Newtonianism

Newtonianism is a philosophical and scientific doctrine based on Isaac Newton's ideas and methods. It describes the universe as governed by rational and understandable laws based on mechanistic principles, emphasizing the primacy of mathematical formalism in modeling natural phenomena.

Isaac Newton was an empiricist, meaning that he rejected speculative knowledge about the world for sake of observation and experimentation. He famously said, "Hypotheses non fingo" ("I frame no hypotheses"), meaning that there should be no speculative hypotheses without any empirical base in science.

Newton's writings reveal his deep knowledge of early Church teachings. He sided with Arius in the Athanasius-Arius conflict over the Trinity, viewing Christ as a divine mediator subordinate to God. He considered the worship of Christ as God to be idolatry, the fundamental sin. Newton's religious studies were extensive, producing works on biblical criticism and prophecy. For example, he dated biblical apocalypse for 2060 AD through analysis of the scripture.

Newton rejected the pantheism of Spinoza, advocating for an ordered universe understood through reason. He believed in evidence of divine design in the universe, though he acknowledged that divine intervention was necessary to correct instabilities over time. This view was mocked by Leibniz, who argued for a self-sustaining universe.

According to Newton, structure of the world can be explained mathematically. He considered God to be creator of the universe, which perfectly tuned all physical aspects of the world through divine reason.

Newton built his view of the universe based on Cartesian mechanism, but he rejected fully materialistic philosophy, claiming that God isn't passive, distant creator, but sometimes intervenes to stabilize the world if necessary.

Newton argued that space and time are absolute, unchanging and independent from perception.^[2] Spacetime in Newtonian physics and philosophy is static, eternal and existing entirely even without any relational or perceived object. This approach to spacetime differs from his contemporaries, such as Leibniz and Berkeley.

While Newton wanted there to be a preferred frame, his own laws of motion made it impossible to detect. Because the laws are the same in all inertial frames (frames moving at constant velocity), there is no experiment you can do to prove you are "at rest" versus "moving constantly." Newton realized that if you have one inertial frame, any other frame moving at a constant velocity relative to it is also inertial. This principle, known as Galilean Relativity, means the physics doesn't tell you which frame is "truly" at rest. Therefore, while Newton himself believed that absolute space and time existed, he acknowledged that the only measures of space or time accessible to experiment are relative.

Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. While Gottfried Wilhelm Leibniz was the first to clearly state the rules of calculus, Isaac Newton developed the use of calculus in his laws of motion and universal gravitation.

Newton's laws of motion are three fundamental principles that describe how objects move and interact with forces. These laws, first presented in his 1687 work Philosophiæ Naturalis Principia Mathematica, can be summarized as follows:

1. Law of Inertia: An object remains at rest or moves at a constant speed in a straight line unless acted upon by a force.
2. Law of Acceleration: The net force on an object equals its mass times its acceleration, or the rate of change of its momentum.
3. Law of Action and Reaction: When two objects exert forces on each other, the forces are equal in magnitude and opposite in direction.

The first law was a refinement of existing work by Galileo Galilei and René Descartes, while the second and third laws were developed in order to mathematically prove why planets move in ellipses.

Aristotle observed that moving objects on Earth eventually come to rest. He described two kinds of motion: "violent" or "unnatural motion", such as that of a thrown stone, and "natural motion", such as that of a falling object. For violent motion, as soon as the agent stops causing it, the motion stops also: in other words, the natural state of an object is to be at rest (since Aristotle did not address friction). He concluded rest was the "natural" state, and motion required a continuous cause, like air pushing a projectile forward. Hipparchus later found Aristotle's air-push explanation incoherent, reasoning that the same medium could not both sustain motion and resist it. Instead, he proposed that the throwing force is transferred directly into the projectile itself at the moment of release, dissipating gradually.^[3] Still, this left unexplained why motion persisted at all once contact ceased, and Philoponus instead proposed that the thrower imparts an internal impetus, making motion a property of the body rather than the medium.^[4]

Avicenna agreed that an impetus is imparted to a projectile by the thrower, but unlike Philoponus, who believed that it was a temporary virtue that would decline even in a vacuum, he viewed it as persistent, requiring external forces such as air resistance to dissipate it. Avicenna made distinction between "force" and "inclination" (mayl), and argued that an object gained mayl when the object is in opposition to its natural motion. Therefore, he concluded that continuation of motion is attributed to the inclination that is transferred to the object, and that object will be in motion until the mayl is spent. He also claimed that a projectile in a vacuum would not stop unless it is acted upon, which is consistent with Newton's concept of inertia.

