tag:blogger.com,1999:blog-3427479692989285926.post8926980788528173616..comments2024-03-17T11:54:10.124+11:00Comments on Journeyman Philosopher: Nature’s Layers of Reality: from Cosmology to QED to The Standard ModelPaul P. Mealinghttp://www.blogger.com/profile/14573615711151742992noreply@blogger.comBlogger20125tag:blogger.com,1999:blog-3427479692989285926.post-11811751695753651392009-11-04T17:31:57.729+11:002009-11-04T17:31:57.729+11:00Hi Timmo,
Yes, it helps a great deal. I appreciat...Hi Timmo,<br /><br />Yes, it helps a great deal. I appreciate the time and effort you've given to your 'appraisal'.<br /><br />I agree with your comments about both string theory and the so-called multiverse.<br /><br />You make me realise how much I don't know and that is a very good thing.<br /><br />I'll give you an acknowledgement in the original post.<br /><br />Best regards, Paul.Paul P. Mealinghttps://www.blogger.com/profile/14573615711151742992noreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-69923622683411242242009-11-04T04:30:13.521+11:002009-11-04T04:30:13.521+11:00Hope that helps! :-)Hope that helps! :-)Timmohttps://www.blogger.com/profile/04095596090336782085noreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-45922881228882849632009-11-04T04:29:08.855+11:002009-11-04T04:29:08.855+11:00Hi Paul,
...String Theory, explaining how it beca...Hi Paul,<br /><br /><i>...String Theory, explaining how it became the latest paradigm in our search for theoretical answers... the idea of a multiverse (very popular, I might add...Therefore, I don’t expect we’ll find a ‘Theory of Everything’ that encompasses all levels of nature in one mathematical expression, but a lot of people, including many who work in the field, seem to think we will.</i><br /><br />Did string Theory ever become a paradigm? The development of String Theory had promised to provide a quantum theory of gravitation. But, and I sense this is part of its current decline and demise, no feasible experimental checks have been offered by the theory. The hypotheses of String Theory, to the best of my knowledge, remain beyond experimental probing -- it's just speculation until we can go make some measurements. It's not a theory of everything so much as a theory of nothing.<br /><br />Multiverses are popular? It's too bad if that's the case. The claim that there are is a multi-verse is pseudo-scientific bunk -- it's neither here nor there when it comes to developing explanatory theories or giving experimentalists something to look for. Maybe it's true, but this is just wild speculation. <br /> <br />Personally, I think it is irresponsible, unprofessional, unethical for scientists to publically engage in these kinds of speculations and mislead people into thinking this is part of the science.Timmohttps://www.blogger.com/profile/04095596090336782085noreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-80398772472037244602009-11-04T04:15:20.889+11:002009-11-04T04:15:20.889+11:00Hello Paul,
I’ve always believed that scale plays...Hello Paul,<br /><br /><i>I’ve always believed that scale plays a role in the laws of physics...Huang’s exposition has highlighted the apparent reality that the laws of physics, therefore nature, are scale dependent. Many people overlook this, and talk about quantum physics as if it really works at all scales, including the one we are familiar with, and the mathematics doesn’t contradict this, just the reality we observe</i><br /><br />Quantum mechanics <i>does</i> work at all scales. Through Ehrenfest's theorem, you can show that F = ma comes out as a special case of quantum mechanics. Moreoever, I just gave you an example of classical results coming out of Feynman's approach. If you stray too far from the path of least action -- the classical trajectory -- the phases can vary at random and make the arrows cancel.<br /><br />There is something else here though. The laws of physics are not scale-invariant in the following way: I cannot just double the size of everything in the universe and get the same results I had before. Feynman talks about this in Six-Not-So-Easy pieces.<br /><br /><i>when time becomes purely imaginary it reduces quantum theory to statistical mechanics, so that time relates to absolute temperature...It is tempting to think that this mathematical relation arises from the fact that entropy is the only physical law we know of that gives a direction to time, with entropy being related to temperature, but Huang doesn’t make this connection, so there probably isn’t one.</i><br /><br />This is just a formal thing. In statistical mechanics, one tries to calculate what is called the partition function Z. If you can calculate Z, then you can derive all of the thermodynamic properties you are interested in (e.g. the chemical potential, heat capacity, phase transition temperatures). So, various schemes for calculating Z have been developed. The 'imaginary-time formalism' allows you to import all of the techniques of Feynman's path integral formulation of quantum mechanics to the project of calculating Z. It's just a mathematical or formal thing.Timmohttps://www.blogger.com/profile/04095596090336782085noreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-46384099358484011152009-11-04T04:03:50.125+11:002009-11-04T04:03:50.125+11:00Hello Paul,
