arXiv subjects

Daniel Grimmer

Publications and source records attributed to Daniel Grimmer.

At least 19 recordsLinked to original sources

arXiv2026

Direct From Darwin: Deriving Advanced Optimizers From Evolutionary First Principles

Evolutionary computation has long promised to deliver both high-performance optimization tools as well as rigorous scientific simulations of Darwinian evolution. However, modern algorithms frequently abandon evolutionary fidelity for physics-inspired heuristics or superficial biological metaphors. This paper derives a suite of advanced gradient-based optimization algorithms directly from evolutionary first principles. We introduce Darwinian Lineage Simulations (DLS) to prove that, in an asexual context, Fisher's and Wright's historically opposed views of evolution are actually formally equivalent; One can partition Fisher's deterministically-evolving total population into Wright's randomly-drifting sub-populations. We prove that proper bookkeeping requires introducing a specific kind of structured noise (the DLS noise relation). Crucially, any bookkeeping choices which satisfy this relation will yield a faithful simulation of evolution. Using this vast representational freedom, we prove that a broad family of battle-tested optimization algorithms are already perfectly compatible with evolutionary dynamics. These include: Stochastic Gradient Descent as well as many regularizations/approximations of Newton's method and Natural Gradient Descent. By simply adding DLS noise (i.e., evolutionarily faithful genetic drift), these algorithms become scientifically valid in silico simulations of Darwinian evolution. Finally, we demonstrate that even the state-of-the-art Adam optimizer can be brought into evolutionary compliance through a minor mathematical surgery.

cs.NE↗

arXiv2024

Spacetime Representation Theory: Setting the Scope of the ISE Method of Topological Redescription

Spacetime dualities arise whenever two theories -- despite being structurally equivalent in some sense -- seemingly provide us with two radically different spatiotemporal descriptions of the world. This often involves radical differences in how the two theories topologically stage their states; Whereas one theory is about *this* type of particle/field on *this* smooth manifold, the other theory is about *that* type of particle/field arranged differently on *that* smooth manifold. For instance, the AdS-CFT correspondence relates a certain theory set in the bulk (our 3+1 dimensional spacetime) to another theory set on the boundary (a 2+1 dimensional spacetime). Another example (new in this paper) is the Möbius-Euclid duality: a theory about a certain type of particle floating around on the Euclidean plane can be topologically redescribed as instead being about a different type of particle living on a Möbius strip, and vice versa. The possibility of such alternative spacetime framings raises some significant questions about the epistemology and metaphysics of space and time. For instance, what are our topology selection criteria? Are they objective or conventional? Moreover, given that two spacetime theories are topological redescriptions of each other, what is the common core which they are equivalent descriptions of? As a step towards answering such questions, this paper develops a general framework (spacetime representation theory) for understanding our ability to topologically redescribe our spacetime theories. With this framework established, I will then discuss the ISE Equivalence Theorem which sets the scope of the recently developed ISE Method of topological redescription.

physics.hist-ph↗

arXiv2023

From Humean Laws to a Neo-Kantian Spacetime: A Dynamics-First View of Topology

Do the spacetime manifolds which feature in our best scientific theories reflect anything metaphysically weighty in the world (e.g., any fundamental substances or relations)? Should we extend our notions of space and time beyond the epistemological roles they play in helping us codify the dynamical behavior of matter? Kant famously answered ``No'' to both of these questions, contra Newton and Leibniz. This paper introduces novel technical and philosophical support for such a (Neo-)Kantian perspective on the metaphysics of space and time. To begin, I will make an explicit analogy between broadly Humean views of laws (e.g., Lewis, Demarest, etc.) and dynamics-first views of geometry (e.g., Brown). I will then continue this line of analogous views beyond the metaphysics of laws debate and the dynamical vs geometric spacetime debate by extending it into the context of spacetime topology. Namely, I will put forward a dynamics-first view of topology (in answer to Norton's problem of pre-geometry). This dynamics-first view of topology is supported by some powerful new techniques for topological redescription which I have recently developed in Grimmer (2023a) and Grimmer (2023b), namely the ISE Method. These new techniques allow us to remove and replace the topological underpinnings of our spacetime theories just as easily as we can switch between different coordinate systems. For instance, a theory set on a Möbius strip might be redescribed as being set on the Euclidean plane and vice versa. Indeed, as Grimmer (2023b) has proved, the ISE Method gives us access to effectively every possible spacetime framing of a given theory's kinematical and dynamical content. Given this overabundance of candidate spacetime framings, it is then conceivable that one can pick out a theory's topological structure via something analogous to a Best Systems Analysis.

