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Slide 2 Robert Ehrlich George Mason University mason.gmu.edu/~rehrlich Youtube:Einstein on faster-than-light speeds? 6 Observations consistent with being a m 2 = - 0.11 eV 2 Tachyon Slide 3 The six values 2 eV Slide 4 Summary of talk 3 A bit about tachyons & neutrinos How I became a tachyon hunter --review of some earlier work A non-cosmologists view of cosmology The six observations How to tell for sure A bit of philosophy Slide 5 Theoretical problems & possible solutions 4 Violation of causality by tachyons: Need not be a problem for near zero tachyon masses (Jentschura & Wundt) Instability of the tachyon vacuum: Instability in boson field leads to condensation, but not necessarily true for spin field (Chodos) Violation of Lorentz invariance: Many of the same results of LI from other subgroups (VSR: Cohen & Glashow, LCR: Chodos) Slide 6 The phantom of the OPERA Sent bunches of neutrinos from CERN to a detector 730 km away Compared their time of flight to that of light, c Measured neutrino speed higher than c by 0.0000237 % photon Experiment has been redone by OPERA and others, and all now show a departure from c within the experimental uncertainty -- just the latest of a number of false sightings. This is not the greatest time to make the case for superluminal (FTL) neutrinos! The OPERA experiment (2011) NOT the way experiment was done! Slide 7 Nothing can go faster than light if it travels in in vacuum if it carries energy or information if it started out slower than light if it is measured locally within the space Slide 8 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). How can you define the rest mass of tachyons which can never be at rest? Slide 9 The only known candidates for being tachyons are one of the 3 types of neutrinos. Only neutrinos have masses so close to zero that within the experimental uncertainty we do not know if m 2 > 0 or m 2 < 0, but we do know that m 2 is non-zero. Slide 10 Super-K detector Ive done something terrible. I have predicted an undetectable particle They come in 3 flavors: electron, muon, and tau Each flavor state is a quantum mechanical mixture of 3 states having specific masses. The flavor states can oscillate from one to another Originally, they were thought to be massless, but existence of oscillations means they are not They are the only candidates among the known particles to be tachyons What we now know about neutrinos Wolfgang Pauli (1929) Slide 11 If you want to learn if neutrinos have v > c, do not bother to measure their speed! 10 Measuring their mass is a much more sensitive test Conventional wisdom: Only have upper limits from cosmology & particle physics so far for each flavor, e.g., 2 eV for electron neutrino Slide 12 More on mass and flavor states Flavor eigenstates Effective masses: Neutrinos emitted and absorbed in flavor states Currently only have mass limits Mass eigenstates: From oscillation experiments we have good values for Each mass propagates with an energy-dependent speed: Absolute scale of masses is unknown Important to keep in mind for SN data m2m2 Slide 13 12 Slide 14 Can only set an upper limit so far Tritium Beta Decay Slide 15 How I became a tachyon hunter? 14 Chodos et al. (1985): Electron neutrinos as tachyon candidates. Their prediction: Energetically forbidden processes like proton beta decay become allowed at high enough energies if the neutrino is a tachyon. Slide 16 distance time 15 p n e v proton beta decay In rest frame need E v < 0 E v > 0 E v < 0 Slide 17 distance time 16 p n e v Lab frame: proton beta decay Slide 18 distance time 17 n v p e In proton rest frame Looks like: Only tachyons can change the sign of their energy from one frame to another Slide 19 High energy cosmic rays 18 Primary cosmic rays create showers of secondary particles Source?? Slide 20 An unconventional proposal: lost protons for E > E knee The cause of the knee? Slide 21 Missing protons interpreted as being due to the onset of proton beta decay for E > E knee Two 1999 Phys Rev articles: (1)Using Chodos et al idea can relate knee position to tachyon mass yields (2) Proton decay above knee leads to pile-up of neutrons just above knee a small peak at ~ 4.5 PeV. Peak claimed using Cygnus X-3 data). (Could reach us given a decay chain n p n p n p Slide 22 Why Cygnus X-3? An X-ray binary with a 4.79 h period One of the most intrinsically luminous sources in the galaxy During flares luminosity increases a thousandfold! Source appears to have a jet pointing almost right at us --see Can get an excellent background subtraction using phase cut Also, reports of deep underground muons from Cygnus X-3 Numerous reports of PeV cosmic rays in the 1970s & 80s 21 Cygnus X-3 animation Lloyd-Evans The skunk Slide 23 2 nd 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 suppression 22 1 PeV 10 PeV 100 PeV 5 PeV Reception to