General Physical Principles and Non‐Linear Group Realizations

1974 ◽  
Author(s):  
Max Dresden
Author(s):  
Ciarán M. Lee ◽  
Matty J. Hoban

Quantum theory presents us with the tools for computational and communication advantages over classical theory. One approach to uncovering the source of these advantages is to determine how computation and communication power vary as quantum theory is replaced by other operationally defined theories from a broad framework of such theories. Such investigations may reveal some of the key physical features required for powerful computation and communication. In this paper, we investigate how simple physical principles bound the power of two different computational paradigms which combine computation and communication in a non-trivial fashion: computation with advice and interactive proof systems. We show that the existence of non-trivial dynamics in a theory implies a bound on the power of computation with advice. Moreover, we provide an explicit example of a theory with no non-trivial dynamics in which the power of computation with advice is unbounded. Finally, we show that the power of simple interactive proof systems in theories where local measurements suffice for tomography is non-trivially bounded. This result provides a proof that Q M A is contained in P P , which does not make use of any uniquely quantum structure—such as the fact that observables correspond to self-adjoint operators—and thus may be of independent interest.


2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
James Bonifacio ◽  
Enrico Pajer ◽  
Dong-Gang Wang

Abstract Our understanding of quantum correlators in cosmological spacetimes, including those that we can observe in cosmological surveys, has improved qualitatively in the past few years. Now we know many constraints that these objects must satisfy as consequences of general physical principles, such as symmetries, unitarity and locality. Using this new understanding, we derive the most general scalar four-point correlator, i.e., the trispectrum, to all orders in derivatives for manifestly local contact interactions. To obtain this result we use techniques from commutative algebra to write down all possible scalar four-particle amplitudes without assuming invariance under Lorentz boosts. We then input these amplitudes into a contact reconstruction formula that generates a contact cosmological correlator in de Sitter spacetime from a contact scalar or graviton amplitude. We also show how the same procedure can be used to derive higher-point contact cosmological correlators. Our results further extend the reach of the boostless cosmological bootstrap and build a new connection between flat and curved spacetime physics.


Soft Matter ◽  
2020 ◽  
Vol 16 (12) ◽  
pp. 3106-3124 ◽  
Author(s):  
Aurore Loisy ◽  
Jens Eggers ◽  
Tanniemola B. Liverpool

Modelling a cell as a deformable drop of active matter, we classify the types of cell locomotion on solid surfaces based on general physical principles. Previous models are special cases of our framework and we identify a new self-propulsion mode.


Development ◽  
1987 ◽  
Vol 101 (3) ◽  
pp. 479-489 ◽  
Author(s):  
A. Gierer

In the formation of projections that map one area of the nervous system onto another, guidance of axonal growth cones by directional cues encoded in target tissues is well established by observations on misrouted fibres, though other mechanisms contribute to the precision of connectivity patterns. General physical principles indicate that, if there is directional guidance of normally as well as misrouted axons, leading them toward their appropriate target positions, the inference for a role of graded distributions of molecules is a strong one. As explained in this paper, curving, meandering, branching and shifting connections are fully consistent with a crucial role of directional cues encoded by graded molecular distributions. A model is proposed according to which slight directional cues are strongly enhanced within the axonal growth cone; if the proximal part of the growth cone is activated indicating that the growth cone points in an entirely wrong direction, then a discontinuous directional change such as branching is elicited. Pathways are corrected in this way, and near the appropriate target position the terminal arbour is formed because from there all routes point towards less optimal positions, leading to multiple branching.


2021 ◽  
Vol 288 (1949) ◽  
Author(s):  
Ratan Othayoth ◽  
Qihan Xuan ◽  
Yaqing Wang ◽  
Chen Li

To traverse complex three-dimensional terrain with large obstacles, animals and robots must transition across different modes. However, the most mechanistic understanding of terrestrial locomotion concerns how to generate and stabilize near-steady-state, single-mode locomotion (e.g. walk, run). We know little about how to use physical interaction to make robust locomotor transitions. Here, we review our progress towards filling this gap by discovering terradynamic principles of multi-legged locomotor transitions, using simplified model systems representing distinct challenges in complex three-dimensional terrain. Remarkably, general physical principles emerge across diverse model systems, by modelling locomotor–terrain interaction using a potential energy landscape approach. The animal and robots' stereotyped locomotor modes are constrained by physical interaction. Locomotor transitions are stochastic, destabilizing, barrier-crossing transitions on the landscape. They can be induced by feed-forward self-propulsion and are facilitated by feedback-controlled active adjustment. General physical principles and strategies from our systematic studies already advanced robot performance in simple model systems. Efforts remain to better understand the intelligence aspect of locomotor transitions and how to compose larger-scale potential energy landscapes of complex three-dimensional terrains from simple landscapes of abstracted challenges. This will elucidate how the neuromechanical control system mediates physical interaction to generate multi-pathway locomotor transitions and lead to advancements in biology, physics, robotics and dynamical systems theory.


Modern developments of atomic theory have required alterations in some of the most fundamental physical ideas. This has resulted in its being usually easier to discover the equations that describe some particular phenomenon than just how the equations are to be interpreted. The quantum mechanics of Heisenberg and Schrodinger was first worked out for a number of simple examples, from which a general mathematical scheme was constructed, and afterwards people were led to the general physical principles governing the interpretation, such as the superposition of states and the indeterminacy principle. In this way a satisfactory non-relativistic quantum mechanics was established.


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