Here is what **I promised for MINOS: **

( — * in general the energy-time uncertainty relation in particle detectors, in terms of speed-time uncertainties for any particle*)

**gamma** and **gamma(c)** are **NOT 1,** but **large numbers** given by binomial factors.

( — * a mistake that, I said previously, gamma=1*)

**I reviewed and the gammas do not really turn out to be very large numbers**, in fact to** 20th** power of **beta** **gammas** go to **order of 5.002,** *in the right units*** everything fits in so well** we will get a **very exact number** for **minimum energy uncertainty** in the order of **eV**, most likely **~4 eV**.

So **OPERA** must **come clean** on **total energy uncertainties** *below* **say 4 eV** *to* **claim** **superluminal neutrinos**, *at their* **quoted levels of uncertainty** *on* **time**.

This is **also in line with an article** *I wrote* on **31/October/2011** .

**In that article**: *citing Weinberg’s results from his text book*, Weinberg’s results were for **uncertainty** *on* **proper-time** *of* **neutrino** *in the same order* **we find** *our* **speed-uncertainty*** to be*, which only means the **7.5 km/second quoted by OPERA-experiment **will be **washed away** *by* as **little** as **4 eV** **uncertainty** *on* **energy**.

This is also **most likely, and I seriously think IT IS,** that **MINOS-experiment** *does* **NOT** see any **speed excess** *consistent* with their **significance** as they had **kinematically and combinatorially** *factored-in their neutrino mass*, **to be in the order of ~50 MeV**.

It is **NOT** the **uncertainty-in-energy** *or* **uncertainty-in-time** *howsoever small or large they may be* **that is** causing such excesses to be **meaningful ***or*** meaningless**. It is the** uncertainty relations** *of* **energy-time**, **speed-time** or (**proper-time**)**-time** that is in the** order of h-cross,** which is **good enough ***to*** void ***or*** invalidate** any claims of **superluminal attributes neutrinos ***were* **thought to have**.

**Below you will only have to remove a 2,** *that* I **mistakenly** **put** *in-front* of **h-cross**. **SO** the** minimum-error ***is* **2.61 mm/second** *NOT* **5.22 mm/second**, *and so on*. BUT **other ideas are correct**, *eg* *the idea that you have to fit the* del(

**E**).del(

**T**) =

**0.75**

**eV-nanosecond**

*might actually be fitted*to

**0.375 eV-nanosecond**.

*This is because*

**while E, v, p, m, t**are all

**equivalent**,

*mathematically*( — that is as an additional

**constraint**)

**E = p.p / 2.m = (1 / 2).m.v.v**.

( — with a **gamma** nearly **= 1**) *Do you* **SEE** the **2** *now*? ( — or will it be further **changed**?)

Here is an** additional note** I would make to place a **relevant concept** as befits the above few lines. ( — wrote today: **26.11.2013**) **Whats meant by equivalent?**

And whats use of saying additional constraint? **Theory of Relativity or Einstein’s work** centers about whats called the **equivalence principle**. Here is what its all about. When a contribution to *variable* **A** comes from **B, C, D, E …, F** and so on, we say **A is equivalent to all those variables**. But it would be **mathematically inconsistent** to* replace the equivalence with a sign of equality*. **Because** *only* **a part of eg B comes into A** and we need to know what part, **exactly**. Or else we would be mathematically inconsistent and therefore **Physics: Laws of nature** will be wrong or rather incorrect.

The **laws of nature or laws of Physics** are nothing but a **mathematical statement of the constraints on a Physical system**. So once we know **what exact part of A is contributed by say B**, we say (this part of ) **A comes exclusively from B**. So its only **partly A that comes exclusively from B** and that part is equal to B with addition of Physics Unit-and-Dimension scheme.

Similarly **A is contributed exclusively by C, D and so on**. If you add Quantum Mechanics here that would mean there has to be a finite or infinite set of variable that only contribute to the variable A. So whats equivalent is a Physical Attribute that a particular variable contributes to another. But whats equal is a mathematical constraint or equation and when its available for a Physical System we say its a Law of Nature.

Here those equations are **E = p.p / 2.m = (1 / 2).m.v.v**. Only such and such forms have been found to be correct and these additional constraints must be applied. Here is a popular mistake committed by the luminaries when they say eg **Mass is equivalent to Energy**. So in natural units they set them equal; **E = m**. So-far-so-good this is **inconsistent** if you are to remember **E(squared) = P(squared) + m(squared)** in **natural units.**

— a **natural unit** is again when **c =1**, so we set to write **E, p, m ***all as*** electron-Volts**, but in other units one has to be cautioned not to do that.

