Using a positron beam to measure the speed of light anisotropy - - PowerPoint PPT Presentation

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Using a positron beam to measure the speed of light anisotropy - - PowerPoint PPT Presentation

Sep 01, 2022 353 likes •763 views

Using a positron beam to measure the speed of light anisotropy Bogdan Wojtsekhowski, Jefferson Lab Physics landscape Search for new beyond-the-Standard-Model physics Positron & electron test of the theory of special relativity

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September 14, 2017 Positrons at Jefferson Lab, JPos17

Bogdan Wojtsekhowski, Jefferson Lab

Using a positron beam to measure the speed of light anisotropy

  • Physics landscape
  • Search for new beyond-the-Standard-Model physics
  • Positron & electron test of the theory of special relativity
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September 14, 2017 Positrons at Jefferson Lab, JPos17

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Physics

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September 14, 2017 Positrons at Jefferson Lab, JPos17

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Quantum Gravity

  • Black hole radius
  • Quantum scale
  • Quantum

gravity scale

no escape (Schwarzschild) radius: rS =

2Gm c2

Compton wave length: λ =

h mc

Planck mass: λ = rS or MP l = q

~c G

MP l = 1019 GeV LP l = 10−19 fm

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September 14, 2017 Positrons at Jefferson Lab, JPos17

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Quantum Gravity

  • Black hole radius
  • Quantum scale

no escape (Schwarzschild) radius: rS =

2Gm c2

Compton wave length: λ =

h mc

q

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September 14, 2017 Positrons at Jefferson Lab, JPos17

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Quantum Gravity

  • Black hole radius
  • Quantum scale
  • Planck scale

no escape (Schwarzschild) radius: rS =

2Gm c2

Compton wave length: λ =

h mc

Planck mass: λ = rS or MP l = q

~c G

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September 14, 2017 Positrons at Jefferson Lab, JPos17

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Quantum Gravity

  • Black hole radius
  • Quantum scale
  • Quantum

gravity scale

no escape (Schwarzschild) radius: rS =

2Gm c2

Compton wave length: λ =

h mc

Planck mass: λ = rS or MP l = q

~c G

MP l = 1019 GeV LP l = 10−19 fm

The proton size is one fermi: 10-13 cm Quantum EM scale is an atom size : 10-8 cm

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September 14, 2017 Positrons at Jefferson Lab, JPos17

7

Quantum Gravity

  • Black hole radius
  • Quantum scale
  • Quantum

gravity scale

  • QG:

no escape (Schwarzschild) radius: rS =

2Gm c2

Compton wave length: λ =

h mc

Planck mass: λ = rS or MP l = q

~c G

MP l = 1019 GeV LP l = 10−19 fm

The proton size is one fermi: 10-13 cm Quantum EM scale is an atom size : 10-8 cm

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September 14, 2017 Positrons at Jefferson Lab, JPos17

8

Quantum Gravity

  • Black hole radius
  • Quantum scale
  • Quantum

gravity scale

  • QG:

no escape (Schwarzschild) radius: rS =

2Gm c2

Compton wave length: λ =

h mc

Planck mass: λ = rS or MP l = q

~c G

MP l = 1019 GeV LP l = 10−19 fm

The proton size is one fermi: 10-13 cm Quantum EM scale is an atom size : 10-8 cm

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September 14, 2017 Positrons at Jefferson Lab, JPos17

9

Quantum Gravity

  • Black hole radius
  • Quantum scale
  • Quantum

gravity scale

  • QG:

no escape (Schwarzschild) radius: rS =

2Gm c2

Compton wave length: λ =

h mc

Planck mass: λ = rS or MP l = q

~c G

MP l = 1019 GeV LP l = 10−19 fm

The proton size is one fermi: 10-13 cm Quantum EM scale is an atom size : 10-8 cm

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September 14, 2017 Positrons at Jefferson Lab, JPos17

