Rethinking Foundations of Physics 2017
Saturday March 11 - Saturday March 18 2017
Traditional conferences and subject-specific workshops offer little room for having in-depth discussions about the foundations of physics in an open, creative and speculative way. Since the first meeting in 2013, this workshop has offered a platform for engaging in such discussions.
The workshop centers on discussions in small groups. The aim of these is to reveal implicit assumptions in physics, to clarify the conceptual core of its guiding ideas and to explore new ways of thinking about problems in basic research. Ideally, the workshop thus bridges the gap between deep critical thinking and creative brainstorming. To lay the ground for these sessions, there will be talks given by the participants.
The following general questions convey the spirit of the workshop and may serve as guidelines for more specific subjects of the discussion sessions:
- Which mathematical, conceptual, and experimental paradigms underlie modern formulations of QM, GR, and QFT?
- Can they be relaxed or changed? If so, how?
- Which new mathematical developments could be relevant for future foundations?
- Are there promising new or non-standard experimental possibilities?
The workshop is aimed at PhD students and Postdocs in physics, mathematics and philosophy. Participants are not required to have substantial knowledge in all modern physical theories, nor do they have to be currently working on basic research questions. We look forward to applications from people who are passionate about conceptual questions, open to other fields and, most importantly, eager to engage in deep discussions.
Date: Saturday, March 11 - Saturday, March 18, 2017
Place: Mountain Cabin, Dorfgastein, Austria
Workshop fee: 350 Euros (includes accommodation, shuttle to the cabin, all meals, and nonalcoholic beverages, financial support for both workshop fee and travel expenses is available*)
The workshop will take place in a beautiful, cosy mountain cabin which offers all necessary luxuries (a bath, showers, a sauna - and even a toilet). However, we want to point out that a mountain cabin is not a hotel: Accommodation will be in dorms with bunk beds, there are no single rooms and bathrooms have to be shared. Also, internet is not available.
There is no catering provided - we will do the cooking ourselves. To this end, we form cooking teams of two or three to prepare breakfast, lunch and dinner.
Statement of Inclusiveness
We affirm that scientific events have to be open to everybody, regardless of race, sex, religion, national origin, sexual orientation, gender identity, disability, age, pregnancy, immigration status, or any other aspect of identity. We believe that such events have to be supportive, inclusive, and safe environments for all participants. Discrimination and harassment cannot be tolerated. We are committed to ensuring that this workshop follows these principles, and that all participants are treated with dignity and respect.
(This statement is part of a larger initiative among the scientific community which we invite you to discover here.)
Flavio Del Santo
Pau Enrique Moliner
Diego A. Quiñones Valles
John H. Selby
The Role of Metric Geometry in Physics
In most formulations of physics, including approaches to quantum gravity, the concept of a metric background is taken for granted. That is, a metric field, either classical or quantum, determining distances is assumed to exist, and once solved for it gives an objective way to determine distances between points of a manifold without direct reference to any other fields living on the manifold. This is still true in general relativity and in any theory of quantum gravity which in some sense has a quantum version of the metric or the connection as a fundamental variable. However, from a fundamental point of view, it appears that such a pre-determined concept of distances is non-physical: in order to do any measurement of distance in the real world, we must actually look at other fields in the theory and consider their interaction. In this sense it appears that we should be able to dispense with the concept of a metric manifold, and simply consider for example correlations between the electromagnetic field in scattering processes, defining geodesics as the paths of free electromagnetic radiation, without ever referring to a metric. The proposed discussion would concern theories which in some sense implement this and the various consequences such a "metric free hypothesis" would have.
Criteria to Decide Between Different Interpretations of Quantum Mechanics
Is it possible to find criteria that would let us decide which interpretation of Quantum Mechanics is more satisfactory, thereby rejecting the attitude according to which choosing between them is a question of mere taste? We will especially try to see in which way one could envision criteria other than empirical prediction.
