Equivalence principle, antigravity Equivalence principle, antigravity of antimatter and all thatof antimatter and all that

Savely G Karshenboim

D.I. Mendeleev Institute for Metrology (St. Petersburg)and Max-Planck-Institut für Quantenoptik (Garching)

Antigravity and equivalence Antigravity and equivalence principle for antimatterprinciple for antimatter

(i) Antigravity of (i) Antigravity of antimatter:antimatter:

Precision Precision spectroscopy of spectroscopy of fundamental fundamental atoms, containing atoms, containing antiparticles, in the antiparticles, in the presence of presence of galactic and Solar galactic and Solar gravitygravity

Equivalence principle and antigravity

Equivalence Equivalence principle:principle: in free fall we could not recognize gravitation (if neglecting the gradients)

Antigravity:Antigravity: no equivalence

principle

while the matter is falling free

the antimatter is rising free

Red shift = {(E=mc2) + (mi=mg) + Newtonian gravity}

All clocks upstairs are blue shifted, photon frequencies are not shifted.When photon is going up it disagrees with the clock by / = (gh/c2).

E = m0c2 + m0gh

E = m0c2

h

E = (m0+m) (c2 + gh)

E = (m0+m)c2 h0 = mc2

hh = m(c2+gh)

ground state excited state transition frequency

Gravitational and motional effects

I will discuss gravitational effects and ignore motional effects.

That is possible because I am interested in differential effects.

Motional effects are closely related to gravitational and often cancel them.

However, differential motional effects such as Doppler effect are equal to zero.

Red shift = {(E=mc2) + (mi=mg) + Newtonian gravity}

E = m0c2 + m0gh

E = m0c2

h

E = (m0+m) (c2 + gh)

E = (m0+m)c2 h0 = mc2

hh = m(c2+gh)

ground state excited state transition frequency

All clocks upstairs are blue shifted, photon frequencies are not shifted.When photon is going up it disagrees with the clock by / = (gh/c2).

Red shift = {(E=mc2) + (mi=mg) + Newtonian gravity}

E = m0c2 + m0gh

E = m0c2

h

E = (m0+m) (c2 + gh)

E = (m0+m)c2 h0 = mc2

hh = m(c2+gh)

ground state excited state transition frequency

All clocks upstairs are blue shifted, photon frequencies are not shifted.When photon is going up it disagrees with the clock by / = (gh/c2).

The shift is universal for all clocks once the gravity is proportional to their inertial mass and thus the shift by itself cannot be detected.

Red shift = {(E=mc2) + (mi=mg) + Newtonian gravity}

E = m0c2 + m0gh

E = m0c2

h

E = (m0+m) (c2 + gh)

E = (m0+m)c2 h0 = mc2

hh = m(c2+gh)

ground state excited state transition frequency

All clocks upstairs are blue shifted, photon frequencies are not shifted.When photon is going up it disagrees with the clock by / = (gh/c2).

The shift is universal for all clocks once the gravity is proportional to their inertial mass and thus the shift by itself cannot be detected. That is correct for all clocks of matter. Once we suggest antigravity for

antimatter – that is not correct for antimatter anymore!

Red shift = {(E=mc2) + (mi=mg) + Newtonian gravity}

E = m0c2 + m0gh

E = m0c2

h

E = (m0+m) (c2 + gh)

E = (m0+m)c2 h0 = mc2

hh = m(c2+gh)

ground state excited state transition frequency

All clocks upstairs are blue shifted, photon frequencies are not shifted.When photon is going up it disagrees with the clock by / = (gh/c2).

The shift is universal for all clocks once the gravity is proportional to their inertial mass and thus cannot be detected. That is correct for all clocks of matter. Once we suggest antigravity for

antimatter – that is not correct for antimatter anymore!

Gravitational red shift is a generic property of any relativistic theory of gravitation.

Can we measure the absolute red shift (in respect to zero gravity r=∞) ?

Hydrogen: Gravity

mmgg = m = mii

Spectroscopy 1s-2s Other

transitions Theory

calculable frequency in terms of me and

Ry

Antihydrogen: [Anti]gravity

mmgg = – m = – mii

Spectroscopy 1s-2s ? HFS ?

