Abstract:

"Three different approaches show that, contrary to a longstanding conviction older than 160 years, the advance of Mercury's perihelion can be achieved in Newtonian gravity with a very high precision by correctly analyzing the situation without neglecting Mercury's mass. General relativity remains more precise than Newtonian physics, but Newtonian framework is more powerful than researchers and astronomers were thinking till now, at least for the case of Mercury.

The Newtonian formula of the advance of planets' perihelion breaks down for the other planets. The predicted Newtonian result is indeed too large for Venus and Earth. Therefore, it is also shown that corrections due to gravitational and rotational time dilation, in an intermediate framework which analyzes gravity between Newton and Einstein, solve the problem. By adding such corrections, a result consistent with the one of general relativity is indeed obtained.

Thus, the most important results of this paper are two: (i) It is not correct that Newtonian theory cannot predict the anomalous rate of precession of the perihelion of planets' orbit. The real problem is instead that a pure Newtonian prediction is too large. (ii) Perihelion's precession can be achieved with the same precision of general relativity by extending Newtonian gravity through the inclusion of gravitational and rotational time dilation effects. This second result is in agreement with a couple of recent and interesting papers of Hansen, Hartong and Obers. Differently from such papers, in the present work the importance of rotational time dilation is also highlighted.

Finally, it is important to stress that a better understanding of gravitational effects in an intermediate framework between Newtonian theory and general relativity, which is one of the goals of this paper, could, in principle, be crucial for a subsequent better understanding of the famous Dark Matter and Dark Energy problems."]]>

Abstract:

This essay questions what is perhaps the most fundamental assumption of quantum theory, which is that states should be represented as vectors in a Hilbert space. As the essay explains, an alternative formalism is possible in which states (and indirectly any higher-level particles observed to be part of the states) are represented as sets, specifically, as extremely sparse sets of fundamental units of far smaller scale than any particles of the Standard Model. This physical theory is borrowed over from an information-processing theory. The connections between the original information processing theory, Sparsey, and my proposed physical theory are further elaborated in an earlier essay, The Classical Realization of Quantum Parallelism.]]>