tag:blogger.com,1999:blog-5418994588621362010.post3120267634005077419..comments2023-11-15T10:08:56.796-08:00Comments on the blog formerly known as The Statistical Mechanic: the measurement problemWolfganghttp://www.blogger.com/profile/07086991199438418163noreply@blogger.comBlogger16125tag:blogger.com,1999:blog-5418994588621362010.post-32665566998980039322009-01-31T05:09:00.000-08:002009-01-31T05:09:00.000-08:00You can download Rational Thermodynamics here.You can download Rational Thermodynamics <a href="http://www.addebook.com/tech/chemistry/rational-thermodynamics_2378.html" rel="nofollow">here</a>.Ponder Stibbonshttp://www.blogger.com/profile/18387561315863534902noreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-65840283720568285132009-01-26T07:47:00.000-08:002009-01-26T07:47:00.000-08:00Also 'Six Lectures in Modern Natural Philosoph...Also 'Six Lectures in Modern Natural Philosophy', 'A First Course in Rational Continuum Mechanics', and, probably above all, 'Rational Thermodynamics' (2nd edition).Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-45833709702407967572009-01-25T02:40:00.000-08:002009-01-25T02:40:00.000-08:00I will try to find out more about Clifford Truesde...I will try to find out more about <a href="http://en.wikipedia.org/wiki/Clifford_Truesdell" rel="nofollow">Clifford Truesdell</a>. <br><br>The title "The Tragicomical History of Thermodynamics" sounds <a href="http://www.jstor.org/pss/3104457" rel="nofollow">interesting</a>...wolfganghttp://tsm2.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-22165660172244232732009-01-25T02:31:00.000-08:002009-01-25T02:31:00.000-08:00>> But some quantum physicists one day awoke...>> But some quantum physicists one day awoke and thought they had found a new problem; while, as Wolfgang say if I understand him/her correctly, this 'problem' or non-'problem' had always been there.<br><br><br>Just to clarify this one point. I think quantum physicists certainly found new problems, but they also stumbled over some 'problems' that have always been there, just not made explicit.wolfganghttp://tsm2.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-36548620835483681752009-01-24T17:26:00.000-08:002009-01-24T17:26:00.000-08:00I'd like to put what Bryan said above slightly...I'd like to put what Bryan said above slightly differently. The values taken by a mathematical symbol representing a physical quantity, e.g. temperature or position, are intended to represent the numbers that experimenters report and call 'temperature' or 'position' (I'm paraphrasing Truesdell here). And this correspondence cannot really be made more precise than that. It is a matter of agreement and discussion, and is subject to historical development and change; it is 'soft' and cannot be precisely formalised. I find it very interesting and exciting precisely because of this. In some cases we analyse those experiments by means of the theory itself in which the name 'position' is used, or by means other theories. But in doing so we use other physical quantities, for which the same 'problem' and soft correspondence remains. This is the 'regress', but is not infinite because at some point it resolves in agreement, convention, or is subject to further discussion - indeed, I don't mean that it should not be discussed and analysed in every instance. Only, it cannot be dispelled once and for all. This remark is similar to Bryan's and Hilbert's. <br><br>After all, the same 'problem' appears when we apply geometry. When you calculate the area of a geometrical figure in front of you, how do you know whether to use the formula for the triangle or that for the circle? Justify that. Strange that people insist on discussing about what certain mathematical entities (like 'position') correspond to, but not others (like 'triangle'). It is a social and historical matter of how strong the respective conventions are. <br><br>This 'soft' correspondence has always been there, and has been made very explicit in classical mechanics from around the fifties, after the work of mathematicians like Noll, Truesdell, Serrin, Coleman, Owen, and many others (whose existence is ignored by most quantum physicists). And I think that many classical authors were aware of that (I am ingnorant here, since I haven't read their works and don't believe in textbook summaries and other second-hand information of that kind). But some quantum physicists one day awoke and thought they had found a new problem; while, as Wolfgang say if I understand him/her correctly, this 'problem' or non-'problem' had always been there.<br><br>This in part explains also why we use different mathematical objects to represent e.g. 