the two 1999 papers? -- partly my fault! Slide 24 Some cosmological data & connection to neutrinos 23 Slide 25 Steadily improving presicision of observations 24 Launched 1989 2001 2009 Just see the dipole Slide 26 Cosmological parameters from data 25 plus more derived quantities Image of sky after filtering out galaxy & Doppler Effect Slide 27 Massive neutrinos leave an imprint on CMB 26 Small angular scale Large angular scale Is sum over mass or flavor states? Flavor sum: Nonzero mass shifts strength & position of peaks Slide 28 The effective number of neutrinos 27 During the radiation epoch (T > 10,000 K) the energy density of radiation controls the rate of expansion. Radiation includes both photons (~60%) & neutrinos (~40%): is the effective number of neutrino species + any other weakly interacting particles (but not sterile neutrinos) -- need not be an integer & can vary with cosmological time -- standard model value = 3.046 -- (0.046 correction due to decoupling) -- values other than 3.046 require new physics -- much less well-known than all other cosmological parameters -- found mainly from CMB & big bang nucleosynthesis -- especially the amount of He 4 in the universe Strange parameter Slide 29 Now the new results 6 observations consistent with the electron neutrino having 28 Slide 30 Tachyonic neutrino mass based on dark energy (Davies & Moss) 29 Using a more up-to-date value: We obtain an actual value & not an upper limit: 1 DM use: Slide 31 CMB & Lensing data fit used to find: 30 Now suppose electron neutrino is a tachyon, which can have 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 2 Conventional interpretation: Slide 32 Chodos model 31 Chodos suggests new discrete symmetry: Light cone reflection (LCR) & develops a theory of neutrinos as tachyons Theory requires that neutrinos come in + m 2 (tachyon-tardyon) pairs, which requires at least one sterile neutrino: Can have any odd number of sterile nus (more + m 2 pairs, e.g. 3 active +3 sterile) With 3 sterile neutrinos many solutions exist with these pairings: Based on 3 + 1 fit to CMB fluctuations & lensing data sterile neutrino mass found To be 0.450 +/- 0.124 eV, so with this pairing: 3 Slide 33 Fine structure in CR spectrum above knee 32 Published data from Tunka Collaboration Excess counts after subtracting two straight lines shown 4 Slide 34 2 nd Knee in CR spectrum 33 Interpret 2 nd knee as threshold for alpha decay 5 Slide 35 6 Result contested by other negative experiments Only possible if neutrino is a Majorana particle Unknown sign of m 2 Slide 36 Summary of the six observations 35 eV Slide 37 The six observations 36 1 2 3 4 5 6 Slide 38 Summary so far 37 Introduction to tachyons & neutrinos Two 1999 Cosmic ray analyses based on an idea by Chodos et al that led to the hypothesis the electron neutrino is a 0.25 + 0.13 eV 2 tachyon Some comments about cosmology from a non-cosmologist New results: 6 observations from data involving particle physics, cosmology & cosmic rays are all consistent with the electron neutrino being a tachyon & value consistent with original hypothesis & yields a much more precise mass How to get definitive proof? Slide 39 The KATRIN tritium beta decay experiment: Main spectrometer for Katrin being transported through the village of Leopold shafen en route to Karlsrube in 2006. Katrin should start taking data in 2016 & expects to achieve a 1 sigma uncertainty of Could see a 0.35 eV tardyon at the level of German precision! Slide 40 39 0.33 eV tardyon 0.33 eV tachyon 3 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 12000 KATRIN Simulations for a m = 0 neutrino 19 for m 2 < -40 39 for m 2 > 40 Slide 41 2 nd test ms-fine structure in SN (Ellis et al.) Two possibilities: If ms-fine structure seen must have |m| < 0.02 eV & could easily disprove If fine structure not seen, can deduce neutrino mass by unsmearing data (finding time distribution at SN) by subtracting from the measured arrival time the neutrino travel time : Slide 42 3 rd test: Look for predicted 4.5 PeV cosmic ray peak 41 I dont have the time to wait for the next supernova! Good possibility: Cygnus X-3 Very important to: (1)use a very accurate ephemeris when doing a phase selection (2)have a sizable fraction of data near 4.5 PeV Slide 43 A bit of philosophy on different ways to make big discoveries 42 Slide 44 Two types of physicists seeking to make fundamental discoveries Pack hunters (6,000 Higgsians)Lone wolves Massive $10 Billion apparatus & many years spent in preparation Analyze existing data in a novel way & takes little time to complete Problems: getting funding & you wont get the Nobel prize Problems: getting access to someone elses raw data & most of the time you will be wrong Advantage of getting advice from many highly knowledgeableexperts Advantage of not getting advice from many experts or crackpots Its better to be lucky than smart. Lone wolves