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Register a new userA quantum gravity tensor equation formally integrating general relativity with quantum mechanics
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Xu Duan
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Extending black-hole entropy to ordinary objects, we propose kinetic entropy tensor, based on which a quantum gravity tensor equation is established. Our investigation results indicate that if N=1, the quantum gravity tensor equation returns to Schrodinger integral equation. When N becomes sufficiently large, it is equivalent to Einstein field equation. This illustrates formal unification and intrinsic compatibility of general relativity with quantum mechanics. The quantum gravity equation may be utilized to deduce general relativity, special relativity, Newtonian mechanics and quantum mechanics, which has paved the way for unification of theoretical physics.
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Can a simple microscopic model of space and time demonstrate Special Relativity as the macroscopic (aggregate) behavior of an ensemble ? The question will be investigated in three parts. First, it is shown that the Lorentz transformation formally stems from the First Relativity Postulate (FRP) {it alone} if space-time quantization is a fundamental law of physics which must be included as part of the Postulate. An important corollary, however, is that when measuring devices which carry the basic units of lengths and time (e.g. a clock ticking every time quantum) are `moving uniformly, they appear to be measuring with larger units. Secondly, such an apparent increase in the sizes of the quanta can be attributed to extra fluctuations associated with motion, which are precisely described in terms of a thermally agitated harmonic oscillator by using a temperature parameter. This provides a stringent constraint on the microscopic properties of flat space-time: it is an array of quantized oscillators. Thirdly, since the foregoing development would suggest that the space-time array of an accelerated frame cannot be in thermal equilibrium, (i.e. it will have a distribution of temperatures), the approach is applied to the case of acceleration by the field of {it any} point object, which corresponds to a temperature `spike in the array. It is shown that the outward transport of energy by phonon conduction implies an inverse-square law of force at low speeds, and the full Schwarzschild metric at high speeds. A prediction of the new theory is that when two inertial observers move too fast relative to each other, or when fields are too strong, anharmonic corrections will modify effects like time dilation, and will lead to asymmetries which implies that the FRP may not be sustainable in this extreme limit.
This paper studies the nature of fractional linear transformations in a general relativity context as well as in a quantum theoretical framework. Two features are found to deserve special attention: the first is the possibility of separating the limit-point condition at infinity into loxodromic, hyperbolic, parabolic and elliptic cases. This is useful in a context in which one wants to look for a correspondence between essentially self-adjoint spherically symmetric Hamiltonians of quantum physics and the theory of Bondi-Metzner-Sachs transformations in general relativity. The analogy therefore arising, suggests that further investigations might be performed for a theory in which the role of fractional linear maps is viewed as a bridge between the quantum theory and general relativity. The second aspect to point out is the possibility of interpreting the limit-point condition at both ends of the positive real line, for a second-order singular differential operator, which occurs frequently in applied quantum mechanics, as the limiting procedure arising from a very particular Kleinian group which is the hyperbolic cyclic group. In this framework, this work finds that a consistent system of equations can be derived and studied. Hence one is led to consider the entire transcendental functions, from which it is possible to construct a fundamental system of solutions of a second-order differential equation with singular behavior at both ends of the positive real line, which in turn satisfy the limit-point conditions.
We present two projects aiming to probe key aspects of the theory of General Relativity with high-precision quantum sensors. These projects use cold-atom interferometry with the aim of measuring gravitational waves and testing the equivalence principle. To detect gravitational waves, a large multi-sensor demonstrator is currently under construction that will exploit correlations between three atom interferometers spread along a 200 m optical cavity. Similarly, a test of the weak equivalence principle is currently underway using a compact and mobile dual-species interferometer, which will serve as a prototype for future high-precision tests onboard an orbiting satellite. We present recent results and improvements related to both projects.
Canonical quantization applied to closed systems leads to static equations, the Wheeler-deWitt equation in Quantum Gravity and the time independent Schrodinger equation in Quantum Mechanics. How to restore time is the Problem of Time(s). Integrating developments are: a) entanglement of a microscopic system with its classical environment accords it a time evolution description, the time dependent Schrodinger equation, where t is the laboratory time measured by clocks; b) canonical quantization of Special Relativity yields both the Dirac Hamiltonian and a self adjoint time operator, restoring to position and time the equivalent footing accorded to energy and momentum in Relativistic Quantum Mechanics. It introduces an intrinsic time property {tau} associated with the mass of the system, and a basis additional to the usual configuration, momentum and energy basis. As a generator of momentum displacements and consequently of energy, it invalidates Paulis objection to the existence of a time operator. It furthermore complies with the requirements to condition the other observables in the conditional interpretation of QG. As Paulis objection figures explicit or implicitly in most current developments of QM and QG, its invalidation opens to research the effect of this new two times perspective on such developments.
Two-photon states produce enough symmetry needed for Diracs construction of the two-oscillator system which produces the Lie algebra for the O(3,2) space-time symmetry. This O(3,2) group can be contracted to the inhomogeneous Lorentz group which, according to Dirac, serves as the basic space-time symmetry for quantum mechanics in the Lorentz-covariant world. Since the harmonic oscillator serves as the language of Heisenbergs uncertainty relations, it is right to say that the symmetry of the Lorentz-covariant world, with Einsteins $E = mc^2$, is derivable from Heisenbergs uncertainty relations.
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