aa r X i v : . [ phy s i c s . pop - ph ] A p r Reviving Gravity’s Aether in Einstein’s Universe
Niayesh Afshordi
1, 2, ∗ Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5,Canada Department of Physics and Astronomy, University of Waterloo,200 University Avenue West, Waterloo, ON, N2L 3G1, Canada
Einstein’s theory of general relativity describes gravity as the interaction of particles with space-time geometry, as opposed to interacting with a physical fluid, as in the old gravitational aethertheories. Moreover, any theoretical physicist would tell you that, despite its counter-intuitive struc-ture, general relativity is one of the simplest, most beautiful, and successful theories in physics, thathas withstood a diverse battery of precision tests over the past century. So, is there any motivationto relax its fundamental principle, and re-introduce a gravitational aether? Here, I give a shortand non-technical account of why quantum gravity and cosmological constant problems provide thismotivation.
Ask any good student of freshman physics and, happilyquoting their textbooks, they will tell you that gravity isthe weakest force of nature. After all, when you lift apen, the electromagnetic dipoles of the molecules in yourhand can easily counteract the gravitational pull from theentire planet Earth. It may thus come as a surprise thatthroughout history, understanding gravity has been oneof the strongest drivers of breakthroughs in theoreticalphysics, and yet it still remains its deepest mystery.After Newton’s discovery of universal laws of gravityand mechanics, physicists and philosophers often won-dered how gravitational forces could act over large dis-tances, while other forces of nature only act in extremeproximity. In fact, this was one of Einstein’s philosophi-cal motivations to introduce metric, or space-time geom-etry, as a medium that mediates gravitational forces, as“action at a distance” cannot be physical. But we arejumping ahead of ourselves!Long before Einstein’s celebrated invention of GeneralRelativity, over the course of the 16th to 19th centuries,many mechanical models of gravity were put forth andthen discarded. In these theories, an invisible medium,called “the gravitational aether”, mediated the particles,vortices, streams, or waves that exchanged gravitationalforce between massive bodies [16]. For example, in 1853,Riemann proposed that gravitational aether was an in-compressible fluid which sinks toward massive objectswhere it is absorbed, at a rate proportional to their mass.He speculated that the absorbed aether is then emittedinto another spatial dimension [1].The most famous refutation of aether theories (eventhough it did not directly concern the gravitationalaether) came from the Michelson-Morley experiment [2],which showed that the speed of light is constant, and in-dependent of reference frame, as opposed to being onlyconstant and isotropic in the aether’s frame of reference.Indeed, the absence of a preferred reference frame, oth-erwise known as the principle of relativity, was the keyassumption in the development of special, and then gen- ∗ Electronic address: [email protected] eral relativity.
I. REVIVING THE INCOMPRESSIBLEGRAVITATIONAL AETHER
Einstein’s theory of general relativity describes gravityas the interaction of particles with space-time geometry,as opposed to interacting with a physical fluid, as in theold gravitational aether theories. Moreover, any theo-retical physicist would tell you that, despite its counter-intuitive structure, general relativity is one of the sim-plest, most beautiful, and successful theories in physics,that has withstood a diverse battery of precision testsover the past century. So, is there any motivation torelax its fundamental principle, and re-introduce a grav-itational aether?Let us consider an interesting analogy with Newtoniangravity. A hypothetical 19th century philosopher, Dr.John Smith, proposes that the laws of gravity are set bythree fundamental principles:1-Bound orbits in the two-body problem must be closed.2-There exist unbound orbits in the two-body problem.3-Gravitational forces obey linear superposition.These principles uniquely fix the formulation of New-tonian gravity and celestial mechanics. However, we nowknow that Principle (1), which fixes the inverse squarelaw [17], is based on an accidental symmetry between ra-dial and angular frequencies. General relativity violatesthis symmetry, which is the origin of Mercury’s anoma-lous perihelion precession. Nevertheless, Dr. Smithwould have ruled out Einstein’s general relativity, as itdid not respect his fundamental principles of gravita-tional theory, as stated above.The lesson from this story is that the underlying prin-ciples or symmetries of an effective theory might be ac-cidental or emergent symmetries of a more fundamentaltheory. As powerful as the principle of relativity mighthave been in the development of Einstein’s theory of grav-ity, it might need to be broken/re-examined, e.g. , by hav-ing a preferred reference frame, or a gravitational aether,in a more complete theory of gravity.But is there any reason to think that general relativityis not the fundamental theory of gravity?The main motivation for this comes from quantummechanics, the other hugely successful physical theoryof the 20th century: both general relativity and quan-tum mechanics have been incredibly successful in de-scribing macroscopic and microscopic phenomena respec-tively. However, any attempt to apply the rules of quan-tum mechanics to general relativity seems to lead to di-vergences that impair the predictive power of the the-ory. The effective theory of gravity breaks down whenthe macroscopic and microscopic worlds meet and a hugeamount of energy is packed into small scales, i.e., energydensities exceeding the Planck density of 10
