1 - Sketch of the Universe - (Mostly) Classical Mechanics

The History and Limitations of Classical Mechanics Galileo introduces the concepts of force and constant acceleration in Mechanics (1623), then Newton introduces his Laws of Motion in Mathematical Principles of Natural Philosophy ,and later, in De Mundi Systemate, described orbital motion with his Universal Law of Gravitation. Some of the more complex aspects of Newtonian Mechanics, such as the motion of rigid bodies, were addressed by Euler's equations of motion. In the 19th century, the use of conservation principles helped solve the problems of thermodynamics, and later became important in how we conceptualize mechanics (e.g with the conservations of energy, momentum, angular momentum). More complex Newtonian models began to be used in continuum mechanics to describe the behavior of waves (e.g fluid mechanics, wave mechanics and electromagnetism). The Michelson-Morley experiment (1887) ruled out the possibility of space being a fluid medium, which eventually resulted in Einstein's special theory of relativity (1905), which described the motion of objects at very high velocities and the non-Newtonian nature of space and time. Statistical mechanics related the microscopic properties of individual atoms to their macroscopic thermodynamic properties. Quantum mechanics explained the failed predictions of classical mechanics used on a very small scale (e.g. with heat capacity.) The law of general relativity corrected certain errors in classical notions of gravity.

Feynman Lecture 1 Atoms in Motion 1-1 Introduction Physical laws summarize knowledge, but we can't learn physics in a purely deductive fashion, giving the laws on one page, and showing the results of those laws in their different permutations. "First, we do not yet know all the basic laws: there is an expanding frontier of ignorance." Secondly, physical laws are written in mathematical notation, so our 'sentences' or elements may be concise, but we first need to understand what the words mean. Because "The test of all [scientific]knowledge is experiment" we can, essentially, only prove theories wrong, correcting or abandoning laws as we discover exceptions. Our laws are philosophically approximate and can never be shown, deductively, to be correct. Example: mass is not constant. 1-2 Matter is made of atoms In the event of apocalypse: 'all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.' We look really closely at a drop of water, 10^-10 meters closely (scale: 'if an apple is magnified to the size of the earth, then the atoms in the apple are approximately the size of the original apple'). These water atoms are always moving (and we call this movement heat), but they don't fly apart, because they're attracted to each other. If, however, we were to heat them enough, they would have enough energy to escape the pull of the water droplet and become steam. These atoms continue to knock against each other and their surroundings, this force (which we call pressure) can be measured on average. If we look at a piston, compressing a given volume, we have to apply a certain amount of force to keep the gas from moving it. So it stand to reason that the force is proportional to the area, since the volume stays the same, but we roughly double the number of collisions. The same logic applies if we double the number of atoms in a given volume; the pressure is proportional to the density. Likewise, if we compress a gas very slowly, it increases the temperature. If we look in the other direction, and decrease the temperature of our water droplet, the atoms are less likely to jostle each other out of place, so they eventually form a crystalline array with a definite place for every atom. Normally these crystal structures would take up less space, but ice is less dense than water, helium never freezes but we can make it solidify etc. 1-3 Atomic processesThen we look at water in air. The atoms always have some energy, so some of them will break away from time to time and become. water vapor. This evaporation takes away heat, and so cools the water. The atoms in the water will also attract other atoms, and if these processes balance each other out, the water will appear to be static. Of course this also happens with 'air atoms' as well, and gases dissolve into the water (mention of the bends). Solids, like salt, can also dissolve into, and crystallize out of, water, but there is no way of knowing which direction the process is going in without more information. It is a dynamic process, just like evaporation. Normally an increase in temperature will increase the rate of dissolution, but not always. 1-4 Chemical reactionUnlike the preceding physical processes, atoms change 'partners' in chemical reactions. Consider coal burning, which is, in a sense, a physical process, but which is also a chemical process, where carbon atoms bond with oxygen atoms to form carbon monoxide. This releases kinetic energy, and if enough energy is released, produces light. Of course, atoms have 'preferred' configurations, and carbon dioxide is more energetically favorable, carbon monoxide tends to form when a combustion reaction takes place very quickly. But how do we know all this? Take the smell of violets for example, which, we hypothesize, is a molecule also made up of atoms in a particular configuration ( 4-(2, 2, 3, 6 tetramethyl-5-cyclohexenyl)-3-buten-2-one), how do we know the shape of this molecule? [Essentially, we figure it out from the behavior and subcomponents of the molecule.] But how do we know? Our atomic hypothesis explains and predicts a number of phenomena, such as the constant random movement of atoms (for example: Brownian motion), x-ray crystallography also shows that the crystal structures are what we would expect from 'layers' of molecules of a certain shape.