Planck-scale physics: facts and beliefs

This review consists of two parts. The first part establishes certain astrophysical bounds on the smoothness of classical spacetime. Some of the best bounds to date are based on the absence of vacuum Cherenkov radiation in ultrahigh-energy cosmic rays. The second part discusses possible implications of these bounds for the quantum structure of spacetime. One conjecture is that the fundamental length scale of quantum spacetime may be different from the Planck length.

A critical length has recently been identified that appears to provide a fundamental limit distinguishing quantum behavior from classical behavior. Because of the unique association between critical length and mass, it appears that we can correlate the mass of an object with the size over which its quantum behavior is manifested. When the expression for the critical length is set equal to the Planck length, we find an associated mass value that in magnitude corresponds to an ...

The search for a theory of quantum gravity faces two great challenges: the incredibly small scales of the Planck length and time, and the possibility that the observed constants of nature are in part the result of random processes. A priori, one might have expected these to be insuperable obstacles. However, clues from observed physics, and the discovery of string theory, raise the hope that the unification of quantum mechanics and general relativity is within reach.

In this letter, I show that Planck's quantum of action $\hbar$ varies proportionally to Newton's constant $G$ in entangled relativity, which manifests an explicit connection between the quantum and the gravitational worlds. On the other hand, the quantum parameter that appears in the phase of the path integral formulation of the theory is a quantum of energy squared $\epsilon^2$ -- instead of a quantum of action. I show that the value of this quantum of energy is set to be th...

The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients for the appearance of this minimum length are quantum mechanics, special relativity and general relativity. As a consequence, classical notions such as causality or distance between events cannot be expected to be applicable at this scale. T...

We present a necessary and sufficient condition for an object of any mass m to be a quantum black hole (q.b.h.): The product of the cosmological constant lambda and the Planck constant h, lambda and h corresponding to the scale defined by this q.b.h., must be of order one in a certain universal system of units. In this system the numerical values known for lambda are of order one in cosmology and about 10^122 for Planck scale. Proving that in this system the value of the cosm...

This author's recent proposal of interferometric tests of Planck-scale-related properties of space-time is here revisited from a strictly phenomenological viewpoint. The results announced previously are rederived using elementary dimensional considerations. The dimensional analysis is then extended to the other two classes of experiments (observations of neutral kaons at particle accelerators and observations of the gamma rays we detect from distant astrophysical sources) whi...

It is generally believed that any quantum theory of gravity should have a generic feature --- a quantum of length. We provide a physical ansatz to obtain an effective non-local metric tensor starting from the standard metric tensor such that the spacetime acquires a zero-point-length $\ell _{0}$ of the order of the Planck length $L_{P}$. This prescription leads to several remarkable consequences. In particular, the Euclidean volume $V_D(\ell,\ell_{0})$ in a $D$-dimensional sp...

After a brief review of the first phase of development of Quantum-Gravity Phenomenology, I argue that this research line is now ready to enter a more advanced phase: while at first it was legitimate to resort to heuristic order-of-magnitude estimates, which were sufficient to establish that sensitivity to Planck-scale effects can be achieved, we should now rely on detailed analyses of some reference test theories. I illustrate this point in the specific example of studies of ...

The Planck scale is considered to be a natural minimum scale, made up as it is solely of fundamental constants. However the Planck scale is well beyond the scales encountered in real life, these latter being at least of the order of the Compton scale. The Compton scale too is fundamental in the same sense -- it is made up of fundamental micro physical constants, though it is $10^{20}$ orders higher than the Planck scale. We discuss here a mechanism by which the Planck scale m...