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We review a few topics in Planck-scale physics, with emphasis on possible manifestations in relatively low energy. The selected topics include quantum fluctuations of spacetime, their cumulative effects, uncertainties in energy–momentum measurements, and low energy quantum-gravity phenomenology. The focus is on quantum-gravity-induced uncertainties in some observable quantities. We consider four possible ways to probe Planck-scale physics experimentally: (i) looking for energy-dependent spreads in the arrival time of photons of the same energy from GRBs; (ii) examining spacetime fluctuation-induced phase incoherence of light from extragalactic sources; (iii) detecting spacetime foam with laser-based interferometry techniques; (iv) understanding the threshold anomalies in high energy cosmic ray and gamma ray events. Some other experiments are briefly discussed. We show how some physics behind black holes, simple clocks, simple computers, and the holographic principle is related to Planck-scale physics. We also discuss a formulation of the Dirac equation as a difference equation on a discrete Planck-scale spacetime lattice, and a possible interplay between Planck-scale and Hubble-scale physics encoded in the cosmological constant (dark energy).

We re-examine the brick-wall model in the context of spacetime foam. In particular we consider a foam composed by wormholes of different sizes filling the black hole horizon. The contribution of such wormholes is computed via a scale-invariant distribution. We obtain that the brick wall divergence appears to be logarithmic when the cutoff is sent to zero.

Here we present explicit expressions for quantum fluctuations of spacetime in the case of (4+n)-dimensional spacetimes, and consider their holographic properties and some implications for clocks, black holes and computation. We also consider quantum fluctuations and their holographic properties in ADD model and estimate the typical size and mass of the clock to be used in precise measurements of spacetime fluctuations. Numerical estimations of phase incoherence of light from extra-galactic sources in ADD model are also presented.

We argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy–momentum space. We discuss the freezing of vacuum energy in such a dynamical energy–momentum space and present a phenomenologically viable seesaw formula for the cosmological constant in this context.

The properties of a dynamic wormhole are investigated. Using a particular equation of state for the fluid on the wormhole throat, we reached an equation of motion for the throat (a hyperbola) that leads to a negative surface energy density σ. The throat expands with the same acceleration 2π|σ| as the Ipser–Sikivie domain wall. We found the Lagrangian leading to the above equation of motion of the throat. The associated Hamiltonian corresponds to a relativistic free particle of a time-dependent negative energy -ℏc/R, where R is the throat radius, similar in form with the Casimir energy inside an expanding spherical box.

Naive calculations in quantum field theory suggest that vacuum fluctuations should induce an enormous cosmological constant. What if these estimates are right? I argue that even a huge cosmological constant might be hidden in Planck-scale fluctuations of geometry and topology — what Wheeler called “spacetime foam” — while remaining virtually invisible macroscopically.