clocks and cold atoms for testing electromagnetism - uzh · a. sakharov (nyu - cern) e....

Clocks and cold atoms for testing electromagnetism

M. Bentum (Twente)L. Bonetti (Orleans)

L. dos Santos (CBPF Rio de Janeiro)J. Ellis (King’s College London - CERN)J. Helayel-Neto (CBPF Rio de Janeiro)

N. Mavromatos (King’s College London - CERN)A. Retino (LPP Paris)

A. Sakharov (NYU - CERN)E. Sarkisyan-Grinbaum (Arlington - CERN)

A. Spallicci (Orleans)A. Vaivads (IRFU Uppsala)

Observatoire des Sciences de l’Univers, Universite d’OrleansLPC2E, UMR 7328, Centre Nationale de la Recherche Scientifique

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Alessandro D.A.M. Spallicci ACES Workshop, 29 June 2017 Zurich

Highlights of the talk

Motivations and considerations.Non-linear theories (Born-Infeld, Heisenberg-Euler). Magnetar.The experimental state of affairs of photon mass.Massive photons from SuSy and LoSy breaking. One possibility.The de Broglie-Proca (dBP) theory, ....+ others (Schrodinger...).Solar wind and fast radio bursts upper limits .LOFAR NenuFAR OLFAR open the MHz, sub-MHz regions.Measurement with ACES and future for clocks .Investigation: non-linear electromagnetism, effective photon massand dissipation.Bentum M.J., Bonetti L, Spallicci A.D.A.M., 2017. Dispersion by pulsars, magnetars and non-Maxwellianelectromagnetism at very low radio frequencies, Adv. Space Res, 59, 736, arXiv:1607.08820 [astro-ph.IM]Bonetti L., dos Santos L.R., Helayel-Neto A. J., SpallicciI A.D.A.M., 2017. Massive photon from Super and LorentzSymmetry breaking, Phys. Lett. B., 764, 203, arXiv:1607.08786 [hep-ph]Bonetti L., Ellis J., Mavromatos N.E., Sakharov A.S., Sarkisyan-Grinbaum E.K.G., Spallicci A.D.A.M., 2016. Photonmass limits from Fast Radio Bursts, Phys. Lett. B, 757, 548, arXiv:1602.09135 [astro-ph.HE]Bonetti L., Ellis J., Mavro,matos N.E., Sakharov A.S., Sarkisyan-Grinbaum E.K.G., Spallicci A.D.A.M., 2017. FRB121102 casts new light on the photon mass, Phys. Lett. B, 768, 326, arXiv:1701.03097 [astro-ph.HE]Bonetti L., Perez-Bergliaffa S., Spallicci A.D.A.M., 2017. Electromagnetic shift arising from the Heisenberg-Euler

dipole, in 14th Marcell Grossmann Meeting, 12-18 July 2015, M. Bianchi, R.T. Jantzen, R. Ruffini, World Scientific,in print, arXiv:1610.05655 [astro-ph.HE]Retino A., Spallicci A.D.A.M., Vaivads A., 2016. Solar wind test of the de Broglie-Proca’s massive photon withCluster multi-spacecraft data, Astropart. Phys., 82, 49, arXiv:1302.6168 [hep-ph] 2/26


Investigating non-Maxwellian (nM) theories: motivations

Though GW detection - from Sept. 2015 - understanding of the universebased on electromagnetic observations.

As photons are the main messengers, fundamental physics has a concern intesting the foundations of electromagnetism.

96% of the universe is dark (unknown), and yet precision cosmology.

Striking contrast: complex and multi-parameterised cosmology - linear andnon dissipative electromagnetism from the 19th century.

Conversely to the graviton, photon mass isn’t frequently assumed. Thesame for alternatives to GR.

There is no theoretical prejudice against a photon small mass, technicallynatural, in that all radiative corrections are proportional to mass (’t Hooft).

Electromagnetic radiation must have zero rest mass to propagate at c , butsince it carries momentum and energy, it has non-zero inertial mass.Hence, for the EP, it must have non-zero gravitational mass, and so, lightmust be heavy (’t Hooft).

The Einstein demonstration of the equivalence of mass and energy (wagon at rest on

frictionless rails, photon shot inside end to end) implies a massive photon.

Regularisation of the singularities of point particles, e.g. Born-Infeld.3/26


Investigating non-Maxwellian (nM) theories: motivations

The photon is the only free massless particle of the Standard Model.

The SM successful but shortcomings : Higgs is too light, neutrinos aremassive, no gravitons...

