The Mechanical Universe...and Beyond

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Science Documentary hosted by Aaron Fletcher, published by CPB in 1986 - English narration

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The Mechanical Universe...and Beyond This series helps teachers demystify physics by showing students what it looks like. Field trips to hot-air balloon events, symphony concerts, bicycle shops, and other locales make complex concepts more accessible. Inventive computer graphics illustrate abstract concepts such as time, force, and capacitance, while historical re-enactments of the studies of Newton, Leibniz, Maxwell, and others trace the evolution of theories. The Mechanical Universe helps meet different students' needs, from the basic requirements of liberal arts students to the rigorous demands of science and engineering majors. This series is also valuable for teacher professional development.

[edit] Introduction

Provocative questions begin the quest of The Mechanical Universe. This introductory preview enters an Aristotelian world in conflict, introduces the revolutionary ideas and heroes from Copernicus through Newton, and, like a space shuttle from past to present, links the physics of the heavens to the physics of the Earth.

[edit] Derivatives

The function of mathematics in physical science. From a theoretical concept to a practical tool, the derivative helps to determine the instantaneous speed and acceleration of a falling body. Differentiation is developed further to calculate how any quantity changes in relation to another. The power rule, the product rule, the chain rule -- with a few simple rules, differentiating any function becomes a simple mechanical task.

[edit] The Law of Falling Bodies

With the conventional wisdom of the Aristotelian world view, almost everyone could see that heavy bodies fell faster than lighter ones. Then along came Galileo. His genius deduced that the distance a body has fallen at any instant is proportional to the square of the time spent falling. From that, speed and acceleration follow with the help of a mathematical tool called a derivative

[edit] Inertia

The rise of Galileo and his fall from grace. Copernicus conjectured that the Earth spins on its axis and orbits around the sun. Considering its implications, a rather dangerous assumption that prompted rather risky questions: Why do objects fall to Earth rather than hurtle off into space? And in this heretical scheme of things in which the Earth wasn't at the center, where was God? Risking more than his favored status in Rome, Galileo helped to answer such questions with the law of inertia.

[edit] Vectors

Physics must explain not only why and how much, but also where and which way. Physicists and mathematicians invented a way of describing quantities that have direction as well as magnitude. Laws that deal with such phenomena as distance and speed are universal. And vectors, which describe quantities such as displacement and velocity, universally express the law of physics in a way that is the same for all coordinate systems.

[edit] Newtons Laws

For all the phenomena of The Mechanical Universe, Isaac Newton laid down the laws. A refinement on Galileo's law of inertia, Newton's first law states that every body remains at rest or continues in uniform motion unless an unbalanced force acts on it. His second law, the most profound statement in classical mechanics, relates the causes to the changes of motion in every object in the cosmos. Newton's third law explains the phenomenon of interactions: for every action, there's an equal and opposite reaction.

[edit] Integration

Newton and Leibniz sprint for the calculus. Winning the longest race in scientific history -- more than 2000 years, from the Golden Age of Greece to the end of the seventeenth century in Europe -- Newton and Leibniz arrived at the conclusion that differentiation and integration are inverse processes. Their exciting intellectual discovery, dramatically rerun to reflect the times, ended in an extremely controversial dead heat.

[edit] The Apple and the Moon

The first authentic steps toward outer space. Seeking an explanation for Kepler's laws, Newton discovered that gravity described the force between any two particles in the universe. From an English orchard to Cape Canaveral and beyond, Newton's universal law of gravity reveals why an apple but not the moon falls to the Earth.

[edit] Moving in Circles

The original Platonic ideal, with derivatives of vector functions. According to Plato, stars are heavenly beings that orbit the Earth with uniform perfection -- uniform speed and perfect circles. Even in this imperfect world, uniform circular motion make perfect mathematical sense.

[edit] Fundamental Forces

All physical phenomena of nature are explained by four forces. Two nuclear forces -- strong and weak -- dwell within the atomic nucleus. The fundamental force of gravity granges across the universe at large. So does electricity, the fourth fundamental force, which binds the atoms of all matter.

[edit] Gravity Electricity Magnetism

Forces at play in the Physics Theater. The gravitational force between two masses, the electric force between two charges, and the magnetic force between two magnetic poles -- all these forces take essentially the same mathematical form. Newton's script suggested connections between electricity and magnetism. Acting on scientific hunches, Maxwell saw the matter in an entirely new light.

[edit] The Millikan Experiment

How does science progress? Through painstaking trial and error, illustrated with a dramatic re-creation of Robert Millikan's classic oil-drop experiment. Understanding the electric force on a charged droplet and viscosity, the measured the charge of a single electron.

[edit] Conservation of Energy

The myth of the energy crisis. According to one of the major laws of physics, energy is neither created nor destroyed.

[edit] Potential Energy

The nature of stability. Potential energy provides a clue, and a powerful model, for understanding why the world has worked the same way since the beginning of time.

