# What is the (f)utility of Sheldon Glashow’s paper towards OPERA result.

It’s probably a week that this remarkable result of OPERA neutrinos crossing photon speed emphatically, was publicized. If you check this blog site of mine on WordPress (infyinfo)  I had opened only a few weeks ago, my main blog site (webmohan) has all my previous articles with slightly more than 5000 total spam free hits.

This site has gotten only a 100 hits but in my opinion has some of my most interesting articles of physics. Out of this about 10 are on neutrino result, the links are all put in one of my articles and a few others on OPERA which I haven’t put in that article as they were written later. This is one of them.

At the outset: the only skepticism that has come from the theory side, all the top names, only Sheldon Glashow has something nontrivial to say. I will mostly talk about his paper which I read last night and in an hour came with my ideas why this does not convince me as a basic physicist and as an experimentalist, to throw the neutrino result as a piece of wrapper on my burger.

What surprises me is the elan with which some are saying this result is “no good no more”. Hold on and hold your breath.

At the outset again my first few remarks about this result were ferociously skeptical, even the night, before the results were publicized and I knew of it, let alone read the staggering 20 pages, I had written a long article “why OPERA result could be potentially wrong”.

Since then I have seen the remarkable nature of this experiment and all the nitty-gritty  which countered some of my spontaneous and independent of “method of the experiment” remarks. eg Here one needs to consider only a baseline and energy of the beam and the time difference.

There are plenty of issues from the theory and experiment perspective but quantum mechanics has come to rescue of this experiment. I have described all these very nicely in several hand weaving but valid reasoning. The skeptics definitely did not read my conclusions — I am not sure just wild guessing.

Weinberg — one of my fave theory man, says it is like fairy tale. That is his only skepticism and he has a place everywhere as a formidable scientist who can be taken as an argument against the result, blows my mind just for that.

But I had come with one of my article where I described why the spread in energy of the neutrino mass is serving as a very useful method. It made the rest energy uncertain hence the time very precise, *time* is the only significant parameter because the baseline is a fixed one, for both beams, irrespective of the collective eigenstates of flavor being assigned to one single mass, not an individually assigned mass per the mass states.

I described with reason several malformed opinions about this result, why they are futile. eg Lawrence Krauss’s claim that a 10 MeV neutrino from supernovae and a 17 GeV neutrino from a proton decay must move at the same speed. They would not because:

1. the neutrino is not mass-less *compared to the photon*,

2. there is an energy loss as per basic relativistic physics which depends on rest energy, the more you have of it, the more you lose it.

3. The sufficiency of energy uncertainty to clad a result of the energy loss is significant if the time sensitivity or time uncertainty window is very small. But here the time uncertainty is of the order nano-seconds. That means a $\sim 10^{-7}\hspace{3pt} eV$ energy error.

That energy band is sufficient to reason that photon is mass-less — say PDG best value of : $10^{-18} \hspace{3pt} eV$,  but the neutrino is not, neutrino being an “eV order rest-energy” particle is sufficiently above the energy-error-band of $10^{-7} \hspace{3pt} eV$.

The neutrino is a million times above the energy resolution. Hence for any relativistic calculation that must respect quantum mechanics at the same time there is visible/real energy loss from the rest-mass/energy of the neutrino. Remember this point — 3, when I explain why Sheldon Glashow’s conclusions are disobeying some of the bounds of quantum mechanics.

4. The 4th point is: the neutrino does not lose energy like other particles of mass since they just do not have “interaction channels” like these other particles I will counter Glashow’s claims of energy loss by another reasoning though.

5. The 5th point is: the supernovae does not have enough info about where exactly the observed flashes came from, etc since the energy, mass, distance etc are not clear. Only one thing is clear. Quantum mechanics says we must respect all experimentally valid observations, parameters, facts. We can not disregard one because others are not clear.

I don’t have the 1976 paper of neutrino study that the MINOS quoted. I shouted in a forest for somebody to give me this paper but nobody returned the voice-mail. I was shouting in the forest as I thought “science has really gone to the wolves“.

Now the only guy who has so far said anything important is Sheldon Glashow. George Smoot is the only experimentalist in the list of these formidable skeptics who hasn’t to my knowledge so-far come up with any arguments. I just happen to know from his 2006 biographies that he is a great fan of Einstein who was his childhood role model and that he used to watch a moon moving along when he saw it from inside his car during his family travels.

So why there is so much elated responses that the OPERA result is losing it’s significance?

On another note: and I have mentioned it in one of my articles that this could be at-last a blessing in disguise towards having a successful theory of quantum gravity. Perhaps the zero photon mass is the problem and for the 1st time an experiment is very successfully hitting at that base.

If you (c)heck my article — The neutrino speed excess  as a function of energy, you will see that the error bars which I have not shown on the y-axis of “speed excess in ppm” gives us an uncertainty in time, since distance is fixed, as a function of energy.

