Cosmic Background Radiation and `ether-drift' experiments

0.22 MB·

by  M. Consoli

epl draft
Cosmic Background Radiation and ‘ether-drift’ experiments
M. Consoli 1, A. Pluchino 2,1, A. Rapisarda 2,1
1 INFN, Sezione di Catania - Via S. Sofia 64, I-95123 Catania, Italy
2 Dipartimento di Fisica e Astronomia, Universita` di Catania - Via S. Sofia 64, I-95123 Catania, Italy
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1
0
2 PACS 98.70.Vc–Background radiations
PACS 07.60.Ly–Interferometers
n
a PACS 89.75.Fb–Structuresand organization in complex systems
J
Abstract. - ‘Ether-drift’ experiments have played a crucial role for the origin of relativity.
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Though, a recent re-analysis shows that those original measurements where light was still prop-
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agating in gaseous systems, differently from the modern experiments in vacuum and in solid

] dielectrics, indicate asmall universalanisotropy which is naturally interpretedin terms ofa non-
O local thermalgradient. Weargue thatthiscould possibly betheeffect, on weakly boundgaseous
C matter, of the temperature gradient due to the Earth’s motion within the Cosmic Background
Radiation (CBR). Therefore, a check with modern laser interferometers is needed to reproduce
.
h the conditions of those early measurements with today’s much greater accuracy. We emphasize
p
that an unambiguous confirmation of our interpretation would have far reaching consequences.
-
o Forinstance, it would also imply that all physical systemson themovingEarth are exposed to a
r tinyenergy flow, an effect that,in principle, could induceforms of self-organization in matter.
t
s
a
[

1
v
Premise. – Over the years, particular efforts have [3–6])orinahighvacuum(asin[7–9])orinsidedielectrics
8
1been devoted to improve the sensitivity of those ‘ether- with alargerefractiveindex (as in[2,10])andthere could
5drift’ experiments which look for the possible existence of be physical reasons which prevent such a straightforward
6a preferred reference frame through an anisotropy of the comparison. In this case, the difference between old ex-
0
two-way velocity of light c¯ (θ) (for a general review see periments (in gases)and modern experiments (in vacuum
γ
.
1e.g.[1]). Thisistheonlyonethatcanbemeasuredunam- orsoliddielectrics)mightnotdependonthetechnological
0biguously and is defined in terms of the one-way velocity progress only but also on the different media that were
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c (θ) as tested.
1γ
2 c (θ)c (π+θ)
v: c¯γ(θ)= γ γ (1) Another possible objection concerns the traditional
i cγ(θ)+cγ(π+θ) analysis of the data. The model assumed so far of slow,
X periodic time modulations, associated with the Earth’s
Here θ represents the angle between the direction of light
rpropagationandtheEarth’svelocitywithrespecttoahy- rotation and its orbital revolution, derives from simple
a
pothetical preferred frame Σ. By defining the anisotropy spherical trigonometry. Here, there might be a logical
gap. The relation between the macroscopic Earth’s mo-
∆c¯ =c¯ (π/2+θ)−c¯ (θ) (2) tion and the microscopic propagation of light in a lab-
θ γ γ
oratory depends on a complicated chain of effects and,
the most recent result from Nagel et al. [2] amounts to ultimately, on the physical nature of the vacuum. By
a fractional accuracy (|∆c¯ |/c) . 10−18. With this new comparing with the motion of a body in a fluid, the stan-
θ
measurement, by looking at their Fig.1 where all ether- dard view corresponds to a form of regular, laminar flow
drift experiments are reported, one gets the impressionof where global and local velocity fields coincide. However,
a steady, substantial improvement over the original 1887 some arguments (for a list of references see [11]) suggest
Michelson-Morley [3] result (|∆c¯ |/c).10−9. that the vacuum might rather resemble a turbulent fluid
θ
Though,this firstimpressionmightbe misleading. The where large-scaleand small-scale flows are only indirectly
various measurements were performed in different condi- related. Inthisotherperspective,themacroscopicEarth’s
tions, i.e. with light propagating in gaseous media (as in motioncouldjustgivetheorderofmagnitudebyfixingthe
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M. Consoli 1, A. Pluchino 2,1, A. Rapisarda 2,1
typical boundaries for a microscopic velocity field which the sidereal time. These experimental velocities, lying in
is irregular and intrinsically non deterministic. Although the range 7÷10 km/s, imply that the fringe shifts in the
it cannot be computed exactly, one could still estimate various experimental sessions were about 10 ÷ 20 times
its statistical properties by numerical simulations [11,12]. smaller than those expected classically for the Earth’s or-
To this end, one could assume forms of turbulence or in- bital value v = 30 km/s (the minimum anticipated drift
termittency which, as in most models, become statisti- velocity).
cally isotropic at small scales. This could easily explain
the irregular character of the data because, whatever the
macroscopic Earth’s motion, the average of all vectorial
quantities (such as the Fourier coefficients extracted from
a fit to the temporal sequences in modern experiments or
thefringeshiftsoftheoldexperiments)wouldtendtozero
by increasingmoreand morethe statistics. In this frame-
work, is not surprising that from an instantaneous signal
of given magnitude one ends up with smaller and smaller
averages. Thistrend,byitself,mightnotimplythatthere
is no physical signal.
