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Copy of Coherent vs random motion

Page history last edited by Joe Redish 7 years, 7 months ago

In the motions we have considered so far in this class -- a ball thrown upward, a box pushed along a floor, a bird poking a hole in a tree -- the motions have been coherent. That is, we can treat the motion as if all parts of the object move together in the same way. This is an appropriate way of treating a complex object if the object is reasonably rigid: it doesn't deform or break during the motion.


It isn't only macroscopic objects that can be treated this way. When two atoms or molecules in a gas collide, we can treat each atom or molecule as moving coherently (i.e. we can ignore the internal motions of the electrons).


However, atoms and molecules in a gas collide extremely frequently with each other, rapidly changing direction.  We may not want to measure and analyze all collisions and instead be interested how the gas moves in a second, rather than a nanosecond between collisions.  We refer to this description of motion as random motion.  


The Twentieth-century physicists showed that predicting the future position and velocity of atoms and molecules is not possible: The laws of Quantum mechanics, discovered in the early 20th century, showed that it is not possible to measure the position and velocity of atoms and molecules absolutely accurately at the same time.  A few decades later physicists working on chaos theory showed that even a very small uncertainty about the current position and velocity makes it impossible to predict position and velocity of an object much into the future.  Chaos theory is most famously stated as the "butterfly effect", which illustrates how small perturbations generated by a butterfly could grow into a hurricane.  To see for yourself how small uncertainties about the initial position of an object make it hard to predict the future motion of the object imagine dropping one basketball on top of another basketball that is sitting on the floor.  You know their positions quite accurately.  But in which direction will the top ball bounce off the bottom ball is hard to tell!  Molecules or atoms moving around have many such collisions that make it impossible to predict their future position and velocity.


As you know from your earlier science classes, all matter is made up of atoms and molecules. These atoms and molecules all are in constant motion, a motion that is a reflection of the object's temperature. Atoms and molecules in solids vibrate pretty much around a fixed location, but atoms and molecules in liquids are in continual and unconstrained motion, wandering from place to place, and atoms in typical gases move long distances (compared to their sizes) before colliding with other atoms and molecules and changing their direction. We refer to this internal motion of an object's atoms and molecules as random motion (sometimes also known as incoherent or thermal motion).


The critical property that differentiates coherent from random motion is that when the parts of an object are in coherent motion, the object carries a net momentum. When the parts of an object are in random motion, the sum of all the internal momentum cancels out.


Since a lot of what happens at the microscopic level in biological and chemical systems depends heavily on the properties of the random motion happening in a gas or fluid, we will study how what we know of the properties of motion from studying Newton's laws leads to an understanding of the properties of random motion. This will lead us to important phenomena such as random walk, diffusion, and entropy.


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Joe Redish 10/22/12



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