Still on that note: you take a sharp energy on x-axis it means time must be very uncertain a fact reflected by OPERA’s 21.9 to 28 ppm. That shooting up at a sharp energy of 17 GeV is a result of quantum mechanical uncertainty, translated from energy-time to speed-time for mass-less photon and momentum-time for “relativistic” neutrino, as it does have a finite mass at-least as the photon in picture is somewhere between $10^{7} - 10^{27}$ less than neutrino mass.

— See point — 3 above, PDG best value of $10^{-18} \hspace{3pt}eV$. In the end that means a photon has a horizontal line and a neutrino has a 3rd power like increase in energy of the speed excess.

Sheldon Glashow points out a few more data-points not included in my graph of 4 points, T2K and SK, but I am not aware of these results as of now, I need to read them. There is no problem here.

If at higher higher energy these speed-excess comes down even what is occurring at 15 or 30 GeV — these latter being TeV range neutrinos, we still do not have a problem from a speed-limit and speed-constancy view-point because these two are being broken anyway, emphatically.

In this later scenario of TeV speed-excess below GeV speed excess we have an epoch or a vertical saturation of speed excess, occurring at lesser energy than TeV. That tells that at these extreme energies Bremsstrahlung like processes or other energy loss schemes are available to the neutrino, but not at the GeV range or immediate-above-GeV range.

I will explain this: why Bremsstrahlung is rather a virtual process at the range at which we are observing the current neutrino effects of above-photon-speed nature. The epoch merely gives an energy-specified speed limit of neutrino, well above the photon. Whether or not at TeV range the neutrino goes through energy losing schemes has to do with what is available to neutrinos, it’s got nothing to do with how much respect or disrespect towards photon is allowed for neutrinos.

The photon being so less of a mass perhaps it’s power-law of “energy increase” is not visible to us. If that were really so, the neutrino is the 1st hint that quantum gravity is on the anvil. We just need to know exactly what we can infer from an energy dependence of the neutrino speed excess and what changes to make to our theory of relativity.

Perhaps then the quantum gravity will start showing consistent attributes. The 1st thing to note is photon mass is not absolute zero and photon speed limit is not absolute c. Neutrino and other particles could break this speed limit although on a different scale, this scale of phenomena is naturally that of energy.

Quantum mechanics is like a natural scale-bar which tells us what uncertainty we lose and what accuracy we gain. It is not just between two commutative parameters but through the physical relationship of all variables, transmits to other variables. I have already given plenty of example: eg my article; “motion blur, earlier title: With a high profile camera why the pictures blurriness is more prominent”.

We need to formulate the right theory of relativity as per energy and scale — perhaps multiple of them, and everything would unify like cream in a pastry.

But here is what I think of Glashow’s paper;

Let us start here: $\Delta E \times \Delta T \geq h \hspace{3pt} (= 4.136 \times 10 ^{ -15}\hspace{3pt} eV.s)$check here.

Glashow assumes that at a high energy level — and we are talking only 17 GeV, the electron and neutrino mass are simultaneously negligible — i.e. zero. We must remember that we already have photon mass as zero, when in actuality the photon mass is at-least $10^{7}$ times smaller than the neutrino mass, at the nano-second time accuracy, check point — 3 above, and at the same accuracy of time the neutrino mass is $10^{6}$ times smaller than electron mass. Electron rest-mass or rest-energy is ~0.5 Mev, and more actually between neutrino-photon if you are using $10^{-18}\hspace{3pt} eV$ for photon-mass.

Let us see what he is doing? He is forcing on us an uncertainty of either rest-mass-energy or kinetic-energy or both, of ~GeV order. Because for the electron to be mass-less in the same calculation of photons and neutrinos being mass-less as per Glashow’s wish one must respect a similar time accuracy and one must also see the fact that only for a GeV mass order it makes sense to talk of an electron being mass less, which is of MeV order, 1/1000 only.

In other words henceforth one must realize that Glashow is forcing 1 GeV or more uncertainty on energy, while at the same time we can only enjoy a nano-second time error. Anything below the nano-second has to come from Glashow’s theory, not the OPERA experiment because they claim only nano-second accuracy.

As I have already shown an eV inaccuracy entails a $10^{-20}s$ inaccuracy and anything beyond GeV entails from $10^{-29}s$ towards smaller inaccuracy/accuracy. — check here.

We simply do not have that privilege in this experiment so Glashow has to find an experiment where this privilege is inherent. Our nano-second accuracy corresponds to a micro-eV order of energy. That is it considers the photons mass-less but not the neutrinos which is eV range. Since we measure these neutrinos in terms of energy and time accuracy, which are fixed for each other, Glashow’s claims are misleading for this experiment.