[edit] Conservation of Momentum

If The Mechanical Universe is a perpetual clock, what keeps it ticking away till the end of time? Taking a cue from Descartes, momentum -- the product of mass and velocity -- is always conserved. Newton's laws embody the concept of conservation and momentum. This law provides a powerful principle for analyzing collisions, even at the local pool hall.

[edit] Harmonic Motion

The music and mathematics of nature. The restoring force and inertia of any stable mechanical system cause objects to execute simple harmonic motion, a phenomenon that repeats itself in perfect time.

[edit] Resonance

The music and mathematics of nature, Part II. As Galileo noted, the swings of a pendulum increasingly grow with repeated, timed applications of a small force. When the frequency of an applied force matches the natural frequency of a system, large-amplitude oscillations result in the phenomenon of resonance. Resonance explains why a swaying bridge collapsed in a mild wind, and how a wineglass can be shattered by a human voice.

[edit] Waves

The medium disturbances of nature. With an analysis of simple harmonic motion and a stroke of genius, Newton extended mechanics to the propagation of sound.

[edit] Angular Momentum

An old momentum with a new twist. Kepler's second law of planetary motion, which is rooted here in a much deeper principle, imagined a line from the sun to a planet that sweeps out equal areas in equal times. Angular momentum is a twist on momentum -- the cross product of the radius vector and momentum. A force with twist is torque. When no torque acts on a system, the angular momentum of the system is conserved.

[edit] Torques and Gyroscopes

Why a spinning top doesn't topple. When a torque acts on a spinning object, the angular momentum changes, but the object only precesses. The object may be a child's toy, or a part of a navigation system, or Earth itself.

[edit] Keplers Three Laws

The wandering mathematician. Kepler's three laws described the motion of heavenly bodies with unprecedented accuracy. However, the planets still moved in paths traced by the ancient Greek mathematicians -- the conic section called an ellipse.

[edit] The Kepler Problem

The combination of Newton's law of gravity and F = ma. The task of deducing all three of Kepler's laws from Newton's universal law of gravitation is known as the Kepler problem. Its solution is one of the crowning achievements of Western thought.

[edit] Energy and Eccentricity

The precise orbit of any heavenly body -- a planet, asteroid, or comet -- is fixed by the laws of conservation of energy and angular momentum. The eccentricity, which determines the shape of an orbit, is intimately linked to the energy and angular momentum of the heavenly body.

[edit] Navigating in Space

Getting from here to there. Voyages to other planets require enormous expenditures of energy. However, the amount of energy expended can be minimized by using the same principles that guide planets around the solar system.

[edit] From Kepler to Einstein

The orbiting planets, the ebbing and flowing of tides, the falling body as it accelerates -- these phenomena are consequences of the law of gravity. Why that's so leads to Einstein's general theory of relativity, and into the black hole, but not back out again.

[edit] Harmony of the Spheres

A last lingering look back at mechanics to see new connections between old discoveries.

[edit] Beyond the Mechanical Universe

Provocative questions begin the quest of Beyond The Mechanical Universe. This introductory preview enters the world of Electricity and Magnetism, goes on to 20th-century discoveries of Relativity and Quantum mechanics. The brilliant ideas of Faraday, Ampere, Maxwell, Einstein, Schrödinger, Heisenberg add to The Mechanical Universe of Newton.

[edit] Static Electricity

To understand materials, one must first understand electricity, and to understand electricity, one must first understand materials. Eighteenth century electricians understood neither, but they knew what it took to spark the interest of an audience and put on an electrifying show. Coulomb's law and the principles of static electricity.

[edit] The Electric Field

Michael Faraday's vision of lines of constant force in space laid the foundation for the modern idea of the field of force. Electric fields of static charges; Gauss' law and the conservation of flux.

[edit] Potential and Capacitance

Benjamin Franklin, the great 18th-century American scientist, who later dabbled in politics, was the first to propose a successful theory of the Leyden Jar. He gave positive and negative charges their names, and invented the parallel plate capacitor. Electrical potential, the potential of charged conductors, equipotentials and capacitance.

[edit] Voltage Energy and Force

In a world of electric charges and currents, field, forces and voltages, what really matters? When is electricity dangerous or benign, spectacular or useful? The electric potential and its gradient; the potentials of atoms and metals; electric energy, and why sparks jump.

[edit] The Electric Battery

Electricity changed from a curiosity to a central concern of science and technology in 1800, when Alessandro Volta invented the electric battery. Batteries make use of the internal properties of different metals to turn chemical energy directly into electric energy.

[edit] Electric Circuits

Design and analysis of currents flowing in series and parallel circuits of resistors and capacitors depend not only on the celebrated laws of Ohm and Kirchhoff, but also on the less celebrated work of Charles Wheatstone.

