Seminars
To keep our momentum going we will regularly (~ once per month) organize virtual causal set seminars. If you would like to speak about something, or would like to hear someone else speak please contact one of the organizers.
A number of past talks have been recorded and can be found on youtube in these playlists:
https://youtube.com/playlist?list=PLf8k6WnJtiEevJuiIkpELkhAg7sT0QmkI
https://www.youtube.com/playlist?list=PLDoI0l0KazzQuToTcRs-rlCviQtwR4Fq7
Alternatively, click on a talk title to go to the recording (if available) of that talk.
30th April (2024), 17:30 CET
Talk by Marián Boguñá
In the first part of the talk, I will discuss some unexpected connections between complex networks (dealing with systems such as the Internet, social networks, and biological networks) and causal sets. In the second part, I will introduce a new approach to measuring proper distances between space-like separated events in Minkowski spacetimes of any dimension. Interestingly, this approach allows us to measure distances up to the Planck scale with arbitrary precision. It also enables us to define reference frames and evaluate some kinematic quantities along time-like paths.
5th March (2024), 16:30 CET
Talk by Karen Yeats
I will describe a common framework that covers both growth models such as classical sequential growth (CSG) in causal set theory and simple tree classes corresponding to solutions to combinatorial analogues of the Dyson-Schwinger equations of quantum field theory. Then I will present a result on when CSG-type models give subHopf algebras of the poset Hopf algebra. Joint work with Stav Zalel.
General Discussion
6th February (2024), 16:30 CET
12th December (2023), 16:30 CET
Talk by Rafael Sorkin - slides
A stochastic dynamics for classical sequential growth (CSG) was devised long ago, based on principles which include ``Bell causality'', but the lack of a quantal counterpart for this principle has blocked the formulation of a QUANTAL dynamics of sequential growth (QSG). As Stav will describe, an alternative path to CSG is known that seems more amenable to generalization to the quantal case. Following this hint, I will propose an Ansatz for QSG in which the decoherence-functional is the product of a complex amplitude with a second factor that governs the degree of interference between histories. In fleshing out this ansatz one must satisfy a consistency and a positivity condition.
preceded by an introduction by Stav Zalel on - slides
The Classical Sequential Growth (CSG) models are classical dynamics for causal sets, a precursor to the much-anticipated quantum dynamics. The CSG models were first derived by formulating and solving a causality condition, and the difficulty in formulating a quantum causality condition has been a major obstacle in adapting these classical models to the quantum case. I will review an alternative derivation of the CSG due to J. Wien which replaces the causality condition with an ansatz for the form of the transition probabilities and suggest that formulating the right ansatz for the form of the decoherence functional could be a way forward to deriving a quantum dynamics.
7th November (2023), 17:00 CET
Talk by Vid Homšak and Stefano Veroni
We present the first numerical study of the thermodynamics of a Schwarzschild black hole in the framework of Causal Set Theory, focusing on the entropy of a black hole as embodied in the distribution of horizon molecules.
To simulate causal sets we created a highly parallelised computational framework in C++. It allowed us to generate causal sets with over a million points, the largest recorded causal set in any non-conformally flat spacetime.
Our results confirm that the horizon molecules model agrees with the Bekenstein-Hawking formula and yields a fundamental discreteness scale in the order of Planck length.
The entropy is found to live on the surface of the black hole in accordance with the holographic principle.
Finally, interesting connections with the information paradox are drawn. In particular, we show how the horizon molecules model could yield a finite black hole temperature cut-off and prevent full black hole evaporation.
26th September (2023), 16:30 CEST
Talk by Astrid Eichhorn
I will argue that a fruitful strategy to make progress in quantum gravity is to connect distinct approaches and transfer methods and ideas from one approach to another. As a concrete example, I will explain recent results in causal-set quantum gravity. The first, namely the construction of a higher-order curvature operator in causal sets, is motivated by the idea to use causal sets as a Lorentzian regularization of the gravitational path integral, in which one can search for asymptotic safety. The second, namely an upper bound on the mass of scalars is inspired by the "matter matters" program in asymptotically safe quantum gravity, in which observational tests of quantum gravity are based on gravity's interplay with matter. I will argue that a similar program for causal sets can provide new, observationally motivated constraints on causal set quantum gravity. To provide background and motivation for these results, I'll provide brief introductions into the key features and key open challenges of asymptotically safe quantum gravity.
8th June (2023), 17:00 CET
Talk by Eitan Bachmat
Discretized versions of space-time domains, obtained from sampling the volume form appear naturally in several settings unrelated to physics. Early examples include I/O scheduling in disk drives and airplane boarding.
I will discuss some recent settings. One can consider the case of college admissions where students have GPA and SAT scores and we wish to rank them in a manner consistent with the data (if person A has better SAT and GPA scores than person B, they should be ranked higher). The ranking problem also appears in the medical decision making process (my motivation for considering it).
I will also mention hyperbolic meta-materials which also offer an exciting domain of potential applications.
