Misplaced Pages

Revision as of 15:48, 7 September 2006

${\displaystyle N_{inputs}=\sum _{j}S_{ij}*(1+(\sum _{k}S_{jk}*(1+\sum _{l}S_{kl})))}$

${\displaystyle N_{inputs}=\sum _{j}S_{ij}*(1+(\sum _{k\not =j}S_{ik}*(1+\sum _{l}S_{kl})))}$

Quantum Mechanics and Statistical Mechanics

I think it's interesting to notice the similarities between the mathematics of quantum mechanics and statistical mechanics.

Both theories use the exponential function heavily, (although only quantum mechanics uses exponentials of complex numbers, whereas statistical mechanics sticks to the real numbers), and both theories are math-heavy with a single constant that connects them with reality. For quantum mechanics the constant is Planck's Constant, and for statistical mechanics the constant is the Boltzmann Constant.

There are a couple thoughts I've had about the philosophy of quantum mechanics in general:

• I'm not sure I believe in the wave/particle duality. I believe there are only waves in the universe. Nobody can determine the position of a point charge to infinite precision, therefore performing a position measurement must yield a quantum state that has a finite ${\displaystyle \langle x-{\bar {x}}\rangle ^{2}}$, in other words, an arbitrarily narrow wave.

• I'm also not sure I believe in quantum indeterminism. Einstein was also suspicious of this, but Bell showed that no local hidden variable theory could be compatible with quantum mechanics. I guess my position is that the universe cannot have local reality. This makes sense to me, and should even make sense in terms of classical physics, as every particle in the universe affects every other particle via electrostatics, gravity, etc. even there.

• It would seem to me, that a lot of the former confusion around these issues arose from the fact that people insisted on viewing experimental measurement as the end-all be-all of a theory. But, they forget that the very act of measurement, and the nature of the measuring apparatus itself as another "piece" of the quantum state of the system, (not to mention the rest of the universe), prevents us from making "perfect measurements" of our experimental systems, even in principle.

Those are just my conjectures...

Vital Data

Name: Edward Joseph Sanville

Home: Loughborough, Leicestershire, United Kingdom, Earth

Interests: Chemistry, Physics, Mathematics, Biology

Born: September 28, 1980 in Laconia, New Hampshire, United States, Earth

List of my favorite scientists and mathematicians

20th Century: Albert Einstein, Paul Dirac, Erwin Schrodinger, Philo T. Farnsworth

19th Century: James Clerk Maxwell, Ludwig Boltzmann

18th Century: Benjamin Franklin, James Watt, Leonhard Euler, Jakob Bernoulli

17th Century: Isaac Newton, Gottfried Leibniz

16th Century: Johannes Kepler, Leonardo da Vinci, Galileo Galilei

15th Century: Nicolaus Copernicus

End of Classical Civilization, beginning of the Dark Ages: Hypatia of Alexandria

Ancient: Pythagoras (the father of science, math, and philosophy), Euclid, Archimedes, Democritus, Eratosthenes

Article Data

Articles I started

Electrostatic force (can't believe nobody created this one yet)

Fock matrix

Overlap matrix

Post-Hartree-Fock

Articles I contributed to substantially

Heat capacity (the theoretical gas phase background)

Equipartition theorem

Hartree-Fock

Basis sets used in computational chemistry

Roothaan equations

Thermodynamics

Statistical mechanics

Message Data

Feel free to leave me a message here. Don't make fun of my articles too much though.

Basis sets

Greetings. You kind of anticipated me in writing Basis sets used in computational chemistry - I noticed it was missing some time ago. So nice work! I'm just wondering if maybe a more appropriate name would be teh generic basis set (chemistry)? Karol July 2, 2005 15:35 (UTC)

Wow! You're quick ;). I made the dismabig at basis set. Cheers! Karol July 2, 2005 15:39 (UTC)

Zlatiborian

Thank you for that correction! I am a Zlatiborian and English is not my native language. Some Serbian nationalist Wikipedians dissagree with Zlatiborian language. However, I would like others to see the reality. I also would like to create a new Misplaced Pages in Zlatiborian language. Can I have your support? George D. Bozovic