Physics beyond the Standard Model

10

Ø Neutrino masses Ø Dark matter Ø Searches in PVDIS, Moller, QWeak

The proposed experiment has sensitivity to reach the onset of Quantum Gravity

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September 14, 2017 Positrons at Jefferson Lab, JPos17

Einstein’s postulates of physics

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The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion. Any ray of light moves in the “stationary” system

  • f coordinates with determined velocity c, whether

the ray be emitted by a stationary or by a moving body. Einstein, Ann. d. Physik 17 (1905)

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September 14, 2017 Positrons at Jefferson Lab, JPos17

The speed of light measurement

The speed of light is said to be isotropic if it has the same value when measured in any/every direction. The constancy of the one-way speed in any given inertial frame is the basis of the special theory of relativity.

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A B

  • ne-way: v1 = dAB/tAB

How do we measure the speed?

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September 14, 2017 Positrons at Jefferson Lab, JPos17

The speed of light measurement

The speed of light is said to be isotropic if it has the same value when measured in any/every direction. The constancy of the one-way speed in any given inertial frame is the basis of the special theory of relativity.

13

A B

round-trip (two-way): v2 = (dAB+dBA)/(tAB+tAB)

How do we measure the speed?

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September 14, 2017 Positrons at Jefferson Lab, JPos17

One-way speed and two-way speed: What is the difference? What is experimentally investigated most often is the round-trip speed (or "two-way” speed of light) from the source to the detector and back.

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The speed of light

The speed of light is said to be isotropic if it has the same value when measured in any/every direction. The constancy of the one-way speed in any given inertial frame is the basis of the special theory of relativity.

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September 14, 2017 Positrons at Jefferson Lab, JPos17

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The speed of light is said to be isotropic if it has the same value when measured in any/every direction.

Michelson-Morley experiment

two-way speed accuracy scale: 1µm / 10m ~ 10-7

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September 14, 2017 Positrons at Jefferson Lab, JPos17

The most recent experiment

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ARTICLE

Received 17 Jan 2015 | Accepted 25 Jul 2015 | Published 1 Sep 2015

Direct terrestrial test of Lorentz symmetry in electrodynamics to 10 18

Moritz Nagel1,*, Stephen R. Parker2,*, Evgeny V. Kovalchuk1, Paul L. Stanwix2, John G. Hartnett2,3, Eugene N. Ivanov2, Achim Peters1 & Michael E. Tobar2

DOI: 10.1038/ncomms9174

OPEN

Lorentz symmetry is a foundational property of modern physics, underlying the standard model of particles and general relativity. It is anticipated that these two theories are low-energy approximations of a single theory that is unified and consistent at the Planck

  • scale. Many unifying proposals allow Lorentz symmetry to be broken, with observable effects

appearing at Planck-suppressed levels; thus, precision tests of Lorentz invariance are needed to assess and guide theoretical efforts. Here we use ultrastable oscillator frequency sources to perform a modern Michelson–Morley experiment and make the most precise direct terrestrial test to date of Lorentz symmetry for the photon, constraining Lorentz violating

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Communications/Nature

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September 14, 2017 Positrons at Jefferson Lab, JPos17

The speed of light measurement

The speed of light is said to be isotropic if it has the same value when measured in any/every direction. The constancy of the one-way speed in any given inertial frame is the basis of the special theory of relativity.

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A B

  • ne-way: v1 = dAB/tAB

How do we measure the speed?

Two clocks and stable distance A-to-B

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Tests of Lorentz Invariance

  • Two-way speed via rotating cavities: Δc2/c < 10-18
  • One-way speed via asymmetric optical ring: Δc1/c < 10-14

At what level could we expect a Lorentz Invariance violation?

dispersion equation in some LI violation models see, Mattingly, Living Rev.Rel. 8 (2005) 5

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Tests of Lorentz Invariance

  • Two-way speed via rotating cavities: Δc2/c < 10-18
  • One-way speed via asymmetric optical ring: Δc1/c < 10-14

At what level could we expect a Lorentz Invariance violation?