20th April (2023), 17:00 CET
Talk by Arad Nasiri
Everpresent Lambda has been one of the most interesting ideas rooted in causal sets and unimodular gravity that tries to bridge the gap between IR and UV physics. In this talk, I will discuss our findings about the statistics of Model 1 of Everpresent Lambda and its late-time behavior, the role of the initial conditions, and the auto-correlation time of Lambda. As for the cosmological data, I will discuss the success of the model with SN1a and its shortcoming with CMB. SN1a data picks those realizations of the model that behave less matter-like at z<1.5. CMB seems to generally disfavor large oscillations in the dark energy sector. Possible avenues for future work will be discussed.
Observables for Cyclic Growth Models
8th March (2023), 17:00 CET
Talk by Stav Zalel
In causal set theory, cycles of cosmic expansion and collapse are modelled by causal sets with “breaks” and “posts” and a special role is played by cyclic growth models in which the universe goes through perpetual cycles. In this talk, I will discuss the observables in these models and their interpretation as statements about unlabeled stems with a single maximal element. Based on work with Fay Dowker (arXiv:2212.01149).
1st November (2022), 16:30 CET
Talk by Fay Dowker
In this talk will develop Rafael D. Sorkin's heuristic that a partially ordered process of the birth of spacetime atoms in causal set quantum gravity can provide an objective physical correlate of our perception of time passing. I will argue that one cannot have an external, fully objective picture of the birth process because the order in which the spacetime atoms are born is a partial order. I propose that live experience in causal set theory is an internal "view'' of the objective birth process in which events that are neural correlates of consciousness occur. In causal set theory, what "breathes fire'' into a neural correlate of consciousness is that which breathes fire into the whole universe: the unceasing, partially ordered process of the birth of spacetime atoms.
22nd September (2022), 17:30 CEST
Talk by Callum Duffy and Joshua Jones
In order to better understand entanglement entropy in the causal set framework, we investigate the entanglement entropy of a 1+1D scalar field in various spacetime configurations. These include the cases of disjoint subintervals, as well as a treatment of a subregion at the edge of the global interval. These calculations involve a truncation scheme for the spacetime commutator and correlator, the Pauli-Jordan and Wightman functions. We extend an existing entanglement entropy truncation scheme to disjoint regions, explain the rationale behind truncation schemes, and give what we believe to be the means of constructing them generally. We then show the numerical results from setups including two and three disjoint causal diamonds, as well as a single causal diamond that shares a boundary with a larger global causal diamond. In all these cases, our results agree with the expected area laws calculated via the continuum theory. The ease of our calculations indicate our methods to be a useful tool for numerically studying such systems, and potentially applicable to systems that are currently beyond analytic treatment in the continuum.
28th July (2022), 17:30 CEST
Talk by Théo Keseman and Hans Muneesamy
Entanglement entropy in causal sets offers a fundamentally covariant characterisation of quantum field degrees of freedom. A known result in this context is that the degrees of freedom consist of a number of contributions that have continuum-like analogues, in addition to a number of contributions that do not. The latter exhibit features below the discreteness scale and are excluded from the entanglement entropy using a "truncation scheme". This truncation is necessary to recover the standard spatial area law of entanglement entropy. In this talk we will discuss previous work on the entanglement entropy of a massless scalar field on a causal set approximated by a 1+1D causal diamond in Minkowski spacetime, as well as new insights into the truncated contributions, including evidence that they behave as fluctuations and encode features specific to a particular causal set sprinkling. We will present new results on Rényi entropies and the massive theory. We will also discuss the implications of our work for the treatment of entanglement entropy in causal sets in more general settings.
6th July (2022), 17:30 CEST
Talk by Steven Johnston
This talk gives an overview of the work presented in arXiv:2111.09331 for embedding a causal set into an interval of Minkowski spacetime. The method defines causal set analogs of Minkowski inner products which are used to construct matrices of inner products. These matrices are then factored using the singular value decomposition to give coordinates in Minkowski spacetime. We show good results for embeddings for dimensions d=2,3,4. The method offers a new way to define spatial orientation and spacelike distances in a causal set. The talk will also present some other ideas and perspectives not included in the paper.
If time had no beginning: growth dynamics for past-infinite causal sets
19th April (2022), 17:30 CEST
Talk by Stav Zalel
General Relativity traces the evolution of our Universe back to a Big Bang singularity. To probe physics before the singularity—if indeed there is a “before”—we must turn to quantum gravity. Causal sets let us to do just that by allowing us to consider cosmologies in which time has no beginning. I will discuss recent work with Bruno Bento and Fay Dowker on whether such past-infinite causal sets are compatible with the growth dynamics paradigm.
25th January (2022), 17:30 CET
Discussion led by Rafael Sorkin (a continuation of the previous discussion)
The problems are: (1) a small problem concerning the uniqueness or lack thereof of Poisson sprinkling (2) an idea for a proposal
for a quantum growth dynamics for causal sets (3) a problem on topology change in four continuum dimensions.
14th December (2021), 17:30 CET
Discussion led by Rafael Sorkin
The problems are: (1) a small problem concerning the uniqueness or lack thereof of Poisson sprinkling (2) an idea for a proposal
for a quantum growth dynamics for causal sets (3) a problem on topology change in four continuum dimensions.