'momentum' in classical and quantum physics. In classical physics an experiment is understood as giving always the same numerical result given the same experimental conditions (otherwise we make a more detailed study of the conditions until we find what is the origin of the fluctuations). In quantum mechanics istead it is assumed that an experiment can give different results, given the same experimental conditions, and so we need a mathematical object that encodes not only the numerical results, but also their frequencies - or sometimes the latter alone. This is the role of Hermitean operators - or of positive-operator-valued measures (resolutions of identity). In principle we could play the same game without these mathematical objects though, using the classical symbols together with probability distributions over them.<br><br>Interestingly, here we can have again the discussion of whether it is justified to call the Hermitean operators ^x and ^p 'position' and 'momentum'. Some think that these are misnomers because the experiments they correspond to are not in the same 'category' as the classical ones with the same name. (For example, in Bohmian mechanics the operator ^x may not directly correspond to the position of any particle in that theory).<br><br>Sorry for the partly polemic and partly lecturing tone, folks!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-79748528723611528282009-01-15T01:58:00.000-08:002009-01-15T01:58:00.000-08:00> given an initial stateIn order to determine o...> given an initial state<br><br>In order to determine or prepare the initial state you must interact with (each molecule of) the cat.wolfganghttp://tsm2.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-6293481796381835662009-01-14T14:42:00.000-08:002009-01-14T14:42:00.000-08:00>> Do you believe we could use GR+QM to pred...>> Do you believe we could use GR+QM to predict the movement of a cat in a closed box?<br>>> I doubt that this is possible even in principle. Measuring the initial state of all neurons (or perhaps of all molecules) in the cat's brain would most likely kill it.<br><br>We have to be careful not conflate <em>schrodinger/unitary evolution</em> with the <em>act of measuring</em>. The former is deterministic, even though the latter isn't. That is, given an initial state (say, inside the box before we close it), quantum theory says it will undergo a <em>unique</em> time-evolution. There's only one possible future for the state of the cat, as long as state reduction does not occur!<br><br>So, I still don't see how our 'in principle' inability to interact with every particle in the cat is a problem.Bryanhttp://www.blogger.com/profile/07379669532781325751noreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-29596729190104596142009-01-14T10:48:00.000-08:002009-01-14T10:48:00.000-08:00Perhaps I should be more explicit about the main p...Perhaps I should be more explicit about the main point of this example.<br><br>There is of course no infinite regress, nobody uses other rulers to determine the distance from a mass point to the markings of the 1st ruler.<br><br>The measurement ends at step 2 when you look at the ruler and 'read the result from the measurement device'.<br>Your eyes and finally your brain terminate the 'infinite regress' early on - and we honestly dont really know how they do it 8-)<br><br>The 'translation' (or perhaps better: correspondence) of classical mechanics to our direct conscious experience is usually not considered to be an important issue - and is usually not even discussed as part of classical physics. (Ernst Mach was the only classical physicist who emphasized that there even is an issue.)<br><br>But when physicists discuss the measurement process within quantum theory, all of a sudden there is an issue, because the 'translation' from QM to our conscious experience is no longer so easy to ignore.wolfganghttp://tsm2.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-49026393903210141972009-01-13T17:20:00.000-08:002009-01-13T17:20:00.000-08:00Just out of curiousity, why can't taking the l...Just out of curiousity, why can't taking the limit of the sequence of infinite regress givee for a well-defined position?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-38099765200180821192009-01-11T10:35:00.000-08:002009-01-11T10:35:00.000-08:00>> If you believe our best theories (GR and ...>> If you believe our best theories (GR and QM under some important constraints), then dynamical evolution is deterministic. So there's no question about the value of x(t).<br><br>Do you believe we could use GR+QM to predict the movement of a cat in a closed box?<br>I doubt that this is possible even in principle. Measuring the initial state of all neurons (or perhaps of all molecules) in the cat's brain would most likely kill it.