PHZ3400-09 Emergence in Condensed Matter: Difference between revisions
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==Defining Macroscopic Bodies== | ==Defining Macroscopic Bodies== | ||
A macroscopic body is made up of many microscopic bodies usually on the order of at least one mole. The amount of particles in one mole is given by Avagadro's number, on the order of <math>\N_A=10^{23}</math>. Were every particle to be watched, there would be something on the order of <math>e^{10^{23}} </math> states to solve for. A significantly high number. | A macroscopic body is made up of many microscopic bodies usually on the order of at least one mole. The amount of particles in one mole is given by Avagadro's number, on the order of <math>\N_A=10^{23}</math>. Were every particle to be watched, there would be something on the order of <math>e^{10^{23}} </math> states to solve for. A significantly high number capable of being too much for even the best computers. | ||
Rather than doing that, most of the time only the center of mass is needed to draw a complete picture about the object. The Center of Mass is found using the following expression: | Rather than doing that, most of the time only the center of mass is needed to draw a complete picture about the object. The Center of Mass is found using the following expression: | ||
Revision as of 14:31, 11 January 2009
I want you to type, and type, and type here... add as much information as comes to mind... formulas, links... whatever helps make the story more convincing... This is the Age of Wikipedia, after all...
Do we have to watch every atom?
The answer to this depends on the context of the problem. If one is looking at the motion of a soccer ball the answer is no. The particles of the air inside the ball can move randomly. These particles can appear to move erratically. However, if one were to look at the overall motion, the center of mass motion, of the aggregate, the motion of the group is greatly simplified. On the other hand, if one wanted to know the air pressure inside the ball, knowing properties of the individual particles is probably more convenient.
If one wants to know if one should look at every atom, one should decide based on whether the property desired is macroscopic or microscopic.
Defining Macroscopic Bodies
A macroscopic body is made up of many microscopic bodies usually on the order of at least one mole. The amount of particles in one mole is given by Avagadro's number, on the order of . Were every particle to be watched, there would be something on the order of states to solve for. A significantly high number capable of being too much for even the best computers.
Rather than doing that, most of the time only the center of mass is needed to draw a complete picture about the object. The Center of Mass is found using the following expression:
Many phases of matter
How important is Quantum mechanics?
Why don't we suffer the fate of Rumpelstinskin (drop through the floor)? This is because objects are solid. But is solidity a quantum or classical phenomena? Solidity is most likely a macroscopic property as solids contain many particles. But classical physics gives no reason for objects to be solid other than molecular vibrations from the temperature of the solid. So ideally one could manipulate the temperature and affect the solidity of the floor. Except for the extreme case where the temperature is brought to the level where the floor dissociates, the temperature does not affect solidity. However, quantum mechanics can solve this problem. Heisenberg's uncertainty forces the electrons of the floor to be discrete values. This also means that the orbitals are incompressible unless the electrons can orbit in the same energy level. Pauli's exclusion principle and Fermi-Dirac statistics show that this is also not a possibility (because electrons are fermions). So despite solidity being macroscopically observed, it is quantum mechanics that keeps solids from passing through each other.
