Interferometric evidence for brane world cosmologies ∗ Ghenadie N. Mardari Rutgers University, 89 George Street, New Brunswick, New Jersey, 08901 (Dated: February 1, 2008) The hypothesis of brane-embedded matter appears to gain increasing credibility in astrophysics. However,itcanonlybetrulysuccessfulifitsimplicationsonparticleinteractionareconsistentwith existing knowledge. This letter focuses on the issue of optical interference, and shows that at least one brane-world model can offer plausible interpretations for both Young’s double-slit experiment, andtheexperimentsthat fitlessneatlywith it. Thebasic assumption isthatparticles caninteract atadistancethroughthevibrationsinducedbytheirmotiononthebrane. Thequalitativeanalysis ofthismechanismsuggeststhatfringevisibilityinsinglephotoninterferencedependsontheenergy levels and the interval between interacting particles. A double-slit experiment, performed with coherent single red photons should reveal the disappearance of interference when the time delay 3 betweenindividualparticlesisincreasedover2.18seconds. Inthecaseofinfraredphotonswiththe 0 frequency of 9·1013Hz,interference must vanish already at theinterval of one second. 0 2 PACSnumbers: 95.30.-k,12.60.-i,42.50.-p,03.75.-b n a Analyses of recent galaxy clustering data and CMB of the cornerstones of quantum mechanics. The essence J measurements demand special explanations for the ap- of the mystery of double-slit interferometry is that in- 3 parent flatness of the Universe, as well as for its accel- dividual photons are emitted and detected as particles, 2 erated expansion. Initial attempts to provide a simple yet they seem to pass through the two slits as waves 4 answer in terms of vacuum energy ran into well-known (non-locality). Any attempt to detect the trajectory of v theoretical difficulties. Quantum field theories yielded photonsdestroystheinterferencefringesonthedetecting 7 unrealistic values for the cosmological constant [1, 2], screen. This is the basis for the conclusion that which- 7 while various solutions to the problem required addi- pathinformationandfringevisibilityarecomplementary, 0 4 tional explanatory variables. In contrast, many of the just like the information about momentum and position 0 most recent brane world cosmologies are offering expla- of particles [12, 13]. The evidence in favor of this inter- 2 nations that appear to be both theoretically promising pretation is almost overwhelming, and does not need to 0 and empirically testable. Most of these involve scenar- be listed here. Nevertheless, there are two special cases / h ioswithmatterlocalizedonflatdomainwalls(3-branes), that do not exactly fit into the mainstream picture. For -t embedded in higher dimensional bulk space-times. Fol- reasons that will become obvious later on, these excep- p lowing the successful generalformulationof Randall and tions need to be presented here in brief. e Sundrum [3, 4], brane-worldcosmologieswere applied to One of these odd cases is the interference of particles h : many problems, including the cosmological constant [5], emitted by independent sources [14]. Just like in the v cosmologicalphase-transitions[6], inflation [7, 8], baryo- double-slit experiment, photons produced by indepen- i X genesis [9]. Consistency with cosmological observations dentsourcesproduceinterferencefringes,evenwhenonly r hasalsobeen suggested[10, 11]. Itshouldbe alsonoted, one of them is present in the system at the same time. a however, that the idea of matter localized on a brane ThisphenomenonwasinitiallydemonstratedbyPfleegor cannot be entirely satisfactory theoretically, unless it is andMandelinthe1960’s[15],andconclusivelyconfirmed also shown to have plausible implications for small scale by Hariharan et al. in 1993 [16]. The problem with this phenomena. (How can it be essential for large scale dy- phenomenon is that it provides partial which-path in- namics, and absent on smaller scales?). In other words, formation without destroying interference. Initially, an it must also have quantum-level implications that would interlocking mechanism between the two sources was as- be consistent with existing interpretations in terms of sumed, in the attempt to suggest that which-path infor- non-classic principles, such as non-locality, uncertainty, mation would still be unavailable. Subsequent experi- complementarity. However, if it were indeed possible to ments with optically isolated photon sources ruled out show that a brane model could offer a full explanation this interpretation [17]. However, even if quantum pro- of particle interactions, then those mentioned principles cesses washed which-path information away, the fact re- wouldbecomeredundant. Thepurposeofthisletteristo mains that each photon was only emitted by one source. showthatatleastonesuchmodelispossible,andthatits This clearly shows that individual photons do not need implications can be verified with optical interferometric to go through more than one slit at the same time in or- equipment. der to produce interference. Moreover, the fringes were Few other tests in physics are as conceptually impor- only presentwhen at least two sources were active. This tant as the double-slit experiment. Because it reveals so opens up the possibility that photons might not inter- clearly the non-classical properties of matter, it is one ferewiththemselves,ascommonlyassumed. Theycould 2 alsoaffectthe trajectoryofsubsequentparticlesthrough Doppler effect. Moreover, this force has to decay as it some hidden mechanism. propagates, according to the inverse square law. Conse- The other odd case, related to single-photon interfer- quently,the spatialeffectofphotonsmustbe temporary, ence,referstothe possibilitythatinterferencemightdis- anditcanonlybeeffectiveindeflectingthetrajectoryof appear entirely at extremely low emission rates of pho- other photons that cross their trails. When the trajec- tons. It was reported in the 1960’s by Dontsov and Baz tory of a photon is significantly bent under the influence [18], who obtained reliable evidence in favor of this ef- of an external force, its lateral neutrality must be dis- fect, but had no means to detect its parameters with rupted. Consequently, photons can produce other forces high precision. This experiment is in clear contradiction in special environments, as detected e.g. in the case of with existing theories and seems to stand