Quote of the Day

Thanks to Ohwilleke for pointing out this 2009 paper on neutrino condensates and dark energy. It should have been cited earlier by Graham and me, even though the analysis is only in terms of traditional CMP thinking. Notable quotes include:

OPERA Act III

The pole $\zeta (1)$ of the Riemann zeta function is associated to a Hagedorn temperature $T_{H}$. That is, when a particle's energy matches this special temperature, such as the CMB in the case of mirror neutrinos, we get the argument $s = E / kT_{H} = 1$, and the partition function diverges. For quarks, $T_{H}$ marks the transition to a quark gluon plasma.

Theory Update 115

As number 26 suggests, the Riemann zeta value $\zeta (-3)^{-1} = - 120$ is associated to the four dimensional quaternions, whereas $\zeta (-7)^{-1} = - 240$ is associated to the octonions. The three parallelizable spheres give the triplet $( \zeta(-1), \zeta(-3), \zeta(-7) )$. Under the functional switch $s \mapsto 1 - s$ of zeta arguments, we obtain the triplet $(2,4,8)$ of dimensions for the corresponding number fields. In categorical scattering theory, we often note that $\zeta (n)$ is associated to $n+3$ particles, giving the triplet $(5,7,11)$ of primes for the exceptional Galois groups.

In the moduli triplet of twistor dimension, the genus $2$ orbifold characteristic was $\zeta (-3)$. The number $120$ counts the vertices of the three dimensional permutoassociahedron, which is obtained by turning each vertex of the $24$ vertex permutohedron into a pentagon. Hence, $120 = 24 \times 5$. In the complex case we have the string regulator, $\zeta (-1)^{-1} = -12$, like the $12$ pentagons that tile the Riemann sphere for the complex moduli space $M_{0,4}$, or the $12$ sides of the planar permutoassociahedron.

And if my calculator hand is working, real arguments give nice real numbers like $\zeta (26) = 1.0000000149$.

More OPERA II

Some people need to see the pretty pictures, so let us draw the full pink line for tachyons.
Although I have not worried about the correct scaling for the curve, the only essential adjustment to relativity is the existence of a minimum $v > c$, given by $\Delta v/c = 2.5 \times 10^{-5}$. If photons always travel at the same local speed, why not particles of very small rest mass.

Superluminal Astrophysicists

While the rest of us are blogging, the true glory seekers have shut themselves in their offices to write papers. Seriously, I have seen them do exactly this. Now, courtesy of Collider Blog, the arXiv onslaught begins: an arXiv paper on the superluminal neutrinos.

More OPERA

Collider Blog has been fitting the three data points for the local $\Delta v/c$, from MINOS and OPERA. I have amended the graph with a constant pink line for crazy theory, which many string theorists appear to have endorsed.

Now what about the supernova results? Four detectors were operating during the day of the SN 1987A event. Wikipedia tells us what they observed: (1) Kamiokande $11$ $\overline{\nu}$, IMB $8$ $\overline{\nu}$, Baksan $5$ $\overline{\nu}$ over $13$ seconds, three hours before the photons, (2) Mont Blanc $5$ $\nu$ (yes, neutrinos) over $7$ seconds, six hours before the photons. The Mont Blanc events are generally not thought to be correlated with SN 1987A.

Let us now do the crazy theory thing and consider the possibility that astronomers do not understand supernovae. That is, from our Earth bound perspective we assume a simultaneity of both photon and neutrino output from the burst. The antineutrinos still travel at a speed very close to $c$, in order to arrive at roughly the same time as the photons (which has already been pointed out a gazillion times on the blogosphere), but we find that all $\nu$ and $\overline{\nu}$ are traveling at a speed greater than $c$.

Theoretical consistency then begs the question: why does the pink line drop to zero for large distances, in a vacuum, in the MeV range? Note that there are already several variables to play with here. First, assume that the MeV range is not the culprit (think MiniBooNE). Perhaps the pink line really is a local result, obtaining the maximum $\Delta v/c$, whereas the SN 1987A neutrinos are only tachyonic as they pass through (all very classical thinking) the stellar debris (someone already suggested this somewhere).

Many possibilities. Another crazy one is the following. What if the tachyonic neutrinos left the burst long after (as in years) the photons, so that $\Delta v/c$ matched the constant. Who are we to say that this is not the case in our frame.