Now, by taking into account these two ingredients,
namely a) the specificity of the various media and b)
the possibility of a genuine, but irregular, physical sig-
nal, there are substantial changes in the interpretation of
the experiments. We believe that the main conclusions
ofthis re-analysis,andthe possible ultimate implications, Fig. 1: The velocities obtained with Eq.(3) in various experi-
are sufficiently important to be summarized in a concise ments, as reported by Miller [4].
formandthusbroughttotheattentionofawideaudience.
At the same time, although much smaller than the ex-
CBR and ether-drift experiments. – Let us first
pected value, the measured fringe shifts were often non
observethat the discoveryof an anisotropyof the Cosmic
negligible [4,12] as compared to the extraordinary accu-
Background Radiation (CBR) [13,14] has introduced an
racyoftheinterferometers. Thissuggeststhat,insomeal-
important new element. Indeed, the standard interpre-
ternativeframework,thesmall,andirregular,effectscould
tation of its dominant dipole component (the CBR kine-
acquireadefinite physicalmeaning. Sofar,theirinterpre-
maticdipole[15])isintermsofaDopplereffectduetothe
tationhas been in terms of unimportant, mainly thermal,
motion of the solar system with average velocity v ∼ 370
disturbances. However,whatabouta‘non-local’tempera-
km/stowardapointintheskyofrightascensionα∼168o
ture effect? An observer moving through the CBR would
and declination δ ∼ −7o. This makes the existence of a
see different temperatures in different directions and, in
preferred reference frame more than a simple possibility.
thiscase,thesituationcouldchangecompletely. Thisalso
Inspite ofthis,itis generallyassumedthatthis motion
suggests to concentrate the attention on the experiments
cannot be detected in a laboratory by optical measure-
ingaseoussystemsbecausetheelementaryconstituentsof
ments. This belief derives precisely from the ether-drift
such weakly bound matter can be set in motion by ex-
experiments, at least when interpreted as a long sequence
tremely small thermal gradients.
of ‘null results’ with better and better systematics. Still,
To estimate this effect, let us recall that, due to the
overthe years,greatestexperts[4,16]haveseriouslyques-
motion of an observer with velocity v, a pure black-body
tioned the traditional null interpretation of the early ex-
spectrum of temperature T becomes Doppler shifted in
periments. Intheiropinion,thesmallresidualsshouldnot o
thevariousdirectionsθaccordingtotherelation(β =v/c)
be neglected. To have an idea of their magnitude, let us
recallthat,atthebeginning,thefringeshiftsproducedby
T 1−β2
o
therotationoftheinterferometerswereanalyzedbyusing T(θ)= (4)
1−βcosθ
the classical formula p
Therefore, if one sets T ∼ 2.7 K and β ∼ 0.0012 as for
o
(∆λ/λ) ∼(L/λ)(v2/c2) (3)
class v = 370 km/s, there is an angular variation
where v is the projection of the Earth’s velocity in the
∆T(θ)∼T βcosθ ∼±0.003 K (5)
o
plane of the interferometer, L the length of the optical
path and λ the light wavelength. Quantitatively,the very A more accurate estimate for an ether-drift experiment
early measurements are summarized in Fig.1 (from ref. would first require to replace the value v = 370 km/s
[4]) where the velocities obtained with Eq.(3) in various with its projection in the plane of the interferometer and
experiments are reported and compared with a smooth then evaluate the effects onthe observationsite. We have
curve fitted by Miller to his own results as function of not attempted this non-trivial task. However, for Miller’s
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Cosmic BackgroundRadiation and ‘ether-drift’ experiments
Table1: The average velocity observed (or the limits placed) by the classical ether-drift experiments in the alternative interpre-
tation where the fringe shifts are given by Eq.(6) and the relation between the observable vobs and the kinematical v is governed
by Eq.(7). For the dots in the Michelson-Pease-Pearson case we address the reader to ref. [12].
Experiment gas in the interferometer v (km/s) v(km/s)
obs
Michelson-Morley(1887) air 8.4+1.5 349+62
−1.7 −70
Morley-Miller(1902-1905) air 8.5±1.5 353±62
Kennedy(1926) helium <5 <600
Illingworth(1927) helium 3.1±1.0 370±120
Miller(1925-1926) air 8.4+1.9 349+79
−2.5 −104
Michelson-Pease-Pearson(1929) air 4.5±... 185±...