alone in its the photoelectric effect. field. However,the hypothesis of delayed interaction be- Despitethequalitativenatureofthisdescription,itcan tweenphotons,suggestedinthepreviousparagraph,also be used to make estimates of the maximum duration of requires the disappearance of interference beyond a cer- the stipulated delayed photonic effects. Essentially, we tain interval between individual particles. So, either the need to calculate the distance (r) travelled by a trans- hypothesis is wrong, or there is something special about verse wave on a string, until enough of its energy leaks the suggested hidden variable that might explain with into the brane to disable its effect on other photons. Di- greater success these findings. Thus, we need a model vidingthisdistancebythespeedofpropagation,wecould that could explain not only the classical double-slit ex- get an idea about the amount of time that it takes for periment,butalsoits”anomalies“. Inlightofthe above, these photonic trails to fade away (r/c=t). Under the themoststraightforwardwaytoconceiveofsuchamodel assumption that particles always interact through brane isbyassumingthatthebraneitselfisthehiddenvariable. waves, the known energy of photons (Emax = hν) must Recall that the turning point in the development of be equal to their maximum effect on the spatial strings. brane-world cosmologies was the realization that a 3- Moreover, the impact of photons on strings must have dimensional domain wall could be embedded in a bulk a constant increment value during chosen units of time. with extra non-compactified dimensions [3,4]. But the This basic unit of action must be equal to h. Hence, same reasoning can be applied to a lower level: one di- the total energy of the photon comes from the cumula- mensional infinite strings with perfect elasticity could tive number of such interactions. This also means that be embedded in the domain wall. Accordingly, longi- a string will always be able to deflect the trajectory of tudinal waves propagating on the strings would be ex- a photon if its own vibrations have an action potential pected to leak into the domain wall at a rate that is comparable to h. Yet, when the waves on a string have inversely related to the distance of propagation, while already decayed to E′ =ν′h, with ν′ =10−3Hz, the de- transverse waves would leak according to the inverse flectionoftheweakestphotoncannotexceed0.06degrees square law. The entire brane (actually, a superstructure (small enough to eliminate interference build-up in most ofsuchstrings)wouldhavetobepreciselytuned,sothat experimental settings). Thus, the value of r corresponds both s-waves and p-waves would propagate at the speed tothe distancetravelledbyastringwaveuntilitsenergy of light. Correspondingly, particles of matter would be Emax decaystoE′. (r02Emax =r2E′,wherer0 istheunit movingthroughthebranebyexcitinganinfinitenumber of distance corresponding to the system of units used to ofstrings. The collectiveeffect ofsuchexcitations would measure E). The equation for the corresponding time amount to the production of fields that are capable to simplifies to t=r0√ν/c√ν′. affect other particles on the same brane. (This provides This conclusion enables us to calculate the maximum an alternative to virtual particles). timedelaybetweenindividualcoherentphotonsofknown In conformity with such a model, the elastic collisions frequency,atwhichinterferencefringesmightstillbevis- ofparticles andtheir remote interactionsare assumedto ible. For the red photons (the most widely used in inter- be mediated by the oscillating brane. The photons (as- ferometric experiments), t =2.18 seconds. Other visible sumed here to be particles) represent a special case, be- colors can produce interference at even larger intervals. causetheyusuallyappeartoproducenoforces. Thiscan At the same time, infrared photons with ν = 9 1013Hz · beexplainedthroughthefollowingconsiderations. First, must loose their fringe visibility at t=1 second. Hence, photons travel in space at the speed of light, which is it is only normal for the double slit experiment (and for also the speed of wave propagationin the brane. Hence, settingswithindependentlyemittedcoherentphotons)to their effect on the brane cannot precede them. Second, produce interference fringes, even when just one particle they must produce equal amounts of symmetric waves passes through the system at the same time, provided in the plane that is perpendicular to their direction of the gap (t) is below its critical values. motion. Thus, photons canbe neutral, while still having Consider the following experimental setting. A strong a real effect on the brane. Third, their effect in reverse coherent red laser beam is divided into two jets with a must correspond to that of a very narrow electrostatic beam splitter. The jets are focused with two mirrors in beam, but it should be extremely weak, because of the frontofascreen,producinginterferencefringesvisibleto 3 the naked eye. A disc, connected to a source of angular falsification becomes highly unlikely. motion, is placed in front of the focal point such as to As a final note, these two experiments should not be cut off both jets. The disc has just one small hole close perceivedas contradictoryto existing scientific data, be- to its edge, and is calibrated such as to open the access cause they are based on non-invasive methods of path to the screen of only one jet at a time, when it is spin- detection. Traditionally, which-path information is ob- ning. In other words, this is an alternator switch, whose tained with filters or detectors, both of which affect the frequency can be adjusted by controlling its angular ve- spatio-temporal properties of photons. In other words, locity. Whenthedischasaverysmallvelocity(lessthan these techniques have a real (negative) impact on coher- one revolutionper minute), there canbe no interference. ence. It is a well-established fact that coherence is a However, at very high velocities the interference fringes necessary condition for interference. Therefore, previous should reappear on the screen, just like in all the other experiments are not reliable as tests of locality and/or experimentswithindependentsources. Atthispoint,two realism. videocamerasareintroducedintothelab. Oneisusedto film the switch; the other is focused on the screen. 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