I can't agree more! A Zlatiborian, a Croat, a Serb, a Montenegrin, and a Bosniak can understand each other without of any translation. That's why about twenty years ago all of these languages were considered as one single language, called Serbo-Croatian or Croato-Serbian. However, some differences exist, and that must be admitted! The only problem is that Zlatibor today is a part of Serbia... Croatia and Bosnia are independent, so they could promote their languages separate from Serbian. Zlatibor and Montenegro are not, so their languages are promoted as a part of Serbian (Perhaps you heard about Montenegrin language? That's the same situation as with Zlatiborian - Serbs claim that there are no such languages, as they claimed that there were no Croatian and Bosnian a few years ago...). You are right, that's all about politics. Zlatiborian is called a dialect of Serbian, although it is not. Of course, there are a lot of similarities, because those languages belong to the same group. I already said it - a Zlatiborian, a Croat, a Serb, a Montenegrin, and a Bosniak can understand each other without of any problems! Some word is different, and the script, but Serbs make no difference! George D. Bozovic

Loughborough

Hi Ed,

I come from Loughborough and went to school there but I don't live there now and didn't go to uni there. The nightlife is crap, there are two or three nightclubs, but the pubs aren't bad if you're not into clubbing particularly. Nottingham and Leicester are not far away if you have a pressing desire to get properly wankered. There are good transport links with the M1 and MML. It's nothing great, but it's not terrible either. Dunc|☺ 11:28, 13 August 2005 (UTC)

Oh and you can get a good curry - I can recommend the Eastern Garden by Sainsbury's. Dunc|☺ 20:58, 14 August 2005 (UTC)

Re: conjectures

Edsanville, I like your contributions. Far more pragmatic than my own ranting. I'm curious about your conjectures on,

"Both theories use the exponential function heavily, (although only quantum mechanics uses exponentials of complex numbers, whereas statistical mechanics sticks to the real numbers), and both theories are math-heavy with a single constant that connects them with reality. For quantum mechanics the constant is Planck's Constant, and for statistical mechanics the constant is the Boltzmann Constant."

A electronic engineer friend of mine said that resistance matching has to do with real numbers, and impedance matching has to do with complex numbers. Do you think this resistance-impedance relation might bare any relation to the statistical mechanics-quantum mechanics relation that you have observed? (And then would one do analogs of resistance matching in statistical mechanics, and impedance matching in quantum mechanics to do optimisations?) Sholto Maud 00:56, 19 December 2005 (UTC)

Gas phase heat capacity table in Heat Capacity

Ed, I think you're responsible for the table of molar gas-phase Cv heat capacities for diatomics in the article above. I don't like your numbers! First of all, of course, all this needs to be defined at some temp, since the values all converge to (7/2) R at higher temps. But even at 300 K, the graphs I've been able to find have Br2 Cv about 3.2 R and I2 about 3.4 R. Those numbers illustrate the discussion point much better than the number you give for B2 at 3.8 R (and what temp?). And a value for I2 is needed. This needs checking. See http://www.pcl.ox.ac.uk/~rkt/tutorials/heatcap/heatcap.html (these are Cp's, so of course subtract R).

BTW, gases are theoretically easy compared to liquids. Even solids are well-behaved at higher temps. But the molar heat capacity for bromine *liquid* (25 C) is about 4.55 R per mole-atom (see the Wiki for the bromine). Pretty impressively larger than 3, eh? Have any idea on how liquids store the extra potential?

Anyway, I'm sure we'll be talking more, since I intend to spend a little time making this article more accessable to the average user, by adding some less technical lead-in's to some of the sections. Sbharris 01:42, 13 March 2006 (UTC)

See my talk page. I don't like your explanation, and I've said why, there.

Thanks. Sbharris 22:14, 14 March 2006 (UTC)

Ed: See the Wiki entry for bromine. These little elemental articles are nice because they all have molar heat capacities, albeit for the element in just one form. For Br2 it's given at temp of "25 C" so I'm sure they're talking about the liquid. Mole-specific heat is given at 75.69 J/(mole*K) which is (divide by 8.31) 9.1 R/mole Br2 which is 4.55 R per mole Br.

You have to be right about electronic heat capacity contributing if such numbers aren't mismeasurements. Gram-atom-specific C's greater than 3R seem to show up in heavier elements like lead (3.4). Liquid mercury at 25 C is high at nearly 3.4 R. Atom-mole-specific for liquid Br2 is by far the largest I can find. Most other metals at this temp are remarkably close to 3R, so there's definitely something fishy going on, and there with just a few elements.