[edit] Magnetism

William Gilbert, personal physician by appointment to her Majesty Queen Elizabeth I of England, discovered that the earth behaves like a giant magnet. Magnetism as a natural phenomenon, the behavior of magnetic materials, and the motion of charged particles in a magnetic field.

[edit] The Magnetic Field

All magnetic fields can be thought to be produced by electric currents. The relationship between a current and the magnetic field it produces is a little peculiar geometrically, and takes some getting used to. The law of Biot and Sarvart, the force between electric currents, and Ampere's law.

[edit] Vector Fields and Hydrodynamics

At first glance, replacing the old idea of action at a distance by the new idea of the field of force seems to e an exercise in semantics. But it isn't, because fields have definite properties of their own suitable for scientific study. For example, electric fields are different in form from magnetic fields, and both kinds can better be understood by analogy to field of fluid flow.

[edit] Electromagnetic Induction

After Oersted's 1820 discovery that electric currents create magnetism, it was obvious that in some way magnetism should be able to create electric currents. The discovery of electromagnetic induction, in 1831, by Michael Faraday and Joseph Henry was one of the most important of the 19th century, not only scientifically, but also technologically, because it is the means by which nearly all electric power is generated today.

[edit] Alternating Current

Electromagnetic induction makes it easy and natural to generate alternating current. Use of transformers makes it practical to distribute ac over long distances. Although Nikola Tesla understood all this, Thomas Edison chose not to, and thereby hangs a tale. Alternating current circuits obey a differential equation identical to the harmonic oscillator resonance equation.

[edit] Maxwells Equations

By the 1860s all the pieces of the electricity and magnetism puzzle were in place, except one. The last piece, discovered by James Clerk Maxwell and called (unfortunately) the displacement current was just what was needed to produce electromagnetic waves called (among other things) light.

[edit] Optics

Maxwell's theory says that electromagnetic waves of all wavelengths, from radio waves to gamma-rays and including visible light, are all basically the same phenomenon. Many of the properties of light are really just properties of waves, including reflection, refraction and diffraction. Ordinary light can be used to see things on a human scale, X-rays to "see" things on an atomic scale.

[edit] The Michelson Morley Experiment

In 1887, in Cleveland, Ohio, an exquisitely designed measurement of the motion of the earth through the aether resulted in the most brilliant failure in scientific history.

[edit] The Lorentz Transformation

If the speed of light is to be the same for all inertial observers (as indicated by the Michelson-Morley experiment) the equations for time and space are not difficult to find. But what do they mean? They mean that the length of a meter stick, or the rate of ticking of a clock depends on who measure it.

[edit] Velocity and Time

Unlike Lorentz, Albert Einstein was motivated to perfect the central ideas of physics rather than to explain the Michelson-Morley experiment. The result was a wholly new understanding of the meaning of space and time, including such matters as the transformation of velocities, time dilation, and the twin paradox.

[edit] Energy Momentum and Mass

The new meaning of space and time make it necessary to formulate a new mechanics. Starting from the conservation of momentum, it turns out among other things that E = mc 2.

[edit] Temperature and the Gas Law

The ups and downs of scientific research are reflected in Boyle's experiments, and Charles' investigations. Hot new discoveries about the behaviours of gases make the connection between temperature and heat, and raise the possibility of an absolute scale.

[edit] The Engine of Nature

The Carnot engine, part one, beginning with simple steam engines.

There was a young man named Carnot
Whose logic was able to show
For a work source proficient
There's none so efficient
As an engine that simply won't go.

[edit] Entropy

This program illustrates the genius of Carnot, Part II, and the second law of thermodynamics. The efficiency of Carnot's ideal engine depends on the ratio between high and low temperatures in the running cycle. Carnot's theory begins with simple steam engines and ends with profound implications for the behavior of matter and the flow of time throughout the universe.

[edit] Low Temperatures

Solids, liquids, and gases are the substance of every substance in the physical world. With the quest for low temperatures came the discovery that, under the right conditions of temperature and pressure, all elements can exist in each of the basic states of matter.

[edit] The Atom

This program explores the history of the atom, from the ancient Greeks to the early 20th century, when discoveries by J.J. Thomson and Ernest Rutherford created a new crisis for the world of physics.

[edit] Particles and Waves

Even before the crisis of the atom, there was evidence that light, which was certainly a wave, could sometimes act like a particle. In the new physics, called quantum mechanics, not only does light come in quanta called photons, but electrons and other particles also interfere like waves.

[edit] Atoms to Quarks

Electron waves confined by electric attraction to the nucleus help resolve the dilemma of the atom and account for the periodic table of the elements. Nucleons themselves obey a kind of period table, following inner rules that lead to the idea of quarks.

[edit] The Quantum Mechanical Universe

A last, lingering look at where we've been, and perhaps a timid glance into the future, marks the close of the series The Mechanical Universe and Beyond....