This article was original written on 16.12.2011.

Edit: 25.11.2013, 17.10.2018. 


This article tries to put on record exactly why OPERA neutrino anomaly, FLYBY of Galileo anomaly and PIONEER anomalies are not at-all anomalies, based upon my research from late 2011. On 25.11.2013 I sat for couple hours and reviewed the article written from 2011 and added contents. Since I am reading after couple of years I reminded myself exactly why these are not anomalies: and here is why. 

Anomaly from OPERA experiment involving neutrino base line:

The mass of elementary particles is equivalent to a proper-time and in another way to the Compton-wavelength. Compton wavelength is defined as \lambda_{Compton} = \frac{h}{mc} where c is the speed-of-light in appropriate units, m is the mass of a given particle, note that h is the Planck’s constant, not the reduced Planck’s constant, usually found in quantum mechanical treatments.

So in case of the OPERA experiment, the neutrino howsoever it challenged the physical validity of the sanctity of proper-time of photon — that proper time of photon is always zero and minimum among all elementary particles, because its a tiny little smurf with hardly any-mass, it could not run faster, because it has mass.

Again the energy uncertainties of the experimental detector would equivalently add mass to the neutrino, a fact completely over-looked by OPERA experiment collaboration.

Photon proper-time is defined to be least, because its mass is zero, hence neutrino must always take more time than photon, for traversing the same distance, but OPERA claimed otherwise. All in all Relativity + Quantum Mechanics restores the anomaly to its nemesis. 

Anomaly from FLYBY of Galileo and PIONEER satellites:

For an explanation of the anomalies while equivalence or relativity of mass, momentum, energy, wavelength etc are not needed here, whats simply needed is mass. This mass is a Newtonian concept but rather refined by Einstein’s theory known as Theory of Relativity which branches into two aspects 1. special theory and 2. general theory.

This theory was simply not applied correctly — and the bewilderment spooked the author,  not applied for 3 decades. Given then you can see the relativity or equivalence of mass and radius, the radius-effect of earth and other such objects were not taken into account.

I told you Einstein not only equivalenced mass and energy, that’s only gossip when luminaries tell you that, who wants physics anyway? He also told us several other things, namely: mass-energy-momentum, distance-time, mass-distance, electricity-magnetism and so on, are equivalents. 

For earth’s mass, a radius effect is of the order of less than 1 cm, a property known by the name Schwarzschild-radius, hence no-matter which trajectory our satellite moves on, an error of less than 1 cm a priori is understood from theory of relativity. For sun’s mass  that would be 3 km effect, valid for the satellite known as Pioneer, but in this case our radars are on earth and pioneer is too far away from sun’s surface as a consequence the effect again comes to level of millimeters. 

This is a a technical article explaining the mumbo jumbo of advance concepts of physics but also sprouted with humor like the following: 

1. But I did not find that article after trying all sorts of search parameters I could on my own web-site. This is one of the time when you realize web-sites are like spouses. Even if its your own spouse, you may not find the answer from him, her at your will. 

2. Thank You and leave physics (alone) if you are not smart, she already has a lot of problems of her own, they are sometimes known to break the hearts of her most ardent lovers. 

Some interesting discussions in the comment section of this article. 


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 on my language analysis.

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 (neutrinos) are faster than the photons. This 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. Photon 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. The speed-of-light is conveniently in various contexts taken to be \beta = c = 1. Therefore, anything that has mass corresponds to 1 > \beta \geq 0.

Neutrino is one funny elementary particle which we have discovered since 8 decades but know not pretty much about it. Neutrinos elude 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 at-most as massive as 2 eV, as per our finding as of today. 

In other words: 2 eV is an upper-limit on neutrino mass, in the terminology of particle physics and eV is the unit of mass in particle physics, actually \frac{eV}{c^2} is the unit of mass, as eV is the unit of energy but in particle physics the most attractive units of physics called as natural units are used, where in c is always 1, hence the units do not show up explicitly, but when one needs consistency as in the case when one keeps changing between various units, one shall be very careful. 