So when this **2nd equation** comes about it reminds us the **variable ***that*** E is**, is *NOT only* **equivalent to m** but also **equivalent** *to the* **variable p**. **E** is therefore equivalent to **m** and **E** is equivalent to **p**. So **Energy is not only equivalent to mass but also momentum**. Its a **catch-22** because in-case of **photon** you simply **can’t ***say ***E = m or E = m.c(squared)** because **that** would *make* **all energy equal to zero**. **YES** *Photon always be a mass zero*, it just does not have that property called mass. Its like **Mr Ding just doesn’t know Tagalog** *or* **has never studied anthropology**.

So a **photon does not have ***guess what* **a rest-frame or a rest-mass** etc. These are all spurious, dubious terms for Physics. **One shall only go home with the idea that Photon; all it has is energy and momentum.** Which makes photon’s invariant mass to be zero since momentum and energy are exactly equal, a case only when mass is exactly zero all the time.

( — invariant and single photon mass for all you puritans, a point which always explains why all confusion regarding photon can easily be dealt, eg **why in medium photons are slower than say electron, because invariant mass of photon is no longer zero, **it would explain everything else eg why photon bends under gravity because its invariant mass is no loner zero, a single photon would also bend but for the reason that it has got energy and momentum which have equivalent effect as that fof mass, but don’t say photon has an effective mass, thats hot-water, and perhaps wrong also. One could easily say according to Gravity Theory of Einstein not only mass interacts with mass through gravity but momentum and energy will be equivalently respond to or create gravity)

** Given that;** one shall always remember the 2nd equation **E(squared) = P(squared) + m(squared)** as a constraint. So we see immediately that once **E = m = 0**, (only mass-less particles) the 2nd equation known as Einstein’s relativistic equation or energy-mass-momentum relation gives: **E = p**. A fact you all know is associated with Photons. All of Photon’s energy ALWAYS comes from its momentum only as it does not have a property called mass, and thats the beginning of Quantum-Mechanics (or wave-particle duality) since its only waves that have momentum and energy but no mass. **Voila**. Photon bothered the scientists so much that it brings new kind of understanding. **If you bother us we will figure you out**.

My finding was thus, as you see in the equation described in the above analysis (image), if OPERA finds it’s **neutrino** with **energy-error** in the order of **1 eV** such that its **time-error** is in the order of **1 nanosecond** it will see **speed excess** (or anomaly) in the order of **7.5 km/second** **consistent** with **theory of Relativity** and **Quantum Mechanics** taken together.

In other words OPERA-experiment must fit **energy-time uncertainty relation del(E).del(T) = a.h-cross** and if it gets **a = 0.75 eV-nanosecond**, it’s **claim** *of*** superluminal neutrinos** vanish ideally. For a **1 nanosecond** *time* **accuracy** this means **0.75 eV** *energy* **accuracy**. All they need to do is see if they have this accuracy in energy, in their experimental detector.

Note that we **fit,** so any **fluctuation** in **time error** reflects in *fluctuation* in **energy error** which is why **distance** becomes **erroneous** and **distance/time = speed** is **erroneous** by *that* **given amount**. Just an observation in this order (off the top of mail paper which is freely available in surplus) is sufficient to see that they can not claim superluminal attributes because it leads to the doubt that they may have to do everything more cautiously, when (in actuality) they will make more errors than their claims. This was to be thought-out prior to the performance of the experiment or at-least publication of results if not publicizing of what they have obtained, in mass media. **

** This is the **reason** why most people *shout* **extraordinary claims require extraordinary evidence**. But I think also, it is our **responsibility** in the name of **diligence** that we take our pen and paper even if we are countering a claim that we would like to prove bogus. I do not think OPERA did a bogus thing. Although they will later agree that they caused a great ripple around the world for which they might have come with a little more caution. For one thing I did plenty of work in the last 2 months and some of these works are paper quality works (although ArXiv rejected my work on OPERA-anomaly not only once but twice) and I hope will serve in the future for other studies whenever **Relativity** is concerned. I have already** 1 paper** that has been written and will be submitted soon. (actually submitted and accepted by many archives, 2 years ago, at the time of these analysis)

I doubt their **anomaly** *will* **hold** any claim since we **do not measure energy to this accuracy** unless a dedicated measurement is performed with this in mind. Their paper does not mention a single word on this or any error of energy. It just deals with errors on time. This is equivalent to saying the distances were measured to mm accuracy (the least epoch theory of Relativity allows in the vicinity of the surface of earth, so to say, the best one would do) but when the analysis was done it was not kept in mind that errors on distance and energy are correlated, hence allowing an energy error they have actually blown up the distance error in their analysis.

The **GPS system is evidently fine** as it is safe from how you use and interpret it. The details for non-superluminal claims are shown in the 3 pages I uploaded below. I will upload **1 more** when that is ready, but that mainly would deal with **MINOS** situation, where they can use my analysis and perhaps come with a much more significant yet null excess result.

SO you can go and **celebrate that Relativity has not been broken**. Also all the money that was going to be spent for redoing all these experiments and all the textbooks that were going to be reviewed and rewritten has been made **redundant**.

## 2 thoughts