The journal Foundations of Physics commemorates “Forty Years of String Theory.” Vijay Balasubramanian (University of Pennsylvania) steps back and ask what we do not understand about time. What is time? Within the broader quantum gravity community outside string theory there has also been considerable thinking about time. Traditionally, in the study of quantum gravity the “problem of time” arises because the Schrödinger equation when promoted to the diffeomorphism invariant context of gravity, becomes the Wheeler-de Witt equation which simply says nothing about time evolution. This is sometimes interpreted as saying that saying that in a quantum diffeomorphism-invariant universe time is meaningless. Vijay Balasubramanian presents nine questions and several lines of attack in string theory in his paper “What we don’t know about time,” ArXiv, 14 Jul 2011. Let me summarizes his ideas.
Why is there an arrow of time? A common idea is that the arrow of time is cosmologically defined by the macroscopic increase of entropy (the second law of thermodynamics). But this raises the associated question of why the universe starts in a low entropy state. This approach also suggests that the notion of time is inherently connected to the coarse graining of an underlying quantum gravitational configuration space.
Why is there only one time? Geometrically, time is different from space because the geometry of spacetime is locally Minkowski (Lorentzian metric signature (1, 3)), not Euclidean (metric signature (0, 4)). From a geometrical point of view we could equally well imagine a signature (2, 2), with two times, which is more symmetric between space and time. In the context of string theory with its many extra dimensions one can ask why we seem to have extra spatial dimensions, not temporal dimensions.
Is there a connection between the existence of a time, and the quantumness of the universe? The difference between time and space is somehow implicated in the difference between quantum mechanics with its characteristic features of quantum interference and entanglement, and classical statistical physics which lacks these features. This kind of difference appears in nonrelativistic quantum mechanics, in quantum field theory, and even in string theory.
Could the real, Lorentzian structure of conventional spacetime be simply a convenient way of summarizing analytic information about an underlying complexified geometry? Physical quantities seem to be described by analytic functions of space and time in both quantum field theory and string theory.
How can singularities localized in time be resolved in string theory or some other quantum theory of gravity? A prediction of General Relativity is that spacetime singularities exist, either timelike (i.e. localized in space), lightlike (i.e. localized on a null curve), or spacelike (i.e. localized in time). One of the goals of a quantum theory of gravity such as string theory is to resolve such singularities.
Why is the area of a horizon, a causal construct, related to entropy, a thermodynamic concept, and can this entropy be given a statistical explanation for general horizons? Semiclassical analyses of quantum mechanics in spacetimes containing horizons like black holes and accelerating geometries such as de Sitter space suggest that inertial observers perceive the horizon as having an entropy proportional to area and a temperature proportional to the surface gravity at the horizon. Neither is there any explanation of why entropy becomes associated to a geometrical construct – the area of a horizon.
How precisely is physics beyond a black hole horizon encoded in a unitary description of spacetime? The “information loss paradox” for black holes is due to the non-unitary semiclassical evolution of quantum states in Hawking radiation. The apparent loss of unitarity can be traced ultimately to the causal disconnection of the region behind the horizon. A solution is required since there is simply no room in the full quantum theory for information loss in black holes.
Can time be emergent from the dynamics of a timeless theory? In the AdS/CFT correspondence, string theory in a (d+1)-dimensional, asymptotically Anti-de Sitter (AdS) spacetime is exactly equivalent to a d-dimensional quantum field theory defined on the timelike boundary of such a universe. Thus, the radial dimension of AdS spacetime (as well as any additional compact dimensions of the bulk string theory) must be regarded as somehow “emergent” from the dynamics of the d-dimensional field theory. The field theory contains a time and the emergent gravitational theory inherits its time directly from the field theory.
Are time and space concepts that only become effective in “phases” where the primordial degrees of freedom self-organize with appropriate relations of conditional dependence and entanglement? The spacetime and its metric are generally be thought of as a coarse-grained description of some underlying degrees of freedom which may, or may not, be organized with the proximity and continuity relations associated to smooth spacetime. The spacetime can be viewed as an emergent description of relations of conditional dependence of underlying fundamental variables.
If you have enjoyed the questions, please refer to the paper “What we don’t know about time” for possible lines of research in order to obtain the answers in string theory.