Theory needs me+ &

mp-

otherwise: all is the same as for H

Can we measure the absolute red shift (in respect to zero gravity r=∞)?

Hydrogen: Gravity

mmgg = m = mii

Spectroscopy 1s-2s Other

transitions Theory

calculable frequency in terms of me and

Ry

Antihydrogen: [Anti]gravity

mmgg = – m = – mii

Spectroscopy 1s-2s ? HFS ?

Theory needs me+ &

mp-

otherwise: all is the same as for H

To be blue shifted (∞).To be red shifted (∞).

Can we measure the absolute red shift (in respect to zero gravity r=∞) ?

Hydrogen: Gravity

mmgg = m = mii

Spectroscopy 1s-2s Other

transitions Theory

calculable frequency in terms of me and

Ry

Positronium: [Anti]gravity

mmgg = 0 = 0

Spectroscopy 1s-2s HFS

Theory needs me+ &

me-

calculable frequency in terms of me and

Antihydrogen: [Anti]gravity

mmgg = – m = – mii

Spectroscopy 1s-2s ? HFS ?

Theory needs me+ &

mp-

otherwise: all is the same as for H

To be blue shifted (∞).To be red shifted (∞). To be not shifted.

Can we measure the absolute red shift (in respect to zero gravity r=∞)?

Hydrogen 1s-2s Equivalence for H

mg = mi

Frequency is calculable in terms of me and

Positronium 1s-2s Antigravity:

mg = 0

Frequency is calculable in terms of me and

Can we measure the absolute red shift (in respect to zero gravity r=∞) ?

Hydrogen 1s-2s Equivalence for H

mg = mi

Frequency is calculable in terms of me and

Positronium 1s-2s Antigravity:

mg = 0

Frequency is calculable in terms of me and

while neglecting gravity

Can we measure the absolute red shift (in respect to zero gravity r=∞)?

Hydrogen 1s-2s Equivalence for H

mg = mi

Frequency is calculable in terms of me and

Positronium 1s-2s Antigravity:

mg = 0

Frequency is calculable in terms of me and Comparison of theory against experiment for Ps is the same

as comparison of H and Ps, because theory of Ps speaks in terms of Ry from H

Can we measure the absolute red shift (in respect to zero gravity r=∞) ?

Hydrogen 1s-2s Equivalence for H

mg = mi

Frequency is calculable in terms of me and

Positronium 1s-2s Antigravity:

mg = 0

Frequency is calculable in terms of me and Comparison of theory against experiment for Ps is the same

as comparison of H and Ps, because theory of Ps speaks in terms of Ry from H

Can we measure the absolute red shift (in respect to zero gravity r=∞)?

Hydrogen 1s-2s Equivalence for H

mg = mi

Frequency is calculable in terms of me and

Positronium 1s-2s Antigravity:

mg = 0

Frequency is calculable in terms of me and Comparison of theory against experiment for Ps is the same

as comparison of H and Ps, because theory of Ps speaks in terms of Ry from H

The results are consistent at level of about few parts in 109.

Can we measure the absolute red shift (in respect to zero gravity r=∞) ?

Hydrogen 1s-2s Equivalence for H

mg = mi

Frequency is calculable in terms of me and

Positronium 1s-2s Antigravity:

mg = 0

Frequency is calculable in terms of me and Comparison of theory against experiment for Ps is the same

as comparison of H and Ps, because theory of Ps speaks in terms of Ry from H

The results are consistent at level of about few parts in 109

suggesting no gravitational effects.

How large is absolute red shift?

Motion around center of galaxy:

v = 10-3 c / = 10-6

Motion around Sun

v =10-4 c /=10-8

Basic equations:a = v2/Ra = U/RU = a·R/ = U/c= v2/c2

It is huge!

va

R

Can we measure the absolute red shift?

Hydrogen 1s-2s Equivalence for H

mg = mi

Frequency is calculable in terms of me and

Positronium 1s-2s Antigravity:

mg = 0

Frequency is calculable in terms of me and

The results are consistent at level of about few parts in 101099.