This question is important in that different interpretations of Quantum Mechanics, even those that give us similar empirical predictions - such as the Copenhagen interpretation and the Bohmian (ontological) interpretation -, necessitate having very different epistemological assumptions regarding the very definition of physics. For example whether the task of physics is to study the natural world and its inherent characteristics or whether it has to provide a systematic knowledge of the way that we perceive nature.
Moreover, it can be shown that because of the probabilistic nature of empirical predictions in Quantum Mechanics, the non-empirical dimensions acquire a very important status and that within the framework of Quantum Mechanics, the attitude that considers these non-empirical aspects to be a question of mere taste, or of mere philosophical curiosity, is not really consistent. From the very inception of Quantum Mechanics, it has been asked whether this probabilistic nature could be overcome later on by creating a more fundamental physical theory or by having access to a more fundamental physical level or not. And for all of those physicists who have refused to consider Quantum Mechanics as a temporary, make-do kind of theory, the primary role of the non-empirical dimensions is to respond to this question: why in spite of the probabilistic nature of empirical predictions in Quantum Mechanics, the latter should be thought of as a definitive theory? Those physicists who are not happy with any of the responses given to this question within different interpretations, and if they do not manage to come up with a satisfactory response, they may prefer to spend their time working out a different physical theory instead of contributing to the development of Quantum Mechanics on its present base. We know that Einstein was one such physicist.
Discussing this question makes it also possible to clarify the different mathematical, conceptual and experimental paradigms that underlie different interpretations, but also to shed some light on the different kinds of relationship that exist between the mathematical, conceptual and experimental aspects within each interpretation.
What Quantum Communication Complexity has to say on Non-Locality and on Macroscopic Realism
Flavio Del Santo
To which extend is QM non-local? Is it only because of Bell's theorem that QM is accepted to be non-local, or it is enough to exploit the effect of quantum superpositions to ensure a more efficient communication? If the latter case would be confirmed, does this represent an independent test of non-locality?
The increasing attention that quantum information processes received in recent years, led to a general more profound understanding of fundamental problems of QM, and on the other hand to the exploitation of such phenomena. In particular, this begs the question whether genuine quantum effects (quantum superposition and entanglement) can actually be advantageous to transmit information, without conflicting with causality. Starting from some results of the so called "quantum communication complexity", it is possible to show that there are certain tasks which are more efficient in a quantum case, if compared to their classical counterpart. This stimulates a discussion on the fundamental value of such a comparison between quantum and classical systems, in terms of information.
Categorical Thinking as a Source of New Foundations
Pau Enrique Moliner
Category theory provides us with a way to study mathematical structures and the relations between them in general, by abstracting away from the details. The goal of this talk is to give an idea of how this way of thinking may lead to better foundations of mathematics and of physics. This talk will consist of two parts and will be given in collaboration with Pierre Martin-Dussaud. In the first part, I will focus mostly on describing the categorical way of thinking in relation to the foundations of mathematics. In the second part, Pierre will focus mostly on the idea of a general science of systems and processes between them (which is based on categorical thinking) in relation to the foundations of physics. In what follows, I will describe in more detail my part of the talk.
Traditionally, most of the basic intutitions on which foundations are based come directly from our experience with the natural world: forming collections of things, counting, observing natural phenomena, etc. This has ultimately led to set theory as a successful foundation of mathematics. However, the major ideas that have allowed such success are difficult to translate into the physical sciences, if possible at all. Now, for the first time in history, we start to have an important amount of basic intuitions coming from the interplay between mathematics and theoretical computer science, which gives us an opportunity to find new foundations. More importantly, some of the basic features that would make such new foundations successful could be easier to translate into the physical sciences.
