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Natural Science Forum / Physics / Relativity / August 2005Heisenberg, and Boltzman, vs. Newton
In statistical thermodynamics, the books cite the example of the all the air molecules in a room suddenly moving to one side (or something similar), with the comment, "It could happen, but very very unlikely!" Now hold the phone - that would violate Newton's 3rd, would it not? I.e. a sudden unmotivated shift in the system's center of mass. My point is, conservation of momentum constrains the possibilities/probabilities of the configuration space - it can't just do any random thing whatever. Right/wrong? An analagous question involves the Uncertainty Principle. In the single slit experiment, for example, as the slit narrows, the unpredictability (variance) of the electron's momentum increases. So picture the electron entering the apparatus at 9 o'clock, then it can exit at any vector from 12 to 6 o'clock. Waitaminnit - if its direction entering was due east, then a moment later it's traveling northeast, don't we have a 3rd Law violation? -- Rich > In statistical thermodynamics, the books cite > the example of the all the air molecules in a [quoted text clipped - 5 lines] > 3rd, would it not? I.e. a sudden unmotivated > shift in the system's center of mass. Wrong. You're forgetting collisions with the walls. > An analagous question involves the Uncertainty > Principle. In the single slit experiment, for [quoted text clipped - 6 lines] > later it's traveling northeast, don't we have > a 3rd Law violation? Not necessarily. See the point above. Also, think about conservation of momentum with regards to a red shifted photon. >In statistical thermodynamics, the books cite >the example of the all the air molecules in a [quoted text clipped - 9 lines] >space - it can't just do any random thing >whatever. Right/wrong? You're not talking about a cloud of molecules and nothing else but about a cloud of molecules *in a room*. The room has walls which are attached to the foundations which are attached to the Earth. So, in the context of the problem, it can be consideered to be of infinite mass, i.e. an infinite momentum reservoir (meaning it can provide or accept arbitrarily large amounts of momentum while changing its velocity by negligible amounts. Thus, the situation described above no more then the fact that you can get of your chair and walk to the other end of the room does. >An analagous question involves the Uncertainty >Principle. In the single slit experiment, for [quoted text clipped - 6 lines] >later it's traveling northeast, don't we have >a 3rd Law violation? Same thing, the apparatus can be considered an infinite momentum reservoir. Note, however, that one can include those considerations in the problem if one so wishes. In the "air in the room problem", well, the standard stat mechanics distributions are derived assuing that the only constant of motion is energy (since momentum and angular momentum can be freely exchanged with the walls). It is possible, though, to derive more general distributions where momentum and angular momentum are also constants of motion. Rarely done since in most cases you get pretty much same results (with way more complexity) but perfectly feasable. Mati Meron | "When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same" > >In statistical thermodynamics, the books cite > >the example of the all the air molecules in a [quoted text clipped - 19 lines] > no more then the fact that you can get of your chair and walk to the > other end of the room does. The argument could be rephrased to say we have gas in a region without the walls.  SignatureAsk yourself, what would God think of your ideals, religion and beliefs? Observations of Bernard - No 83 > > You're not talking about a cloud of molecules and nothing else but > > about a cloud of molecules *in a room*. The room has walls which are [quoted text clipped - 8 lines] > The argument could be rephrased to say we have gas in a region without > the walls. Then you are right: the center of mass could not move. However, even constrained by the stationarity of the center of mass, there are many nearly impossible things we could imagine -- after all, that only contrains 3 degrees of freedom out of 10^24, give or take. >> > You're not talking about a cloud of molecules and nothing else but >> > about a cloud of molecules *in a room*. The room has walls which are [quoted text clipped - 10 lines] > >Then you are right: the center of mass could not move. This has been addressed in the original answer. Mati Meron | "When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same" statistical mechanics is an advanced field. an understanding of analytical mechanics is required. dynamics of particles and rigid bodies, the 2-body central force problem, lagrangian formulation, hamilton's principle, and inertia tensor are topics found in analytical mechanics. also an understanding of or an introduction to quantum physics is required. atomic spectroscopy and wave mechanics are topics found in quantum physics. in addition, an understanding of the application of schroedinger theory to the harmonic oscillator and hydrogen atom, orbital angular momentum and spin-orbit interaction, quantum statistics, and topics from quantum theory