Planck-scale physics: facts and beliefs

I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear effects can be of comparable magnitude to the linear ones and still be highly suppressed at low energies. This can offer alternative approaches to quantum gravity and to the evolution of the early universe.

It is generally assumed that the search for a consistent and testable theory of quantum gravity is among the most important open problems of fundamental physics. I review the motivations for this search, the main problems on the way, and the status of present approaches and their physical relevance. I speculate on what the situation could be in 2050.

A satisfactory theory of quantum gravity may necessitate a drastic modification of our perception of space-time, by giving it a foamy structure at distances comparable to the Planck length. It is argued in this essay that the experimental detection of such structures may be a realistic possibility in the foreseeable future. After a brief review of different theoretical approaches to quantum gravity and the relationships between them, we discuss various possible experimental t...

We suggest that there are time-varying quanta of mass (gomidia) and of length (somia), thus pointing to a quantization of geometry and gravitation. The present numerical value of the gomidium and somium, are, 10 to the power minus 65 grams, and 10 to the power minus 91 centimeters. Gomidia may be responsible for dark matter in the Universe; Heisenberg's principle, confirms the numerical estimates for gomidia and somia, either for the present Universe, or for Planck's time.

Physical research looks for clues to quantum properties of the gravitational field. On the basis of the common Schr\"odinger theory, a simple model of the quantization of a Friedmann universe comprising dust and radiation is investigated. With regard to energy quantization, the result suggests a universal limitation of the energy spacing between neighbouring quantum states by the Planck energy. Applied to black-body radiation, a modified Planck radiation law follows. If this ...

The question whether the invariant speed c, Planck constant h/, and gravitational constant G can be or should be put equal to 1 is analyzed. The discussion is based on fundamental considerations concerning the notion of physical quantity. It is found that the issue is not a matter of appropriate unit selection. Further it is shown that classical space-time geometry and quantum mechanics can be formulated in such a way that the invariant speed and the action quantum are truly ...

The fact that mass has an effect on surrounding space is the first essential element of general relativity. This paper unifies this mass/space distinction of general relativity with Newtonian gravity at a subatomic scale and with reported experimental findings of the last century. The subatomic distinction of mass concentration mainly in nucleons surrounded by empty space as we know it now was not known when the general relativity was written. The author uses this distinction...

A new idea of quantum gravity is developed based on {\it Gravitational Complementary Principle}. This principle states that gravity has dual complement features: The quantum and classical aspects of gravity are complement and absolutely separated by the planck length into planckian and over-planckian domains, respectively. The classical Einstein equations are correct at the fundamental level at over-planckian domain and general relativity is not a low energy limit of a more f...

We describe a recently introduced principle of relative locality which we propose governs a regime of quantum gravitational phenomena accessible to experimental investigation. This regime comprises phenomena in which $\hbar$ and $G_N$ may be neglected, while their ratio, the Planck mass $M_p =\sqrt{\hbar / G_N}$, is important. We propose that $M_p$ governs the scale at which momentum space may have a curved geometry. We find that there are striking consequences for the concep...

The mass equivalency [m*c^2 = h*f] applies to gravitational mass just as to inertial mass. From that, the gravitational mass has a corresponding, associated, equivalent frequency, f. Using that frequency a new result is obtained in which the significance of the Planck Length is clarified. The Planck Length is fundamental to gravitation and in effect supercedes G in that role because it is found that there is operational or mechanical significance to the role of the Planck Len...