<br><br>I even doubt that it makes sense to assign a wave function to the macroscopic brain of the cat - assuming it exists but we just dont know it.<br>The wave function of the cat would be entangled with the environment in a most complicated way and one would ultimately have to deal with the wave function of the universe.<br><br>I have linked to my thoughts about this earlier...wolfganghttp://tsm2.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-10833460151257146002009-01-11T07:03:00.000-08:002009-01-11T07:03:00.000-08:00Nice post! The second part about the cat in the bo...Nice post! The second part about the cat in the box doesn't seem too pressing. If you believe our best theories (GR and QM under some important constraints), then dynamical evolution is deterministic. So there's no question about the value of x(t). If you don't, then the point is moot.<br><br>The first part about the measurement regress is very interesting. However, I don't see why you think "we need to measure the distance of each mass point to the markings on the ruler". I've got a negative and a positive comment about this.<br><br><em>Negative.</em> Using a ruler to measure another ruler in this case is very bad methodology (indeed, the very idea smacks of absurdity). I'm reminded of Hilbert's maxim: we cannot use just any mathematical methods to justify mathematical practice itself, for that would be circular; a practice can only be justified by <em>more stringent</em> methods of justification. Similarly here -- if we want to justify the practice of measuring length with rulers, we can't use a ruler to do it!<br><br><em>Positive.</em> I actually don't think 'measurement with rulers' is the kind of thing that needs much justification. When we learn to make measurements, we learn a reliable, standardized practice. This could involve a ruler, or it could involve the Stern-Gerlach apparatus. But much of the practice itself is conventional -- we <em>define</em> what counts as a measurement, and then proceed to compare 'measurements' according to that definition. No further justification seems possible, and none seems necessary.Bryanhttp://www.blogger.com/profile/07379669532781325751noreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-14413872736217669802009-01-10T09:27:00.000-08:002009-01-10T09:27:00.000-08:00There is perhaps a similarity with Dedekind cuts.A...There is perhaps a similarity with <a href="http://en.wikipedia.org/wiki/Construction_of_the_real_numbers#Construction_by_Dedekind_cuts" rel="nofollow">Dedekind cuts</a>.<br><br>And perhaps I could have added <a href="http://en.wikipedia.org/wiki/Dedekind_cut#Allusions" rel="nofollow">some Bergson</a> to this thing 8-)wolfganghttp://tsm2.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-58515841757961665812009-01-10T07:30:00.000-08:002009-01-10T07:30:00.000-08:00Actually, the position that the infinite regress i...Actually, the position that the infinite regress is the measurement reminds me of a rather strange-sounding remark in one of Bertrand Russell's books (<i>The Analysis of Matter</i>, I think), that it is possible to start with extended spatio-temporal events and a relationship "overlaps with", and recover point-instants as a kind of equivalence class of overlapping events. I should revisit this now that I know more math.Cosmahttp://bactra.org/weblog/noreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-75023423688223512892009-01-09T13:40:00.000-08:002009-01-09T13:40:00.000-08:00Thank you.And thank you for the link and the nice ...Thank you.<br>And thank you for the link and the nice words...wolfganghttp://tsm2.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-70742433574632261112009-01-09T11:43:00.000-08:002009-01-09T11:43:00.000-08:00This is a classic post, wolfgang, I greatly enjoye...This is a classic post, wolfgang, I greatly enjoyed it.Dave Baconhttp://www.blogger.com/profile/03506030153326411733noreply@blogger.comtag:blogger.com,1999:blog-5418994588621362010.post-81627558874146922192009-01-09T01:46:00.000-08:002009-01-09T01:46:00.000-08:00Apparently, one reader understood this post as &qu...Apparently, <a href="http://delicious.com/cshalizi" rel="nofollow">one reader</a> understood this post as "A parable".<br><br>But I think it really is just a (more or less accurate) report about an important historical debate about the foundations of classical mechanics.<br><br>The fact that it never happened does not mean it was not important.<br><br>(Physicists who believe in the many [classical] worlds interpretation will understand what I mean.)wolfganghttp://tsm2.blogspot.comnoreply@blogger.com