The extra term leads to a directional variation of the speed of light.

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Tests of Lorentz Invariance

  • Two-way speed via rotating cavities: Δc2/c < 10-18
  • One-way speed via asymmetric optical ring: Δc1/c < 10-14

At what level could we expect a Lorentz Invariance violation?

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September 14, 2017 Positrons at Jefferson Lab, JPos17

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Tests of Lorentz Invariance

  • Two-way speed via rotating cavities: Δc2/c < 10-18
  • One-way speed via asymmetric optical ring: Δc1/c < 10-14

MZ/MP l ∼ 10−17 At what level could we expect a LI violation?

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Measurement of the speed

Relative speed would be enough: light vs. beam Stable beam of electrons photons

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Measurement of the speed

Relative speed would be enough: light vs. beam Stable beam of electrons photons The difference (c-v) defines the Lorentz factor.

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September 14, 2017 Positrons at Jefferson Lab, JPos17

Speed of light variation and Lorentz factor

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γ =

c

√

(c−v)·(c+v)

When the value of the speed v is fixed, a tiny variation of c in the direction

  • f motion leads to a large variation of γ,

which provides a powerful enhancement

  • f sensitivity to a possible variation of c.

∆γ γ

= γ2 · ∆c

c

v-c γ

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September 14, 2017 Positrons at Jefferson Lab, JPos17

A concept of a new Lorentz Invariance test

Ø Explore the difference of (v-c) in opposite directions of v Ø Use a very small value of (v-c)/c ~ 10-9, ultra relativistic electrons The method (BW in EPL, 108 (2014) 31001; arXiv:150902754 )

  • Momentum measurements at the opposite ends of the arc:

B

A B O p p

A

time 1

δc ∝ R ∆R(t) · sin ⇥ ω⊕t + φ ⇤ dt

ω⊕

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R =

PA PB

sensitive direction

, ratio of momenta in segments A and B

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September 14, 2017 Positrons at Jefferson Lab, JPos17

Beam in an accelerator

as a first-order estimate using the dispersion along the orbit:

  • Hor. displacement = Dispersion times Momentum deviation

x(s) = xβ(s) + η(s) × ∆p

p

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ηlarge ∼ 1.5m , σx ∼ 50µm

A large number of Beam Position Monitors could be used for higher accuracy.

σ h pA−pB

paver

i = σ h xA

ηA

i ⊕ σ h xB

ηB

i ∼ 0.5 · 10−4

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September 14, 2017 Positrons at Jefferson Lab, JPos17

Beam in an accelerator

consider the first term statistics over 100 seconds:

x(s) = xβ(s) + η(s) × ∆p

p

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σ∆p p

= σ h ∆ x

η

i ⊕ x

η · σ

time η

η

σ∆p p

= 0.5 · 10−4 × q

2.5·10−6 100

∼ 10−8

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September 14, 2017 Positrons at Jefferson Lab, JPos17

Beam in an accelerator

a short time ~100 s A measurement over 24 hours => a few days’ experiment: δc/c ~ 10-18 It would be 10,000 times better than the current limit for the one-way δc/c

  • Hor. displacement = Dispersion times Momentum deviation

x(s) = xβ(s) + η(s) × ∆p

p

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σ∆γ γ

= 3 · 10−10

σ∆p p

= 10−8

Back to statistical estimations:

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September 14, 2017 Positrons at Jefferson Lab, JPos17

Accelerator stability

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It would be great to have a 10-10 level of magnet and geometry stability (over 24 hours). However, typical stability is of 10-6! Analysis of the frequency will help, but .. The solution is two beam operation: positrons and electrons, moving in opposite directions.

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September 14, 2017 Positrons at Jefferson Lab, JPos17

Cornell electron/positron storage ring

Experiment analysis is in progress. The first result will be posted in 2017. 99 BPMs, two single-bunch beams Four 5-8 hour data runs were taken.

