To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure firstname.lastname@example.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Quantum gravity by causal dynamical triangulation has over the last few years emerged as a serious contender for a nonperturbative description of the theory. It is a nonperturbative implementation of the sum-overhistories, which relies on few ingredients and initial assumptions, has few free parameters and – crucially – is amenable to numerical simulations. It is the only approach to have demonstrated that a classical universe can be generated dynamically from Planckian quantum fluctuations. At the same time, it allows for the explicit evaluation of expectation values of invariants characterizing the highly nonclassical, short-distance behaviour of spacetime. As an added bonus, we have learned important lessons on which aspects of spacetime need to be fixed a priori as part of the background structure and which can be expected to emerge dynamically.
Quantum gravity – taking a conservative stance
Many fundamental questions about the nature of space, time and gravitational interactions are not answered by the classical theory of general relativity, but lie in the realm of the still-searched-for theory of quantum gravity: What is the quantum theory underlying general relativity, and what does it say about the quantum origins of space, time and our universe? What is the microstructure of spacetime at the shortest scale usually considered, the Planck scale lPl = 10-35m, and what are the relevant degrees of freedom determining the dynamics there?
What is more natural than constructing space from elementary geometric building blocks? It is not as easy as one might think, based on our intuition of playing with Lego blocks in three-dimensional space. Imagine the building blocks are d-dimensional flat simplices all of whose side lengths are a, and let d > 2. The problem is that if we glue such blocks together carelessly we will with probability one create a space of no extension, in which it is possible to get from one vertex to any other in a few steps, moving along the one-dimensional edges of the simplicial manifold we have created. We can also say that the space has an extension which remains at the “cut-off” scale a. Our intuition coming from playing with Lego blocks is misleading here because it presupposes that the building blocks are embedded geometrically faithfully in Euclidean ℝ3, which is not the case for the intrinsic geometric construction of a simplicial space.
By contrast, let us now be more careful in our construction work by assigning to a simplicial space T – which we will interpret as a (Euclidean) spacetime – the weight e−S(T), where S(T) denotes the Einstein action associated with the piecewise linear geometry uniquely defined by our construction. As long as the (bare) gravitational coupling constant GN is large, we have the same situation as before.
Email your librarian or administrator to recommend adding this to your organisation's collection.