Since the energy dependence of the neutrinos speed comes from their definite rest-mass, for their observability, the eV range accuracy of energy must be kept intact, OPERA has chosen to keep a micro-eV range intact for the energy in order to reach the nano-second range time resolution.

The MINOS had a wider energy error ~50 MeV? that entailed it theoretical calculations towards the $10^{-26}s$ but what time resolution they had? One must always match with what is experimentally available.

By choosing a GeV and more energy error, he is claiming an energy loss through electron pair production from the original neutrinos, this he parameterized through two variables: one the decay-width and the other the energy gradient over space.

For both of these he did a dimensional analysis but put the numerical constants by hand, that is, these constants are arbitrary and no reason is given for their validity. The energy is reduced at an arbitrary rate through a pair of Bremsstrahlung electrons which being real should be observed.

His paper suggests from this energy loss that the neutrinos do not reach the target or are splashed dissipatively but that is not the case. We observe a statistically significant and systematically accurate 15000 neutrinos.

One needs to check the decay-width and branching rates of the neutrinos from the proton luminosity and Glashow should come with his calculations with all the processes involved not just the hypothetical Bremsstrahlung pair so that the branching rates of all the processes can be compared with the experimentally observed rates.

At one point he is saying there is a 50 GeV error for OPERA measurement, I am confused where he got this value, we need clarifications there, this error means OPERA had gotten a magic clock that read $10^{-29} s$.

Our energy resolution is far more higher so we can not admit his ideas. If you use the uncertainty in-equation above, Glashow’s ideas entail a time uncertainty of far below a nano-second. far far far below. From $10^{-30} s$ towards smaller time-ticks >>> that’s a string theoretic approach.

The MeV corresponds to $\sim 10^{-26}s$ , a 100 million part of an atto-second, that is, if a real electron is cladding the value of energy by being misidentified or effect of some state-of-the-science measurement artifact, in that case our nano-second range GPS clocks would be no good.

The neutrino and photons would be ticking at far below our capability and we would lose them. But no, Glashow is asking for a concession of the GeV level, which is $10^{20}$ part of the present sensitivity: a few nanoseconds. So his hypothesized Bremsstrahlung pair are actually a pair of virtual electrons, they can not escape with the energy, they take this energy and merge-back with the neutrino again so that the neutrino actually goes to the target.

Another thing to note that Glashow is hypothesizing this process at a very small distance scale where the energy is essentially lost to a virtual electron pair. That distance corresponds to what light would travel in that time. Light would travel $3\times 10^{8} \frac{m}{s} \times 10^{-29} s > \sim 10^{-21} m$ — of the order but slightly larger than this value.

We do not measure that distance. Anything happening in that distance must be considered to be virtual. Ministry of internal affairs deals with that. The present sensitivity of distance is $10^{-18} m$, I had written an article a year or two ago, LIGO experiment measures this distance of 100th the size of a proton. $10^{-21} m$ would be a million times smaller than the size of the atom.

If Glashow needs further energy loss by forcing as large an energy uncertainty, he is talking about string theoretic distances, at that scale neutrinos may not break the speed limit of photon, but that is not what this experiment is all about. This experiment is about scales at which present experiments are being performed and neutrinos break the photon “machismo” comfortably.

Glashow is essentially talking about scales of string theory where neutrino may not be thought to cross the photon speed. There is an additional point I want to make although I see in my mind why Glashow’s idea is futile at the scale on which this measurement has been performed.

He used arbitrary numerical constants without any explicit reasoning where he gets these. One can only put these by hand to show consistency with a hypothesis, but not contradict an independent result, that too an experimental measurement.

The other point is his calculations of branching rates — or decay widths. He computed these from the energy calculation, analysis but applies only to a hypothetical Bremsstrahlung and makes a claim of neutrinos not making it to the target, but we see that neutrinos actually make to the target, so what is he saying here. He is saying the neutrino result is nullifying his Bremsstrahlung hypothesis, not the other way round.

He also did not calculate the rates of all the processes and compare with actual results calculable from the source luminosity of protons.

He is silent on how the electron pair can actually combine back to the neutrino thereby conserving the energy of the neutrino, or rather that these are just virtual electrons and that must be the case.

But it is clear that his paper isn’t proving anything can be refuted about the neutrino speed excess.

But I don’t see where the science community is going with, reason and shear reason or big names and brands and futility and erroneous logic.

6th October 2011,

from a family break,

Bangalore, India

I slightly edited this tonight, the break did not give me enough time and internet to publish these as soon as I made most of the points, a blessing of sorts since I got more quality time to think these through my head. A silly error had crept in but didn’t in essence dilute the gross miss-thinking of Glashow, I have removed that error. That is the reason why I published this on 6th October but kept it private after I realized my error as soon as I published.