Starting from the basic assumptions and equations of Big Bang theory, we present a simple mathematical proof that this theory implies a varying (decreasing) speed of light, contrary to what is generally accepted. We c...Starting from the basic assumptions and equations of Big Bang theory, we present a simple mathematical proof that this theory implies a varying (decreasing) speed of light, contrary to what is generally accepted. We consider General Relativity, the first Friedmann equation and the Friedmann-Lema?tre- Robertson-Walker (FLRW) metric for a Comoving Observer. It is shown explicitly that the Horizon and Flatness Problems are solved, taking away an important argument for the need of Cosmic Inflation. A decrease of 2.1 cm/s per year of the present-day speed of light is predicted. This is consistent with the observed acceleration of the expansion of the Universe, as determined from high-redshift supernova data. The calculation does not use any quantum processes, and no adjustable parameters or fine tuning are introduced. It is argued that more precise laboratory measurements of the present-day speed of light (and its evolution) should be carried out. Also it is argued that the combination of the FLRW metric and Einstein’s field equations of General Relativity is inconsistent, because the FLRW metric implies a variable speed of light, and Einstein’s field equations use a constant speed of light. If we accept standard Big Bang theory (and thus the combination of General Relativity and the FLRW metric), a variable speed of light must be allowed in the Friedmann equation, and therefore also, more generally, in Einstein’s field equations of General Relativity. The explicit form of this time dependence will then be determined by the specific problem.展开更多
An infinite horizon linear quadratic optimal control problem for analytic semigroup with unbounded control in Hilbert space is considered.The state weight operator is allowed to be inddefinite while the control weight...An infinite horizon linear quadratic optimal control problem for analytic semigroup with unbounded control in Hilbert space is considered.The state weight operator is allowed to be inddefinite while the control weight operator is coercive.Under the exponential stabilization condition,it is proved that any optimal control and its optimal trajectory are continuous.The positive real lemma as a necessary and sufficient condition for the unique solvability of this problem is established.The closed-loop synthesis of optimal control is given via the solution to the algebraic Riccati equation.展开更多
文摘Starting from the basic assumptions and equations of Big Bang theory, we present a simple mathematical proof that this theory implies a varying (decreasing) speed of light, contrary to what is generally accepted. We consider General Relativity, the first Friedmann equation and the Friedmann-Lema?tre- Robertson-Walker (FLRW) metric for a Comoving Observer. It is shown explicitly that the Horizon and Flatness Problems are solved, taking away an important argument for the need of Cosmic Inflation. A decrease of 2.1 cm/s per year of the present-day speed of light is predicted. This is consistent with the observed acceleration of the expansion of the Universe, as determined from high-redshift supernova data. The calculation does not use any quantum processes, and no adjustable parameters or fine tuning are introduced. It is argued that more precise laboratory measurements of the present-day speed of light (and its evolution) should be carried out. Also it is argued that the combination of the FLRW metric and Einstein’s field equations of General Relativity is inconsistent, because the FLRW metric implies a variable speed of light, and Einstein’s field equations use a constant speed of light. If we accept standard Big Bang theory (and thus the combination of General Relativity and the FLRW metric), a variable speed of light must be allowed in the Friedmann equation, and therefore also, more generally, in Einstein’s field equations of General Relativity. The explicit form of this time dependence will then be determined by the specific problem.
基金Supported by National Natural Science Foundation of China （60574016）, the National Science Foundation for Distinguished Young Scholars of China （60825304）, and the Taishan Scholar Program of Shandong Province
基金This work is partially supported by the National Key Project of Chinathe National Nature Science Foundation of China No.19901030NSF of the Chinese State Education Ministry and Lab.of Math.for Nonlinear Sciences at Fudan University
文摘An infinite horizon linear quadratic optimal control problem for analytic semigroup with unbounded control in Hilbert space is considered.The state weight operator is allowed to be inddefinite while the control weight operator is coercive.Under the exponential stabilization condition,it is proved that any optimal control and its optimal trajectory are continuous.The positive real lemma as a necessary and sufficient condition for the unique solvability of this problem is established.The closed-loop synthesis of optimal control is given via the solution to the algebraic Riccati equation.