physics.hist-ph↗

arXiv2023

Decoding Quantum Field Theory with Machine Learning

We demonstrate how one can use machine learning techniques to bypass the technical difficulties of designing an experiment and translating its outcomes into concrete claims about fundamental features of quantum fields. In practice, all measurements of quantum fields are carried out through local probes. Despite measuring only a small portion of the field, such local measurements have the capacity to reveal many of the field's global features. This is because, when in equilibrium with their environments, quantum fields store global information locally, albeit in a scrambled way. We show that neural networks can be trained to unscramble this information from data generated from a very simple one-size-fits-all local measurement protocol. To illustrate this general claim we will consider three non-trivial features of the field as case studies: a) how, as long as the field is in a stationary state, a particle detector can learn about the field's boundary conditions even before signals have time to propagate from the boundary to the detector, b) how detectors can determine the temperature of the quantum field even without thermalizing with it, and c) how detectors can distinguish between Fock states and coherent states even when the first and second moments of all their quadrature operators match. Each of these examples uses the exact same simple fixed local measurement protocol and machine-learning ansatz successfully. This supports the claim that the framework proposed here can be applied to nearly any kind of local measurement on a quantum field to reveal nearly any of the field's global properties in a one-size-fits-all manner.

quant-ph↗

arXiv2023

The Pragmatic QFT Measurement Problem and the need for a Heisenberg-like Cut in QFT

Despite quantum theory's remarkable success, many philosophers worry that it nonetheless lacks some crucial connection between theory and experiment. One under-discussed aspect of the Quantum Measurement Problems is that it is sometimes unclear how to model our measurement processes in order to extract experimental predictions. Without a solution to these pragmatic worries, quantum theory would be at risk of losing both its evidential support and its physical salience. Avoiding these risks requires solving the Pragmatic Measurement Problem. For non-relativistic quantum theory, this problem has been solved as follows: One can model each of quantum theory's key experimental successes on a case-by-case in terms of measurement chains and Heisenberg cuts. From here, one can then strive for a wide-scoping measurement theory capable of modeling all (or nearly all) possible measurement processes. Indeed, for non-relativistic quantum theory this leads us to our usual projective measurement theory. But how does this story have to change when we move into the context of quantum field theory (QFT)? It is well known that in QFT almost all localized projective measurements violate causality, allowing for faster-than-light signaling. Despite this, I will argue that we can proceed largely as we did in the non-relativistic case. We first ought to build up a case-by-case measurement framework for QFT by using measurement chains and Heisdenberg-like cuts (where we switch from a QFT model to a non-QFT model). We can then strive for both a new measurement theory for QFT and an empirically meaningful characterization of its observables. It is at this point that significantly more theoretical work is needed. This paper ends by briefly reviewing the state of the art in the physics literature regarding the modeling of measurement processes involving quantum fields.

physics.hist-ph↗

arXiv2023

Introducing the ISE Methodology: A Powerful New Tool for Topological Redescription