As a real-life example of work in this direction, I will introduce the main ideas behind homotopy type theory and the univalent foundations program. More concretely, how our foundational understanding can benefit from the interplay between category theory, type theory, and logic. Categorical Quantum Mechanics (CQM) is a field that in particular aims to establish a new paradigm for the mathematical foundations of quantum theory by seeing it as an example of abstract theory of systems and processes, but, in order to avoid overlap, these ideas will mostly be covered by Pierre.
Discussion: How could the advantages of thinking categorically in mathematics be translated into physics? It seems possible to get a good notion of general theory of systems and processes, and to view certain parts of physics (e.g. quantum theory) as an example. However, at the moment, in order to select quantum theory out of all possible theories, a number of ad hoc choices have to be made which are just motivated by the mathematical structure of standard quantum theory. How could we find a set of physically or informatically motivated axioms that select quantum theory out of all possible theories?
Could the fact that the univalent foundations program is an approach to the foundations of constructive mathematics represent a serious limitation?
What are the philosophical implications of CQM? Since CQM is a new field, this question has not yet received a lot of attention.
How could dagger Frobenius algebras be interpreted physically? These algebras are a key ingredient of CQM, in relation to how classical and quantum information are modelled in this context.
Boundary Conditions, Causality and Time-Asymmetry
Should the state of physical systems depend only on boundary conditions in the past, and not in the future? At the macroscopic scale, it seems obvious that this answer to this question is 'yes': everyday events are always preceded in time by their causes. However, given the fundamental time symmetry of most of our physical laws, it is interesting to ask whether this is necessarily still true at the quantum level.
The question is compelling even at this abstract level, but there are also more concrete physical reasons to be interested. Many no-go theorems in quantum mechanics, such as Bell's theorem, rule out local hidden variable theories given certain assumptions. One of these is that the state of the quantum system is uncorrelated with the future state of the detector. This is an explicitly time-asymmetric assumption – we do of course expect the past state to be relevant – and it is interesting to consider what the implications of relaxing it are.
This idea is not new but has remained rather unexplored, perhaps partly because of its unintuitive nature. However it has been popularised to some extent by Huw Price, among others, and has started to attract more attention in quantum foundations – one recent example would be Leifer and Pusey, Is a time symmetric interpretation of quantum theory possible without retrocausality? (arxiv/1607.07871). The possibility of a local, spacetime-based quantum theory that is still compatible with quantum no-go theorems is attractive enough that it seems worth investigating
Reductionism, ad absurdum?
Contemporary physics seems to be inwrought with reductionist ideologies, which hold that everything, i.e. every phenomenon, will ultimately be explained in terms of basic physical entities and laws thereof. Whereas many physicists would concede that such a reduction has not yet been established, the idea that one could proof the opposite, namely that reductionism is wrong, seems false, if not ludicrous to most.
Yet, in the first chapter of his 2010 book, David Chalmers, a famous philosopher from NY University, sets out to do exactly this: To proof that reductionism is simply false. He establishes that there are phenomena which, according to his argumentation, cannot in principle be reduced to physical notions.
I think his argumentation, and the underlying question, concern an important border-stone of physics and may have implications for the fundamental methodology of this science. Therefore, I would like to propose a critical discussion of Chalmers' argumentation which aims at elaborating the extend to which his conclusion applies to physics.
As a preparation for this discussion, I would gladly offer to give a talk where I present Chalmers' argument in a detailed but brief way. Furthermore, I would add my thoughts about his reasoning and could, if time permits, sketch a slightly different argumentation which is more adapted to foundations of physics. In the subsequent discussion session, depending on the preferences of the participants, we could focus on aspects of Chalmers' argument and its criticism, or also evaluate my different proposal.
I think this topic very much aligns with the goals of the workshop because it concerns (and invites to rethink) the most general, and hence most deep, paradigms of modern physics.
Is Black Hole Thermodynamics Thermodynamics After All?