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nM theories: considerations

non-Maxwellian theories are non-linear (initiated by Born and Infeld;Heisenberg and Euler) or massive photon based (de Broglie-Proca).

Massive photon and yet gauge invariant theories include: Bopp, Laude,Podolsky, Stueckelberg, Chern-Simons, Carroll-Field-Jackiw.

Impact on relativity? Difficult answer: variety of the theories above;removal of ordinary landmarks and rising of interwoven implications.

Massive photons evoked for dark matter, inflation, charge conservation,magnetic monopoles, Higgs boson, redshifts; in applied physics,superconductors and ”light shining through walls” experiments. The masscan be considered effective, if depending on given parameters.

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Non-Maxwellian (nM) theories: Heisenberg-Euler

The Heisenberg-Euler Lagrangian

L = −FµνFµν

4+

e2

~c

Z ∞

0

dηe−η

η3·

iη2

2FµνF ∗µν ·

·cos

»η

Ek

q−FµνFµν

2+ iFµνF ∗µν

–+ cos

»η

Ek

q−FµνFµν

2− iFµνF ∗µν

–cos

»η

Ek

q−FµνFµν

2+ iFµνF ∗µν

–− cos

»η

Ek

q−FµνFµν

2− iFµνF ∗µν

–+ |Ek |2 +

η3

6· FµνFµν

ff(1)

F ∗µν = εµνρσF ρσ (2)

Photon-Photon interaction and Photon splitting since HE theoryrelates to second order QED.

Vacuum polarisation occurs for Ec > 1.3× 1018 V/m orBc > 4.4× 1013 G.

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HE theory application to a dipole (magnetar)

Heisenberg-Euler on magnetars overcritical magnetic field. Blue or redshift depending on polarisation for a photon emitted up to similar valuesto the gravitational redshift.

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Experimental limits 1: Particle Data Group limits, early 2017

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Experimental limits 3: dBP photon

Laboratory experiment (Coulomb’s law) 2× 10−50 kg.

Dispersion-based limit 3× 10−49 kg (lower energy photons travel at lower speed).Note: quantum gravity affects high frequencies (GRB, Amelino-Camelia).

Ryutov finds mγ < 10−52 kg in the solar wind at 1 AU, and mγ < 1.5× 10−54 kgat 40 AU (PDG value). These values come partly from ad hoc models. Limits:(i) the magnetic field is assumed exactly always and everywhere a Parker’s spiral;(ii) the accuracy of particle data measurements (from e.g. Pioneer or Voyager)has not been discussed; (iii) there is no error analysis, nor data presentation.

Speculative lower limits from modelling the galactic magnetic field: 3× 10−63 kginclude differences of ten orders of magnitude on same data.

New theoretical limits from black holes stability, gravitational light bending, CPTviolation.

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Experimental limits 4: Warnings

Quote ”Quoted photon-mass limits have at times been overlyoptimistic in the strengths of their characterisations. This is perhapsdue to the temptation to assert too strongly something one knowsto be true. A look at the summary of the Particle Data Group(Amsler et al.. 2008) hints at this. In such a spirit, we give here ourunderstanding of both secure and speculative mass limits.”Goldhaber and Nieto, Rev. Mod. Phys., 2000

The lowest theoretical limit on the measurement of any mass isdictated by the Heisenberg’s principle m ≥ ~∆tc2, and gives3.8× 10−69 kg, where ∆t is the supposed age of the Universe.

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SuSy and LoSy breaking 1. Where the mass could come from?

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SuSy and LoSy breaking 2

Extensions of the Standard Model (SM) address issues like theHiggs boson mass discrepancy, the dark universe, neutrinooscillations and their mass.

We focus on models involving Super and Lorentz symmetriesbreaking and analyse four general classes of such models in thephoton sector. All dispersion relations show a non-Maxwellianbehaviour for the, phenomenologically both present, CPT(Charge-Parity-Time reversal symmetry) even and odd sectors.

In the latter, a massive photon behaviour in the group velocitiesemerges.

Then, we extract a massive and gauge invariant Carroll-Field-Jackiwterm in the Lagrangian and show that the photon mass isproportional to the background vector.

The mass is lower than 10−18 eV or 10−55 kg.

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de Broglie-Proca (dBP) theory 1

The concept of a massive photon has been vigorously pursued byLouis de Broglie from 1922 throughout his life. He defines the valueof the mass to be lower than 10−53 kg. A comprehensive work of1940 contains the modified Maxwells equations and the relatedLagrangian.