This paper introduces a powerful new tool for topological redescription, the ISE Methodology. These tools allow us to remove and replace a theory's topological underpinnings just as easily as we can switch between different coordinate systems. Aspirationally, these novel topological redescription techniques can be used to provide new support for a roughly Kantian view of space and time; Rather than corresponding to any fundamental substances or relations, we can see the spacetime manifolds which appear in our theories as merely being an aspect of how we represent the world. This view of spacetime topology parallels the dynamic-first view of geometry as well as a Humean view of laws; The spacetime manifolds which feature in our best theories reflect nothing metaphysically substantial in the world beyond them it being one particularly nice way (among others) of codifying the dynamical behavior of matter. A parallel publication (namely, Grimmer (2023)) will explicitly characterize the power and scope of the topological redescription techniques offered to us by the ISE Methodology. The modest goal of this paper is simply to introduce the ISE Methodology by applying it to two example theories. Firstly, to familiarize ourselves with these techniques, I will show how they can be used to redescribe a spacetime theory via a Fourier transform. Secondly, I will show how the exact same techniques can be used to redescribe a lattice theory (i.e., a theory set on a discrete spacetime, M=RxZ) as existing on a continuous spacetime manifold,M=RxR.

physics.hist-ph↗

arXiv2022

Deflating Spacetime: A Dynamics-First View of the Spacetime Manifold

What, if anything, can help us explain the dynamical behavior of matter? One may be tempted here to appeal to the laws of nature, or to the world's geometric structure, or even to the smooth topological structure of the spacetime manifold itself. Some think, however, that the metaphysics involved in such explanatory strategies is excessively spooky. Indeed, some opt to reverse the arrow of explanation, putting dynamics first. For instance, one can use Lewis's Best Systems Analysis (BSA) to view the laws of nature as merely being codifications of certain patterns in the dynamical behavior of matter. Similarly, one can use Huggett's Regularity Relationism to achieve an analogous view of the world's geometric structure. At present, however, there is no such dynamics-first view of the spacetime manifold itself. This dissertation puts forward such a view: The spacetime manifold is merely a codification of certain patterns in the dynamical behavior of matter. This dissertation develops powerful mathematical tools for investigating and negotiating between a wide variety of spacetime settings for a wide range of spacetime theories. From here, a competition between different spacetime codifications is invoked analogous to the competition between different law-like codifications in Lewis's BSA. Whereas the BSA judges law-like codifications based on their balance of simplicity and strength, spacetime codifications are to be judged by how well they fit the theory's dynamics and kinematics.

physics.hist-ph↗

arXiv2022

A Discrete Analog of General Covariance -- Part 1: Could the world be fundamentally set on a lattice?

A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a theory's substantive content from its merely representational artifacts. It is an indispensable tool for a modern understanding of spacetime theories. Motivated by quantum gravity, one may wish to extend these notions to quantum spacetime theories (whatever those are). Relatedly, one might want to extend these notions to discrete spacetime theories (i.e., lattice theories). This paper delivers such an extension with surprising consequences. One's first intuition regarding discrete spacetime theories may be that they introduce a great deal of fixed background structure (i.e., a lattice) and thereby limit our theory's possible symmetries down to those which preserve this fixed structure (i.e., discrete symmetries). However, as I will discuss, these intuitions are doubly wrong and overhasty. Discrete spacetime theories can and do have continuous translation and rotation symmetries. Moreover, the exact same theory can be given a wide variety of lattice structures and can even be described with no lattice at all. As my discrete analog of general covariance will reveal: lattice structure is rather less like a fixed background structure or part of an underlying manifold and rather more like a coordinate system, i.e., merely a representational artifact. Thus, the world cannot be "fundamentally set on a square lattice" (or any other lattice) any more than it could be "fundamentally set in a certain coordinate system". Like coordinate systems, lattice structures are just not the sort of thing that can be fundamental; they are both thoroughly representational. Spacetime cannot be discrete (even when it might be representable as such).

physics.hist-ph↗

arXiv2022

A Discrete Analog of General Covariance -- Part 2: Despite what you've heard, a perfectly Lorentzian lattice theory