The paradigm of black hole thermodynamics is likely to provide a stepping stone towards a theory of quantum gravity. But does black hole thermodynamics form an instance of genuine thermodynamics—as it is typically believed after the discovery of Hawking radiation—or merely an analogy to thermodynamics proper? The question will be of interest to any one working on gravity, QFT in curved spacetime, foundations of thermodynamics and, more philosophically, the distinction between analogy and identity. It also nicely touches a general problem of physics at the frontier of current knowledge: what kind of theoretical principles to trust in when the right empirical data is missing.
Various Meanings of Symmetries in Physical Theories
Symmetries are regarded as central components of all modern physical theories. However, it seems that not much can be said about them in general and the most important work in their analysis should be devoted to finding crucial differences between various types of symmetries.
All symmetries can be understood as functions determined on a set of (kinematically) possible states of a given theory. The first important distinction (Caulton 2015) is between analytic and synthetic symmetries. Analytic symmetries are these which do not change any physically real properties of any state; they are merely redescriptions of a physical system and operate only on 'superfluous structure' of a theory which does not have any physical content. (The term 'gauge symmetry' is often used in a similar way.) Synthetic symmetries change some physically real properties of at least some states, but there are another physically real properties which are left unchanged by them. The second important distinction (Kosso 2000) is between symmetries that have direct empirical significance (that is, can be tested by performing appropriate transformation and observing appropriate invariance) and these that do not have direct empirical significance (it does not mean that they do not have empirical significance at all – but in this case it is only indirect, e.g. via Noether's theorems).
The aim of my presentation is to explain in more details these two abstract distinctions, consider possible relations between them (my hypothesis is that under some plausible understanding of being physically real and of empirical significance these two distinctions should coincide) and try to connect them with more 'concrete' divisions of symmetries, for which we can easily provide well known examples, namely discrete vs. continuous, global continuous vs. local continuous, internal vs. external.
Discussion: What is a relation between analytic vs. synthetic symmetries on the one hand and symmetries having direct empirical significance vs. symmetries having only indirect empirical significance, on the other?
Which of known symmetries belong to which of these four types? How can we decide this question?
Can we understand the notion of empirical significance in a non-anthropocentric way?
Does it make sense to consider a status (with respect to the above distinctions) of a symmetry in a theory which is only approximately true?
Categories: A General Science of Systems and Processes?
The theory of categories, developed in particular by Grothendieck, offers a very general formalism that enables to draw links between physics, topology, logic and computation. At the opposite of the exponential rate of ramification of the tree of science, could it be a path for gathering over-specialized scientists by showing their problems are nothing but the same object watched from different point of views?
Information as a Common Quantity in Physics
Diego A. Quiñones Valles
Is information a fundamental concept of Physics? Information theory has bridged the gap between Quantum mechanics and Thermodynamics, solving the Maxwell's demon conundrum and offering the exciting possibility of using information as a source of usable energy (Szilárd engine). Recent works have proposed that Gravity is an entropic force, one even suggesting that Dark energy can be explained from Quantum information principles (E. Verlinde, 2016), further cementing the relevance of the concept of information. Nonetheless, some critical axioms of Quantum mechanics and Relativity have been subject of much debate, like the information's speed limit and the information conservation principle, opening to question how fundamental information is in physics.
The question examines the possibility that one the core concepts in Physics may not be essential, as usually assumed. It allows a discussion about how necessary physical information is for other theories to remain consistent and also about the possibility that information might be even more fundamental than previously thought.
Causality in Physical Theories
Few notions in physics are as fundamental as causality. Yet, we rarely pay much attention to how causality enters into our physical theory of choice, beyond perhaps ensuring the absence superluminal signalling. But how does causality enter into physics? And exactly how do we ensure that superluminal signalling is
In this talk I will first give a short introduction to how causality is treated in philosophy as opposed to in the natural sciences. I will then provide a comprehensive overview of how causality is incorporated into four of the main theories in physics: Newtonian mechanics, quantum mechanics, general relativity and quantum field theory. We will then examine the above theories one by one and divide them into two distinct categories; those that have a fixed causal structure and those that have a dynamic causal structure. In the process, we will see how the causal structure of the theories can guide us in the search for quantum gravity. Lastly, I will present the notion of indefinite causal structures and the causal inequality, along with a brief overview of in which direction current research efforts in the quantum foundations community are heading.