I did know of one other molecule where electronic transitions influence C at room temp, and that's nitric oxide .NO, where that one unpaired electron is in a pi* MO where it has lots of room to wiggle. Halogen dimers have all those MO's filled, but perhaps with big ones there are electrons in MO's derived from d orbitals that are loosely bound...

Anyway, I'm going to make the point to a greater extent that calculating "specific" molar heat capacities per mole of *molecules* really introduces an artificial parameter which makes the things less "intensive" (even though they still look intensive), because the larger the molecule, the better this number looks! That fakes out a lot of students. Diatomic gases at high temps go to 3.5 R, but that's really only 1.75 R per mole of atoms. For (linear) triatomic gases at full vibration you have 9-3-2 = 4 vibration modes so you get 4R + 5/2 R = 13/2 R = 6.5 R, which sounds like a lot. Until you divide by 3 and find it's only 2.17 R per atom. The bigger the molecule, the closer this gets to 3 R per atom (because the vibrational mode number goes up fast and swamps the rest).

Liquid water has a heat capcity of 9 R per mole which looks very impressive until you see that it's really 3 R per mole of atoms, so it's more or less the same as for solids with larger atoms. The amazing thing about water's heat capacity is NOT how large it is in specific terms: per mole of atoms, it's the same as for most metals. The amazing thing is that liquid water manages to do that at room temp, even with all the light H atoms thrown in. That's the hydrogen bonds and (I suspect) rotational modes storing potential energy (which can only happen in a liquid), which odd modes are like speed bumps and stand in for (and sort of ARE) vibrational modes that would otherwise be frozen out at these temps by the lightness of H (as happens in solid ice, where the per atom heat capacity is cut in half). Remarkable. Sbharris 19:20, 16 March 2006 (UTC)

Mass-to-charge ratio - who has ever said this is dimensionless

Edsanville: some people claim that m/z is a dimensionless quantity. It unfortunately is also the official policy of the UIPAC, which you find here. Of course it nonsense. This is why I am currently fighting to replace the dimensionless m/z by the correct m/q on the m/z misconception page. Unfortunately some people want to delete this page (Misplaced Pages:Articles_for_deletion/M/z_misconception). Please support me if you have time. Kehrli 23:26, 1 April 2006 (UTC)

this might be old, but Kehrli made some recent edits to Physical constant that appears to be based on the same kind of issue you guys have with mass spectrometry and dimension. may i suggest that you take a look at natural units, planck units, nondimensionalization and some of the lit in physics about this. just as when one counts tick marks (a dimensionless number) on a ruler when they measure length, when we use any measuring instrument to read a physical quantity it was designed for results in a fundamentally dimensionless number. it's in the interpretation of that reading and knowledge of what it uses as a standard to measure the physical quantity, that we attach units to the reading. r b-j 02:11, 5 September 2006 (UTC)

Dimensionless quantities

You said:

"just as when one counts tick marks (a dimensionless number) on a ruler when they measure length, when we use any measuring instrument to read a physical quantity it was designed for results in a fundamentally dimensionless number. it's in the interpretation of that reading and knowledge of what it uses as a standard to measure the physical quantity, that we attach units to the reading."

That's all fine and good, but you can use the same logic to show that everything in the universe is unitless. Ed Sanville 07:23, 5 September 2006 (UTC)

if you measure everything in Planck units, it is. if you were to measure everything in Planck units, there simple is no c (it's 1), G (also 1), ${\displaystyle \hbar \ }$, or Coulomb constant (1/(4 π ε₀)). it is not uncommon that physicists use Planck units to describe other quantities as dimensionless numbers. everything from the age of the universe to the cosmological constant to the elementary charge (it's e = ${\displaystyle {\sqrt {\alpha }}\ }$, a dimensionless number). certainly there is debate about which set or definition of natural units to use (a lot of people think that normalizing e is more natural and in MS, when they express m/q in dimensionless values, it appears to be normalizing e and the atomic mass unit, u that they are using as a standard of measurement - that's what they use to calibrate the instrument). anyway, i didn't want to jump into the MS debate of standard practice, only to say to you and Kehrli that what you guys call "misconception" or "idiocy" might not be.

since i originally left a message here, it makes sense to keep the conversation at one place. but it could be at my place, if you want (then please copy everything over). r b-j 15:00, 5 September 2006 (UTC)