Joos(1930) helium 1.8+0.5 330+40
−0.6 −70
observations this analysis was carried out by Kennedy, goodagreementamongthe various determinations ofv in
Shankland(see p.175 of [17], in particular the footnote16) Table 1 provides enough evidence for the existence of a
andJoos[18]. Theirconclusionwasthatperiodictempera- non-local effect that should be understood.
turevariationsofabout±0.001Kor±0.002Kintheairof
Derivation of the observed anisotropy. – Within
the optical arms could be responsible for Miller’s average
thetraditionalthermalinterpretation,theultimateexpla-
fringe pattern. Now, on the one hand, these temperature
nation of the observed universal anisotropy proportional
values agree well with Eq.(5). On the other hand, such
to ǫ(v/c)2 wassearchedfor [12,20]inthe fundamentalen-
interpretation of the residual effects would also fit with
ergy flow which, on the basis of general arguments, is ex-
Miller’s conclusion [19] that the needed temperature vari-
pectedinaquantumvacuumwhichisnotexactlyLorentz
ations could not be due to a uniform heating (or cooling)
invariant and thus sets a preferred reference frame. How-
ofthelaboratorybutshouldhavebeenthoseproducedby
ever,the agreementbetweenEq.(5) andthe old estimates
a directional effect, as it would be with the CBR dipole.
of Joos, Kennedy and Shankland introduces now a new
With this premise, it becomes important to check if
argumentand providesthe mostnaturalinterpretationin
the small residuals indicate a non-local phenomenon that
terms of the CBR itself.
could be interpreted as a universal temperature gradient.
TotrytounderstandEqs.(6)and(7),onecanfirststart
To this end, we summarize in Table 1 the main results
from standard assumptions, namely:
of ref. [12] which represents the most complete analysis
i) light anisotropy should vanish when both the ob-
performed so far of the classical experiments in gaseous
serverand(thecontainerof)themediumwherelightprop-
media (Michelson-Morley [3], Miller [4], Illingworth [5],
agatesaretakenatrestinthehypotheticalpreferredframe
Joos [6]...). For the typical projections v associated with
Σ, for instance the system where the CBR looks exactly
an Earth’s velocity of 370 km/s, by introducing the gas
isotropic
refractive index N =1+ǫ, the experimental fringe shifts
ii) light anisotropy should also vanish if light prop-
producedbytherotationoftheinterferometerswerefound
agates in an ideal vacuum, i.e. for a medium refractive
to scale as
index N =1 so that c coincides with c
γ
(∆λ/λ) ∼(L/λ)(v2 /c2) (6) Thismeansthat,inthephysicalcasewhereinsteadboth
EXP obs
the observer and (the container of) the medium are at
with an ‘observable’ velocity rest in the laboratory S′ frame, any possible anisotropy
should vanish identically in the limit of velocity v = 0
vo2bs ∼2ǫv2 (7) when S′ ≡Σ. Therefore, if we restrict our analysis to the
Notice that the effect vanishes in the ǫ → 0 limit, as ex- region N = 1+ǫ of gaseous media, one can expand in
pected when the velocity of light c approaches the ba- the two small parameters β = v/c and ǫ = N −1. Then,
γ
sic parameter c entering Lorentz transformations. Thus any possible anisotropy will start to O(ǫβ) for the one-
one gets (v2 /c2).10−9 for air at atmospheric pressure, wayvelocitycγ(θ) andtoO(ǫβ2) forthe two-wayvelocity
obs
where N ∼ 1.00029, or (v2 /c2) . 10−10 for helium at c¯γ(θ) which, by its very definition, is invariant under the
obs
atmospheric pressure, where N ∼ 1.000035. To appre- replacement β → −β. At the same time, for any fixed
ciate the strong suppression effect, one should compare β, c¯γ(θ) is also invariant under the replacement θ → π+
with the corresponding classical prediction Eq.(3). For θ. Thus, to lowest non-trivial level O(ǫβ2), one finds the
instance, for air, the fringe shifts for v = 370 km/s are general expression
about10 times smaller thanthose expected classicallyfor
∞
themuchlowervelocityv =30km/s. Forgaseoushelium, c¯ (θ)∼ c 1−ǫβ2 ζ P (cosθ) (8)
γ 2n 2n
the effect is even 100 times smaller. We believe that the N " #
n=0
X
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M. Consoli 1, A. Pluchino 2,1, A. Rapisarda 2,1
Here, to account for invariance under θ → π+θ, the an-
gular dependence has been given as an infinite expansion
of even-order Legendre polynomials with arbitrary coeffi-
cients ζ =O(1).