The first one to grasp this persistent motion by itself was William of Ockham. Applying Ockham's Razor, the principle that if a body is already moving, no secondary "thing" is needed to explain its persistence, Jean Buridan transformed earlier concepts into a quantitative impetus theory, defining impetus as proportional to speed and mass.^[5][6] Being influenced by Beeckman that all objects without external interference move indefinitely in a straight line, and seeking a mechanical philosophy based on clear principles, René Descartes formulated his First Law of Nature as "Each thing, insofar as it is simple and undivided, remains in the same state as far as it can, and never changes except by external causes." Descartes explicitly endorsed straight-line inertial motion, assumed a plenum (no vacuum), and explained planetary orbits through vortices.

Newton's revolutionary idea was to redefine uniform motion not as an effect requiring a cause, but as a state identical to rest, meaning force is only necessary to change a state, via acceleration or deceleration, rather than to maintain it. For this, Newton adopted Galileo's idea of inertia, referring to it as "innate motive force,"^[7] and reframed it as a fundamental property of persistence: Every body perseveres in its state of rest, or of uniform motion in a straight line, unless it is compelled to change by forces impressed upon it. He required this axiom to define an inertial frame—the reference state against which forces (such as gravity) could be measured. To Newton, an inertial frame was a frame that was either at rest or moving at a constant speed relative to absolute space. Without that reference state, he felt he couldn't justify why things moved in straight lines or why centrifugal forces happened.^[8] The modern understanding of Newton's first law is that no inertial observer is privileged over any other. It is a special case of the second law, derived by setting the net force to zero.

Newton's Law of Acceleration is mainly due to Kepler's data of planetary orbits as well as Galileo's and Huygens' experiments which determined the equations for a body undergoing uniform acceleration and centripetal acceleration, respectively. Newton, much like Descartes, viewed circular motion as a "state of equilibrium" between opposing forces. This perspective relied on the existence of "innate forces," balancing the external pull of gravity (centripetal force) against an inherent internal "entity" known as centrifugal force. Newton initially used this balance to fulfill the principle of inertia, however, he moved away from this "equilibrium" model by introducing mass as the universal constant of proportionality. This allowed him to redefine force not as an inherent property of an object, but as an external agent acting upon it.

The Law of Acceleration is usually presented as a definition of force, i.e., a force is that which exists when an inertial observer sees a body accelerating. This is sometimes regarded as a potential tautology (acceleration implies force, force implies acceleration). To break this circular logic, specific independent force laws, like universal gravitation, must be applied. By inserting such an expression for force into Newton's second law, an equation with predictive power can be written.

In the late 1660s, the collective work of Johannes Wallis, Christopher Wren, and Christiaan Huygens had firmly established that in a closed system of colliding bodies, the total momentum is always conserved. Newton's original contribution was applying this law to action-at-a-distance forces like gravity. Newton reasoned that if momentum is conserved in a system, then the net change of momentum is zero. According to the Law of Acceleration, force is defined as that which changes momentum. Therefore, for the total momentum of the system to remain unchanged, the net internal force within that system must be zero.^[9]

The labels "action" and "reaction" have the misleading suggestion of causality, as if the "action" is the cause and "reaction" is the effect. It is therefore easy to think of the second force as being there because of the first, and even happening some time after the first. In reality, these forces are simultaneous and symmetric. While human volition (like kicking a ball) makes it feel like the player's strike is the "action" and the force by the ball on the player the "reaction," the physics treats the interaction as a single event where labels can be flipped without changing the analysis. Overly brief paraphrases of the third law, like "action equals reaction", may also cause misunderstanding because the "action" and "reaction" apply to different bodies. For example, consider a book at rest on a table. The Earth's gravity pulls down upon the book. The "reaction" to that "action" is not the support force from the table holding up the book, but the gravitational pull of the book acting on the Earth.

Newtonian Mechanics is based on Newton's laws of motion. Newton and most of his contemporaries hoped that through a unified mechanical theory they would be able to explain all entities, including (in the form of geometric optics) light. Over time, additional concepts like energy further developed Newtonian mechanics. However, Newton's laws have limitations, requiring new theories for objects moving at high speeds (special relativity), very massive objects (general relativity), or very small particles (quantum mechanics).