A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a theory's substantive content from its merely representational artifacts. It is an indispensable tool for a modern understanding of spacetime theories. Motivated by quantum gravity, one may wish to extend these notions to quantum spacetime theories (whatever those are). Relatedly, one might want to extend these notions to discrete spacetime theories (i.e., lattice theories). This paper delivers such an extension with surprising consequences, extending Part 1 (arXiv:2204.02276) to a Lorentzian setting. This discrete analog of general covariance reveals that lattice structure is rather less like a fixed background structure and rather more like a coordinate system, i.e., merely a representational artifact. This discrete analog is built upon a rich analogy between the lattice structures appearing in our discrete spacetime theories and the coordinate systems appearing in our continuum spacetime theories. I argue that properly understood there are no such things as lattice-fundamental theories, rather there are only lattice-representable theories. It is well-noted by the causal set theory community that no theory on a fixed spacetime lattice is Lorentz invariant, however as I will discuss this is ultimately a problem of representational capacity, not of physics. There is no need for the symmetries of our representational tools to latch onto the symmetries of the thing being represented. Nothing prevents us from using Cartesian coordinates to describe rotationally invariant states/dynamics. As this paper shows, the same is true of lattices in a Lorentzian setting: nothing prevents us from defining a perfectly Lorentzian lattice(-representable) theory.

gr-qc↗

arXiv2021

Measurements in QFT: Weakly coupled local particle detectors and entanglement harvesting

We present a comparison of the AQFT-based Fewster-Verch framework with the Unruh-DeWitt particle detector models commonly employed in relativistic quantum information and QFT in curved space. We use this comparison to respond to a recent paper [arXiv:2103.13400] in which it was argued that the Reeh-Schlieder theorem prevents weakly coupled local particle detectors from harvesting vacuum entanglement from a quantum field. Their claim can be traced back to the mixedness that a local particle detector cannot escape from because of the entanglement that it must have with the quantum fields outside of the localization area. We argue that for any realistic scale of localization for physical particle detectors the effect of that mixedness is negligible, and that weakly coupled localized particle detectors are not impeded from harvesting vacuum entanglement.

quant-ph↗

arXiv2021

Dimensional reduction of cavities with axial symmetry: A complete analysis of when an optical fiber is approximately one-dimensional

Intuition dictates that a very long, very thin cavity (e.g., a fiber optic cable) could perhaps be modeled as an approximately one dimensional system. In this paper we rigorously explore the validity of such intuition from the perspective of a localized probe coupling to a quantum field inside a cavity (e.g., an atom or an Unruh-DeWitt particle detector in a fiber optic cable). To do so, we introduce the notion of subfield decomposition in which a $D+1$ dimensional quantum field in an axially-symmetric cavity can be reduced to an infinite collection of uncoupled, massive $1+1$ dimensional fields. We show that the ability to approximate a higher-dimensional scenario by a $1+1$ dimensional model is equivalent to making a certain change of the probe's shape in the higher-dimensional space. The approximation is justified whenever this change of shape is "small enough". In this light, we identify the dynamically relevant norm by which the magnitude of these changes in probe shape ought to be judged. Finally, we explore this approximation in particular setups corresponding to quantum optics and superconducting circuits.

quant-ph↗

arXiv2020

The Unruh effect in slow motion

We show under what conditions an accelerated detector (e.g., an atom/ion/molecule) thermalizes while interacting with the vacuum state of a quantum field in a setup where the detector's acceleration alternates sign across multiple optical cavities. We show (non-perturbatively) in what regimes the probe `forgets' that it is traversing cavities and thermalizes to a temperature proportional to its acceleration. Then we analyze in detail how this thermalization relates to the renowned Unruh effect. Finally, we use these results to propose an experimental testbed for the direct detection of the Unruh effect at relatively low probe speeds and accelerations, potentially orders of magnitude below previous proposals.

quant-ph↗

arXiv2020

Interpolated Collision Model Formalism

The dynamics of open quantum systems (i.e., of quantum systems interacting with an uncontrolled environment) forms the basis of numerous active areas of research from quantum thermodynamics to quantum computing. One approach to modeling open quantum systems is via a Collision Model. For instance, one could model the environment as being composed of many small quantum systems (ancillas) which interact with the target system sequentially, in a series of "collisions". In this thesis I will discuss a novel method for constructing a continuous-time master equation from the discrete-time dynamics given by any such collision model. This new approach works for any interaction duration, $δt$, by interpolating the dynamics between the time-points $t = n\,δt$. I will contrast this with previous methods which only work in the continuum limit (as $δt\to 0$). Moreover, I will show that any continuum-limit-based approach will always yield unitary dynamics unless it is fine-tuned in some way. For instance, it is common to find non-unitary dynamics in the continuum limit by taking an (I will argue unphysical) divergence in the interaction strengths, $g$, such that $g^2 δt$ is constant as $δt \to 0$.

