**James Overduin, Richard Conn Henry**

Pythagoras’ theorem lies at the heart of physics as well as mathematics, yet its historical origins are obscure. We highlight a purely pictorial, gestalt-like proof that may have originated during the Zhou Dynasty. Generalizations of the Pythagorean theorem to three, four and more dimensions undergird fundamental laws including the energy-momentum relation of particle physics and the field equations of general relativity, and may hint at future unified theories. The intuitive, “pre-mathematical” nature of this theorem thus lends support to the Eddingtonian view that “the stuff of the world is mind-stuff.”

Read more https://arxiv.org/abs/2005.10671

# Category Archives: History and Philosophy of Physics

# Memory and entropy

**Carlo Rovelli**

I study the physical nature of traces (or memories). Surprisingly, (i) systems separation with (ii) temperature differences and (iii) long thermalization times, are sufficient conditions to produce macroscopic traces. Traces of the past are ubiquitous because these conditions are largely satisfied in our universe. I quantify these thermodynamical conditions for memory and derive an expression for the maximum amount of information stored in such memories, as a function of the relevant thermodynamical parameters. This mechanism transforms low entropy into available information.

Read more at https://arxiv.org/pdf/2003.06687.pdf

# Roland Eotvos: scientist, statesman, educator

**András PATKÓS**, Institute of Physics, Eötvös University

This lecture recalls the memory of Baron Roland Eötvös, an outstanding figure of the experimental exploration of the gravitational interaction and “funding father” of applied geophysics. Beyond the scientific achievements his contribution to the development of the modern Hungarian schooling and higher educational system, most importantly, the foundation of an innovative institution of teacher’s training did not lose its contemporary significance. This lecture has been invited by the organizers of this Conference in response to the decision of UNESCO to commemorate worldwide the death centenary of the most outstanding Hungarian experimental physicist of modern times.

Read more at https://arxiv.org/ftp/arxiv/papers/2002/2002.05743.pdf

# Joseph Polchinski: A Biographical Memoir

**Raphael Bousso, Fernando Quevedo, Steven Weinberg**

Joseph Polchinski (1954-2018), one of the the leading theoretical physicists of the past 50 years, was an exceptionally broad and deep thinker. He made fundamental contributions to quantum field theory, advancing the role of the renormalization group, and to cosmology, addressing the cosmological constant problem. Polchinski’s work on D-branes revolutionized string theory and led to the discovery of a nonperturbative quantum theory of gravity. His recent, incisive reformulation of the black hole information paradox presents us with a profound challenge. Joe was deeply devoted to his family, a beloved colleague and advisor, an excellent writer, and an accomplished athlete.

Read more at https://arxiv.org/pdf/2002.02371.pdf

# Maxwell’s Demon and Its Fallacies Demystified

**Milivoje M. Kostic**

A demonic being, introduced by Maxwell, to miraculously create thermal non-equilibrium and violate the Second law of thermodynamics, has been among the most intriguing and elusive wishful concepts for over 150 years. Maxwell and his followers focused on ‘effortless gating’ a molecule at a time, but overlooked simultaneous interference of other chaotic molecules, while the demon exorcists tried to justify impossible processes with misplaced ‘compensations’ by work of measurements and gate operation, and information storage and memory erasure with entropy generation. The illusive and persistent Maxwell’s demon fallacies by its advocates, as well as its exorcists, are scrutinized and resolved here. Based on holistic, phenomenological reasoning, it is deduced here that a Maxwell’s demon operation, against natural forces and without due work effort to suppress interference of competing thermal particles while one is selectively gated, is not possible at any scale, since it would be against the physics of the chaotic thermal motion, the latter without consistent molecular directional preference for selective timing to be possible. Maxwell’s demon would have miraculous useful effects, but also some catastrophic consequences.

Read more at https://arxiv.org/ftp/arxiv/papers/2001/2001.10083.pdf

# Nonconservation of Energy and Loss of Determinism

**I. Infinitely Many Balls**

**David Atkinson, Porter Johnson**

An infinite number of elastically colliding balls is considered in a classical, and then in a relativistic setting. Energy and momentum are not necessarily conserved globally, even though each collision does separately conserve them. This result holds in particular when the total mass of all the balls is finite, and even when the spatial extent and temporal duration of the process are also finite. Further, the process is shown to be indeterministic: there is an arbitrary parameter in the general solution that corresponds to the injection of an arbitrary amount of energy (classically), or energy-momentum (relativistically), into the system at the point of accumulation of the locations of the balls. Specific examples are given that illustrate these counter-intuitive results, including one in which all the balls move with the same velocity after every collision has taken place.

Read more at https://arxiv.org/pdf/1908.10458.pdf

**II: Colliding with an Open Set**

An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite number of elements. With this restriction indeterminism, energy non-conservation and (creatio ex nihilo) no longer occur. A numerical analysis of finite systems of colliding balls is given, and the asymptotic behavior that corresponds to the potentially infinite system is inferred.

Read more at https://arxiv.org/pdf/1908.09865.pdf

# Exploring Gravitational Lensing

**Tilman Sauer, Tobias Schütz**

In this article, we discuss the idea of gravitational lensing, from a systematic, historical and didactic point of view. We show how the basic lensing equation together with the concepts of geometrical optics opens a space of implications that can be explored along different dimensions. We argue that Einstein explored the idea along different pathways in this space of implication, and that these explorations are documented by different calculational manuscripts. The conceptualization of the idea of gravitational lensing as a space of exploration also shows the feasibility of discussing the idea in the classroom using some of Einstein’s manuscripts.

Read more https://arxiv.org/pdf/1905.07174.pdf