A force in physics is anything that causes an object's velocity to change, that is, making it accelerate. Forces come from fields like electrostatic (from static electrical charges), electromagnetic (from moving charges), or gravitational (from mass).

Newton was the first to mathematically express the relationship between force and momentum. Some physicists interpret Newton's second law of motion as a definition of force and mass, while others consider it a fundamental postulate, a law of nature.^[10] Either interpretation has the same mathematical consequences. So long as the force acting on an object is known, Newton's second law is sufficient to describe the motion of an object. Once independent relations for each force acting on an object are available, they can be substituted into Newton's second law to obtain an ordinary differential equation, which is called the equation of motion.

Newton's third law can be used to deduce the forces acting on an object when in a closed system. If it is known that one object exerts a force on another object, it follows that the second must exert an equal and opposite reaction force on the first. Conservative forces are defined as forces for which the work done in moving an object between two points is independent of the path taken. The strong form of Newton's third law requires that these forces act along the line connecting the two objects, and these forces are defined as central forces. However, central forces are an approximation since objects that are at rest are only at rest with respect to one another. This limitation to Newton's third law can be shown using the Coulomb force, where charges must remain stationary with respect to a nonaccelerating frame of reference.

When dealing with non-central forces like the Lorentz force, the weak form of Newton's third law is used by identifying conservation of momentum. Illustrations of the weak form of Newton's third law can be found for magnetic forces like the Lorentz force while discussing the curl or cross product of vectors. Thus, the forces acting on objects cannot be identified without accounting for relative acceleration and direction by utilizing reference frames.

Work and energy are closely related because the energy from the object doing work is transferred to the other objects it interacts with when work is being done. The work-energy principle states that an increase in the kinetic energy of a rigid body is caused by an equal amount of positive work done on the body by the resultant force acting on that body. Conversely, a decrease in kinetic energy is caused by an equal amount of negative work done by the resultant force. Thus, if the net work is positive, then the object's kinetic energy increases by the amount of the work. If the net work done is negative, then the object's kinetic energy decreases by the amount of work.

Conservative forces, like gravity or spring forces, can be described using potential energy. This energy is stored and can be converted into kinetic energy when the object moves. Conservation of energy says that the total energy, the sum of kinetic and potential energy, remains constant over time.

After Kepler had produced his laws of planetary motion, Newton developed the idea that these laws must also apply to the orbit of the Moon around the Earth and subsequently to all objects on Earth. Newton's law of universal gravitation combined his laws of motion with new mathematical analysis to explain Kepler's empirical results. It describes gravity as a force by stating that every object in the universe attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This means objects attract each other as if all their mass were concentrated at their centers.

Newton himself was famously deeply unsettled by the fact that his law required gravity to act instantaneously across any distance. Because the formula does not contain a variable for time, if the Sun were to suddenly disappear, the Earth would feel the loss of gravitational pull immediately. This contradicts the modern understanding (from Special Relativity) that no information or influence can travel faster than the speed of light.

By the 19th century, astronomers noticed a tiny but persistent error in the predicted orbit of Mercury. Mercury's elliptical orbit rotates (precesses) over time. While Newton's formula accounted for the pull of other planets, there was a remaining shift of about 43 arcseconds per century that his theory could not explain. This discrepancy occurs because Mercury is so close to the Sun that the intense gravitational field requires the more precise description of gravity that would ultimately be provided by Einstein's general relativity.

• Christianity - This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. But trinitarianism is not real.
• Classical Liberalism - I was a Whig in the United Kingdom.

• Cartesianism - Your vortex theory is flawed, but at least you are a mechanist.
• Einsteinianism - Improved on my work. Wait a minute, you're an agnostic
• Aristotelianism - You were good, but objects don't have a desire to stay at rest!

• Atheism - You are all senseless. Look at the solar system. That cannot have formed by chance.
• Catholicism - The trinity is a false teaching!
• Leibnizianism - I am the inventor of calculus!
• Wolffianism - Too abstract for a science.

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• Newtonianism
• Newton's law of universal gravitation

• The little known story of F = ma and beyond by Amitabha Ghosh
• Newton’s generalized form of second law gives F=ma by Ajay Sharma