of atoms, molecules, solids, nuclei and particles is required. topics such as the laws of thermodynamics, thermodynamic potentials, kinetic theory, phase transitions, equilibrium ensembles and related formalism with applications to classical and quantum systems are found in the study of statistical mechanics. such topics as the theoretical foundations of thermodynamics and statistical mechanics for equilibrium and nonequilibrium systems. applications to bose and fermi assemblies, real gases, liquids, solids, solutions, phase transitions, and chemical reactions are found in more advanced studies of statistical mechanics. http://en.wikipedia.org/wiki/Statistical_thermodynamics > In statistical thermodynamics, the books cite > the example of the all the air molecules in a [quoted text clipped - 23 lines] > -- > Rich > In statistical thermodynamics, the books cite > the example of the all the air molecules in a [quoted text clipped - 20 lines] > later it's traveling northeast, don't we have > a 3rd Law violation? Aside from the obvious, what is the chance of 10^23 honest coins all flipping heads? 0.1% of them? SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf > Aside from the obvious, what is the chance of 10^23 honest coins all > flipping heads? 0.1% of them? Two chances: Slim and None. Bob Kolker > > Aside from the obvious, what is the chance of 10^23 honest coins all > > flipping heads? 0.1% of them? > > Two chances: Slim and None. > > Bob Kolker It is not none. From the point of view of a thought experiment, slim is all you need to make it a real issue. So QM it is solvable but for Newton and relativity its a real problem. SignatureAsk yourself, what would God think of your ideals, religion and beliefs? Observations of Bernard - No 83 >> > Aside from the obvious, what is the chance of 10^23 honest coins all >> > flipping heads? 0.1% of them? [quoted text clipped - 7 lines] > >So QM it is solvable but for Newton and relativity its a real problem. What problem? There is no problem. Mati Meron | "When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same" > >> > Aside from the obvious, what is the chance of 10^23 honest coins all > >> > flipping heads? 0.1% of them? [quoted text clipped - 12 lines] > Mati Meron | "When you argue with a fool, > meron@cars.uchicago.edu | chances are he is doing just the same" Correct if you ignore the question. SignatureAsk yourself, what would God think of your ideals, religion and beliefs? Observations of Bernard - No 83 >> >> > Aside from the obvious, what is the chance of 10^23 honest coins all >> >> > flipping heads? 0.1% of them? [quoted text clipped - 14 lines] > >Correct if you ignore the question. The question was answered. If you think otherwise, kindly repost the question and point whih part of it wasn't answered. Mati Meron | "When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same" > >> >> > Aside from the obvious, what is the chance of 10^23 honest coins all > >> >> > flipping heads? 0.1% of them? [quoted text clipped - 17 lines] > The question was answered. If you think otherwise, kindly repost the > question and point whih part of it wasn't answered. The issue is that in relativity, the laws of conservation of energy/mass and momentum must be conserved in all probablity distributions. Here it does not appear to be. > Mati Meron | "When you argue with a fool, > meron@cars.uchicago.edu | chances are he is doing just the same" >> >> >> > Aside from the obvious, what is the chance of 10^23 honest coins all >> >> >> > flipping heads? 0.1% of them? [quoted text clipped - 21 lines] >energy/mass and momentum must be conserved in all probablity >distributions. *Only* for closed systems. > Here it does not appear to be. I explained it already. 1) The standard "canonical distribution" in statistical mechanics is derived assuming that the system is contained and that the container acts as momentum and angular momentum source/sink, thus the *only* conserved quantity is energy. No contradiction with either relativity or Newtonian mechanics since the system is not closed. 2) In cases where no container is present, it is quite straighforward to generalize the canonical distribution so that it conserves not only energy but momentum and angular momentum as well. The procedure employs Lagrange multipliers and is discussed in numerous stat mechanics textbook. The reason that it is rarely used is simply because there is rarely need for it. 3) If you assume a containerless system and use one of the more general distributions discussed in (2) then, of course, you cannot have all the particles of the system concentrating in a small neighborhood of one location unless this location happens to coincide with the CM of the system. You can, however, have all but one of the particles concentrating in the neighborhood of an arbitrary location, with the remaining particle being at some other (far away) location so that the center of mass remains fixed. Since stat mechanics routinely deals with very large ensambles of particles, the difference between "all" and "all but one" is devoid of significance. See Ed Green's response. 