Workshop: Exploring gravity with quantum mechanics and vice versa

Participants

External

• Angelo Bassi (University of Trieste)
  
• Daniel Bedingham (Imperial College)
• Nick Huggett (University of Illinois at Chicago)
• Tim Koslowski (University of New Brunswick)
• Ward Struyve (Rutgers University)

Local (UNAM)

• Pedro Aguilar
• Pablo Barberis
  
• Yuri Bonder
• Pedro Cañate
  
• Chryssomalis Chryssomalakos
• Alejandro Corichi
  
• Edgar Guzmán
• Hector Hernández
  
• Jorge Manero
• Sujoy Modak
  
• Porfirio Morales
  
• Elias Okon
  
• Leonardo Ortiz
  
• Igor Peña
  
• Erandy Ramírez 
• Saul Rodríguez
• Marcelo Salgado
  
• Tatiana Salazar
• Fernanda Samaniego
• Gerardo Sanjuan
  
• Eduardo Serrano
• Daniel Sudarsky

Program and Abstracts

Alejandro Corichi: Loop quantum cosmology

In this talk we shall review the main conceptual foundations of loop quantum cosmology, together with its 'successes' and its current status as a consistent, complete theory of the early universe.

Nick Huggett: Searching for Quantum Mechanics and for Quantum Gravity 

The organizing question for my seminar is “How is the search for an ‘interpretation’ of QM related to the search for a quantum theory of gravity?”. I will pose that question explicitly (mainly to invite answers from the audience!) in the final section of the presentation, where however it is also partly a way to tie together two more loosely connected themes, which I want to discuss first: (1) why do foundational/philosophical questions — such as those raised in this meeting — arise in physics at all? (2) One possible answer to my main question is that the searches are independent, and one sense in which gravity and QM might be independent is if gravity is not quantized at all, but rather couples to quantum matter through a semi-classical theory. I want to reject some arguments against this possibility (but mention some others).

(1) Natural scientists – for instance, Descartes, Newton and Leibniz – in the 17th Century faced a rather similar situation to that facing physics today – that of developing a radically new systematic theory (including radically new empirical and mathematical frameworks) from scattered theory fragments and empirical clues. Of course it’s hard for us to see the leaps they had to take from our standpoint after the dust has settled, and especially bizarre seeming today, at the center of the development was a debate about the nature of motion, absolute or relative (and relative to what?). Looking at the thinkers’ different proposals for mechanics shows how such philosophical arguments were essentially tied to the physics they were developing — and I hope, gives a perspective on the contemporary situation, and the role of foundational issues. I will draw on philosophical thought about the development and logic of science to offer an explanation of why such foundational debates are likely to arise during the development of new physics.

(2) By semi-classical gravity I primarily have in mind a theory in which a classical gravitational field (typically represented by the metric tensor) interacts with quantum matter (represented by a quantum state) — most simply by dependence on an expected value for the state. The main argument against semi-classical gravity that I want to consider is that of Eppley and Hannah (1977), who (broadly) argue that the interactions of quantum mechanical matter with a classical field can neither collapse (on pain of violating energy conservation) nor not collapse (on pain of superluminal communication) the quantum state. I will discuss Callender and Huggett (2001), in which we find loopholes in their arguments against both options (and some other response that have been made). It will emerge that in semi-calssical gravity gravity and the quantum are not independent in the sense of my organizing question.

(3) So, how is the search for an ‘interpretation’ of QM related to the search for a quantum theory of gravity? By ‘QM’ here I mean the assumption of a Hilbert space formalism, with unitary evolution, and the Born Rule — (more than) enough to generate the measurement problem, whose solution is what I primarily mean by an ‘interpretation’ of QM. Other aspects of the interpretation of QM (especially QFT), to do with locality, existence, renormalization, for example, seem more obviously dependent on quantum gravity. In the first place I intend the question as a methodological one: is it a promising strategy to pursue quantum gravity without first unequivocally solving the measurement problem? (For the purposes of the meeting I hope we are assuming that at least there are competing solutions; certainly I am for this seminar.) I see three options: (a) the two searches are independent, and so quantum gravity can be pursued without considering the interpretation of QM; (b) QM must be interpreted adequately before gravity can be quantized; (c) gravity is the key to interpreting QM, and so quantization will occur simultaneously with solving the measurement problem. I hope that the audience will discuss where different approaches to the searches stand on the issues, and indeed whether it is a useful framework at all.

Ward Struyve: Bohmian mechanics

I will give an introduction to Bohmian mechanics, which is an alternative to standard quantum theory that describes actual particles moving under the influence of the wave function. I will discuss how it deals with the conceptual problems of quantum theory, its present status and scope, and topics for future research.

Angelo Bassi: Collapse models: from theoretical foundations to experimental verifications

Collapse models modify the Schroedinger equation by including nonlinear stochastic terms, which tend to localize wave functions in space in a dynamical manner. These terms have negligible effects on microscopic systems - therefore their quantum behaviour is practically preserved. On the other end, since the strength of these new terms scales with the mass of the system, they become dominant at the macroscopic level, making sure that wave functions of macro-objects are always well-localized in space.  We will discuss why modifications of the Schroedinger equation which include nonlinear stochastic terms have to be of the form used in collapse models. Therefore, in a precise sense, collapse models are the only consistent modifications of quantum mechanics, preserving general physical principles. We will also present models which differ from the GRW or CSL model, and explain why they are important. By changing the dynamics of quantum systems, collapse models make predictions, which are different from standard quantum mechanical predictions. We will discuss the most relevant scenarios, where such deviations could possibly be observed.

Dan Bedingham: Relativistic dynamical state reduction models

I will give a pedagogical overview of relativistic dynamical state reduction models. Dynamical state reduction models are an attempt address the measurement problem by unifying Schroedinger dynamics and quantum state reduction in one mathematical framework. I will discuss some of the conceptual and technical problems encountered when we try to include relativity and present some possible resolutions and open issues.

Sudarsky, Okon, Ortiz, Peña and Modak: Benefits of Objective Collapse Models for Cosmology and Quantum Gravity

We will display a number of advantages of objective collapse theories for the resolution of long-standing problems in cosmology and quantum gravity. In particular, we will examine applications of objective reduction models to three important issues: the origin of the seeds of cosmic structure, the problem of time in quantum gravity and the information loss paradox; we will try to show how reduction models contain the necessary tools to provide solutions for these issues.

Tim Koslowski: Gravity is the evolution of spatial conformal geometry

"Shape Dynamics" describes gravity as the evolution of spatial conformal geometry. This combines relational ideas proposed by Barbour and collaborators with the conformal approach to the initial value problem developed by York and Choquet-Bruhat. The new ingredient is the observation that gauge symmetries can be traded while keeping all physical predictions unchanged. In particular, the gauge freedom of choosing a foliation can be traded for a gauge freedom of choosing a local scale. Once this is explained, there are several questions to explore and I will adjust my presentation due to requests by the audience. The possibilities are: (1) What happens with singularities if the conformal evolution is the fundamental description of gravity and space-time is only a derived concept? (2) How is space-time abstracted from the evolution of spatial conformal evolution? (3) What are the implications of the shape dynamics picture for quantum field theory and in particular quantum gravity?