Joules (or10 kilograms) per cubic meter. Although it is hard toachieve such densities in laboratories, Penrose and Hawk-ing [3] showed that singularities with infinite densities areinevitable in the future and past of general relativistic dy-namics. While they may not be immediately accessibleto us, they should be prevalent in the universe, residingat the centers of millions of astrophysical black holes inour galaxy, and possibly present at the first moment ofthe cosmological big bang. It is generally believed thata fundamental theory of quantum gravity should give aself-consistent description of physics close to these singu-larities (and thus avoid their formation). General rela-tivity plus quantum mechanics does not.Most physicists agree on the status of the problem atthis level. However, they diverge on their approachesfrom this point on. One approach is the interesting pos-sibility of relaxing the requirement of no preferred refer-ence frame (or Lorentz invariance). While the geometricnature of gravity is ubiquitous, there might still exist aphysical gravitational aether, which only interacts withgeometry (or matter) at very high energies.Recently Petr Hoˇrava generated a lot of excitement bysuggesting that if the speed of propagation of gravitonsincreases with energy as E / at very high energies, thenthe theory of gravity might have a well-defined quantiza-tion [4]. This of course introduces a preferred frame inwhich the energy E is measured.While breaking Lorentz invariance may sound hereticalto many physicists, it comes easily to cosmologists. Afterall, even though our laws don’t seem to have a preferredframe of reference, the universe hasn’t had much troublein picking one. For example, a relativistic electron in theuniverse will eventually come to stop in the rest frameof the cosmic microwave background (CMB), where theCMB dipole vanishes. That is why analogues of the in-visible aether, such as dark matter, dark energy, and theinflaton exist and play crucial roles in the standard modelof cosmology.While it is typical to spontaneously break Lorentz sym-metry on cosmological scales, normal matter on verysmall scales/high energies decouples from this cosmolog-ical frame. Nevertheless, it is easy to find theories thatdo not behave this way, and yet are consistent, at leastup to some high energy cut-off. For scalar field theories, this can be done through covariant actions that are notquadratic in field gradients. An extreme example of thisis the “cuscuton action” [5, 6], defined as: S = Z d x √− g h µ p ∂ µ ϕ∂ µ ϕ − V ( ϕ ) i , (1)which represents an incompressible fluid, implying thatperturbations around any uniform density backgroundare non-dynamical. It is interesting to note that Hoˇrava’sgravity theory reduces to general relativity minimallycoupled to an incompressible cuscuton fluid at low en-ergies [7].At this point, it is interesting to recall Riemann’s ideaof an “incompressible gravitational aether”, and to en-tertain the possibility that after 156 years, it might turnout to be an actual ingredient of a quantum theory ofgravity. There are, after all, no new ideas under the sun! II. GRAVITATIONAL AETHER AND THECOSMOLOGICAL CONSTANT PROBLEM
Although one may decide to ignore the problem ofquantizing gravity for low energy and large scale obser-vations, there is one aspect of quantum mechanics thatis disastrous for any gravitational observable: the quan-tum vacuum of the standard model of particle physicshas a density of roughly 10 kilograms per cubic me-ter! One does not need precision observations to concludethat this is not realistic, as human bodies, let alone starsand planets would be torn apart by extreme gravitationaltidal forces. Incidentally, there are cosmological precisionmeasurements of the vacuum density, which put it at [8]: ρ vac = (7 . ± . × − kg / m , (2)i.e. some 60 orders of magnitude smaller than the stan-dard model prediction! Of course, there could be otherunknown contributions to the vacuum density, but whyshould they so precisely (but not completely) cancel theknown contributions? This is known as the cosmologicalconstant problem.One way to avoid the problem is to couple gravity tothe traceless part of the energy-momentum tensor, effec-tively decoupling the vacuum energy from gravity:(8 πG ′ ) − G µν [ g µν ] = T µν − T αα g µν + T ′ µν . (3)Eq. (3) is a modification of the celebrated Einstein equa-tion, which couples the space-time curvature, representedby the Einstein tensor, G µν on the left, to the matterenergy-momentum tensor T µν on the right. However,the last two terms on the right are new: the second termsubtracts the trace of T µν , which effectively decouplesthe vacuum from gravity. The last term is there to en-sure energy-momentum conservation T νµ ; ν = 0, as Bianchiidentity enforces zero divergence for the Einstein tensor G νµ ; ν = 0. Therefore, we require T ′ νµ ; ν = 14 T νν,µ . (4) T ′ µν is a new component of gravitational dynamics,which we can think of as a modern-day version of thegravitational aether [9]. Moreover, through the aboveargument, it is an inevitable component of a completetheory of gravity if we decide to decouple the quantumvacuum energy from geometry.Of course, one needs to know more about the proper-ties of aether in order to make predictions in this theory.By now, it may not come to the