tachyon

Robert Ehrlich

George Mason Universitymason.gmu.edu/~rehrlich

Click on image to show video: Einstein on faster-than-light speeds?The hunt for the tachyon:Six Observations consistent with the electron neutrino being a m2 = -- 0.11 + 0.02 eV2 tachyon

10:48 AM1

v> c is verboten

UnlessNo information sentExpansion of space itselfNo infinite energy needed?10:48 AM2In a warped space-time

Why were tachyons first proposed? (1962)

m is imaginary!Bilaniuk, O.-M. P.; Deshpande, V. K.; Sudarshan, E. C. G. "'Meta' Relativity". American Journal of Physics 30 718 (1962).

Ea 2-way barrierNeutrinos: the only candidates

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Best tritium beta decay data(as of 2015)For such a mass no speed measurement could reveal any departure from c(any feasible L & E gives immeasurably small dt)

KATRIN discovery potential(100X smaller uncertainty)

How I became a tachyon hunter?Chodos et al. (1985, 1992): Neutrinos as tachyons

Their prediction: Energetically forbidden processes like proton beta decay become allowed at high enough energies if the electron neutrino is a tachyon the threshold depends on the mass of ve 10:48 AM5Basic idea: Only tachyons can reverse their direction in time when seen in different reference frames

There was a young lady named Bright whose speed was far faster than lightdistancetimepnevLab frame: proton beta decay

distancetimenvpeIn proton rest frameLooks like:

Only tachyons can change the sign of their energy or direction in time from one frame to another

High energy cosmic raysPrimary cosmic rays create showers of secondary particlesSource??10:48 AM8

An unconventional proposal: lost protons for E > EkneeThe cause of the knee?10:48 AM9Missing protons interpreted as being due to the onset of proton beta decay for E > Eknee

Two 1999 articles1,2 applying this idea:

(1) Eknee deduce tachyonic mass value for neutrino:

(2) Corroboration: P decay above knee leads to pile-up of neutrons just above knee or a small peak at ~ 4.5 PeV. Neutrons unlike protons travel in straight lines & might reach us from sources normally considered to distant, because of a decay chain

1. Ehrlich, R., Physical Review D, 60, 17302 (19992. Ehrlich, R., Physical Review D, 60, 73005 (1999)

CRs would point back to source if most of time they are neutrons!

Where to see small 4.5 PeV neutron peak?

10:48 AM11Cygnus X-3 is an X-ray binary with a 4.79 h period

One of the most intrinsically luminous sources in the galaxy

Numerous reports of PeV cosmic rays in the 1970s & 80s, especially when making a 4.79 h phase cut

Only one experiment had enough events for E > 1 PeV to make an energy histogram

2nd 1999 paper in which 4.5 PeV peak claimed for Cygnus X-3

Counts above background vs energy

Signal based on counts in 2.5% wide interval of phase, background based on the other 97.5% -- factor of 40 background suppression1 PeV 10 PeV 100 PeV5 PeVNo signal outside peak10:48 AM1250%Possible reason why other high statistics expts failed to see itPart II: The 6 values of

average eV10:48 AM13Cosmological dataHalf-wayCosmic ray dataNuclear experimentFine structure in CR spectrum above knee(recall earlier 4.5 PeV peak)

2013 data from Tunka Collaboration (dE/E ~ 15%)Excess counts after subtracting two straight lines shown10:48 AM 1475%4.5 PeV1``2nd Knee in CR spectrumInterpret 2nd knee as threshold for alpha decay (supported by sudden lowering of average atomic weight found at that energy)

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1st2nd2The Cosmic Background Radiation (CMB)

17 free parameters in the fit! 3 of them involve neutrinosWhole sky image of CMB after filtering 10:48 AM16A measure of the temperature of space-- A remnant of the big bang (universe 2% its present age)-- Almost isotropic (fluctuations ~ 1 part in 100,000)-- Blue= slightly colder, Green = slightly warmer-- CMB = the primordial seeds for future matter clumpingMultipole expansion to fit the dataLarge scaleSmall scaleAmazing fitBUT

Radiation energy density during early universeis the effective number of neutrinos at the time of CMB decoupling-- need not be an integer-- it controls the rate of expansion & affects the CMB wiggles-- standard model value = 3.01 (other values new physics)

1 Actually, 3.046 0.046 correction due to decoupling

10:48 AM17photonsneutrinos

Calculation based on (Davies & Moss, 2012)

A more up-to-date value:Nollett & Steigman (2014) Gives an actual value & not an upper limit: 3DM use:

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Departure from standard model valueTachyonic neutrino mass

Fit to CMB & other data (Battye & Moss, 2014)

4BM conclude that the 3 flavor masses have nearly same mass: 10:48 AM19Otherwise no agreement with tiny dm2 seen in oscillation data: biggest is

An alternate view of BM fit to sum of 3 neutrino massesSuppose electron neutrino is a tachyon with negative energy.