Depending on where the discussion leads us, the following questions could be interesting to consider. What is the relationship between causality and the notion of measurement? Is it possible to derive causality from some deeper notion, and if so, from what? Quantum entanglement can be seen as the knowledge that two systems have the same origin. Is there a link between causality and entanglement? Lastly, quantum theory respects causality in that it doesn't allow for superluminal signalling. This is however a consequence of the non-uniqueness of mixed states, and not the consequence a deeper causal structure. Are there other ways than this to impose causality onto a system?
The Role of Operationalism and Picturialism in Quantum Theory and Beyond
John H. Selby
There are two guiding principles involved in much of the current research in quantum foundations. Firstly, operationalism, in the sense that: it is a necessity of any physical theory to be able to predict the outcome of experiments, but moreover, that it is desirable that all of the mathematical tools we use to describe a theory have a clear operational interpretation. Secondly, picturalism (or formalism-locality or compositionality or use of diagrams or...): that the mathematics used to describe a physical theory should 'resemble' the physical thing that is being described. More concretely, this leads to the framework of process theories, which use a diagrammatic language such that composition in the diagrammatic language directly corresponds to composition of 'things' in the 'real world'.
This way of thinking has provided an extremely useful way to view the world, and forms the basis of much modern research in quantum foundations. However, I think that there are limitations to any individual perspective on to understand physics, and so I think it would be beneficial to challenge these principles to try to understand what these limitations may be. More specifically, I think there are several aspects to be discussed:
- How valid do we think these two principles are?
- How successful have they been within quantum foundations? (E.g. what have 'reconstructions' of quantum theory actually achieved?)
- What are the limitations of this way of thinking?
- Should we be seeking to apply these principles, and the resulting mathematical tools, more generally? (E.g. to quantum field theory, general relativity, condensed matter theory, ...)
More concretely, I will introduce these principles and the associated mathematical frameworks arising from them, In particular focusing on process theory framework. I will then discuss the role of these principles (and the tension between them) in reconstructing quantum theory.
We will wend our way through the history of the vacuum, focusing on Einstein's varying ideas about the nature of empty space. Arriving at the modern age we will look at some current motivations behind the quantisation of space and time. Finally we dip our toes into the role that quantum foundations might play in an understanding of the properties of emptiness.
Geometry and Energy in Quantum Field Theory
Are there problems concerning the relationship between geometry, energy, and quantum field theory which can elucidate the nature of the latter?
One of the themes which characterize 20th century physics is the relationship between geometry and energy. This relationship is most often associated with general relativity in which energy densities determine the spacetime curvature of a system. But it also exists in quantum physics in the reverse direction: the geometry of a quantum system (specifically, assumptions about the system's boundary conditions) determines the resulting energy spectrum of the system (e.g., for example, the infinite square well potential, or the hydrogen atom).
Given this theme it is worth considering whether it would be possible to explore connections between geometry, energy, and quantum field theory. Such explorations have already been hinted at in work on topological quantum field theory, but I think it could be pushed in new directions by pursuing analogies in the mathematics of quantum field theory systems. Analogies possibly relevant in this direction are
- Self-similarity of fractals and conformal invariance of some quantum field theories.
- Determinants in quantum field theory and geometry.
From Intuitive Observations to Physical Quantities
In an exercise of introspection and metaphysical honesty one realises that any physical theory, however sophisticated, should be formally constructed from the set of our intuitive observations and quotidian experiences - after all, it is the structure of this very set of observations what physical theories will attempt to describe. In principle, one should be able to pinpoint the fundamental constructions (e.g. numbers, proportions, sets...) that underlie any modern physical model at the level of our immediate experience of our existence. In other words, and taking a materialist stance which I, in general, do not take, one should be able to identify how physical concepts are constructed from the set of sensations perceived through our human senses.