may be stronger, more aggressive and far more dangerous than the average wolf that is a member of a pack. However, lone wolves have difficulty hunting, as wolves favorite prey, large ungulates, are nearly impossible for a single wolf to bring down alone. Instead, lone wolves will generally hunt smaller animals and scavenge carrion. Wikipedia entry 43 Slide 45 Tardy- centrism mason.gmu.edu/~rehrlich Slide 46 Tachyons would fill a vacant niche Tachyon luxon tardyon Past light cone Future light cone 3 world lines Spacetime diagram (c = 1.0 here) Slide 47 Tachyons from A to B Tachyon kinematics is consistent with special relativity For v > c particles relativity says M 2 < 0 No passing through the light barrier from either side 3 distinct classes: tachyons, tardyons & luxons Neither required nor forbidden by theory Searches to date have not been conclusive They violate causality -- but maybe not Slide 48 Many false sightings: all speed measurements so far consistent with v = c within experimental uncertainties, but we know that neutrinos (unlike photons) cannot have exactly v = c. Never settled: Negative results on speed measurements cannot rule out neutrinos being tachyons they only set more stringent limits, i.e., v closer to c. Pointless? Many people believe there is no point in even looking since Einstein said v > c is impossible! Conclusions from tachyon searches Slide 49 How are the neutrino masses found? -- For some reaction where neutrino is emitted measure the missing (unobserved) energy E & momentum p -- Calculate the missing mass from: m 2 = E 2 p 2 (relation assumes c = 1) Slide 50 Measuring the neutrino mass E = mc 2 pion muon nu Muon detector Measure the muon kinetic energy (KE) Neutrino (nu) not detected Muon & neutrino have equal magnitude momenta so we can find the neutrino mass by observing the muon energy Assume pion initially at rest Slide 51 Using pion decay to find the neutrino mass 4.120 -1149 +1149 Mass 2 meter # muons Result for muon neutrino: Result for electron neutrino Slide 52 How could we tell if neutrinos are tachyons? 1. Find one type that can outrace light (v > c). 2. Find one type that has an imaginary rest mass, i.e., 3. Look for low energy neutrinos created in a brief pulse arrive before high energy ones Supernovae are the only way it could be done why? 4. Find an energetically forbidden decay in which one is emitted!!! A. Chodos, and V. A. Kostelecky, Phys. Lett. B 150, 431 (1985; Least Sensitive test Wait until 2020 (Katrin) Next SN in galaxy will tell Maybe seen already!!! STATUS New results Need enormous distance to see spread in times due to energy variation. Slide 53 A quiz about proton beta decay: 1.Why is the process considered to be impossible? 2.Why doesnt proton energy matter? 3.Why could process occur if neutrinos are tachyons? 4.Obviously effect would need to occur at extremely high energies (Could not be seen at accelerator energies) p n p __ Threshold for proton decay depends on the mass of the tachyonic (m 2 < 0) neutrino Chodos et. al. (1985) Slide 54 p ne + v pe - v ne + v pe - v ne + v The p n p n p Decay chain Assume n p much slower than p n. Chain continues with energy loss at each step until p drops below the energy of the knee. The result is a pile up of neutrons at an energy a bit above the knee a small peak at around 4.5 PeV (+ 2.2 PeV) After 1999 prediction a 2 nd paper written in same year found a 4.5 PeV peak for CRs pointing back to Cygnus X-3. Chain Offers a way cosmic rays could mostly point back to their sources Slide 55 Any guesses? Reception to 4.5 PeV paper (1999) Was cited by 23 people over the years, but by the wrong ones! Great skepticism (extending to whether all reports of Cygnus X-3 claimed CR signals were genuine), in light of several high statistics subsequent experiments having negative results: The coffin nail CASA-MIA (1996) In addition, conventional wisdom is that except at very high energies, CRs being charged protons or nuclei are randomized sufficiently by galactic B-field so that none point back to sources. Also, neutrons could not survive the trip from any sources 54 Slide 56 Why 4.5 PeV signal from Cygnus X-3 only seen in some experiments? Obviously signal cannot show up in experiments that lack enough CRs with E ~ 4 PeV. CASA-MIA had only 0.09% of its data with E > 1.2 PeV Plus, being a weak signal 4.5 PeV peak only shows up when background suppressed by: -- cut on times of very rare major flares (Tibet & Marshak) -- cut on 2.5% phase window (Lloyd-Evans) 55 Slide 57 New paper supporting 4.5 PeV peak Dont look at any one suspected source, but do a blind search for candidate sources anywhere in the sky, i.e, statistically significant excess of counts above what calculated background See how the excess number of candidate sources depends on energy & look for a peak near E = 4.5 + 2.2 PeV Data Suggests a peak in CR spectrum at 5.86 PeV