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Proposed Terrestrial Experiment to Detect the Presence of Dark Energy Using Atom Interferometry Martin L. Perl ( [email protected]) SLAC National Accelerator Laboratory Holger Mueller Physics Department, University California-Berkeley

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Proposed Terrestrial

Experiment

to Detect the Presence of

Dark Energy

Using

Atom Interferometry

Martin L. Perl ([email protected])

SLAC National Accelerator Laboratory

Holger Mueller

Physics Department, University California-Berkeley

Talk presented at Windows on the Universe, Château Royal de Blois, France,, June 21 -26, 2009


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The majority of astronomers and physicists

accept the reality of dark energy but also

believe it can only be studied indirectly

through observation of the motions of

galaxies [P. J. E. Peebles and B. Ratra, The

Cosmological Constant and Dark Energy

arXiv:astro-ph/0207347v2, (2002)]

This talk opens the experimental question of

whether it is possible to directly detect dark

energy on earth using atom interferometry

through the presence of dark energy density.

The possibility of detecting other weak fields

is briefly discussed


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  • Outline of Presentation

  • Present beliefs about dark energy.

  • Comparison of dark energy density

  • with energy density of weak electric field.

  • 3. Comparison of dark energy density

  • with energy density of terrestrial

  • gravitational field.

  • 4. Our assumptions about dark energy

  • and description of the experimental

  • method.

  • 5. Remarks on dark matter and zero-point

  • vacuum energy.

  • Appendix A: Comparison with other

  • experimental directions for dark

  • energy studies.



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Magnitude of dark energy

density:

Counting mass as energy via

E=Mc2 ,the average density of

all energy is the critical energy

rcrit =9 x10-10 J/m3

rmass» 0.3 x rcrit= 2.7 x10-10 J/m3

rdark energy» 0.7 x rcrit= 6.3 x10-10 J/m3

Use rDE to denote rdark energy


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rDE » 6.3 x10-10 J/m3 is a very small energy density but as shown in the next section we work with smaller electric field densities in the laboratory

Distribution of dark energy

density:

rDE is taken to be at least

approximately uniformly distributed in space


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2. Comparison of dark

energy density with

energy density of weak

electric field.


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rDE» 6.3 ´ 10-10 Joules/m3

Compare to electric field of E=1 volt/m

using rE=electric field energy density.

Then

rE = e0E2/2=4.4 x 10-12 J/m3

This is easily detected and measured. Thus

we work with fields whose energy

densities are much less than rDE


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  • Obvious reasons for ease of working

  • with electric fields:

  • There is a qE force on all charged

  • objects

  • Electron currents offer manifold,

  • sensitive, detection methods

  • Magnetic fields offer manifold,

  • sensitive, detection methods


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  • Obvious reasons for difficulty or

  • perhaps impossibility of working

  • with dark energy fields:

  • Cannot turn dark energy on and off.

  • Cannot find a zero dark energy field

  • for reference.

  • In some hypothesis about

  • dark energy, it may not exert

  • a force on any material object

  • beyond the gravitational force of

  • its mass equivalent.



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  • r terrestrial gravitational fieldG = gravitational energy density =

  • rG=g2/(8pGN)

  • At earth’s surface rG = 5.7´ 10+10 J/m3

  • and rDE/ rG ~ 10-20.

  • The phase change of atoms depends upon the integral of a force over a distance. Hence we are interested in the ratio FDE/FG.

  • We speculate

  • FDE/FG ~ (rDE/ rG)1/2 ~ 10-10


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4. Our assumptions about dark energy and description of the terrestrial gravitational field

experimental method


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  • Assumptions about dark terrestrial gravitational field

  • energy:

  • A dark energy force, FDE, exists other

  • than the gravitational force equivalent

  • of rDE.

  • FDE is sufficiently local and rDE is

  • sufficiently non-uniform so that FDE

  • changes over distance of the order of

  • a meter.