This question, in one way or another, should be addressed satisfactorily in any serious attempt to give a solid conceptual foundation to physics. Thus, any programme that aims at giving a general mathematical description of a physical theory as devised by one single observer should include a mathematical treatment of the fact that abstract, theoretical observers are nothing but an image of our own mental self and the observations/measurements they make are a reflection of the set of our quotidian experiences (or some formal constructions therein).
I will propose a first approach to such treatment focusing on the notion of physical quantity. During the talk I will discuss my thoughts on how to give a mathematical structure to the set of intuitive observations that faithfully represents the characteristics of these that make it possible for us to do science in the way we do, namely, via logical verification, quantitative analysis, etc. Then I will briefly mention how this fits in a programme that aims at describing observer-based description of physical systems. In that context, the mathematical notion of observable is given a very precise mathematical structure (Poisson algebra) and I will try to argue why that structure matches the notion of physical quantity. For instance, a very concrete aspect of this is the relation between the use of physical quantities in real, practical physics (physical units and dimensional analysis) and the mathematical structure of the corresponding theoretical objects (addition, scalar multiplication and associative multiplication of elements of the Poisson algebra).
I can imagine that this topic has been treated extensively in the literature but I intend to present everything in fairly self-contained terms so that the subsequent discussion can yield some conclusive results withing some reasonable boundaries. The only previous knowledge that will be useful for those willing to partake actively after the talk will be that of general mathematical structures well-known to graduate students (some algebra, some differential geometry, a bit of logic and set theory...)
Unified Field Theory. Are Gravity, Electromagnetism, and Weak and Strong Interactions Different Aspects of a Single Underlying Field Theory?
There are certain similarities between general relativity and electromagnetism (or, more generally, Yang-Mills theories): the principles of local symmetry introduce gauge potentials (the metric 'g' or the Yang-Mills gauge fields 'A'), which not only govern the movement of matter, but also satisfy dynamical equations of motion. A closer look at the standard exposition reveals also numerous structural differences between these theories: the gravitational field refers to spacetime diffeomorphisms, whereas Yang-Mills fields to local symmetries in the internal space of the matter fields; the kinetic term for the gravitational field, the scalar curvature 'R', differs from 'F^2' in the Yang-Mills theory (although there exist alternative approaches to gravity, namely, the teleparallel theory of gravity, which makes the two kinetic terms more comparable); and so on.
Nevertheless, it is tempting to look for a theory of a single unified field, of which the known interactions would be merely different manifestations. Yet, my design is not only to assemble the well-established fundamental interactions, but rather find a sufficiently general and elegant framework, which could well contain extra degrees of freedom. These might correspond to new interactions, or provide some insight into the origins of 'quantumness' as captured by the path integral.
After some preliminary discussion, and an overview of attempts to build a unified field theory, I will briefly pursue a point of view where spacetime is put on equal footing with the internal space of the matter fields, thus modifying the usual paradigm of fields as functions living on the spacetime. The requirement of invariance with respect to arbitrary diffeomorphisms of the total space then leads to a gauge field, which can be reduced to Yang-Mills gauge field or the gravitational vierbein field under appropriate restriction of the group of transformations. To this end I will use a rather unorthodox formulation of classical field theory based on the (Hamiltonian) constraint between coordinates and the field-theoretic momentum multivector.
University of Regensburg - Faculty of Mathematics,
DFG Graduate School GRK 1692 "Curvature, Cycles, and Cohomology",
European Research Council Project Philoquantumgravity,
Basic Research Community for Physics e.V.
Prof. Dr. Felix Finster, Department of Mathematics, University of Regensburg