Historical Quote

Goddard and Thorne (1972)

Theory Update 114

The other formula given by number 26 uses $\alpha$, the fine structure constant, starting from the observation that $\alpha^{-1}$ is close to $137$. Many have attempted derivations of the modern non integral value for $\alpha$ using the integer $137$. For instance, the Relativist James G. Gilson discusses the beautiful formula

$\alpha = \frac{\cos (\pi /137)}{137}$

noting that other authors have expressed $137$ as $2^7 + 2^3 + 2^0$, as used by number 26. The integer $163 = 137 + 26$ is a favourite Almost Integer known as Ramanujan's constant. It satisfies

$e^{\pi \sqrt{163}} \simeq 640320^3 + 744$

where the decomposition of the large integer is well known in moonshine circles. Alternatively, we can write

$e^{\pi \sqrt{163}} \simeq (C e^{\pi i/24})^{24} - 24$

for $C = \eta (z) / \eta (2z)$, where $z = (1 + \sqrt{163} i)/2$ and $\eta$ is the Dedekind eta function. The $j$-invariant also appears in interesting studies of CFTs, with central charge $48$. Pundits call all this numerology, but mathematicians most certainly do not. Long live the bosonic string.

Theory Update 113

Under the assumption that neutrinos are tachyonic, while the ordinary antineutrinos are not, the $\overline{\nu}$ may travel at a speed very close to $c$. Then the $\Delta v / c$ measured by OPERA would characterise the difference between canonical speeds for the two species. The simple formula given by number 26 is then rewritten

$\frac{\Delta v}{c} = (26^{\textrm{log} 26})^{-1} = 2.45 \times 10^{-5}$

where as usual $26$ is the dimension of bosonic strings, namely the traceless elements of the $3 \times 3$ octonion Jordan algebra.

Quote of the Week

The Fermilab team will then begin a second stage of their experiment, called Minos Plus, which is even more similar to the Cern trial and will deliver results accurate to one nanosecond, she said.

According to Professor Jenny Thomas from MINOS, in the news.

Theory Update 112

For many years, kneemo has tried to get me interested in the classical geometry much beloved by traditional M theorists. An early push on this front included Szabo's 2002 paper on tachyons and K-homology. So when number 26 made a few remarks at the viXra log neutrino post, sounding for all the world like a numerology robot, it nonetheless caught my attention, because robots don't usually know that $120$ is a very, very interesting number.

Recall that, back in 2006, we were very excited that the orbifold Euler characteristic of the moduli space $M_{2,0}$ of the genus $2$ Riemann surface with no punctures was $-1/120 = 2 \zeta(-7)$, in terms of a zeta value. This is because $M_{2,0}$ belongs to the triplet $(M_{0,6}, M_{1,3}, M_{2,0})$ of moduli spaces of twistor dimension. We already knew that the number of generations for mass quantum number came from the $-6$ for the moduli $M_{0,6}$, by halving. Similarly, we halve the $-1/120$ to get the $\zeta (-7)$ much beloved by number 26.

Not being an expert in classical geometry, I am still rather unsure about some of the things that number 26 said, but I am quite certain that some of the things that number 26 said are in fact closely related to mass generation in quantum gravity. Long live tachyonic neutrinos.

The Seminar

The two hour OPERA seminar, which was extremely clear, is now available from CERN.

Theory Update 111

Commenter number 26 at Phil's blog has noted that M theory can produce the formula

$\frac{v - c}{c} = e^{- \textrm{log}^{2} (26)} = 2.45 \times 10^{-5}$

or more accurately,

$\frac{v - c}{c} = 3 e^{- \sqrt{1/ \alpha}} = 2.48 \times 10^{-5}$

for tachyonic neutrinos. I wonder what version of M theory that would be.

Rumour No More

And so it shall be done. Congratulations to the whole OPERA collaboration for eventually trusting their data.

$\frac{v - c}{c}$ $= 2.48 \pm 0.28 \pm 0.30$ $\times 10^{-5}$

Given the old MINOS results, and other hints, it now seems clear that most, if not all, neutrinos are tachyons. Recall also a low energy excess in the $\nu$ results from MiniBooNE. Not to mention non existent fairies, zombies, wimps, dark forces and more. So although the majority of ill informed punters will immediately tell you to ignore this $6 \sigma$ result from a large professional collaboration who have been working on this for years, you should not.

The CERN seminar can be viewed via live webcast tonight, 4 pm Zurich time. Eek. Anyone feel like recording it for me?

Rumour of the Century III

Due to popular demand, now in the news, ahead of the seminar.

Note that this is not the first experiment to investigate tachyonic behaviour. MINOS measured neutrino speeds in 2007.

Vesta South Pole

From DAWN via Universe Today, this beautiful image of the strange south pole basin on Vesta. Hopefully Louise will tell us more.

