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Motivated by the Dirac idea that fundamental constant are dynamical variables and by conjectures on quantum structure of spacetime at small distances, we consider the possibility that Planck constant $hbar$ is a time depending quantity, undergoing random gaussian fluctuations around its measured constant mean value, with variance $sigma^2$ and a typical correlation timescale $Delta t$. We consider the case of propagation of a free particle and a one--dimensional harmonic oscillator coherent state, and show that the time evolution in both cases is different from the standard behaviour. Finally, we discuss how interferometric experiments or exploiting coherent electromagnetic fields in a cavity may put effective bounds on the value of $tau= sigma^2 Delta t$.
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A simple experimental setup for measuring the Plancks constant, using Landauer quantization of the conductance between touching gold wires, is described. It consists of two gold wires with thickness of 0.5 mm and 1.5 cm length, and an operational amplifier. The setup costs less than $30 and can be realized in every teaching laboratory in two weeks. The usage of oscilloscope is required.
In their Letter, Kentosh and Mohageg [Phys. Rev. Lett. 108, 110801 (2012)] seek to use data from clocks aboard global positioning system (GPS) satellites to place limits on local position invariance (LPI) violations of Plancks constant, h. It is the purpose of this comment to show that discussing limits on variation of dimensional constants (such as h) is not meaningful; that even within a correct framework it is not possible to extract limits on variation of fundamental constants from a single type of clock aboard GPS satellites; and to correct an important misconception in the authors interpretation of previous Earth-based LPI experiments.
Lattice results on sigma terms and global analysis of parton momentum fractions are used to give the quark and glue fractions of the proton mass and rest energy. The mass decomposition in terms of the trace of the energy-momentum tensor is renormalization group invariant. The decomposition of the rest energy from the Hamiltonian and the gravitational form factors are scheme and scale dependent. The separation of the energy-momentum tensor into the traceless part which is composed of the quark and glue parton momentum fractions and the trace part has the minimum scheme dependence. We identify the glue part of the trace anomaly $langle H_{beta}rangle $ as the vacuum energy from the glue condensate in the vacuum. From the metric term of the gravitational form factors, which is the stress part of the stress-energy-momentum tensor, we find that the trace part of the rest energy, dominated by $langle H_{beta}rangle$, gives a {it constant} restoring pressure which balances that from the traceless part of the Hamiltonian to confine the hadron, much like the cosmological constant Einstein introduced for a static universe. From a lattice calculation of $langle H_{beta}rangle$ in the charmonium, we deduce the associated string tension which turns out to be in good agreement with that from a Cornell potential which fits the charmonium spectrum.
Based on Eddington affine variational principle on a locally product manifold, we derive the separate Einstein space described by its Ricci tensor. The derived field equations split into two field equations of motion that describe two maximally symmetric spaces with two cosmological constants. We argue that the invariance of the bi-field equations under projections on the separate spaces, may render one of the cosmological constants to zero. We also formulate the model in the presence of a scalar field. The resulted separate Einstein-Eddington spaces maybe considered as two states that describe the universe before and after inflation. A possibly interesting affine action for a general perfect fluid is also proposed. It turns out that the condition which leads to zero cosmological constant in the vacuum case, eliminates here the effects of the gravitational mass density of the perfect fluid, and the dynamic of the universe in its final state is governed by only the inertial mass density of the fluid.
We derive a model of dark energy which evolves with time via the scale factor. The equation of state $omega=(1-2alpha)/(1+2alpha)$ is studied as a function of a parameter $alpha$ introduced in this model. In addition to the recent accelerated expansion, the model predicts another decelerated phase. The age of the universe is found to be almost consistent with observation. In the limiting case, the cosmological constant model, we find that vacuum energy gravitates with a gravitational strength, different than Newtons constant. This enables degravitation of the vacuum energy which in turn produces the tiny observed curvature, rather than a 120 orders of magnitude larger value.
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