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September 14, 2017 Positrons at Jefferson Lab, JPos17

Experiment at CEBAF

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12GeV

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Positron beam for CEBAF

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injector e- FEL is a source of e+

Always both beams – electron and positron! Minimum new construction.

100 W beam

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September 14, 2017 Positrons at Jefferson Lab, JPos17

Positron beam for CEBAF

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injector e- FEL is a source of e+

Always both beams – electron and positron! Minimum new construction.

100 W beam

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September 14, 2017 Positrons at Jefferson Lab, JPos17

Positron beam for CEBAF

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injector e- FEL is a source of e+

Always both beams – electron and positron! Minimum new construction.

100 W beam

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September 14, 2017 Positrons at Jefferson Lab, JPos17

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Summary

§ The search for a Quantum Gravity effect in the dispersion formula is well motivated. The onset of QG is within current capability. § A search for possible anisotropy of the maximum attainable speed is proposed using the high energy electron and positron beams via beam deflections in the magnetic arcs at CEBAF.

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Backup slides

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Synchrotron Radiation

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Number of emitted photons per revolution = γ/15 ~ 1000 Photon energy ~ 30 keV Jitter of beam energy centroid (in one second) < 1 MeV/106 => 10-10 relative effect

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September 14, 2017 Positrons at Jefferson Lab, JPos17

U-boson search, concept 2006

38 Slow positron

e+

30 cm diameter flywheel

e

1 mA electron beam

30−100 nA positron beam 170 +/ 1.5 MeV

−

positron beam 45 micron emittance 30 +/ 1.5 MeV

Optics 150 kW 160 MeV dump Positron source

  • B. Wojtsekhowski, P. Degtiarenko, A. Freyberger, L. Merminga
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September 14, 2017 Positrons at Jefferson Lab, JPos17

JPos09: JLab positron beam considerations

n = 60 4[mm]2

5000[mm] = 50 µm × rad

σx ∼ 2 mm, βSRF ∼ 5 m

⇥n =

σ2

x

βSRF

e+ emittance: Ee=130 MeV, W 0.5 mm, z = 0.25 mm

Mean ALLCHAN 0.3558E-01 0.2910E-03

!x (mm!rad) N-1

edNe+/d!

Ek = 20 " 1 MeV " # 15$ Red: !x from -0.01 to 0.11 mm!rad

!x (mm!rad) #dNe+(!)

Ek = 20 " 1 MeV " # 15$

Mean ALLCHAN 0.2824E-01 0.2567E-03

!x (mm!rad) N-1

edNe+/d!

Ek = 30 " 1.5 MeV " # 10$ Red: !x from -0.01 to 0.11 mm!rad

!x (mm!rad) #dNe+(!)

Ek = 30 " 1.5 MeV " # 10$

Mean ALLCHAN 0.2811E-01 0.2332E-03

!x (mm!rad) N-1

edNe+/d!

Ek = 40 " 2 MeV " # 8$ Red: !x from -0.01 to 0.11 mm!rad

!x (mm!rad) #dNe+(!)

Ek = 40 " 2 MeV " # 8$

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0.25 0.5 0.75 1 0.25 0.5 0.75 1 0.25 0.5 0.75 1 10

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0.25 0.5 0.75 1 0.25 0.5 0.75 1 0.25 0.5 0.75 1 10

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0.25 0.5 0.75 1 0.25 0.5 0.75 1 0.25 0.5 0.75 1

Ee = 130 MeV, E+ = 20 ± 1 MeV, θ+ < 15

⇥x = x ⇤x

J+ = J− × (max

x

)2 × N+/N−

Production: ~10-4 positrons per each 160 MeV electron into acceptance SRF

N+/N− ∼ 3 × 10−4

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September 14, 2017 Positrons at Jefferson Lab, JPos17

JLab, March 27, 2009 A probe of the u/d ratio at high x