Energy density of a sea of tachyons:Gravitational mass negative for a tachyon since number density cannot be

Let the magnitudes of the 3 masses be equal

10:48 AM204Why

Fixes big problem with previous one: inconsistency with

+ m2 - m2 10:48 AM21Chodos: Neutrinos must come in: + m2 pairs

5Based on BM fit to CMB fluctuations when a sterile neutrino is included its mass is found To be: 0.450 + 0.124 eV. Thus, with the right pairing we have:

4th Sterile flavor stateFlavor states 0

6Result contested by other negative experiments(A,Z) (A,Z-2) +2e--

10:48 AM22Neutrinoless Double Beta DecayKE of 2 electrons

Other issues:Monochromatic!The six values of

B & C are 2 interpretations of same dataAverage if it is dropped

average eVNo known observations in conflict with the claim

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This experiment may be wrongThree tests of claim that(1) Next supernova in our galaxy (only 1-2 per century)

(2) Clear evidence for an E = 4.5 PeV cosmic ray peak

(3) A highly precise tritium beta decay experiment

10:48 AM24Suppose SN emitted neutrinos simultaneously having masses +m2 with a spectrum of energies

1/E2+m2 Lags light- m2 Leads light

arrival time relative to light & T is light travel time from SNSuppose ms-fine structure is seen must have |m| < 0.02 eV claim is false

If not seen Deduce neutrino mass by unsmearing data. Subtracting from the measured arrival time the neutrino travel time with m a fitted parameter :

11:28 AM26Core-collapse model predictionsUnless neutrino mass very tiny the energy-dependent travel times from source will wash out any ms-fine structures in observed neutrinos at detectorSN models predict ms-fine structure

2nd test: Clear 4.5 PeV CR neutron peak

Cygnus X-3 Main cut needed is on the phase of the binary:

Need a very accurate ephemeris to find the phase: Example: need to have time-varying period accurate to 0.00007% for 10 y of data to see a sharp phase peakNeed a data sample covering 1 to 10 PeV to look for a peak in phase histogramEarlier negative experiments may have not seen a signal because they lacked data in the knee region and failed to make the proper cutsBased on a citation search no test of 1999 claim of a 4.5 PeV peak from Cygnus X-3 has ever been made! Test could be done using existing data10:48 AM27Messen Sie die Neutrinomasse ohne Fehler, und finden Sie den ehrlichen Wert!

10:48 AM28My message to KATRIN:Measure the neutrino mass without error and find the honest value.A bit of philosophy on two different approaches to particle physics10:48 AM29Two types of particle physicists

Pack hunters (6,000 Higgsians)Lone wolvesMassive $10 Billion apparatus & many years spent in preparationAnalyze existing data in a novel way & takes little time to completeProblems: getting funding & you wont get the Nobel prizeProblems: getting access to someone elses raw data & most of the time you will be wrongAdvantage of getting advice from many highly knowledgeable expertsAdvantage of not getting advice from many expertsor crackpots

Lone wolves may be far more dangerous than the average wolf that is a member of a pack. However, lone wolves have difficulty hunting, as wolves favorite prey, and will generally hunt smaller animals and scavenge carrion.

Wikipedia entry

Its better to be lucky than smart.

Possible evidence of a bias towards m2 < 0?

Also, 11 out of 13 experiments report best values m2 < 0Kurie plots m2 = + 0.33 eV2 10:48 AM32

10:48 AM33Classical TachyonsOriginally suggested in 1962 as hypothetical v > c particles

Consistent with eqs of special relativity if they have an imaginary mass

Speed c is a 2-way speed barrier & the special speed in the LT & in Maxwell eqs

No definitive sightings despite many searches & erroneous claims Tachyons play a vital role in the Higgs mechanism (a very different sort of tachyon):

Imaginary mass tachyons signal an instability in Higgs field, but no v > c propagation. Instead get a tachyon condensation yielding a m2 > 0 particle, i.e., the Higgs boson.

Many more papers on these than on classical tachyons10:48 AM34Classical tachyon: the Devilparticle?Why most theorists hate them

--Instability of the vacuum

--Cohen-Glashow effect

--Violation of Lorentz Invariance--Violation of causality

On the other hand

(applies to scalar tachyon fields, but not spin 1/2 fields where you cannot lower vacuum energy by creating tachyon anti-tachyon pairs )1

(Only would come into play for |m| > 2me ) -- CG

(Could be very small & alternatives to LI exist. Also v > c OK in some variations of quantum gravity)

(No backward time signaling for |m| > 2me )1

Jentschura & Wundt (2013)

10:48 AM35More on mass and flavor statesFlavor eigenstates Effective masses:Neutrinos emitted and absorbed in flavor statesCurrently only have mass limits

Mass eigenstates:From oscillation experiments we have good values forAbsolute scale of masses is unknown

m2

10:48 AM360.00232 eV 2

(a) Earlier experiments were incorrect(marginal statistics)

(b) Source turned off just when more sensitive searches were made a shy source?