  • FDE acts on atoms


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Beam Deflector terrestrial gravitational field

Interference fringes

detector

Beam source

Beam splitter

Fig. 1 Conceptual design of atom interferometer

  • The method:

  • We use a two beam atom interferometer with arms of unequal length and of extent about 1 meter as shown in Fig. 1


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  • The method continued: terrestrial gravitational field

  • To search for FDE the known forces

  • that change the atomic phase must be nulled out.

  • The effects of electric and magnetic forces are nulled by shielding.

  • The effect of the gravitational force is cancelled by the interferometry since gravity is a conserved force. Cancellation by a factor of 10-10 has been demonstrated and we expect to be able to cancel by a factor 10-17


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  • Sensitivity: terrestrial gravitational field

  • The sensitivity of the experiment can be as good as

  • FDE/FG =f ´10-17

  • where f=0 if our assumptions are false and f of the order of 0.1 if are assumptions are true


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  • Unknown weak fields: terrestrial gravitational field

  • The foregoing discussion applies to any other unknown weak fields.


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5. Remarks on dark matter and zero-point terrestrial gravitational field

vacuum energy.


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Dark Matter: terrestrial gravitational field

We have begun to study the effect of

dark matter on this experiment. Is it a “bug” in the experiment or an additional feature of the experiment.


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Zero-Point Vacuum Energy: terrestrial gravitational field

We have been thinking for time as to whether atomic interferometry can be used to elucidate the maddening infinity problem in zero-point vacuum energy. No progress.



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Idea for fitting zero-point vacuum energy to for dark energy studies.

dark energy by looking for a lower frequency

cutoff

C. Beck et al. [C. Beck and M. C. Mackey,

Electromagnetic dark energy,Int. J. Mod.

Phys., D17,71(2008); C. Beck and C

Jacinto de Matos, arXiv: gr-qc/0709.237v1(2007)]

have proposed that the noise spectrum

in superconductors will decrease for

frequencies above fDE = 4 x 1012 Hz. They

propose using Josephson junctions for

the test and believe that the same cutoff

applies to zero-point energy

This idea is criticized by P.Jetzer and

N. Straumann [P.Jetzer and N. Straumann Has Dark

Energy really been discovered in the Lab?

astro-ph/0411034v2, (2004)] We are skeptical.


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h for dark energy studies.

Idea for looking for effect of dark energy on gravitational inverse square law

It is conventional to define a characteristic

length, LDE, for dark energy

LDE = [ c/ rDE]1/4 = 84 x 10-6 m

and to search if the gravitational inverse

square law breaks down at

distances < LDE = 84 x 10-6 m?

No evidence yet for such a breakdown. [D. J. Kapner

et al., Phys. Rev. Lett. 98, 021101 (2007)]

Also a breakdown could be evidence

for a string theory model and have nothing

to do with dark ednrgy.


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h for dark energy studies.

Idea of looking for effect of dark energy on gravitational inverse square law

It is conventional to define a characteristic

length, LDE, for dark energy

LDE = [ c/ rDE]1/4 = 84 x 10-6 m

and to search if the gravitational inverse

square law breaks down at

distances < LDE = 84 x 10-6 m?

No evidence yet for such a breakdown. [D. J. Kapner

et al., Phys. Rev. Lett. 98, 021101 (2007)]

Also a breakdown could be evidence

for a string theory model and have nothing

to do with dark energy.

Also definition of LDE is based on dimensional

analysis


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h for dark energy studies.

Idea for looking for a dark energy particle

Does dark energy have a particle

nature consistent with our 90 year

old understanding of quantum

mechanics?

Can this be used to detect rDE?

Use the relation between a force of

range L carried by a particle of

mass M:

M x L = /c

With LDE = 84 x 10-6 m

Then MDE = 2.5x10-9 MeV/c2

But if MDE is a conventional

particle it will act as matter not as dark energy


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