I disagree with the statement that everything is unitless when you use Planck units, or atomic units, etc. You are simply using a different set of units in each case. The fact that there are different "sets" of unitless systems is testament to the fact that they do in fact have units, and that you need to use those units to convert between the different "unitless" systems. Being a computational chemist, I use the atomic units quite a bit, by the way... but claiming that they're "unitless" just ain't right! Certain quantities really are unitless, though, and there is a big difference between Planck units and those situations. Quantities that are truly unitless are always the same quantity, no matter what unit system is being used, which does not apply to anything measurable in Planck units or atomic units. An example of a truly unitless quantity would be the proton/electron mass ratio. I hope this didn't come off as rude or arrogant, I only wanted to italicize important stressed words. Ed Sanville 15:14, 5 September 2006 (UTC)

i should have mentioned that (for the time being) i have your talk page on my Watchlist, but feel free to plop anything on my talk page, if you choose to. but. i'll respond if i see you update this on my Watchlist until either of us decide to end the conversation.

i want to change the semantics, for the time being, from "unitless" to "dimensionless". we have lot's of "units" for dimensionless quantities (as well as for dimensionful quantities). for example, dB or decibels is a unit for the dimensionless quantity of log(magnitude). nepers is another unit (and mathematically more natural) for the very same thing and there is a dimensionless factor that is a conversion ratio between the two. likewise with degrees of angle vs. the more natural radian measure. both are dimensionless. the units for degrees and dB are purely anthropometric, made for the convenience of people. the "units" for radians and nepers, really are not units, both are not only dimensionless, but are ratios of like-dimensioned quantity or a mathematical function of ratios of like-dimensioned quantity. i would say (perhaps here you disagree) that nepers and radians are not only measures of dimensionless quantity, but, strictly speaking, are unitless.

okay, so now i have a question for you: what is the unit attached to the quantity L1/L2 where L1 and L2 are both lengths? (or pick an arbitrary ratio of the like-dimensioned quantity of your choice.) r b-j 19:17, 5 September 2006 (UTC)

Yes, I agree that radians are unitless, because it is the ratio of two equal units. Things like decibels must also be unitless, since logarithms always lose their units. But, what is the justification for calling m/z "unitless?" I haven't seen a good one yet! Ed Sanville 12:08, 6 September 2006 (UTC)

i wouldn't call dB "unitless", i would call them "dimensionless" but with these units that differentiate them from nepers which is both dimensionless and unitless. anyway, i thought what they meant with the dimensionless m/z is actually: (m/u)/(q/e) which is dimensionless and a ratio of two dimensionless quantities. r b-j 14:45, 6 September 2006 (UTC)

forgive me for interspersing comments. it's easier for me. if you don't like it, feel free to edit, it's your talk page.

Yes, but you could just as easily do that with anything, and try to call it unitless.

well, with planck units (or some other system of natural units) you can and they do do that in some contexts in physics. i would still prefer to separate the semantics regarding "unitless" and "dimensionless", but i'll try to use your terminology (as i understand it).

It's just a stupid unit trick. Instead of measuring electrical potential in volts, why not divide the charge by the elementary charge, and divide the energy by 1 hartree, and claim that it's unitless?

if the expression is: ${\displaystyle {\frac {eV}{\mathrm {E_{h}} }}\ }$, it is dimensionless and unitless. if the expression is ${\displaystyle V\ }$, it is not.

Well, I actually meant ${\displaystyle V'={\frac {\frac {E}{E_{h}}}{\frac {q}{e}}}}$

appears to be dimensionless, dunno why it's called a voltage, unless it's understood to be a normalized voltage (against atomic units) by convention.

Yeah, it would be the electrical potential, measured in atomic units. It's used all the time by computational chemistry software... but nobody would actually report a value like that without converting it into a "dimensionful" unit. In my view, there's no essential difference between reporting some dimensionless value normalized against some unit, and reporting the value as "X units." The former saves writing, and the latter is much more clear, (unless you have some convention like the mass spectrometrists, I guess). Ed Sanville 15:48, 7 September 2006 (UTC)

If you don't like the hartree, then divide by 1 Rydberg and claim that's unitless. I think it just confuses the issue. Why don't they just use some units? You know, I bet this debate wouldn't even exist if there was a unit which exactly corresponded to the elementary charge.

you mean a "Stoney charge"? e is the unit charge in Stoney units (i know it's a red link, but it shouldn't be).

