The Life and Science of Albert Einstein Lecture 1 - Setting the stage Handout: Physics chapter from "The Development of the Sciences" Regimes of applicability of various physical theories: ======================================================= Humans exist in the Classical World. The characteristic sizes and motions of things in the Classical World are far from the regime where relativity and quantum theory become important. Newton's Laws of Motion and his Law of Universal Gravitation are sufficiently accurate in nearly all cases to describe the motions of objects we experience on Earth and in the heavens (i.e., planets revolving around the sun). A fair question is : How far is the Classical World from the Worlds of Relativity and Quantum Theory? Relativity becomes important for speeds approaching the speed of light (typically denoted by "c") which has the numerical value of 3e5 km/s. [Note exponential notation: 3e5 = 3x10^5 = 300,000]. Here are typical speeds we experience in life : Person walking: 4 mph = 1.8 m/s New Jersey Turnpike: 75 mph = 33 m/s Space Shuttle launch 17,500 mph = 7.8 km/s Speed of Earth in orbit around sun: 2*pi*150,000,000 km / 1yr = 30 km/s Even the latter speed is only 0.01% (1e-4) of c. Effects of relativity in typical human experience can be safely ignored for all but the most precise applications (the Global Positioning Satellite [GPS] system is one exception). Quantum Theory describes the microscale world of individual atoms, molecules, protons, and electrons. Quantum effects become important when the product of the characteristic size ("x") and momentum ("p") of a system become comparable to Planck's constant (typically denoted by "h"), which has the numerical value of 6.6e-34 kg m^2/s. What is the product of characteristic size and momentum ("xp") for a human? The characteristic size is roughly a meter, and the characteristic momentum is m*v = 100 kg * 1 m/s, so xp = 100 kg m^2/s. This value is much much larger than Planck's constant and so again typical human experiences in the classical world are very, very far from the quantum world. The beginning of the 20th century was when physics first began to explore the Worlds of Relativity and Quantum Theory. Previously physics was purely in the Classical domain. Our human experience of the Classical World will not necessarily be helpful as we explore the World of Relativity in this course. One should be alert to the possibility that assumptions (even very basic ones) that we make in the Classical World will have to be modified or even discarded. On the other hand, it is most definitely not the case that "anything goes" in the Worlds of Relativity and Quantum Theory. Conservation Laws must be obeyed, new theories that describe experimental results in the Quantum and Relativistic Worlds must also describe the Classical World. ========================================================== A brief review of physics at the end of the 19th century: There were only two basic origins of force in classical physics: . gravitational mass . electric charge giving rise to the universal gravitational force and electromagnetic forces. We will consider each of these in turn. ******************* Classical Mechanics ******************* The origin of physics as an experimental science is generally traced back to Galileo Galilei (1564-1642), whose experiments in mechanics and interpretation of astronomical observations shattered the Aristotelian world view that had held sway over natural philosophy in Europe for a thousand years. [Aristotle held that heavier objects fell faster than lighter objects.] Galileo conducted careful experiments on the motion of falling bodies using inclined planes to demonstrate that gravity accelerates all objects by the same amount, further showing that the distance they travel increases with the square of the time taken. [Experiment: an observation carried out under highly artificial and carefully pre-arranged conditions.] Galileo's investigations into motion were elaborated upon and codified into Three Laws of Motion by Newton (1643-1727): First Law (Law of Inertia): A body at rest will remain at rest and a body in motion will continue in motion in a straight line at constant velocity (so-called "uniform motion") in the absence of any interaction with the rest of the universe. Second Law (Law of motion): The net force acting upon a body is equal to the product of the mass and the acceleration of the body; the direction of the force is the same as that of the body's acceleration. Third Law (Law of Action-Reaction): When a body exerts a force on another body, the second body exerts a force on the first body of the same magnitude but in the opposite direction. Newton also determined the force law for gravitation ".. all matter attracts all other matter with a force proportional to the product of their masses and inversely proportional to the square of the distance between them." F = G m_1 m_2 / r^2 G = universal gravitational constant = 6.67E-11 N-m^2/kg^2 This allowed him to convincingly explain the tides on Earth, the eccentric orbits of the comets (including Halley's comet), and Kepler's three laws of planetary motion (see below), to name just a few phenomena. Through his researches in mechanics and gravitation, Newton came to the conclusion that there is an absolute space and an absolute time that each exist "without reference to any external object whatsoever." He writes on time (see "Einstein's Theory of Relativity" Max Born, p. 57) "Absolute, True, and Mathematical Time, of itself, and from its own nature flows equably without regard to any thing external, and by another name is called Duration: Relative, Apparent, and Common Time is some sensible and external (whether accurate or unequable) measure of Duration by the means of motion, which is commonly used instead of True time; such as an Hour, a Day, a Month, a Year ... "For the natural days are truly unequal, though they are commonly consider'd as equal, and used for a measure of time: Astronomers correct this inequality for their more accurate deducing of the celestial motions. It may be, that there is no such thing as an equable motion, whereby time may be accurately measured. All motions may be accelerated and retarded, but the True, or equable progress, of Absolute time is liable to no change. The duration and perseverance of the existence of things remains the same, whether the motions are swift or slow, or none at all... and on space: "Absolute space, by its own nature, without regard to any thing external, remains always similar and immoveable. Relative Space is some moveable dimension or measure of the absolute spaces; which our senses determine, by its position to bodies; and which is vulgarly taken for immoveable space..." Newton is making essentially unprovable assertions about the nature of space and time. Yet it was necessary for him to do this in order to arrive at the law of inertia, for example. How can motion be considered uniform if one does not first have a reference system with which to define time and space? Kepler (1571-1630) was the recipient of the voluminous and accurate observations of planetary positions made by Tycho Brahe (1546-1601), which resulted in Kelper's Three Laws of Planetary Motion: (1) The planets move in ellipses with the sun at one focus. (2) The radius vector drawn from the sun to the planet describes equal areas in equal times. (3) The cubes of the major axes of the ellipses are proportional to the squares of the periods of revolution. The first two laws apply to each of the planets while the third law applies to the ensemble. Here we show how Kepler's 3rd law arises from an inverse square force law. We assume a circular orbit of radius r, period T, and orbital speed v. Newton's second law relates the force and acceleration of the planet in its orbit F = m a . So to determine the force law we need to determine the acceleration, which is centripetal and given by a = v^2 / r . The orbital speed is v = 2 pi r / T , where r is the radius of the orbit and T is the orbital period. Combining the last two gives a = 4 pi^2 r / T^2 . Kepler's 3rd law says r^3/T^2 = const = K . Using this to eliminate T in the eqn for acceleration gives a = 4 pi^2 K / r^2 , which is the inverse square force law. The result holds true as well for elliptical orbits (a circle is just a special case of an ellipse with zero ellipticity), although the mathematics is more complicated. ************************* Electricity and Magnetism ************************* Electric force between two charged point sources: Coulomb's law: F_e = 1/(4pi e_0) Q_1 Q_2 / r^2 = k Q_1 Q_2 / r^2 k = 8.99e-9 N-m^2/C^2 e_0 = electric permittivity of free space Which is stronger? Gravity or electrical force? Forces between two electrons at 1 m Mass = 9.11e-31 kg Charge = 1.6e-19 Coulombs F_g = 5.54e-71 N F_e = 2.3e-46 N The electrical force is much stronger than the gravitational force.