanning 60 or more pages on paper and pen. Some of it is available in this website.

Now that these two equations were equivalents intuitively, I sat dowwn and took another 15 minutes to derive my equation from Weinberg’s equation. Bam. It worked like charm.

Now I was confident that OPERA has really no anomaly if we are to apply the basics of Relativity special theory and Quantum Mechanics uncerrtainty principle. So I declared this on my blog here and put all that I had by then. I am writing in more detail and reviewing everything again. I had to follow several important and new mathematical tools to do this.

SO there really is no causality violation. What OPERA is seeing is merely within and much deeply within the allowed limits by Quantum Mechanics. Quantum Mechanics has always saved Relativity from falling from grace.

I hope this answers you …