Should be red shifted (∞). Should be immune.Should be immune.

Theory again?Theory again?

Universality of the red Universality of the red shift for matter sources:shift for matter sources:

Universality of free fall for Universality of free fall for matter:matter:

Applicability of the Dirac Applicability of the Dirac equation for an electron equation for an electron and CPT (mand CPT (me+e+ = m = me-e-):):

Proved experimentally!Proved experimentally!

Proved experimentally!Proved experimentally!

Proved experimentally in Proved experimentally in g-2 experiment!g-2 experiment!

Theory again?Theory again?

Applicability of bound Applicability of bound state QED:state QED:

We do not know the field We do not know the field of our galaxy:of our galaxy:

We do not know about We do not know about the Sun:the Sun:

Proved experimentally in Proved experimentally in H H etcetc. spectroscopy!. spectroscopy!

The Sun gravitation is The Sun gravitation is enough!enough!

Not less than about the Not less than about the

Earth!Earth!

Besides: antiprotonic helium and muonium point in the same direction!

Theory again? Theory again? OK: no galaxy, no CPT, no QEDOK: no galaxy, no CPT, no QED

aphelion: 152.1 Gm perihelion: 147.1 Gm

U/c2 = 3 × 10-10 – quite a large `small’ effect for spectroscopy

Theory again? Theory again? OK: no galaxy, no CPT, no QEDOK: no galaxy, no CPT, no QED

aphelion: 152.1 Gm perihelion: 147.1 Gm

U/c2 = 3 × 10-10 – quite a large `small’ effect for spectroscopy

We consider differential effectsand do not care about Dopplereffect etc.

Theory again? Theory again? OK: no galaxy, no CPT, no QEDOK: no galaxy, no CPT, no QED

aphelion: 152.1 Gm perihelion: 147.1 Gm

U/c2 = 3 × 10-10 – quite a large `small’ effect for spectroscopy

might be done for positronium,muonium, antiprotonic heliumantiprotonic heliumand antihydrogenand antihydrogen

Atoms with antiparticles: just to remind

• positronium:• muonium:

antimuon + electron

• antiprotonic helium: -particle + antiproton

• antihydrogen:

truly neutral in any sense mass of the antiparticle

>> mass of the particle (m=207me)

mass of the antiparticle = ¼ of mass of the particle

there is a small disturbing electron…

I hope you already know I hope you already know what it is: a truly what it is: a truly antiatomantiatom

not yet cold enough, but not yet cold enough, but hopefully will be (winter hopefully will be (winter is coming)is coming)

Atoms with antiparticles: just to remind

• positronium:• muonium:

antimuon + electron

• antiprotonic helium: -particle + antiproton

• antihydrogen:

truly neutral in any sense mass of the antiparticle

>> mass of the particle (m=207me)

mass of the antiparticle = ¼ of mass of the particle

there is a small perturbing electron (let be neglected)

I hope you already know I hope you already know what it is: a truly antiatomwhat it is: a truly antiatom

not yet cold enough, but not yet cold enough, but hopefully will be (winter is hopefully will be (winter is coming)coming)

Effects, uncertainties, sensitivities

Gravitation effect U/c2 Uncertainty/Sensitivity

10-6

10-9

10-12

10-15

Solar gravity (∞)

Galactic gravity (∞)

Solar gravity (perihelion-aphelion)

Moon gravity (day-night)

Earth gravity (100 m)

Ps 1s-2s (th+exp)Mu 1s-2s (th+exp)

H 1s-2s (exp)

H HFS 1s (th + exp)

Anti-p helium

g-2 (Dirac eq)

10-18

Solar gravity (day-night)

Earth gravity (1 m)best clocks

No room for antigravity,but a smallsmall room for `non-universality’

antigravity:antigravity: inertial mass of

particles and antiparticles is [about] the same

gravitational mass = + inertial mass

(matter)= – inertial mass

(antimatter)= [almost] 0 (truly

neutrals) no chance !no chance !

Still possible: a smallsmall violation of

equivalence principle a smallsmall difference in

gravitation for a particle and antiparticle of a certain kind