reader as a surprise thatwe shall assume aether to be incompressible, or morespecifically, to have zero density, but non-vanishing pres-sure. The main motivation, apart from its historical ap-peal and appearance in quantum gravity theories, is thatan incompressible fluid does not introduce new dynami-cal degrees of freedom, which are severely constrained byprecision tests of gravity.What is surprising about this theory is how similarits predictions are to those of general relativity. In fact,the two are only significantly different in objects withrelativistic pressure (such as neutron stars, or the earlyuniverse) or large vorticity [9]. The main effect of thenew terms on the right hand side of Eq. (3) is to cre-ate an effective Newton’s constant which depends on theequation of state of matter, w matt . = p matt . /ρ matt . , theratio of pressure to density: G eff ≃ (1 + w matt . ) G N . (5)While this change is negligible in most astrophysical sit-uations, it significantly changes the dynamics of the earlyuniverse, as the gravitation due to radiation is enhancedby a factor of 4 /
3. To a good approximation, this effectcan be captured in the standard cosmological model byincreasing the number of neutrinos from 3 to 5.5, whilekeeping the gravitational constant fixed. Surprisingly,this is exactly what is found in analysis of the Lyman- α forest in quasar spectra ( N ν = 5 . ± . M B H FIG. 1: From [11]:
Top panel:
The prediction of differ-ent astrophysical black hole formation scenarios (see below)for the effective dark energy equation of state ¯ w ( < z ), giventhat aether pressure scales as inverse cube of the mean blackhole mass, M − BH . This can be compared to constraints fromcosmology. The unshaded area shows the region currentlyallowed at 68% confidence level for this parameter, as mea-sured from cosmological observations [13]. Bottom panel:
The mass-weighted geometric mean of black hole masses, M BH , in units of M ⊙ as a function of redshift. Our fiducialmodel (solid, black line) assumes our best estimates of themass distribution evolution of the black hole mass distribu-tion. Dashed lines indicate the range of uncertainty expecteddue to the unknown relative contribution of supermassive andstellar-mass black holes, while the dotted lines represent theuncertainty in the shape of the star formation density evolu-tion. These correspond to the same models used in the toppanel. shielded from the outside world by event horizons, the in-compressible gravitational aether with an infinite speedof sound is not bound by the horizons. Therefore, theonset of the quantum gravity regime close to the sin-gularity might affect aether pressure outside the blackhole. In [11, 12], it was shown that an incompress-ible gravitational aether ties the geometry close to theblack hole horizon to cosmological scales. AssumingPlanck scale physics close to the horizon, one can showthat the pressure of aether at infinity roughly scales as M − BH , and is comparable to today’s vacuum pressure for M BH = 10 − M ⊙ . Incidentally, this is the typicalmass range for stellar black holes in our universe. There-fore, the gravitational aether scenario could potentiallyexplain today’s acceleration of cosmic expansion, with-out any fine-tuning , by virtue of a quantum gravitationaleffect close to the horizon of stellar black holes. Fur-thermore, Fig. 1 shows that this model makes concretepredictions for the evolution of cosmic acceleration overtime, that appear to match well with current observa-tions. Future observational probes of cosmic accelerationand galaxy formation will be able to definitively rule outor confirm this proposed connection between dark energyand astrophysical black holes over the next decade. III. CONCLUSIONS
Unifying general relativity and quantum mechanics,the two great physical theories of the twentieth cen-tury, has fascinated and puzzled theoretical physicistsfor many decades. As bizarre as it may sound, recyclingdiscarded ideas of the 19th century might provide a wayforward!While gravitational aether is far from the only possibil-ity for solving the problems of quantum gravity, the the-oretical arguments and motivations for its reincarnationare simple and sound, and the coincidence of its predic-tions with cosmological observations is very suggestive.Many questions still remain, and need to be answered in order to have a viable physical theory on par with generalrelativity: Is there an action for this theory with a well-defined quantization? Can a UV completion of the theoryresolve the structure of black hole horizons? What doesblack hole formation look like in this theory? Will therebe smoking guns in the future precision tests of gravity?Is aether consistent with all cosmological observations?What about the anomalies such as those in the integratedSachs-Wolfe [14] and large-angle CMB anisotropies [15]?Looking forward, one expects the revival of gravita-tional aether to lead to many new possibilities in ourtheoretical understanding of quantum gravity and quan-tum cosmology, as well as the phenomenology of astro-physical and cosmological observations. The resolutionof last century’s mysteries may not be too far off afterall.Research at Perimeter Institute is supported by theGovernment of Canada through Industry Canada and bythe Province of Ontario through the Ministry of Research& Innovation. [1] B. Riemann, “Neue mathematische Prinzipien derNaturphilosophie”, Bernhard Riemanns Werke undgesammelter Nachlass (1876) 528–538.[2] A. A. Michelson and E. W. Morley,
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