DARK MATTER CRISIS THREATENS EINSTEIN’S EQUIVALENCE PRINCIPLE

DARK MATTER CRISIS THREATENS EINSTEIN’S EQUIVALENCE PRINCIPLE: 

DARK MATTER CRISIS THREATENS EINSTEIN’S EQUIVALENCE PRINCIPLE Emmanuel T. Rodulfo Physics Department, De La Salle University 2401 Taft Avenue, Manila, Philippines

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ABSTRACT Cosmological models live or die by the ‘sword’ of Einstein’s Equivalence Principle (EP) which states that the laws of physics are the same in all inertial and freely falling frames. Theories of gravity or interpretations of inertia are conventionally required to locally fulfill EP . Under mainstream cosmology, the observed dynamics of stellar structures commands the existence of an enormous amount of non-luminous matter that responds only to gravity. For several decades now, the search for non-baryonic particles supposed to constitute this dark matter (DM) still fail to account for the amount expected by concordance cosmology.

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ABSTRACT This frustration has led some to suspect that perhaps it is our understanding of inertia that may be at fault and that perhaps we shall never be able to find enough exotic particles to fully account for the huge amount of DM expected by concordance cosmology. Attempts to modify the law of inertia without presupposing a colossal amount of DM invariably come into conflict with EP and seem to favor a Machian interpretation of inertia . To demonstrate this quandary, we consider a generalized approach to Modified Newtonian Dynamics (MoND) .

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ABSTRACT We may be at a very privileged position in the history of science where we may witness the universal confirmation of Einstein’s Equivalence Principle and the models built upon it if non-baryonic particles are found (for instance at the Large Hadronic Collider); or, if DM particles are not detected, a possible ‘dark death’ of Einstein’s Equivalence Principle and the emergence of Machian cosmological models.

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REFERENCES: [1] R. B. Tully and J. R. Fisher, Astron. Astrophys. 54, 661 (1977). [2] M. Milgrom, “A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass Hypothesis”, Astrophys. J. 270, 365 (1983). [3] J. M. Romero, A. Zamora, "Alternative proposal to modified Newtonian dynamics", Phys. Rev. D , 73, (027301) 2006. [4] J. D. Bekenstein, Phys. Rev. D 70, 083509(2004); Erratum-ibid. 71, 069901 (2005), astro-ph/0403694. [5] J. D. Bekenstein, “Relativistic gravitation theory for the MOND paradigm”, arXiv:astro-ph/0403694 v6 23 Aug 2005. [6] S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (John Wiley & Sons, New York, 1972).

Dark Matter: 

Dark Matter Conceptually similar to the old problem of unseen planets : dark objects or failure of GR ? 2 famous examples: anomalous Uranus motion Neptune discovery anomalous Mercury motion Discovery of GR ! What do we need today to explain Dark Matter : a new particle … … or a new description of gravity ?

Most favored Cold Dark Matter Candidates : 

Most favored Cold Dark Matter Candidates Supersymmetry (susy) is the basis of most attempts to go beyond the “Standard Model” of particle physics. WIMP s – weakly interacting massive particles Heinz Pagels et al. 1982 PRL pointed out that the lightest superpartner particle should be stable and abundant in the early universe because of R-parity, thus a good candidate for DM . Goldberg 1983 and Ellis et al. 1984 worked out the now-favored susy neutralino WIMP . AXIONs -- a hypothetical particle that remains the best idea to save the strong interactions from violating CP symmetry, could also be the dark matter particle. Dine et al. 1981 Searches for WIMPs and AXIONS.

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MACHOs Brown Dwarfs Exist in the halo of galaxies Attempts to explain Cold Dark Matter without new particles MAssive Compact Halo Objects

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WIMPs Undiscovered non-baryonic particle Interacts only through the weak and gravitational forces High mass corresponds to a lower kinetic energy, making the particle “cold” Weakly Interacting Massive Particles

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WIMPs Several candidates for WIMPs are predicted by supersymmetry Neutralinos are the most probable non-interacting Combination of Z-boson, photon, and Higgs boson superpartners Supersymmetry

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Consensus? No WIMPs have been directly observed Groups studying MACHOs have not found enough objects to account for the missing mass problem Cold Dark Matter probably a mixture of both baryonic and non-baryonic matter

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Universal Composition

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Universal Overview Dark matter slows the universal expansion rate Density of dark matter affects the fate of the universe Low density leads to accelerating expansion High density leads to Big Crunch Dark matter density affects the universal geometry Low density leads to open universe High density leads to closed universe

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Universal Implications  = Actual Density / Critical Density

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The Pioneer Anomaly is at the scale a c : a is approximately 8 10 -8 cm/sec 2 astro-ph/0104064, 0208046

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Non-Keplerian Rotation of Galaxies the orbit speed is observed to be independent of radial distance according to the Tully-Fisher Law ! Instead of the expected decrease of the orbit speed with the radial distance from the galactic center,

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Milgrom’s MoND 1980 Milgrom proposed to modify Newton’s second law to where A new acceleration constant a 0 separates the two asymptotic regions: a > a 0 and a < a 0 . e.g.,

Why MoND wouldn’t go away : 

Why MoND wouldn ’ t go away Flavours of DM in/out fashion as Rotation Curves wiggle MOND consistently fits RCs, rarely needs fine-tuning.

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Far from the center of a galaxy, the gravitational force a star experiences is, with good approximation Assuming that the orbit is essentially circular, Tully-Fisher Law !

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In an effort to accommodate conserved quantities in MoND, Romero and Zamora 2006 proposed: Dynamical Law of Romero and Zamora (2006)

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Linear momentum and time In Special Relativity,

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Linear momentum and time

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Linear momentum and time In some versions of Modified Newtonian Dynamics which provide operational alternatives to the dark matter hypothesis, time earns an acceleration dependence. A universal acceleration constant a 0 separates regimes with differing inertial laws.

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Linear momentum and time In general,

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Lorentz invariance is ensured if we deduce the general expression for the relativistic energy from Substitute our linear momentum We find a general expression for the relativistic energy

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Euclidean Energy-Momentum 4-vector: Euclidean spacetime interval 4-vector:

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Euclidean spacetime interval 4-vector:

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Low accelerations induce spacetime curvature:

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Low accelerations induce spacetime curvature:

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4-acceleration:

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square of 4-acceleration :

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square of 4-acceleration : Recovers Einstein’s Special Relativity :

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acceleration parameter:

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Special Relativity is recovered if Modified Momentum-Energy:

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Note that the asymptotic property required to recover Special Relativity (SR) is just like that of the arbitrary interpolating function of MoND So we make the ansatz:

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Consistent with SR and Romero and Zamora (2006) in the appropriate limits Modified Momentum-Energy:

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Dynamical Law Proposed Law of Romero and Zamora (2006) come as low velocity limit.

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Conservation of Energy Reduces to non-relativistic Law proposed by Romero and Zamora(2006). Energy is conserved if: or if:

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Our ansatz entails time dilation and contraction

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Mach’s Principle?

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Violation of Lorentz invariance

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De Broglie wavelength

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Quantum Indeterminacy diverges in Deep MoND