quant-ph↗

arXiv2020

A classification of Markovian fermionic Gaussian master equations

We introduce a classification scheme for the generators of open fermionic Gaussian dynamics. We simultaneously partition the dynamics along the following four lines: (1) unitary versus non-unitary, (2) active versus passive, (3) state-dependent versus state-independent, and (4) single-mode versus multi-mode. We find that only nine of these 16 types of dynamics are possible. Using this partition we discuss the consequences of imposing complete positivity on fermionic Gaussian dynamics. In particular, we show that completely positive dynamics must be either unitary (and so can be implemented without a quantized environment) or active (and so must involve particle exchange with an environment).

quant-ph↗

arXiv2019

Collisional quantum thermometry

We introduce a general framework for thermometry based on collisional models, where ancillas probe the temperature of the environment through an intermediary system. This allows for the generation of correlated ancillas even if they are initially independent. Using tools from parameter estimation theory, we show through a minimal qubit model that individual ancillas can already outperform the thermal Cramer-Rao bound. In addition, due to the steady-state nature of our model, when measured collectively the ancillas always exhibit superlinear scalings of the Fisher information. This means that even collective measurements on pairs of ancillas will already lead to an advantage. As we find in our qubit model, such a feature may be particularly valuable for weak system-ancilla interactions. Our approach sets forth the notion of metrology in a sequential interactions setting, and may inspire further advances in quantum thermometry.

quant-ph↗

arXiv2019

Thermal Contact: Mischief and Time Scales

We discuss what kind of quantum channels can enable thermalization processes. We show that in order to determine a system's temperature, a thermometer needs to dynamically gain information about the system's local Hamiltonian and not just its state. We illustrate this showing that any temperature measurement protocol that does not resolve the system's local Hamiltonian (such as, e.g., full state tomography) is susceptible to being fooled into measuring any value for the temperature. We will establish necessary conditions for thermal contact for quantum systems. Furthermore, we will show that the intuitive idea of thermalization emerging out of quickly interacting with the microconstitutents of a thermal reservoir cannot be correct.

quant-ph↗

arXiv2019

Zeno Friction and Anti-friction from Quantum Collision Models

We analyze the quantum mechanics of the friction experienced by a small system as it moves non-destructively with velocity $v$ over a surface. Specifically, we model the interactions between the system and the surface with a \textit{collision model}. We show that, under weak assumptions, the magnitude of the friction induced by this interaction decreases as $1/v$ for large velocities. Specifically, we predict that this phenomenon occurs in the Zeno regime, where each of the system's successive couplings to subsystems of the surface is very brief. In order to investigate the friction at low velocities and with velocity-dependent coupling strengths, we motivate and develop \textit{one-dimensional convex collision models}. Within these models, we obtain an analytic expression for the general friction-velocity dependence. We are thus able to determine exactly the conditions under which the usual friction-velocity dependency arises. Finally, we give examples that demonstrate the possibility, in principle, of anti-friction, in which case the system is accelerated by its interaction with the surface, a phenomenon associated with active materials and inverted level populations.

quant-ph↗

arXiv2018

A classification of open Gaussian dynamics

We introduce a classification scheme for the generators of bosonic open Gaussian dynamics, providing instructive diagrams description for each type of dynamics. Using this classification, we discuss the consequences of imposing complete positivity on Gaussian dynamics. In particular, we show that non-symplectic operations must be active to allow for complete positivity. In addition, non-symplectic operations can, in fact, conserve the volume of phase space only if the restriction of complete positivity is lifted. We then discuss the implications for the relationship between information and energy flows in open quantum mechanics.

quant-ph↗