4) Part of the art of doing physics consists of utilizing simplifying assumptions and using, in any practical situation, the simples formulation possible. This means that more often than not you're using approximations, based not only on first principles but on additional assumptions. If, why evaluating one of these formulations, you seem to perceive in some cases discrepancies with basic principle, you'll better evaluate whether those cases are still consistent with the simplifying assumptions as well. If not, you don't have a case. 5) One of the less endearing traits of the products of modern education (which focuses at enhancing self esteem, rather than knowledge) is that when they encounter a discrepancy between the results of a theory and their understanding of said theory, they tend to assume that said discrepancy points to a flaw in the the theory, not in their understanding. Too bad. I'm assuming that you're not a lost cause here (else I wouldn't have been responding) but I keep my eyes open to the possibility that I'm wrong. Any questions? Mati Meron | "When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same" <snip> >5) One of the less endearing traits of the products of modern >education (which focuses at enhancing self esteem, rather than >knowledge) is that when they encounter a discrepancy between the >results of a theory and their understanding of said theory, they tend >to assume that said discrepancy points to a flaw in the the theory, >not in their understanding. There is another problem. All through el-hi, every question had to have one, and only one, correct answer. Then the child is thrust into the real world and everything is compromise. Most do not get more science education, so they continue to think that science is exact, correct and always perfect. <snip> /BAH > >> >> >> > Aside from the obvious, what is the chance of 10^23 honest coins all > >> >> >> > flipping heads? 0.1% of them? [quoted text clipped - 23 lines] > > *Only* for closed systems. Of course. > > Here it does not appear to be. > > [quoted text clipped - 23 lines] > with very large ensambles of particles, the difference between "all" > and "all but one" is devoid of significance. See Ed Green's response. This might work. > 4) Part of the art of doing physics consists of utilizing simplifying > assumptions and using, in any practical situation, the simples [quoted text clipped - 18 lines] > Mati Meron | "When you argue with a fool, > meron@cars.uchicago.edu | chances are he is doing just the same" SignatureAsk yourself, what would God think of your ideals, religion and beliefs? Observations of Bernard - No 83 In article <df1an2$8ss_001@s1242.apx1.sbo.ma.dialup.rcn.com>, jmfbahciv@aol.com writes: >In article <iTUQe.6$45.2173@news.uchicago.edu>, > mmeron@cars3.uchicago.edu wrote: [quoted text clipped - 12 lines] >Most do not get more science education, so they continue to >think that science is exact, correct and always perfect. And, they think that their understanding of science is exact, correct and always perfect. Mati Meron | "When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same" >In article <df1an2$8ss_001@s1242.apx1.sbo.ma.dialup.rcn.com>, jmfbahciv@aol.com writes: >>In article <iTUQe.6$45.2173@news.uchicago.edu>, [quoted text clipped - 16 lines] >And, they think that their understanding of science is exact, correct >and always perfect. The stupid ones do think this. The not-stupid ones don't. Members of my family are not stupid but do have the assumption. This assumption is reinforced by their Church's stance on so-called science. It gets complicated to explain in TTY ASCII but I understand it and the side effects. /BAH BernardZ: >> > Aside from the obvious, what is the chance of 10^23 honest coins all >> > flipping heads? 0.1% of them? [quoted text clipped - 4 lines] > >It is not none. Sure it is. The chance of flipping all heads 1 in 10^23, so it can't be 0.1%. If it were 0.1%, the coins couldn't be fair coins. > BernardZ: > >In article <wIOdnZ2dnZ12HTDKnZ2dnbUjjd6dnZ2dRVn-0Z2dnZ0@comcast.com>, [quoted text clipped - 14 lines] > Sure it is. The chance of flipping all heads 1 in 10^23, so it can't be > 0.1%. If it were 0.1%, the coins couldn't be fair coins. 0.1% referred to a percentage of coins, not a probability. i.e. 10^20 out of the 10^23 coins being heads, which has a non-zero probability of occuring. -- http://cherenkov-radiation.blogspot.com/ > > Aside from the obvious, what is the chance of 10^23 honest coins all > > flipping heads? 0.1% of them? > > Two chances: Slim and None. That an event has probability 1 or 0 does not mean it is certain to occur or not occur. This is true by integrating any probability density function over that precise event (integrating dirac delta over 0 doesn't count). > Bob Kolker Schoenfeld: >> > Aside from the obvious, what is the chance of 10^23 honest coins all >> > flipping heads? 0.1% of them? [quoted text clipped - 3 lines] >That an event has probability 1 or 0 does not mean it is certain to >occur or not occur. No, but it does mean that chances of flipping all heads is 1 in 2^n, and n in this case is 10^23, the chance of flipping all heads is certainly not 0.1%. I have no idea what it means to say the chance of the chance. >This is true by integrating any probability density >function over that precise event (integrating dirac delta over 0 >doesn't count). Which obviously can't be 0.1% for a fair coin. |
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