Instead, the original aim of Alexandru Proca, de Broglie’s student,was the description of electrons and positrons. Despite Proca’sseveral assertions on the photons being massless, his work has beenused.

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de Broglie-Proca (dBP) theory 2: SI equations

L = − 1

4µFαβFαβ − M2

2µAαAα − jαAα (3)

Fµν = ∂µAν − ∂νAµ. Minimal action (Euler-Lagrange) → inhomogeneous eqs.Ricci Curbastro-Bianchi identity ∂λFµν + ∂νFλµ∂µF νλ = 0 → homogeneous eqs.

∇ · ~E =ρ

ε0−M2φ , (4)

∇× ~B = µ0~j + µ0ε0

∂~E

∂t−M2~A , (5)

∇× ~E = −∂~B

∂t, (6)

∇ · ~B = 0 , (7)

ε0 permittivity, µ0 permeability, ρ charge density, ~j current, φ and ~A potential.M = mγc/~ = 2π/λ, ~ reduced Planck (or Dirac) constant, c speed of light, λCompton wavelength, mγ photon mass.

Eqs. (4, 5) are Lorentz-Poincare transformation but not Lorenz gauge invariant,

though in static regime they are not coupled through the potential.

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Cluster data analysis 1: the mission

Highly elliptical evolving orbits in tetrahedron: perigee 4 R⊕ apogee 19.6 R⊕, visited a wide set of magnetospheric regions.

Inter-spacecraft separation ranging from 102 to 104 km. 15/26


Cluster data analysis 8: particle current

The particle current density ~j =~jP = ne(~vi − ~ve) from ion andelectron currents; n is the number density, e the electron charge and~vi , ~ve the velocity of the ions and electrons, respectively.An accurate assessment of the particle current density in the solarwind is difficult due to inherent instrument limitations.jP >> jB (up to four orders of magnitude), mostly due to thedifferences in the i, e velocities, while the estimate of density isreasonable. While we can’t exclude that this difference is due to thedBP massive photon, the large uncertainties related to particlemeasurements hint to instrumental limits.

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Cluster data analysis 9: our mass limit

jP = 1.86 · 10−7 ± 3 · 10−8 A m−2, while jB = |∇ × ~B|/µ0 is3.5± 4.7 · 10−11 A m−2. AH is an estimate, not a measurement.

AH12 (mγ + ∆mγ) = AH

12

(mγ +

∣∣∣∣∂mγ

∂jP

∣∣∣∣ ∆jP +

∣∣∣∣∂mγ

∂jB

∣∣∣∣ ∆jB

)=

k

[(jP − jB)

12 +

∆jP + ∆jB

2(jP − jB)12

]. (8)

Considering jP and ∆jP of the same order, jP = 0.62 ∆jP , and bothmuch larger than jB and ∆jB , Eq. (8), after squaring, leads to

AH12 (mγ + ∆mγ) ∼ k (jP + ∆jP)1/2 . (9)

Table: The values of mγ (according to the estimate on AH).

AH [T m] 0.4 29 (Z) 637

mγ [kg] 1.4× 10−49 1.6× 10−50 3.4× 10−51

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de Broglie-Proca (dBP) theory 3: dispersion relations

From the Lagrangian we get ∂αFαβ +M2Aβ = µjβ. With the Lorentzsubsidiary condition ∂γAγ = 0,[

∂µ∂µ +M2]Aν = 0 (10)

Through Fourier transform, at high frequencies (photon rest energy <the total energy; ν � 1 Hz), the positive difference in velocity for twodifferent frequencies (ν2 > ν1) is

∆vg = vg2 − vg1 =c3M2

8π2

(1

ν21

− 1

ν22

), (11)

being vg the group velocity. For a single source at distance d, thedifference in the time of arrival of the two photons is

∆t =d

vg1− d

vg2' ∆vgd

c2=

dcM2

8π2

(1

ν21

− 1

ν22

)' d

c

(1

ν21

− 1

ν22

)10100m2

γ . (12)

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Plasma dispersion or photon mass?, FRBs

Such behaviour reproduces interstellar dispersion the delay in pulsearrival times across a finite bandwidth. Dispersion occurs due to thefrequency dependence of the group velocity of the pulsed radiationthrough the ionised components of the interstellar medium. Pulsesemitted at lower radio frequencies travel slower through theinterstellar medium, arriving later than those emitted at higherfrequencies.

In absence of an alternative way to measure plasma dispersion, thereis no way to disentangle plasma effects from a dBP photon.