Feynman’s book explains brilliantly, ...Hello Paul,<br /><br /><i>Feynman’s book explains brilliantly, with no equations whatsoever, how one can work something out from the summing of ‘all possible paths’ to produce the path of ‘least action</i><br /><br />Perhaps I can clarify what he is saying. In the first two lectures he lays out the quantum-mechanical laws of motion: <br /><br />(1) The probability P for an event is given by the absolute square of a complex number called the probability amplitude ψ. P = |ψ|^2<br /><br />(2) If an event can happen in alternative ways, 1 and 2, then the amplitude ψ is given by summing the amplitudes for the event to occur via 1 and via 2: ψ = ψ1 + ψ2.<br /><br />(3) If an event occurs in temporally contiguous stages A and B, the amplitude for the event is the product to the amplitudes for each stage: ψ = ψA × ψB<br /><br />Feynman does not state the rules in this way. Complex numbers can be represented as arrows, or vectors on the complex plane, so the rules (1)-(3) I just wrote down can be given in terms of adding and multiplying arrows in terms of the prescription that he gives.<br /><br />What you produce in a given problem is not necessary the path of 'lease action'. He gives the example of a mirror and shows how to regain the classical answer that the beam hits, say, the middle of the mirror and bounces off at the same angle it hits the mirrror. There is an amplitude ψ for the light to hit all of the various parts of the mirror, but, away from the classical path, the phases of all those ψ's, of all those arrows, basically vary at random and cancel. So, you recover the classical answer. And, if you cut away every part of the mirror but the middle you get the same result.<br /><br />But, if we cut away parts of the mirror at regular intervals to prevent the random cancellation away from the path of least time -- thereby making a diffraction grating -- we don't get the 'classical' answer! Whether or not the dominant contribution to the final arrow is the classical path of least time depends on the details of the situation!Timmohttps://www.blogger.com/profile/04095596090336782085noreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-51543097182878516012009-11-04T03:48:23.234+11:002009-11-04T03:48:23.234+11:00Hello Paul,
QED (quantum electrodynamics) is the ...Hello Paul,<br /><br /><i>QED (quantum electrodynamics) is the most successful theory ever... yet no one really understands how it works.</i><br /><br />Feynman is fond of saying that nobody understands quantum mechanics. There is a sense in which that statement is false, a sense in which it is controversial, and a sense it which it is true. <br /><br />We have a very strong <i>technical</i> understanding of quantum mechanics: one can learn the rules and play according to them. We know what the mathematical character of the theory is; we can use it to create models of phenomena we are interested in and compare theoretical predictions to experimental data; we can teach the theory to students and explain it collegues. There is a crystal clear grasp of the functional, operational workings of quantum mechanics.<br /><br />It is controversial whether there is a <i>conceptual</i>, or philosophical, understanding of quantum mechanics: there are rival accounts of what the world is like according to quantum mechanics. My own sympathies lie with Niels Bohr, Aage Petersen, and Leon Rosenfeld who championed the complementarity interpretation of the formalism. But, I notice that there are deep connections between the various interpretations (Bohr and Bohm both emphasize <i>wholeness</i>). Sometimes people say that Bohmian mechanics is just a many-worlds theory in disguise! <br /><br />It is certainly true that we do not have a <i>intuitive</i> grasp of quantum mechanics: the results are shocking, confusing, and leave one asking 'But... how could it be that way?' Though, it is also worth noting that Newtonian mechanics also sometimes defies intuitive expectations, as anyone who has tried to teach it finds out! Even very simple ideas, like the motion of the Earth, were bizarre to the people who were first wrestling with it. Nowadays everyone hears this since they are young and don't see what an incredible claim it is!Timmohttps://www.blogger.com/profile/04095596090336782085noreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-52144366446317563702009-06-05T08:15:27.346+10:002009-06-05T08:15:27.346+10:00Hi Paul,