Here is one article — A tip on speed of light units, which I had written on this web-site clarifying how consistencies call for the usage of the right-unit for variables such as mass, energy and momentum which are all interchangeably expressed as eV by the particle Physicists.

This is so because in natural units where c = 1 this difference of energy being: eV, momentum being energy per speed-of-light, hence \frac{eV}{c} and mass being momentum per speed of light, hence  \frac{1}{c} \times \frac{eV}{c}, which is why mass is energy per speed-of-light squared, \frac{eV}{c^2} does not show up.

— This paradox is easy to remember, de-mystify if you remember E=m.c-squared.

But particle-physicists would very swiftly express mass as eV — eg electron mass is 0.511 MeV, rather than the more explicit, electron mass is 0.511 \hspace{3pt}\frac{MeV}{c^2}, momentum as eV — e.g. the proton was flying with momentum 1 GeV, rather than proton was flying with momentum 1 \hspace{3pt}\frac{GeV}{c} and so on.

But I did not find that article after trying all sorts of search parameters I could on my own web-site. This is one of the time when you realize web-sites are like spouses. Even if its your own spouse, you may not find the answer from him, her at your will.

If you are not very good and comfortable, at using natural units, try expressing everything as their explicit forms would be, which says if you are smart to understand this, that is if you think you are really not smart, do not use natural units. But once you are not using natural units, do not claim you are smart. Thank You and leave physics (alone) if you are not smart, she already has a lot of problems of her own, they are sometimes known to break the hearts of her most ardent lovers. 

But if you are smart, its highly likely you are good and comfortable, at natural units, and you will resort to another method of looking at consistency. Go nuts on how you express mass, momentum and energy all to be expressed in eV. But when you are calculating something be consistent everywhere.

eg if you know that earth’s gravitational potential must be in the order of 10^{-9} and you do not obtain that, try seeing where speed-of-light values must be inserted first, if needed to be, to bring consistency. There is no other hard-and-fast rule, but rather to look at what you know and how to implement it all and to know all that has been solved and found out: e.g. how its been found out that earth’s potential is 10^{-9} for its consistency, in SI units.

As an added note: the speed-of-light entails G = 1 and h = 1 where G is Newton’s Gravitational Constant and h is Planck’s constant. I think that was all that was the jest of the linked article — A tip on speed of the light unit, but I might have had other interesting points there, so kindly notify me if you come across that article. — It seems the article was later found and linked. 

See I write blogs because I can’t remember everything, at once. Its perfectly legit to not remember every damn thing even if its important, more so in physics. But you must figure a way to fall back to tranquility by finding whats needed, in a given situation.

Now lets get back to the neutrino: this mass-limit of 2 eV on neutrino, is as per our latest investigations which are based upon the fact that neutrinos occur in 3 types and they constantly convert into each other, a process known as neutrino oscillation or neutrino flavor oscillation. No other particle has this property. It’s like a showman in a movie who 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 for making by the then movie community, I was often confused and would 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 unthinkable 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 written couple of articles explaining why this is so, prior to the OPERA experiment’s announcement of it’s results –and tons and tons of articles, after the experiment declared its results. 

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 alternate 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 satellites from a theory of relativity perspective. They all — my studies, pointed to a 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 in-fact the basic laws rather than a complicated, one-sided and arbitrarily chosen constants must not have explained sufficiently the observed anomaly.

And in-fact the conclusions drawn by Sheldon et-al 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) theory of relativity only and the other on  theory of relativity as well as quantum mechanics.

— One of these article could be the following linked one, as I have said there have been a large number of articles on these anomalies I pretty soon lost track. But I am just linking because anyway its relevant. Note that the linked article will be thoroughly edited, anytime in the future, because its bedraggled in its appeal at the moment. Article: What is the (f)utility of Sheldon Glashow’s paper towards OPERA result.   