7th September (2021), 18:00 CEST
Talk by Nosiphiwo Zwane
In most theories of quantum gravity, spacetime is taken to have some fundamental structure from which the continuum arises as an approximation at macroscopic scales. In these theories it is important to have some measure of how different the emerging spacetime is from the one it is approximating. In this talk we discuss the use of PF Invariance in distance measure (a way to measure how far two spacetime are from being isometric).
7th July (2021), 18:00 CEST
Talk by David Meyer
A high energy/small scale effective spacetime dimension of 3, or even better, 2, is expected to make a quantum theory of gravity more tractable. Thus, evidence for such dimensional reduction has been sought in several approaches, including causal set theory. We propose a Bayesian framework to deal with the difficulties of estimating the dimension of causal sets at the smallest scale. Our results do not show a reduction in dimension to 3 or below when causal sets are well-approximated by Minkowski space at the smallest scales.
26th May (2021), 17:00 CEST
Talk by Maximilian Ruep
In 1993, Sorkin argued [1] that ideal measurements of most local observables of QFT enable superluminal signaling. In fact, the underlying signaling protocol does not rely on ideal measurements, nor is it tied to Minkowski spacetime. It implies a very general condition for local quantum operations of any local quantum theory defined on a fixed background with a causal structure (e.g., a causal set) to be "causal" (i.e., non-superluminally signaling). In this talk I will show that quantum operations arising from local dynamics are causal and how this renders the measurement theory of [2] (which is based on a local interaction between the system and a probe) causal as well [3]. Moreover, work in progress [4] suggests, that such local probes can be used to perform measurements of (morally) every local observable of the system without superluminal signaling.
[1] Sorkin, R. D. Impossible Measurements on Quantum Fields In: Hu, B.L., Jacobson, T.A. (eds.) Directions in general relativity: Proceedings of the 1993 International Symposium, Maryland, vol. 2, pp. 293–305. Cambridge University Press, Cambridge (1993) arXiv:gr-qc/9302018
[2] Fewster, C. J. & Verch, R. Quantum Fields and Local Measurements Commun. Math. Phys. 378, 851–889 (2020) arXiv:1810.06512
[3] Bostelmann, H., Fewster, C. J. & Ruep, M. H. Impossible measurements require impossible apparatus Phys. Rev. D 103, 025017 (2021) arXiv:2003.04660
[4] Fewster, C. J., Jubb, I. & Ruep, M. H. In preparation (2021)
On the Horizon Entropy of a Causal Set
28th April (2021), 18:00 CEST
Talk by Jinzhao Wang
"In this talk we discuss some kinematical horizon entropy proposals in causal set theory. We extend a recent definition of horizon molecules to a setting with a null hypersurface crossing the horizon. We argue that, as opposed to the spacelike case, this extension fails to yield an entropy local to the hypersurface-horizon intersection in the continuum limit. We then look at the entropy defined via the Spacetime Mutual Information between two regions of a causal diamond truncated by a causal horizon, and find it does limit to the area of the intersection in flat spacetime."
Length of the Longest Chain and Proper Time in Curved Spacetimes
4th March (2021), 17:00 CET
Discussion led by Eitan Bachmat and Fay Dowker on:
"a result proved in 2 dimensions by Deuschel and Zeitouni (which) applies to curved 2 dimensional spacetimes and extends to cover curved spacetimes in all dimensions. (..) Is the constant m_d the same for all intervals in a d dimensional spacetime? Or does m_d depend on the interval (i.e. on the geometry of the interval)? "
20th January (2021), 17:00 CET
Talk by Eitan Bachmat, followed by discussion
Abstract: The theory of causal sets was developed to provide models of gravity. In the talk I will describe other systems which can be considered and analyzed as causal sets, generated by Poisson sampling space-time domains.
In particular, I will describe a particle system which I will call "airplane boarding" and if time permits I will also describe the polynuclear growth process. I will explain how the analysis of such systems can be informed by the causal set program and viceversa, how it can lead to new insights.
Entropy and the Link Action in the Causal Set Path-Sum
17th December (2020), 17:00 CET
Talk by Abhishek Mathur and Anup Anand Singh, followed by discussion
Abhishek and Anup will talk about their recent work on extending the Loomis-Carlip results (https://arxiv.org/pdf/1709.00064.pdf) to KR posets for the link action.
4th November (2020), 17:00 CET
Talk by Marco Letizia, followed by discussion
"In this talk I will present some recent results (arXiv:2008.02291) about Lorentzian spectral geometry in causal sets.
After giving some motivations for this work, I will introduce the strategies used to investigate whether causal sets can be identified through a set of geometric invariants such as spectra without explicitly inspecting the link/causal matrix."
Discussion on Quantum swerves
2nd October (2020), 18:00 CEST
The discussion will be led by Fay, who suggested this topic because
"I think there is a potential there for phenomenology but I get very confused when I think about what a model of quantum swerves might be so maybe I can just involve everyone else in my confusion."
If you want to read up about swerves beforehand Fay recommends this paper: https://arxiv.org/abs/0810.5591