2n
A crucial point for the thermal interpretation is that
Eq.(8) admits a dynamical basis. In fact, exactly the
same form is obtained [12] (see also Appendix 1 of [20])
′
if, in the S frame, there were convective currents of the
gas molecules associated with an Earth’s absolute veloc-
ity v. Both derivations clearly differentiate gaseous sys-
tems from solid and liquid dielectrics (where instead N
differs substantially from unity) and, therefore, one can
understand the difference with strongly bound matter, as
in the Shamir-Fox experiment [10]. Being aware that the
classical measurements could be proportional to ǫ(v/c)2,
Fig. 2: The scheme of a modern ether-drift experiment. The
they selected a medium where the effect of the refrac-
light frequencies are first stabilized by coupling the lasers to
tive index would have been enhanced (i.e. perspex where Fabry-Perot optical resonators. The frequencies ν1 and ν2 of
N ∼1.5). Since this enhancementwasnotobserved,they
the signals from the resonators are then compared in the beat
concluded that the experimental basis of special relativ- note detector which provides the frequency shift ∆ν = ν1 −
ity was strengthened. However, with a thermal interpre- ν2. In present experiments a very high vacuum is maintained
tation, one can reconcile the different behaviors because within the resonators.
in solid dielectrics a small temperature gradient would
mainly dissipate by heat conduction without generating
ThisgivesbackthephenomenologicallysuccessfulEqs.(6)
any appreciable particle motion or light anisotropy in the
and(7). All together,we havefound a consistentdescrip-
rest frame of the apparatus.
tion of the data where symmetry arguments, on the one
Now, Eq.(8) is exact to the given accuracy and pre-
hand, motivate and, on the other hand, find justification
dicts the rightorderof magnitude ǫ(v/c)2 of the observed
′ in underlying dynamical mechanisms.
anisotropy. Therefore, by leaving out the first few ζ s as
freeparametersinthefits,onecoulddirectlycomparewith Conclusions and outlook. – This overall level of
the experimental data. Still, there is one more derivation consistencyrequiresacheckwithanewgenerationofpre-
of the ǫ → 0 limit with a preferred frame which, on the cise laser interferometers in order to reproduce the ex-
basis of other symmetry arguments, permits to get rid of perimentalconditions ofthe oldexperiments withtoday’s
theunknowncoefficients in(8)andtodeduce Eqs.(6)and much greater accuracy. The essential ingredient is that
(7). The reason is that the transformation matrix which the optical resonators that nowadays are coupled to the
connects the space-time metric gµν for light propagation lasersshouldbe filledbygaseousmedia,see Fig.2. Sucha
′
inthelaboratoryS frametothereferenceisotropicmetric typeof‘non-vacuum’experimentswouldbealongthelines
γµν =diag(N2,−1,−1,−1)in the preferredΣ frame, is a ofref.[21]wherejust the use ofopticalcavitiesfilledwith
two-valued function for N →1. As shown in Appendix 2 differentmaterials was consideredas a useful complemen-
of ref. [20], by taking into account this subtlety, there are tary tool to study deviations from exact Lorentz invari-
two solutions: either gµν = γµν or gµν ∼ ηµν +2ǫuµuν ance. The only delicate aspect concerns the high relative
where ηµν is the Minkowskitensor and uµ the dimension- stability in temperature and pressure of the two cavities
′
less S 4-velocity. With the latter choice, from the condi- which is required to prevent possible spurious sources of
tion pµpνgµν = 0, by defining cγ(θ) from the ratio p0/|p| the frequency shifts. However, with present technology
and using Eq.(1), one finds a two-way velocity and technical skill 1, this should not represent a too seri-
ous problem.
c¯γ(θ) ∼ (c/N) 1−ǫβ2 2−sin2θ (9) In units of their natural frequency ν0, we then predict
a frequency shift between the two resonators
(cid:2) (cid:0) (cid:1)(cid:3)
which corresponds to setting in Eq.(8) ζ =4/3, ζ =2/3
0 2
andallζ2n =0forn>1. Eq.(9)isadefiniterealizationof (∆ν/ν0)gas =(∆c¯θ/c)gas ∼(Ngas−1) (v2/c2) (11)
the generalstructure in (8) and provides a partial answer
′
to the problem of calculating the ζ s from first principles. which should be larger by orders of magnitude than the
As such,it representsa modelto compute the time differ- correspondingeffectwithvacuumresonators[7]−[9]. This
ence for light propagation back and forth at right angles substantialenhancementisconfirmedby the onlymodern
along rods of length L (at rest in the S’ frame)
1For instance, an important element to increase the overall sta-
bilityand minimizesystematic effects may consist in obtaining the
∆t(θ)=(2L/c¯ (θ))−(2L/c¯ (π/2+θ))∼(2L/c)(∆c¯ /c)
γ γ θ two optical resonators from the same block of material as with the
(10) crossedoptical cavityofref.[22].
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Cosmic BackgroundRadiation and ‘ether-drift’ experiments
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p-5