Martin L' Perl martinslac'stanford'edu

1
Proposed Terrestrial Experiment to Detect the
Presence of Dark Energy Using Atom Interferometry
Martin L. Perl (martin_at_slac.stanford.edu) 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
2
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 arXivastro-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
3

• 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

4
1. Present beliefs about dark energy
5
Magnitude of dark energy density Counting mass
as energy via EMc2 ,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
6
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
7
2. Comparison of dark energy density with energy
density of weak electric field.
8
rDE 6.3 10-10 Joules/m3 Compare to electric
field of E1 volt/m using rE electric field
energy density. Then rE e0E2/24.4 x 10-12
J/m3 This is easily detected and measured.
Thus we work with fields whose energy densities
are much less than rDE

9

• 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

10

• 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.

11
3. Comparison of dark energy density with energy
density of terrestrial gravitational field
12

• rG gravitational energy density
• rGg2/(8pGN)
• At earths surface rG 5.7 1010 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

13
4. Our assumptions about dark energy and
description of the experimental method
14

• Assumptions about dark
• 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

15

• 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

16

• The method continued
• 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

17

• Sensitivity
• The sensitivity of the experiment can be as good
  as
• FDE/FG f 10-17
• where f0 if our assumptions are false and f of
  the order of 0.1 if are assumptions are true

18

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

19
5. Remarks on dark matter and zero-point vacuum
energy.
20
Dark Matter 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.
21
Zero-Point Vacuum Energy 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.
22
Appendix A Comparison with other experimental
directions for dark energy studies.
23
Idea for fitting zero-point vacuum energy to 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.

24
Idea for looking for effect of dark energy on
gravitational inverse square law
It is conventional to define a characteristic leng
th, LDE, for dark energy LDE c/ rDE1/4
84 x 10-6 m and to search if the gravitational
inverse square law breaks down at distances lt 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.

25
Idea of looking for effect of dark energy on
gravitational inverse square law
It is conventional to define a characteristic leng
th, LDE, for dark energy LDE c/ rDE1/4
84 x 10-6 m and to search if the gravitational
inverse square law breaks down at distances lt 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

26
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