antigravity and equivalence principle savely g karshenboim pulkovo observatory (ГАО) (st....
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Antigravity and Equivalence principle
Savely G Karshenboim
Pulkovo observatory (ГАО) (St. Petersburg)and Max-Planck-Institut für Quantenoptik
(Garching)
Outline EP
Deflection of light Dirac equation Problem of binding
energy
Consistent picture Curved space Inertial systems Red shift for
photons vs. blue shift for clocks
Two-body systems with antiparticles
Matter, antimatter and light We do have an
efficient access to matter to study its gravity, but we do not have an efficient access to antimatter to study gravity.
However, the world does not consist of matter and antimatter. There are purely neutral objects, such as photons.
Matter, antimatter and light However, the
world does not consist of matter and antimatter. There are purely neutral objects, such as photons.
Comparison of light and matter in gravitation field gives a hint, what could we expect from comparison of matter and antimatter.
EP: for light and matter Red shift Deflection of light
Curved space and deflection of light
Curved space and deflection of light Curved space is a
good concept if it universally affects everything, i.e. in case of EP.
Curved space and deflection of light Curved space is a
good concept if it universally affects everything, i.e. in case of EP.
We may also speak about a flat space with the gravitational interaction presented, but nothing remains unaffected.
Curved space and deflection of light Curved space is a
good concept if it universally affects everything, i.e. in case of EP.
We may also speak about a flat space with the gravitational interaction presented, but nothing remains unaffected.
There is no material substance to realize the flat space.
Free falling elevator and deflection of light
Light propagationfrom inside of anelevator
Light propagationfrom outside of anelevator
Falling elevator versus time
Free falling M-elevator and deflection of light
Light propagationfrom inside of anM elevator
Light propagationfrom outside of anM elevator
Falling M elevator versus time
Free falling M and Mbar elevators and deflection of light
Light propagationfrom inside of Mand anti-M elevators,in case of EP
Light propagationfrom outside
Falling elevator versus time
Deflection of light (suggesting antigravity)
matter:hydrogen
antimatter:antihydrogen
Deflection of light (suggesting antigravity)
matter:hydrogen
antimatter:antihydrogen
neutral:positronium,and photonsphotons
Does not look really great!Does not look really great!
Deflection of light (suggesting antigravity)
matter:hydrogen
antimatter:antihydrogen
neutral:positronium,and photonsphotons
Does not look really great!Does not look really great!
Real light behaves in as an ultrarelativistic particle of matter!
Deflection of light and EP There is no way to
simultaneously (but separately) keep exact EP for matter and light, antimatter and light in case of antigravity.
The only possibility is to allow mg/mi to vary for matter and antimatter at the same level as we are able to verify deflection of light as it follows from GR (~1%).
EP: the Dirac equation Dirac equation
describes an electron.
Dirac equation has been checked with a high accuracy.
It predicts a positron with the same mass (rest energy) and opposite charge.
If gravitation for electron and positron is not the same we would arrive at a problem.
Problem of binding energy In case of inertial
mass and in case of EP, binding energy is sufficient to describe a bound state.
In case of non-universal mg/mi for different components, we should rather speak about `bound masses´. I.e. We have to split the binding energy between the components.
E.g. comparing g-2 of e+ and e–, we observe certain energy levels.
Antigravity and inertial systems Inertial system:
a free particle has no acceleration.
Energy may conserve.
Non-inertial system: a free particle may be acceletared. It has no potential energy, but may change its kinetic energy.
Energy cannot be conserved.
Antigravity and inertial systems Non-inertial
system: a free particle may be acceletared. It has no potential energy, but may change its kinetic energy.
Energy cannot be conserved.
Introduce forces of inertia: they immitate potential energy and immitate conservation of energy.
EP and non-inertial systems The force of inertia is
proportional to the inertial mass of a particle.
The force of gravity is proportional to the gravitational mass of the particle.
