The interaction of gravitational radiation with superconductors: A - - PowerPoint PPT Presentation

Invited lecture at the “Time and Matter Conference” in Bled, Slovenia by Raymond Chiao August 28, 2007

The interaction of gravitational radiation with superconductors:

A progress report on experiments at UC Merced at the interface of:

Quantum Mechanics

&

General Relativity

Co-workers

• Students: S. Minter, J. McLane
• Collaborators: C. Rowe, K. Wegter-

McNelly* *Work sponsored by the Center of Theology and Natural Sciences STARS program

Hoover dam is an efficient hydroelectric energy converter of: Gravitational energy electrical energy

Can we convert gravitational wave energy efficiently into electromagnetic wave energy? Answer: YES

What is a gravitational wave?

• It is a time-varying tidal gravitational field (think
• f jello with grapes embedded inside it)

Tidal forces of a gravitational wave

• 5
• 4
• 3
• 2
• 1

1 2 3 4 5

• 5
• 4
• 3
• 2
• 1

1 2 3 4 5

g

• c. m.

One possible GR-to-EM wave converter

Ring with supercurrent I B B Levitated superconducting sphere d(t) I

Ring with supercurrent I B B Levitated superconducting sphere d(t) I

Faraday’s law leads to high conversion efficiency for superconductors

Lenz’s law implies that:

GR EM

= − F F

Power absorbed from GR wave Power emitted into EM wave.

GR rad EM rad

∴ = = − =

⋅ ⋅ F v F v

Similarly, in the time-reversed process

• f EM-to-GR wave conversion

EM GR

= − F F

Power absorbed from EM wave Power emitted into GR wave.

EM rad GR rad

∴ = = − =

⋅ ⋅ F v F v

Wave conversion from gravitational to electromagnetic waves

EM wave out GR wave in

Quantum transducer

Example:

Ring with supercurrent I B B Levitated superconducting sphere d(t) I

Time-reversal symmetry

EM wave in GR wave out

Quantum transducer

Hertz-like experiment

EM wave in EM wave out GR wave

Quantum transducer Quantum transducer

Einstein's field equations

μν μν μν μ μν μν μν μν μν μν μν μν μν

π η η η π T c G t h c h h h h h h g T c G R g R

kk j ij 4 2 2 2 2 , 4 2 1

16 1 ) ( gauge traceless

• e

transvers in the Then . and 1 1 1 1 where fields, For weak 8 − = ∂ ∂ − ∇ = = = << ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛− = + ≈ = −

Maxwell-like equations for weak gravitational fields

where

G G G G G G G G G G G G

t t ρ ε μ ε ∇⋅ = − = ∂ ∇× = − ∂ ∇⋅ = ∂ ⎛ ⎞ ∇× = − + ⎜ ⎟ ∂ ⎝ ⎠ E E g B E B E B j

where

30 2 9

16 3.7 10 SI units 1 1.19 10 SI units 4

G G

G c G π μ ε π

−

= = × = = ×

Gravity wave speed and impedance

8 18 G

1 3.00 10 meters/sec Z 2.79 10 SI units

G G G G

c ε μ μ ε

−

= = × = = ×

Why quantum mechanics?

• Efficiency of quantum transducers

depends on “quantum rigidity”

• Efficiency of quantum gravity wave

antennas depends on “quantum dissipationlessness”

• Both arise from the ENERGY GAP (e.g,

the BCS gap) of the quantum system and the quantum adiabatic theorem.

Energy gap

• f a two-level quantum system

Ground state Excited state ENERGY GAP

What’s the difference between a normal metal and a superconductor?

normal metal superconductor

ω

• ω
• B =
• magnetic field

created by London moment

2

e

m e

B ω =

Reflection of a gravitational plane wave from a normal metal vs. a superconductor

cm

g g

normal metal

• e
• e

+Ze +Ze in presence of gravito-electric field

• ⊗
• G

B

• G

B

• 1 (

)

G

G G G

s E B

μ

= ×

• superconductor

in the presence of gravito-magnetic field +Ze +Ze

• 2e
• 2e

v=0 v=0 G

s

An important application: “Gravity Radio”

• Intercontinental communication by

microwave-frequency gravity waves directly through the interior of the Earth

Gravity waves from the Big Bang

Cosmic Gravitational Wave Background (CGB)

• 20
• 15
• 10
• 5
• 20
• 15
• 10
• 5

5 10 15

Frequency [Log10 f(Hz)] Fractional Energy Density [Log 10 h02Ωgw]

Slow-Roll Inflationary Big Bang Ekpyrotic/Cyclical Model Pre-Big Bang Model Advanced LIGO/VIRGO Sensitivity (ground-based) LISA Sensitivity (space-based) Planck Sensitivity (space-based, indirect EM measurement) Big Bang Observer (space-based, LISA follow-on) 0.9 K Thermal Spectrum (Wien peak f = 53 GHz)

CONCLUSIONS:

• A pair of superconducting bodies can become

an efficient transducer between GR and EM waves.

• Observations of “Cosmic Gravitational-wave

Background” (CGB) should be possible.

• “Gravity radio” communications between

continents should be possible.