Tachyon

Robert Ehrlich

George Mason University

mason.gmu.edu/~rehrlich

ABSTRACT: Despite the apparent conflict with relativity, some physicists have

continued to seek evidence for the existence of hypothetical faster-than-light

particles dubbed tachyons. In the past all claims of tachyons have, however, later

been shown to be incorrect, or at least not reproducible. Nevertheless, the speaker

believes that the tachyon is not some mythical beast, and that we may be on the

verge of proving its existence. Specifically, he believes that the ever-surprising

neutrino, or its electron flavor, is actually a tachyon. It might be useful to check out

the speaker’s youtube video or a press release describing his latest research on the

subject, both of which can be found on his web site: http://mason.gmu.edu/~rehrlich/

ABSTRACTYoutube:“Einstein on faster-than-light speeds?”

5 Observations consistent with being a m2 = - 0.11 eV2 Tachyon6

Consistency of the six values of

2

“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 %

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!

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 withinthe space

Why were tachyons first proposed? (1962)

0

1

2

3

4

0 0.5 1 1.5 2

speed, v/c

mas

s,

m

22

2

/1 cv

mcE

cv 02 m

m is imaginary!

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

pE pE pE

How can you define the rest mass of tachyons which can

never be at rest?

Why?

The only known candidates for beingtachyons are one of the 3 types of neutrinos.

ANSWER: Only neutrinos have masses so close to zero that within the experimental uncertainty we do not know

if m2 > 0 or m2 < 0, but we do know that m2 is non-zero.

Super-K detector

Wolfgang Pauli (1929), “I’ve done something

terrible. I have predicted an undetectable

particle“

They come in 2.98 +/- 0.008 “flavors”

– electron, muon, and a tau neutrinos

Each of the 3 flavor states is a quantum

mechanical mixture of 3 states having specific

masses.

The flavor states can oscillate from one to

another as a beam of neutrinos propagates.

Originally, they were thought to be massless, but

existence of oscillations means they are not

What we now know about neutrinos

e e e

321 ,,

2

1

m

More on mass and flavor states

Flavor eigenstates:Neutrinos emitted and absorbed in these statesFlavor states have an “effective” massCurrently only have mass limits on individual flavors or their sum

Mass eigenstates:From oscillation experiments we have good values forAbsolute scale of masses is unknownEach mass propagates with an energy-dependent speed:

NormalHierarchy

InvertedHierarchy

9

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

eeHeH 33

)4(4.21.1 222 eVeVm

Can only set an upper limit so far

Tritium Beta Decay

Total energy can be negative in new reference frame

How I became a “tachyon hunter?”

12

Chodos et al. (1985): Electron neutrinos as tachyon candidates

For tachyons

High energy cosmic rays

13

Primary cosmic rays create showers of secondary particles

A Radical proposal:Missing protons?

Missing protons interpreted as being due to the onset of proton beta decay for E > Eknee

Normally energetically forbidden -- why?

…but it can occur if neutrino is a tachyon

15

Two 1999 Phys Rev articles:

(1) From energy of knee deduce neutrino is a tachyon with: m2 = -- 0.25 + 0.12 eV2

(2) Proton decay above knee leads to “pile-up” of neutrons just above knee a small peak at ~ 4.5 PeV. Peak seen using Cygnus X-3 data)

distance

tim

e

16p

ne

v

proton beta decay

In rest frame need Ev < 0

Ev > 0Ev < 0

distance

tim

e

17p

ne

v

Lab frame:proton beta decay

distance

tim

e

18

n

v

p

e

In proton rest frameLooks like:

2nd 1999 paper in which peak claimed

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

19

1 PeV 10 PeV 100 PeV

5 PeV

Reception to the two 1999 papers?

Some brand new results

(Could not have been done in 1999)

20

Variety of cosmological parameters & data

21…plus more derived quantities

The “effective” number of neutrinos,

22

During the radiation epoch (T > 10,000 K) the energy density of radiation controls the rate of expansion

Radiation includes both photons, neutrinos & any “neutrino-like” particles:

Photon energy density:

Neutrino energy density:

= the “effective” number of neutrino species -- need not be an integer & can vary with cosmological time-- cosmological data can be used to deduce & hence -- standard model says:-- deviation from standard model:-- Actual value is much less well-known that other cosmological parameters

The six observations

23

Tachyonic neutrino mass based on dark energy (Davies & Moss)

24

Using a more up-to-date value:

We obtain an actual value & not an upper limit:

1

CMB & Lensing data fit: 3 + 0 case

25

But suppose electron neutrino is a tachyon

3 neutrinos must be nearly degenerate

Gravitational mass is negative

Let the magnitudes of the 3 masses be equal

2

Chodos model (2012)

26

Problems with theories of tachyons

Chodos suggests new discrete symmetry: Light cone reflection (LCR)& develops a theory of neutrinos that is VSR & LCR invariant

Theory requires that neutrinos come in + m2 (tachyon-tardyon) pairs

Requires at least one sterile neutrino:

Can have any odd number of sterile nu’s (do need another + m2 pair, i.e., 3 +3)

With 3 sterile neutrinos many solutions exist with these pairings:

Based on 3 + 1 fit to CMB fluctuations & lensing data:

3

“Fine structure” in CR spectrum above knee

27

Published data from TunkaCollaboration

Excess counts after subtracting two straight lines shown

4

2nd Knee in CR spectrum

28

Interpret 2nd knee as threshold for alpha decay

5

6

Controversial

The six observations

30

1

2

3

4

5

6

Summary so far

31

Introduction to tachyons & why neutrinos are the only candidates

Cosmic ray analysis in 1999 based on an idea by Chodos et al led to the hypothesis the electron neutrino is a – 0.25 + 0.13 eV2 tachyon

A 2nd 1999 Phys Rev paper gave further supporting cosmic ray evidence

New paper: 5 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

There are no phenomena that should be observed and are not, assuming the hypothesis is true, as was the case with OPERA

How to get definitive proof?

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 2025.0 eVCould see a 0.35 eV tardyon

at the level of

33

0.33 eVtardyon

0.33 eVtachyon

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

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 :

If the neutrino masses have a very non-standard hierarchy may even see each mass state separately

A bit of philosophy on different ways to make big discoveries

35

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 won’t get the Nobel prize

Problems: getting access to someone else’s 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

“It’s 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

36