The Infra-Red Road to Quantum Gravity

Abstract

We review work in areas ranging from condensed matter physics to quantum gravity, with the following interconnected questions in mind: (i) what is the nature of the vacuum in condensed matter systems, in quantum field theory, and in classical and quantum gravity; (ii) how do analogies between these systems work, how well do they work, and how useful are they; (iii) what modifications can we make to quantum mechanics to deal with quantum gravity, and (iv) how and why low-energy theories of quantum gravity are, in our view, the right way to make progress in this field. We use many different examples to illustrate our arguments.

Figures (11)

• Figure 1: Thought experiment for a $H$ atom in a box. In (a) we show the physical vacuum at $T=0$; one has a simple atom in its ground state. In (b) we shown the same vacuum at $T=2.7$K; for a large enough box the atom dissociates. In (c) we show the vacuum when $T-10^{10}$K; it is now full of thermally excited $e^+/e^-$ pairs. Finally, in (d) we show the system at $T=0$ but with a very strong electric field $E_o \sim 10^{18}~V/m$ applied. The vacuum is now unstable, with $e^+/e^-$ pairs dissociating out of the vacuum, the $H$ atom completely dissociated, and all particle accelerating to infinity.
• Figure 2: Operational definition of a superfluid. In (a) we show the equilibrium state of a superfluid 3-d rotating cylindrical bucket. If $T > T_c$, the superfluid transition temperature, then the normal fluid rotated with the cylinder (and shows a parabolic depression of the fluid surface). Below $T_c$, if the angular velocity $\Omega < \Omega_c$, where $\Omega_c$ is a critical angular velocity, then the superfluid is stationary in a local inertial frame. When $\Omega > \Omega_c$, the equilibrium state has single quantized vortices present. In (b) we show the same situation for a 2-d superfluid on a rotating disc, where the same argument applies, provided no vortex/anti-vortex pairs are excited - these pairs destabilize the superfluid state, even at $T=0$. Note that in (b), we do not show the parabolic depression of the film surface that occurs for a rotating disc above $T_c$.
• Figure 3: The form of the quasiparticle spectrum in Bose superfluids. In (a) we show the result for weak coupling, along with the free particle spectrum. In (b) we show what happens when one increases the coupling strength for a dilute 3D Bose gas; and In (c) we show the result for strongly-coupled 3D $^4$He superfluid. In (c) we show the main quasiparticle spectrum, and just one of the multiparticle branches (the bound roton pair states). In none of these three cases do we show the broad band of incoherent multi-quasiparticle excitations.
• Figure 4: The form of the tunneling potential ${\cal T}({\bf r}_12)$ is shown here in (a) for different external flow velocities $\boldsymbol{v}_{\text{s}}^{0}$. In (b) we show the superflow pattern as the vortex/anti-vortex pair separates. Finally, in (c) we show two other interesting geometries in which one can imagine looking for vacuum tunneling in 2D superfluid films. In the upper figure, superfluid is shown accelerating towards a circular "drain"; in the figure below, through a constriction. The "horizons", defined by the critical crossover velocity $\bar{v}_c({\bf r})$ where vacuum tunneling switches on, are shown by dotted lines; and the superflow directions in (b) and (c) are shown by arrows.
• Figure 5: Some processes that can produce vortices in 3D $^4$He superfluid. In (a) we see a vortex loop nucleating on the surface of a moving ion (whose motion is denoted by an arrow). In (b) we show vortices nucleating at a boundary, past which the the superfluid in flowing. We also show how the vortex loops can escape from the boundary by forming vortex rings). The vortex loops nucleate around boundary regions where the local boundary curvature and the neighbouring superflow velocity are high. Once formed they can migrate along the surface.