Hamilton, Hamiltonian Mechanics, and Causation

Hamiltonian Mechanics is not a mere development of Newtonian Mechanics, but is a true "revolution." It introduces significantly new notions and has new applications relative to Newtonian mechanics. It is not equivalent to Newtonian mechanics in several senses. Various accounts of Equivalence in philosophy of science literature are considered.

Erkenntnis, 1981

Cambridge History of Philosophy of the Scientific Revolution, 2022

2011

One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is yes: I state and prove two technical results, inspired by simple physical arguments about the generic properties of classical systems, to the effect that, in a precise sense, classical systems evince exactly the geometric structure Lagrangian mechanics provides for the representation of systems, and none that Hamiltonian mechanics does. The argument not only clarifies the conceptual structure of the two systems of mechanics, their relations to each other, and their respective mechanisms for representing physical systems. It also provides a decisive counter-example to the semantical view of physical theories, and one, moreover, that shows its crucial deficiency: a theory must be, or at least be founded on, more than its collection of models (in the sense of Tarski), for a complete semantics requires that one take account of global structures defined by relations among the individual models. The example also shows why naively structural accounts of theory cannot work: simple isomorphism of theoretical and empirical structures is not rich enough a relation to ground a semantics. † I thank Robert Geroch for many stimulating conversations in which the seeds of this paper's technical arguments were germinated and, in some cases, fully cultivated. I also thank John Norton for making me explain the technical arguments to him with enough care and thoroughness so as to allow him to offer many useful suggestions about how to give them a simpler, more digestible form, without the need for heavy machinery throughout. I am grateful to Chris Pincock for stimulating and edifying conversations about the semantical view of physical theories, in which he set straight a few misunderstandings I had.

Hamiltonian mechanics is a genuine revolution in physics, not a mere application or version of Newtonian mechanics. Hamilton was heavily influenced by Kant in his understandings of mathematics and physics.

Amazon, 2020

Physics: from the Beginning to Now: History, Philosophy, and Science, Volume I: Classical Mechanics Physics: from the Beginning to Now, have been attempted to consider historical physics events, but this is not the history of physics. But in this book, it has been so focused on the evolution of physic science to explain the development of ideas leading to physical discoveries. Philosophical arguments have been discussed alongside historical events to make the philosophy of physics ornamental of its scientific content. However, this book cannot be considered as philosophical. A deep understanding of the science of physics, regardless of its historical trends and philosophical attitudes, diminishes the attraction of this fundamental knowledge. https://www.amazon.com/gp/product/B08FGK23MK/ref=dbs_a_def_rwt_bibl_vppi_i1

Encyclopedia

This entry presents a historical view of the meaning attributed to the terms mechanics and natural philosophy, from a hint to ancient Greece, the Middle Ages, and the Renaissance to a special focus on the 18th Century, which represents a turning point for the development of modern physics and science in general. Since we are not concerned with the summation of the histories of natural philosophy and mechanics, but only with their interrelations, this makes a detailed description of the two disciplines unnecessary.

The British Journal for the Philosophy of Science, 2014

One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is yes: I state and prove two technical results, inspired by simple physical arguments about the generic properties of classical systems, to the effect that, in a precise sense, classical systems evince exactly the geometric structure Lagrangian mechanics provides for the representation of systems, and none that Hamiltonian mechanics does. The argument not only clarifies the conceptual structure of the two systems of mechanics, their relations to each other, and their respective mechanisms for representing physical systems. It also provides a decisive counter-example to the semantical view of physical theories, and one, moreover, that shows its crucial deficiency: a theory must be, or at least be founded on, more than its collection of models (in the sense of Tarski), for a complete semantics requires that one take account of global structures defined by relations among the individual models. The example also shows why naively structural accounts of theory cannot work: simple isomorphism of theoretical and empirical structures is not rich enough a relation to ground a semantics. † I thank Robert Geroch for many stimulating conversations in which the seeds of this paper's technical arguments were germinated and, in some cases, fully cultivated. I also thank John Norton for making me explain the technical arguments to him with enough care and thoroughness so as to allow him to offer many useful suggestions about how to give them a simpler, more digestible form, without the need for heavy machinery throughout. I am grateful to Chris Pincock for stimulating and edifying conversations about the semantical view of physical theories, in which he set straight a few misunderstandings I had.

HOPOS: The Journal of the International Society for the History of Philosophy of Science , 2013

Although Newton carefully eschews questions about gravity’s causal basis in the published Principia, the original version of his masterwork’s third book contains some intriguing causal language. “These forces”, he writes, “arise from the universal nature of matter”. Such remarks seem to assert knowledge of gravity’s cause, even that matter is capable of robust and distant action. Some commentators defend that interpretation of the text – a text whose proper interpretation is important, since Newton’s reasons for suppressing it strongly suggest that he continued to endorse its ideas. This article argues that the surface appearance of Newton’s causal language is deceptive. What, then, does Newton intend with his causal language if not a full causal hypothesis? His remarks actually indicate a way of considering the force mathematically, something he contrasts to the structure of the force as it really is, in nature. In explaining that, he identifies a notable disjunction between the physical force itself and mathematical ways of considering it; and the text’s signifiance therefore lies in its view of the force’s structure and in the questions raised about the relationship between mathematical representations and the physical world.

2001

It is well known that classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanism. In this article the basic assumptions which underlie those features are discussed. It is shown that these basic assumptions -though universally assumed up to the beginning of the 20th century -are far from obvious. Finally it is shown that -to a certain extent -there is nothing wrong in assuming these basic postulates. Rather, the error lies in the epistemological absolutization of the theory, which was considered as a mirroring of Nature.