Searching for New Forces over Ultrashort Distances

XXXVIIIth RENCONTRES DE MORIOND2003

Ephraim Fischbach

andRicardo Decca

Galina KlimchitskayaDennis KrauseDaniel Lopéz

Vladimir Mostepanenko

Overview• Was Newton Really Right?

– Tests of 1/r2 law– Tests of the equivalence principle– Importance of scale

• Motivations for Non-Newtonian Gravity– New light quanta ⇒ new forces– Unification and extra dimensions

• Experimental Tests– Problems with short-distance experiments– The “iso-electronic” effect– The IUPUI Casimir experiment

• Outlook

Summary of Newtonian Gravity• Newtonian Gravity • Non-Newtonian Gravity

V (r) = −Gm1m2

rV (r) = −

Gm1m2

r1+α 12e

− r / λ{ }r F (r) = −G / m 1m2

r 2ˆ r = / m 1

r a 1 F (r) = −G(r)m1m2

r 2ˆ r

r a 1 = −

Gm2

r2 ˆ r G(r) = G[1+ α12e−r / λ (1+ r /λ)]

a) independent of the nature of m1(Equivalence Principle)

b) varies as 1/r2

doesn’t vary as 1/r2 *

not independent of 1 or 2 *

* Evidence for either of these would point to a new fundamental force in nature.

rm m1 2

Theory of New ForcesA new force can arise from

the exchange of a lightquantum with appropriate properties

scalar(JP = 0+)

vector (JP = 1-)

µ1f 2f

p, e, n, (π0, …) p, e, n, (π0, …)

refQQrV

reffrV

r

r

λ

λ

/2

2112

/

2112

)(

)(

−

−

±=

±=

scalar

vector

Bulk Matter

λ = Range

= h/µc

if µ = 10-9 eV/c2 ⇒ λ = 200 m

Limits on Extra Dimensions and New Forces:Long-Range Limits

Reference: Coy, Fischbach, Hellings, Standish & Talmadge (2003)

Limits on Extra Dimensions and New Forces:Short-Range Limits

Reference: Long, et al., Nature 421, 922 (2003)

Gravitational strengthGravitational strength

Mini-Review #1• The existence of ultra-light particles can produced long-range fields

which behave somewhat like gravity

• The presence of such fields would show up as apparent deviations from the predictions of Newtonian gravity

1/r2 violationsequivalence principle violations

• To search for such violations, experiments must be carried out over many distance scales

• Newtonian gravity is OK down to ~ 0.1 mm.Below ~ 0.1 mm we know relatively little about the behavior of Newtonian gravity

Long-Range Forces Over Sub-mm Scales

• Various mechanisms lead to potentials with and inverse power law behavior

n=2 2-photon exchange; 2-scalar exchange

n=3 2-pseudoscalar exchangen=4n=5 νν -exchange; 2-axion exchange

• Also: String Theory Models …

• Such forces can best be detected in experiments where the interacting bodies are very close to each other, as in the Casimir Effect

• Problems– How to separate out the new

forces from the knownelectromagnetic effects

– Forces are intrinsically small– V(r) ≠ 1/r

1021)(

−

−=

nN

nn rr

rmmGrV α

__

Neutrino Exchange Force

Vνν (r) =GF

2

4π31r 5

1 2

ν

νGF GF

Gravity in 3 + n Non-Compact Dimensions

M M

r

1 2

Potential Energy: VGravity(r) = −GM1M2

r1+n

r F Gravity (r) = −

r ∇ V (r)Force:

Observations ⇒ n = 0

Compact Spatial Dimensions

RR

r >> R → Space appears 3-Dr < R → Extra dimensions appear

Experiment:• All matter sees extra dims ⇒ R< 10-15 m• Only gravity sees extra dims ⇒ R< 10-4 m

Gravity with n Compact Extra Dimensions

VGravity(r) =

− GM1M2

r(1+ α e−r / λ ), r >> R

−G' M1M2

r1+n , r ≤ R

Yukawa Correction

Range of Yukawa: λ ~ RStrength Constant α:

•Models of extra dimensions: α ~ 1-10 •New Force Models: α ~ ????