consistent with previous claim of peak at 4.5 + 2.2 PeV 56 Slide 58 How to look for a peak in spectrum if you do not know where sources are? Define candidate sources: Small region of sky from which cosmic rays of energy E appear to come in excessive numbers (rel. to bkgd.) Excessive is defined in statistical terms p < 1/2000 Candidate sources are not associated with any known objects Find number of candidate sources versus energy & look for a peak many more at some particular energy 57 Slide 59 Calculation of background: Time shuffling method Accurate means needed in order to know what the excess is at any location in the sky (in the absence of a real source) Use the Shuffling method which relies on the data itself & shuffles recorded times between events. Hinges on fact that any sky location (in celestial coordinates RA & declination) connects to many Earth-based coordinates (in azimuth, altitude, and t -- time event recorded. If no real sources the time shouldnt matter Earth-based coordinates: Altitude & azimuth North star Any source with a specific RA & declination changes its altitude & azimuth as the Earth rotates Slide 60 For E = 5.86 PeV energy bin many more large S > 0 excesses than chance predicts & no excess for S < 0 N S Standard Gaussian (sigma = 1) Candidate sources taken to have S > 3.3 sigma excess above background Basis of this definition? 68 candidate sources -- 48 above Gaussian 59 Slide 61 Numbers of excess candidate sources in each energy bin E (PeV) N N No excess seen for candidate sinks Not physically possible Candidate sources S > 3.3 Candidate sinks S < - 3.3 Slide 62 61 Locations of candidate sources Locations of candidate sinks Slide 63 Now some fun stuff: Why v > c neutrinos might imply the ability to send signals back in time First, one-way signaling 62 Slide 64 Tachyons violate causality No absolute distinction between cause & effect! Consider a warning signal sent between approaching saucers to avoid a collision. Assume that the warning signal is sent using v > c tachyons. How would this appear on a spacetime diagram? Slide 65 distance time 64 Slide 66 65 Slide 67 Sending a message to your earlier self? Requires round trip signaling Which famous physicist first showed this could be done if faster-than-light particles existed & could be used to send signals? In what year? Paul Ehrenfest (1911) See wikipedia entry on tachyon anti-telephone for details Slide 68 Mistakes are very useful provided you learn how to spot them (a) Especially mistaken assumptions: time is absolute parity is conserved doctors can do no wrong only long term processes can lead to drastic changes on Earth tachyons are unphysical??? (b) Especially your own mistakes! 67 Slide 69 Mistakes & learning how to spot them (b) especially your own mistakes. The original paper presenting these results was so absurd, no reputable journal should publish it --fortunately for me! Initially: looked at ~20 suspected CR sources, e.g., The Crab put equal weight on MSU data & Tunka data used only one search radius calculated background wrong had no cut N > 50 (fooled by small numbers) focused only on E = 4.5 PeV energy bin thought 2 & 3 sigma signals were meaningful I had the great benefit of having a Russian collaborator Mikhail Zotov at MSU who had access to the Tunka data & who finally declined to be a coauthor. 68 Why? Slide 70 Special thanks to: Leonid Kuzmichev of Moscow State University, Head of the Tunka Collaboration & to Mikhail Zotov also of MSU for providing his analysis of the Tunka data. My web site http://mason.gmu.edu/~rehrlich has a link to a press release, a link to this presentation, and to the scientific paper on which it is based. 69 Slide 71 Why are most physicists tardycentric? Einstein said no v > c Many false sightings Imaginary rest mass Causality violated Instability of vacuum in field theory Flaky associations My guess what Einstein would think about these arguments Slide 72 Apophenia The occupational hazard of tachyon-hunters 71 Apophenia is the experience of seeing patterns or connections in random or meaningless data. The term is attributed to Klaus Conrad [1] by Peter Brugger, [2] who defined it as the "unmotivated seeing of connections" accompanied by a "specific experience of an abnormal meaningfulness", but it has come to represent the human tendency to seek patterns in random information in general, such as with gambling and paranormal phenomena. [3]randomKlaus Conrad [1] [2] [3] Slide 73 Jumping from failure to failure with undying enthusiasm is the secret of success. Savas Dimopoulos, a particle physicist, quoted in the 2/25/14 NY Times in connection with the discovery of the Higgs 72 Ehrlich corollary (courtesy of Kenny Rogers): You've got to know when to hold them & Know when to fold them. Slide 74 Could neutrino mass states arrive separately? R. Cowsik (1988) Neutrino travel time 73 Neutrino arrival time