Rumour of the Century II

This is not the first time that neutrino experiments have exhibited anomalous behaviour. In fact, as anyone who follows neutrinos will tell you, anomalous results are par for the course, giving this insane rumour its suspenseful edge. In particular, Graham notes again that the recent MINOS results are confusing, with the introduction of large new systematic errors required to explain big shifts in the apparent $\Delta m^2$ for $\overline{\nu}$.

We can be inventive when considering such results. Some, for instance, think that neutrinos are tachyonic while antineutrinos are not. Perhaps we should mix up the $(\nu, \overline{\nu})$ sets into tachyonic and ordinary subsets.

But given Louise's cosmology, and a fixed local $c$, a natural thing to ponder is the cosmic time variation of mass. It is important to understand that every observer has a cosmic time, that they observe most simply via their CMB temperature. Since our cosmic epoch corresponds to a large universal mass $M$, we do not expect to detect a variation in $M$ over short laboratory time scales. But maybe the neutrino's tiny rest mass, and hence small associated cosmic period, allows a mass time variation to be observable on human laboratory time scales. Could the strange MINOS results be explained by an oscillation of $\Delta m^2$ values between the limiting $\pm \pi/12$ phases? Such a limitation on the measurement of $\Delta m^2$ would eventually be observable at a number of neutrino experiments. Note that the total mass scale for the triplet of states could be fixed, with the amplitudes for individual states coming from parameters that interpolate between the mixing matrices for neutrinos and their mirror counterparts. This would utterly confuse the measurements of $\theta_{13}$!

Does this have anything to do with tachyons? Recall that the minus sign in the Koide rule occurs for one phase, but not for its mirror conjugate, possibly suggesting only a single tachyonic $\nu$ mass state. Alternatively, five of the six states could be tachyonic, with only one ordinary $\nu$ mass state. On Saturday, we will have many more ideas with which to play.

Rumour of the Century

We don't usually report on unsubstantiated rumours here at AP, but this one is just too spectacular to ignore. Jester thinks its crazy, Phil sounds excited, and Graham says that Tommaso had a post up with a $6.1 \sigma$ result from OPERA, but the post has now disappeared. Given the number of false rumours that get circulated, we should be doubtful at this point. Here is OPERA's last arxiv paper. The CERN seminar is this coming Friday.

So the rumour is that neutrinos arriving at OPERA have travelled at a speed greater than $c$. Forget fairy fields. If this is true, it demolishes establishment thinking in one falcon swoop. Could the minus sign in Brannen's Koide relation for neutrinos be responsible for such tachyonic behaviour? Why not? Or, perhaps all neutrinos are tachyons. Now the minus sign goes with the lightest neutrino mass state. The literature has an annoying tendency to confuse EW and mass states, but we should note that all mass states can occur in $\nu_{\mu}$-$\nu_{\tau}$ oscillations.

Tony's Condensate

Tony Smith has kindly summarised his well known analysis of the correct Higgs mechanism, in light of its relation to MUBs. This prediction of a mass triplet associated to a top quark condensate should be taken far more seriously than anything a stringer, loopie or groupie says about EW symmetry breaking.

For a $3 \times 3$ octonion matrix version of the physics model see this wonderful 1995 paper. I am very sorry, Tony, that I never spotted that before. Now I still think fairies are fairies, but Tony's main prediction is for quark mass states, not for a Higgs boson or other new field. Let us hope he is correct.

And here are Tony's papers at viXra.

WIMPed Out

At TAUP 2011, Maxim Pospelov gives an interesting talk on alternatives to WIMPs for the DAMA, CoGeNT and CRESST data. Much of the talk focuses on a novel neutrino sector, resulting in a keV alternative to apparent WIMP recoils. Note that although recent CRESST results fall into the ballpark DAMA and CoGeNT WIMP mass range, a particle is a particle, and a particle cannot have a different profile at different experiments. One need not take the current form of the neutrino analysis seriously, but the general idea is certainly intriguing. The plot shows a forced fit to the CoGeNT data. Given the failure to date of stringy pseudo-predictions, we will probably see more of these ideas in the near future.

Fermi Shines II

Fermi also confirms the rise in the positron spectrum up to $200$ GeV. This would make stringers happy if there was good evidence for WIMPs, but alas there is not.

Fermi Shines

Fermi shows today that $31$ percent of gamma ray sources in its all sky map are of unknown origin.

It's Wrong

Quote of the Week

While this is a tragedy against womens’ rights, this is pretty normal stuff online. You should have seen what happened when I made the front page of Digg, back when people used Digg. Owwie. But I was okay with this, because I have a strong support network, and when I chose this path, I had a fairly clear idea of the consequences. I chose to be a semi-public figure.

I just didn’t expect the death threats.

Naomi Dunford