As far as these two masses are the same, we cannot locally distinguish a non-inertial frame and an inertial frame with a [different] gravity.
EP and non-inertial systems As far as these
two masses are the same, we cannot locally distinguish a non-inertial frame and an inertial frame with a [different] gravity.
The free falling system looks like an inertial system.
EP and non-inertial systems As far as these
two masses are the same, we cannot locally distinguish a non-inertial frame and an inertial frame with a [different] gravity.
The free falling system looks like an inertial system (for an insider!).
The oudsider may see the source of gravity and thus distinguish (in part) between the gravity and non-inertiality.
EP and non-inertial systems As far as these
two masses are the same, we cannot locally distinguish a non-inertial frame and an inertial frame with a [different] gravity.
The free falling system looks like an inertial system (for an insider!).
The oudsider may see the source of gravity and thus distinguish (in part) between the gravity and non-inertiality.
EP and non-inertial systems The oudsider may
see the source of gravity and thus distinguish in part between the gravity and non-inertiality.
The outsider understands that the free falling system is a non-inertial system with gravity, where forces of inertia and gravity exactly compensate each the other
EP and non-inertial systems The oudsider may
see the source of gravity and thus distinguish in part between the gravity and non-inertiality.
The outsider understands that the free falling system is a non-inertial system with gravity, where forces of inertia and gravity exactly compensate each the other as far as mi=mg.
EP and non-inertial systems The outsider
understands that the free falling system is a non-inertial system with gravity, where forces of inertia and gravity exactly compensate each the other as far as mi=mg.
If mimg then some `free´ particles will have got accelerated. The energy is not conserved
EP and non-inertial systems The outsider
understands that the free falling system is a non-inertial system with gravity, where forces of inertia and gravity exactly compensate each the other as far as mi=mg.
If mimg then some `free´ particles will have got accelerated. The energy is not conserved unless we explicitly introduce the forces of inertia and gravity which do not compensate each the other anymore.
Conservation of energy and `true´ inertial frames All variety of
coordinates in GR and the very possibility to introduce the `curved´ space come from universality of gravity
Conservation of energy and `true´ inertial frames All variety of
coordinates in GR and the very possibility to introduce the `curved´ space come from universality of gravity and from universal cancelation between forces of inertia and forces of gravity.
Not anymore.
Conservation of energy and `true´ inertial frames All variety of
coordinates in GR and the very possibility to introduce the `curved´ space come from universality of gravity and from universal cancelation between forces of inertia and forces of gravity.
Not anymore. Now we have to
introduce the `absolute´ inertial frame with gravity.
Conservation of energy and `true´ inertial frames A good choice is
an inertial system in which we explicitely describe gravity, e.g., the Earth gravity.
We are still free falling in respect to all other gravitation sources, which are not taken into account explicitly, which is not good.
Gravitational and motional effects Now I will discuss
gravitational effects and ignore motional effects.
That is possible because I am interested in differential effects.
Within GR the 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 sameas 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 sameas 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 sameas 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 sameas 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.
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
Effects, uncertainties, sensitivities: now including particle physics
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)
kaons m/m
B mesons m/m
D mesons m/m
Anti-p helium
g-2 (Dirac eq)
10-18
Solar gravity (day-night)
Earth gravity (1 m)best clocks
Testing the equivalence principle
Laboratory (UW): Earth gravity
Laser Lunar Ranging:Solar gravity
where and
Testing the equivalence principle
Laboratory (UW): Earth gravity
Laser Lunar Ranging:Solar gravity
Kaons:galactic field
where and
Other mesons: D B
Theory again? OK: 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 oscillations.
Data on oscillations of Data on oscillations of K, B & D mesons leaveK, B & D mesons leaveno chance for antigravity.no chance for antigravity.
References Atoms with
antiparticles:
Kaons:
To conclude:matter is a `magic´ word
Nucleon structure: three consituent
quarks contains a
combination of sea quarks and antiquarks with admixture of gluons
+ a `label´ which is of matter.