Yes, if it was a little more well-established in non-theoretical usage. Ed Sanville 10:08, 7 September 2006 (UTC)

If we happened to have such a unit, then the mass spectrometrists would claim to use the units "Da/X" or "amu/X" or something, where X is the unit corresponding to the elementary charge. Ed Sanville 22:06, 6 September 2006 (UTC)

i can't really comment on what mass spectrometrists should be using to communicate physical quantity. i can understand if some of them would want to standardize the expression of mass to charge in terms of amu per e (it seems like that's how they might calibrate the gear), and if someone says it's m/q without clarification, i agree with you that this would be ambiguous. but if, for the sake of compact language, the discipline creates a widespread convention that whenever anyone mentions "mass to charge" they mean (m/q) / (u/e) which is dimensionless, i don't see what the problem is. i don't understand Kehrli's problem with it nor the "misconception". it's a convention and that expression is dimensionless. the reason i brought this to your attention was the support you lent on his talk page about this and the fact that i am convinced that Kehrli made changes (which have been reverted) on physical constants that seemed to indicate that he had the misconceptions of the role of units in physical quantities.r b-j 00:30, 7 September 2006 (UTC)

So, you are basically saying that although m/z is not dimensionless, there is no problem with expressing it without using any units? And, although certain quantities are dimensionless by Nature, the choice of using units is up to convention. Do I understand your point correctly? If so, I guess I can understand that. I guess I was just taught that it is always bad practice to express a non-dimensionless quantity without any units. Ed Sanville 10:06, 7 September 2006 (UTC)

i am saying that m/q is not dimensionless, and that (m/q) / (u/e) is dimensionless, and that it doesn't appear to me to be flat out wrong if the MS community wants to establish a convention (for conciseness) that when someone says or writes the words "mass to charge ratio", they mean the latter. especially, if that is how the instruments are calibrated and the dimensionless values read from the "meter" on the box (i imagine it's a peak on a spectrum plot) indicate so. anyway, my real beef was more with Kehrli's changes to physical constants, he completely reversed the meaning of something because he simply "thought it was wrong" where, it was he that had the misconception and it appeared that it was closely related to his issues of dispute with the MS articles. r b-j 14:31, 7 September 2006 (UTC)

Ah yes, I see the errant edit. Of course, it's true that the values of dimensionful physical constants would not be the same, independent of the system of units used (culture). No argument there. Ed Sanville 15:48, 7 September 2006 (UTC)

The Whistling Gypsy

I know this was about a year and a half ago, but since you still seem to be moderately active here, I thought I might tell you that I've labelled the inclusion of lyrics in The Whistling Gypsy as a copyright violation: the song was written around 1950 and the lyrics are still copyrighted in the United States. Thanks. TheProject 02:27, 27 June 2006 (UTC)

I'd love to keep the rest of the article, without the lyrics, but if you look at the last revision, you'll see there's not much in the article outside of the lyrics. Thanks. TheProject 14:52, 27 June 2006 (UTC)

Dartmouth college

Hi Ed, for you to know I switched my user page to User:Sadi Carnot. Thanks for the tip on your correct college, I have amended it per your request. From my point of view, one negative comment is more valuable than any ten positive comments; if, however, you do not want any association with this project just let me know and I'll switch your name to a pseudonym. Adios:--Sadi Carnot 15:30, 9 July 2006 (UTC)

P.S., I am close to finishing a new book on human chemistry, i.e. the science of chemistry between people; if you would be interested in reviewing the first three chapters before the book goes to press, I can email them to you. Your help would be appreciated. Two thermodynamic authors, Georgi Gladyshev and Jing Chen recently reviewed these first chapters several weeks ago and their feed back was very encouraging and helpful. I have about four more chemical engineers and two chemists lined up to help review, but I need more. If interested let me know? Thanks:--Sadi Carnot 16:49, 9 July 2006 (UTC)

Sourcing on Juan Manuel Alvarez?

Hi Edsanville,

You added the following to Juan Manuel Alvarez on 8/15/05 (see revision here):

Police say recent investigations indicate Alvarez may have intended to cause the crash without committing suicide. Authorities have filed additional charges against him for murder with intent.

Do you have any source information on this statement? I was looking to copy this info into the main Glendale train crash article but am hesitant to do so without proper sourcing. I had not heard this information, which is why I'm attempting to verify it.

Thanks! cluth 02:38, 20 August 2006 (UTC)

Found what I was looking for here. I'll source the article accordingly. Thanks! cluth 03:18, 20 August 2006 (UTC)