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

Then I was involved a lot with studying the flyby anomaly where I had to work out on pen and paper about 70 pages or more and I saw very accurately why the flyby Galileo-I is not actually an anomaly, but expected with theory of relativity — general and special aspects of the theory taken together.

When I thought more about it, it was clear that one need to have done all these calculations because one could readily see that the Schwarzschild radii of the earth is only 9 mm, which is in the order of the observed anomaly, of all the satellites, not just Galileo-I. This naturally extends to Pioneer satellite anomaly — another infamous satellite anomaly, as well, and turns out that it is so — that is, they both have same source of explanation.

But till today I haven’t done any further analysis of Pioneer or other satellites. When I summarize my results in a paper or otherwise, it will be clear why all these data fits in there. That will be a test of my results as well — the fact that other satellite anomaly will also be explained by my analysis will be the stringent criteria to judge the validity of my results I think, because they are all in the \frac{mm}{s}  range of speed anomaly.

Before this I had written one article which was based on the equation of Weinberg, constraining the causality violation of relativity theory 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 satellites was over and again based on the handy calculations of Weinberg’s another equation, I saw the exact time-offset of GPS satellites, if any, predicted by theory of relativity.

Working on special relativity was my effort but for general relativity I immediately interpreted from 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 2.43 ms 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 — even in one’s blog.

So I turned my interest back to focus on OPERA anomaly again. Now I saw that I had made a few unscrupulous advent as to why uncertainty-relationship itself might explain: what OPERA experiment 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 satellite motion and relativistic-time-dilation etc that I had calculated.

When I returned my focus I was playing on my newly installed gnu-plot to play with various functions and uncertainty-relationship. I wanted to check to see, if there is any energy excess I (would) see if I extrapolate my binomial analysis functions.

In other words; I haven’t summarized all these results very well, but this can be redone, — once my priority is available, I fitted the uncertainty-equation of energy-and-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 these 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 blog-site.

I continued to obtain various values so I sat doing a more rigorous calculation, in about an hour or two, I was seeing something very concise or elegant. In those couple hours a major thing started coming up. I was up to my blog-site here, to report all these, which is when I wrote the blog: Light Again — Linked article is not the same title: just 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, — there are 3 kinds of wave-lengths, and Compton-wavelength is the one defined by mass, de-Broglie’s wavelength by momentum, for a technical contrast, assuming the nominal-mass used by OPERA-experiment.

In particle-physics experiments such as OPERA-experiment a nominal mass means a so very well-known value for the mass that it be used in situations (1) to verify a hypothesis or (2) to give a hypothetical value to a quantity or (3) to claim the value of mass of a particle.

Momenta on the other hand are arbitrary in the sense its a distribution. When a mass is a distribution its not called a nominal mass, rather a distribution of mass, hence a nominal value means a fixed, acceptable, well known value.

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.

This is the summary of all the Physics analysis I did in the last 3 months. 

When I looked back, like in-case of my flyby anomaly analysis, there was a simpler connection between the causality violation of proper-time of a particle with mass and the mass of the particle. Which is essentially what Weinberg had given in his book, but was not explicit about how this is such a attribute of the relation.

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”  — which I had obtained from energy-time uncertainty before, from the “proper-time violation or uncertainty-due-to-a-mass” and both are therefore in terms of the mass or Compton-wavelength which is equivalent to that mass.  

So energy-time goes to speed-time when you know uncertainty of mass, because energy has speed and mass, then mass is Compton-wavelength and proper-time, all in all the unification achieved by the grand artisans of physics I not only understood in 3 weeks but also applied to “solve-as-per-my-claim-so-far” 2 long-standing fundamental-anomalies and one PIA-anomaly that would have thrown physics into darkness for who-knows- 10 years or 100 years.

I am not claiming a savior I am claiming I did in 3 weeks, what most people did not in 30 years, and I did, sitting like this through hard-work: morning, evening, night, morning cycles for 3 weeks.

This ends up as a beautiful pleasure of the mind where one sees an unified behavior inscribed 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.

3 thoughts

  1. 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?


    1. 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 …


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