Data on FRB 150418 indicate mγ . 1.8× 10−14 eV c−2

(3.2× 10−50 kg), if FRB 150418 has a redshift z = 0.492. In thefuture, the different redshift dependences of the plasma and photonmass contributions to DM can be used to improve the sensitivity tomγ . .

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Other investigations

MMS four satellite data for a Cluster-like data analysis

International collaboration for OLFAR proposed to ESA: a swarm ofnano-satellites opening the 100 KHz-30 MHz window.

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OLFAR nanosatellites: low frequencies and delays due tophoton mass

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ACES

CERGA Grasse (Veillet), ENS Lab. de Spectroscopie HerzienneParis (Salomon), Un. Munchen, Un. Stuttgart, Un. Tubingen-Un.Dresden (Soffel), DLR, DASA-RI 1995. Time & Frequency ScienceUtilization and Space Station Study, Contract 11287/94/NL/VK,ESA (A. Spallicci)

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ACES(-like)

Average distance ISS-ground of 1.5× 106 m (a slant range of 2.6× 106 m, an altitude of 4× 105 m).

Table: S band.

Kg Each Signal 1 pass 1 day 18 months

5 ms 10 minutes Continuous coverage Continuous coverage

10−45 5 ps (5× 10−12 s) 600 ns (6× 10−7 s) 86 µs (8.6× 10−5s) 47 ms (4.7× 10−2s)

10−50 500 ys (5× 10−22 s) 60 as (6× 10−17 s) 8.6 fs (8.6× 10−15s) 4.7 ps (4.7× 10−12s)

10−54 5× 10−30 s 5× 10−25 s 8.6× 10−23s 4.7× 10−20s

∆tS for different observation times. The outcome of the first column 5 ps is to be compared with the ionospheric delay, also

proportional to d/ν2 and amounting to 10−8 and 10−7 s. For detection of an effect in the order of some ps, it would be

necessary to know the ionosheric delay with a precision of 0.01%, which is well beyond the state of the art. The second, third,

and fourth column demand that the cumulation of each delay which at present is not possible with the S band

ACES-PHARAO equipment. Indeed, there is only a downlink.

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ACES(-like)

Table: Ku band, uplink of 14.5 GHz and a downlink of 13.75 GHz.

Kg Each Signal 1 pass 1 day 18 months

5 ms 10 minutes Continuous coverage Continuous coverage

10−45 250 fs (2.5× 10−13 s) 30 ns (3× 10−8 s) 4.3 µs (4.3× 10−6s) 2.3 ms (2.3× 10−3s)

10−50 25 ys (2.5× 10−23 s) 3 as (3× 10−18 s) 430 as (4.3× 10−16s) 230 fs (2.3× 10−13s)

10−54 2.5× 10−31 s 2.5× 10−26 s 4.3× 10−24s 2.3× 10−21s

We draw from the table that an upper limit of 10−47 kg corresponds to a single pass of 10 minutes. Nevertheless, the

positioning error of the ISS corresponds to 10−2 m, and thus 3× 10−11 s.Though not competitive with PDG limits, there are positive features

It represents a novel measurement system never attempted before.

The atmosphere must be well modelled (including cubic terms from ionospheric dispersion in the order of 1 ps, ascientific goals in itself).

It may constitute a first step toward a new application of atomic clocks in space. For instance, if LISA were equippedof atomic clocks and possibly masers, beside lasers, the distance between the satellites would allow a more ambitiousupper limit of a factor at least 104.

Continuous coverage for a day, or 18 months: multi-path, ground station self-synchronisation, synchronisationbetween stations.

The variable distance between ISS and ground station produces a signature hopefully different from ionosphericeffects.

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What about cosmology?

Do nM theories produce redshifts that could complement thecosmological expansion? Work in progress.

How precise are astrophysical data on distances, Hubble constantetc. to attribute redshift solely to expansion?

What about criticism on dark energy? data SN1 consistent withconstant expansion (Nielsen J.T., Guffanti A., Sarkar S., 2015, arXiv1506.01354 [astro-ph.CO]).

Under certain conditions, frequency dependent group velocityproduces an ”effective time dilation”.

For alternative cosmologies passing some tests, see 2017Lopez-Corredoira on Foundations of Physics (Capozziello, Prokopec,Spallicci, Eds.)

Experiment on local expansion? Kennedy-Thorndike experiment(Shamir J., Fox R., 1967, N. Cim. B, 50, 371). Work in progress.

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Grazie per la vostra attenzione

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clocks and cold atoms for testing electromagnetism - uzh · a. sakharov (nyu - cern) e....

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