Newtonian Gravity

Numerical Estimates• It is convenient to introduce an energy scale set by the usual Newtonian

constant G ≡ G4. This is the Planck mass MPl ≡ M4

M4 ≡ MPl = (hc/G4)1/2 = 2.18×10-5 g = 1.22×1019 GeV/c2

• In natural units (h = c = 1) M42 = 1/G4

• The analog of the Planck mass in higher dimensions is called M4+n

• When expressed in terms of M4 and M4+n the previous resultG4 = G5/4R generalizes to

• This forms the basis for current experiments

M42 ≈ Rn(n)M4+n

n+2

How Big is M4+n? How big is n?

1) The usual Planck mass M4 and the associated length scale h/M4c ≈10-33 cm are the scales at which gravitational interactions become comparable in strength to other interactions, and hence can be unified with these interactions

2) It would be nice if this happened at a smaller energy scale ⇒ bigger length scale.A natural choice is ~ 1 TeV = 1012 eV where supersymmetrybreaks down

3) This can happen in some string theories with extra spatial dimensions if ordinary matter is confined to 3-dimensional walls(“branes”), and only gravity propagates in the extra dimensions

How Big is M4+n? How big is n?

4) In such theories M4+n ≈ 1 TeV by assumptionWe then solve:

n = 1 ⇒ R(1) ≈ 2 × 1015 cm Excludedn = 2 ⇒ R(2) ≈ 0.2 = 2 mm Highly Constrained

! n = 3 ⇒ R(3) ≈ 9 × 10-7 cm Unconstrained

( ) cm102)(

)(

17/32

24

24

−

++

×≈

≈

n

nn

n

nR

MnRM

(1019 GeV)2 (1 TeV)n+2

Forces acting between two 1 cm × 1cm × 1mm copper plates separated by distance d (T = 300 K)

Gravity dominates when d >>10-5 m

Casimir forcedominates when 10-10 m < d < 10-5 m

NeutrinoNeutrino

Casimir Review• Casimir force, arising from quantum

fluctuations of vacuum, dominates gravity at short separations.

• Large Casimir background hinders efforts to detect new forces and extra dimensions at short distances.

• Experiments utilizing the iso-electroniceffect should be able to negate this Casimir background.

Casimir Force for Ideal Metals at T = 0

dε= ° ε= °

FF

F(d) = −

π2

240hcd4 A

Zero-Point Fluctuations of Radiation Field +

Boundary Conditions

⇓

Casimir Force for Real Metals at T ≠ 0:Lifshitz Formula

dε(ω) ε(ω)

F (d) = °kB T A

º c31X

l=00ª 3

lZ 11 p2dp f

2

6666664

0

BBBB@

K (iª l) + " ( iª l)pK (iª l) ° " ( iª l)p

1

CCCCA

2e2d(ª l=c)p ° 1

3

7777775

° 1

+

2

6666664

0

BBBB@

K (iª l) + pK (iª l) ° p

1

CCCCA

2e2d( ª l=c)p ° 1

3

7777775

° 19>>>>>>>>=

>>>>>>>>;

where

! = iª l; ª l =2º kB T l

šh;

K (iª l) =2

4p2 ° 1 + " ( iª l )3

51=2

Isotopic Dependence of the Casimir Force?

FIsotope #1Casimir = FIsotope # 2

Casimir

Our strategy

FX = FIsotope # 2Measured − FIsotope #1

Measured

assumes that the Casimir force is the same for two isotopes:

Is this true?

Isotopic Dependence of the Casimir Force:A First Look

1. Casimir Force depends on dielectric properties of interacting bodies

2. Frequency-dependent dielectric constant ε(ω) depends on the lattice spacing a

3. Lattice spacing a depends on isotopic mass through:

• Anharmonicity of Interatomic Potentials

• Zero-Point Motion of Ions

Isotopic Dependence of the Casimir force and New forces and extra dimensions: Logic

Limits on Extra Dimensions and New Forces

Casimir Force

Isotopic Mass Lattice Constant

Plasma FrequencyDielectric Constant

Lifshitz Formula

Dielectric Constant of a Metal

The optical properties of a material depend on its dielectric constant ε(ω).