(c) Something else

Possible explanations of failure to replicate Cygnus X-3 cosmic rays

10:48 AM37Massive neutrinos leave an imprint on CMB

Small angular scaleLarge angular scaleIs sum over mass or flavor states?

FlavorMassDoesnt matter

Sum is based on effect of energy density of neutrinos on expansion. It must be a sum over flavorsNonzero mass shifts strength & position of CMB peaks10:48 AM38Serial apophenism?Ehrlich has been going on and on about this for more than a decade.

Noted by an on-line blogger about the paper1 Ehrlich, R., Physical Review D, 60, 17302 (1999) http://arxiv.org/pdf/hep-ph/0009040.pdfEhrlich, R., Physical Review D, 60, 73005 (1999) http://arxiv.org/abs/astro-ph/9904290Ehrlich, R., Phys. Lett. B, 229-232 (2000)Ehrlich, R., Am. J. Phys., 71 (11) 1109-14 (2003)Ehrlich, R., Astropart. Phys. 35 625-628 (2012) http://arxiv.org/abs/1111.0502Ehrlich, R. Astropart. Phys., 41 16, (2013) http://arxiv.org/pdf/1204.0484.pdfChan, M .H. and Ehrlich, R., Astrophysics and Space Science, 349, (1), 407- 413 (2014), http://arxiv.org/abs/1301.6640Ehrlich, R. (2014) http://arxiv.org/abs/1307.3944Ehrlich, R. ISRN High Energy Physics, vol. 2014, Article ID 408508, 2014. doi:10.1155/2014/408508. http://arxiv.org/abs/1301.3390Ehrlich, R., Astropart. Phys. 66 11-17 (2015) http://arxiv.org/abs/1408.2804

*Three papers shown in bold are the basis of this talk.

10:48 AM3939Improving precision of cosmological observations: Cosmic Microwave Background (CMB)

Launched 1989 2001 2009 Just see the dipole10:48 AM40

0.33 eV tardyon0.33 eV tachyon3 Kurie plots

Makes data for beta decay linear near endpoint for a m = 0 neutrino (dashed line)

Tachyons harder to distinguish from m = 0 than tardyons

Is KATRIN equally sensitive to m2 < 0 values?

12000+ KATRIN Simulations for a m = 0 neutrino10:48 AM41Neutrino mass in single & double beta decay10:48 AM42

Width of band is a reflection of unknown Majorana phases.

For zero phase get equality between the two masses for m > 0.05 eV.If you want to learn if neutrinos have v > c do not bother to measure their speed!Measuring their mass is a much more sensitive test given the claimed mass it is unlikely any Earthly speed measurement could see v > c neutrinos10:48 AM4325%Consistent with With certain assumptions the 6 observations would follow from the electron neutrino being a m2 = - 0.11 eV2 tachyon

We cannot draw the reverse conclusion, because each observation has other more mundane explanations, unlike a direct measurement of m2)

One must recognize the danger of apophenia

Neutrino not observed even in most direct caseprobability against a natural origin = 10-21 Tom Van Flandern 10:48 AM44Summary of talkPart I: BackgroundA bit about tachyons & neutrinosA review of some earlier work

Part II: New results1 A bit about cosmologyThe six observations of the subtitleHow to tell for sure10:48 AM451. Astropart. Phys., 66, 1117 (2015) http://arxiv.org/abs/1408.2804

0.33 eV is the ideal mass to predict!

3 sigma in 1 yr5 sigma in 5 yr10:48 AM46

Super-K detector

Ive done something terrible. I have predicted an undetectable particle

They come in 3 flavors:

Each flavor state is a quantum mechanical mixture of 3 states having specific masses.

The flavor states can oscillate from one to another

Originally, thought to be massless, but existence of oscillations means they are not

Strong hints of additional sterile flavors from experiments

Wolfgang Pauli (1929)

10:48 AM47What we now know about neutrinos

Neutrino oscillations just like coupled oscillators

Mass states normal modes (specific m or f)Flavor states which oscillator is moving

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Conventional wisdom:can only set an upper limit so far Tritium Beta Decay10:48 AM4848The KATRIN tritium beta decay experiment:

Katrin should expects to achieve a 1 sigma uncertainty of

Could see a 0.35 eV tardyon at the level of

The real marvel of German precision!10:48 AM