Alex: I was thinking the "Canonical Ensemble". Do you think if our Universe behaves like a "Grand-canonical Ensemble" or an "Isothermal-isobaric Ensemble"? If you don't know what I am talking about then punish you to drink 3 beers.
Goykhman: The volume, temperature, and chemical potential are held constant in a Grand-Canonical Ensemble. The number of molecules, pressure, and temperature are held constant in an Isothermal-Isobaric ensemble. Neither can work to describe the universe. The volume of the universe is always expanding so the Grand-Canonical cannot be correct. If the universe had a 'pressure' it would have to be in some sort of container, which is impossible if the boundaries are always expanding. If there was any pressure it would be negative pressure, from the accelerating expansion, but this would not be constant pressure (because the expansion isn’t constant) So that kind of scraps the Isothermal-Isobaric ensemble. If I had to pick one, it would be Grand Canonical, because I find the idea of the universe having a ‘pressure’ much more ridiculous than a constant volume. What were your thoughts?
Alex: Ha ha ......LOL~ Very good!
At least you have started thinking more than drinking or smoking more LOL~
The idea of ENSEMBLE is designed for relating the microscopic properties (such as kinetic or potential energy, dipole moment....) of each atom or molecule to the macroscopic properties (such as pressure, temperature, thermodynamic parameters, volume....) of global universe in "Statistical Mechanics/Physics" (by using Partition Function). Maybe my question was not given in clear definition by explaining you more statistical background (in probability theory & mathematical equations). I was actually asking you which fundamental micro-models will better-fit the macroscopic properties of our global universe. The answer, of course is "No Different". Ha ha ha ....this is a trick to test your statistical foundation. Because when the scale of ENSEMBLE increase, the differences that caused by different micro-models will be close to zero. Also, the definition of PRESSURE is nothing to do with container but only to do with force (on surface). Think about the atmosphere (barometer) of the Earth. Is it within a container? Also, we do measure the pressure in vacuum or space (the value is close to 0 but is not zero) with regardless of whether it is inside a container or not. When you touched the argument about the boundary of our Universe, it is another important topic about astrophysics. Go to my wall and read my comment about Olbers' Paradox and you will find something interesting. Keep trying! Don't give up!
Alex: "Olbers' Paradox" is very interesting to me. I have recently read some articles about it. But I hereby want to propose an opposite way to think about it. I would like to ask why our day sky is much brighter than night sky. The day sky on the moon is relatively still dark than it on the earth. So the day sky on the moon is in the true and normal brightness that we should see in our universe. Kepler is actually the first person to notice about this paradox. If either Kepler or Olbers was living on the moon they probably would think it is no big deal because the day sky is only a little bit brighter than the night sky on the moon. The atmosphere of our planet Earth has amplified the brightness of day sky by scattering the sunlight. But Olbers' paradox is still a good observation and argument about the essence of our Universe even the brightness of day sky is not that big different from that of night sky in most planets of our Universe. The big bang theory has even predicted the future night sky will become darker more and more.
Megan Barker: I wish statistics would die. Please die statistics. Someone tell me why I need this class? :( Two more assignments and I'll be halfway done.
Alex: Let's say if you want to design a door (of an elevator or an entrance...whatever...) which its height can allow 95% American adults to pass through it, then you need to know the 95% confidence interval of the average mean of the American adult height. Another example, you want to define the hypertension then you have to know the average mean of the normal blood pressure first. You want to know if your developed medicine does work on patients then you gotta do the statistical test. Simply saying the STATISTICS is the most powerful prediction science in human civilization therefore every modern (industrialized) country has its own "National Statistics Bureau". Statistics can mainly do two kind of things: (1)Descriptive statistics, help you to find out the common features of a given data set. (2)Inferential statistics, help you find out the logical correlation and turn the data to be useful information and ultimately become knowledge. Probability Statistics has been widely used in many stochastic computations to generate many useful knowledge such as Quantum Mechanics, Molecular Evolution, Quantitative Economics ...etc. The modern Mathematics can be simply classified as three domains: Discrete Math, Continued Math (Calculus) and Statistics. If you don't like statistics you will miss a bunch of great math subjects and tools. If you disagree the values of above, then at least you will buy this point. "Statistics related jobs all are high-income jobs." The last word I wanna give you: STATISTICS never lies, STATISTICIAN does!
Sunday, April 3, 2011
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