Free Electron Metal: ε(ω) = 1−ωp

2

ω2

ωp2 =

4πNe2

meV

If ω < ωp, light is reflected by the metalIf ω > ωp, light is transmitted through the metal.

N/V = # of valence electrons/volumePlasma Frequency:

For copper and gold, ωp = 9.3 × 1016 rad/s (λ = 136 nm)

Anharmonicity of Interatomic Potentials : Thermal Expansion of Lattice

r

r − r0 = u =du ue−V (u) /k BT∫du e−V (u) /k BT∫ ≈

b2k2 kBT

a(T ) ≡ r ≈ r0 +b

2k 2 kBT

Thermal average interatomic spacing:

T-dependent lattice spacing:

r - r0

VHr- r0L

V(r − r0 ) ≈12

k(r − r0 )2 −16

b(r − r0 )3

Anharmonic term

⇓⇓

Zero-Point Motion of Atoms:Isotopic Dependence of Lattice Constant

Thermal Oscillations →

kBT →

a(T ) ≡ r ≈ r0 +b

2k 2 kBT aZP ≡ r ≈ r0 +

b4k2 hω→

aZP ≡ r ~ r0 +

bh

4k 3/ 21Mω ~

kM

M = Atomic Mass( ) ⇒

∆aa

=a2 − a1

a1

~ −bh

4k3 /2a1 M1

∆MM1

Relative difference in a for two different isotopes #1 and #2

=

Quantum Zero-Point Motion

12

hω

Isotopic Dependence of a: Experiment

Observed dependence is more complicated!

∆aa

~ − T - dependent constant ( )∆MM⇒

Sozontov, et al., 2001-5.3×10-5 (T = 30 K)-2.2×10-5 (T = 300 K)

70Ge, 76Ge

Batchelder, Losee, and Simmons, 1968

-1.9×10-3 (T = 3 K)-1.6×10-3 (T = 24 K)

20Ne, 22Ne

Covington and Montgomery, 1957-4×10-4 (T = 293 K)6Li, 7Li

Holloway, et al., 1991-1.5×10-4 (T = 298 K)12C, 13C(Diamond)

Kogan and Bulatov, 1962-1.4×10-4 (T = 78 K)5.7×10-5 (T = 300 K)

58Ni, 64Ni

Reference∆a/aIsotopes

Isotopic Dependence of the Casimir Force: Plasma Model

ωp2 ∝

1a3

F(d) ≈ −π2

240hcAd4 1−

163

cωpd

If d ¿

2º c! p

and T øšh c

2kB d,

Since

Relative difference in FCasimir for isotopes #1 and #2

=∆FF

=F2 − F1

F1

~ −8c

ωp,1d∆aa

~ 8c

ωp,1d×10−4 << 10−4

and ∆aa

~ −10−4 ,

Reference: Krause and Fischbach, Phys. Rev. Lett. 89, 190406 (2002)

IUPUI Experiment (Decca, Lopéz, Fischbach, Krause)

IUPUI Experiment (Decca, Lopéz, Fischbach, Krause)

Experimental Parameters:

Experiment of Chan, et al., from Experiment of Chan, et al., from October 2001 October 2001 Physics TodayPhysics Today

Plate: 500 µm × 500 µm × 3.5 µmSphere Radius: 300 µmCoatings:

Sphere: 1 nm Cr with 200 nm AuPlate: Cu and Ni

Sphere/Plate Separation: 200-1200 nmMinimum Force:

Current: 6 fN /Hz1/2

(Note: E. Coli bacterium weight ~ 10 pN)

Experimental Setup for Casimir Force Measurement between Dissimilar Materials

Electrostatic Force Measurements

Casimir Force:Static Measurement

Casimir Pressure:Gradient Measurement

Limits on Extra Dimensions and New Forces:Sub-micron Limits

Reference: Decca, Lopéz, Fischbach, Krause (unpublished)

Future Work

1. Comparing the Casimir force between an Au sphere and a Au-Ge substrate

2. Comparing the Casimir force between an Au sphere and a 58Ni and 64Ni substrate