Saw your addendum, and found the referen...Hi Paul,<br /><br />Saw your addendum, and found the referenced article lucid and interesting (but then, stuff in the New Scientist usually is). And here I thought "string theory" was only good for tying up Schroedinger cats! :) :)PKnoreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-41077648792985401102009-06-03T18:08:38.592+10:002009-06-03T18:08:38.592+10:00Hi PK,
To be fair and honest, I won a prize along...Hi PK,<br /><br />To be fair and honest, I won a prize along with about 12 others I expect. Anyone whose submission was published received a prize. I never saw the result because getting issues here seems to be a hit and miss affair, but I received a prize, which was a book by Raymond Tallis, so that's how I know.<br /><br />I added an addendum to the post if you haven't noticed.<br /><br />Regards, Paul.Paul P. Mealinghttps://www.blogger.com/profile/14573615711151742992noreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-13928140357584508122009-06-03T10:44:11.978+10:002009-06-03T10:44:11.978+10:00Hi Paul,
I think you make a good case, predicated...Hi Paul,<br /><br />I think you make a good case, predicated on his contributions to the form (and even the inception) of the academy as we know it, which stands irrespective of whether I concur with all of his philosophical opinions. Managing (especially as a non-academician) to get an article published in a philosophy magazine -- let alone winning a prize for it! -- is a d*mned impressive achievement, so my sombrero is off to you, in any case! Kudos!<br /><br />Regards, PeterPKnoreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-43741469336603341072009-06-01T22:25:13.728+10:002009-06-01T22:25:13.728+10:00On that subject: I actually wrote a short essay, a...On that subject: I actually wrote a short essay, and won a modest prize when I submitted it to <EM>Philosophy Now</EM>, a UK magazine.<br /><br />You can read the essay <A HREF="http://journeymanphilosopher.blogspot.com/2008/09/who-is-best-philosopher.html" REL="nofollow">here</A>.<br /><br />Regards, Paul.Paul P. Mealinghttps://www.blogger.com/profile/14573615711151742992noreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-65154960030911508872009-06-01T22:22:06.524+10:002009-06-01T22:22:06.524+10:00This is where your education shines through. I've ...This is where your education shines through. I've actually never read Plato's Republic - I've only read some of his Socratic dialogues. In my curtailed course on philosophy (I went overseas and wrote <EM>Elvene</EM>, and never returned to studying it officially) which pretty well sums up my whole education - never finished anything. I never finished that last sentence - in my curtailed course, I studied Aristotle, in particular his <EM>Nicomachean Ethics</EM>, and some of the stoics, both Greek and Roman. <br /><br />So my only knowledge of Plato centres around the influence of Socrates and Pythagoras. I do know (according to Kitty Ferguson, <EM>The Music of Pythagoras</EM>) that Plato adopted Pythagoras's 'quadrivium' of mathematics, geometry, astronomy and music, for his famous 'Academy', from Pythagoras's most successful student, Archytas, whom Plato actively sought out, or so Ms Ferguson claims, and she is a scholar.<br /><br />Regards, Paul.Paul P. Mealinghttps://www.blogger.com/profile/14573615711151742992noreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-14264540450648261092009-06-01T21:43:48.627+10:002009-06-01T21:43:48.627+10:00Hi Paul,
Well, we do disagree on one point, which...Hi Paul,<br /><br />Well, we do disagree on one point, which is that I'm *entitled* to "accuse" you of *anything* ("accuse" having, for me, the pejorative connotation of a sanctimonious, judgmental attitude, which I'd like to hope I mostly avoid; I try to, anyway). We can, on the other hand, amicably agree to disagree, which is fine. I guess at one point I rather blithely and offhandedly expressed my disdain for Plato's writing (though not for *all* of his ideas), but there's a story behind that, which has partly to do with my having been exposed to The Republic at an extremely early age (12), when I regrettably lacked tolerance of anything that didn't seem to me rigorously logical. And then I used to get into public arguments with a colleague from another department (philosophy) who was an enthusiastic Nietzschean as well as a devout Platonist, and I may have let my distaste for the one slop over onto the other, whereas there wasn't really any a priori connection. Also, I had reread Plato's one work on linguistics, The Cratylus, back when I was studying that field, and I think even the most ardent of Platonic apologists have had a hard time maintaining that that particular essay can be interpreted to have any coherent meaning whatsoever. Howsoever, I harbor no animus whatsoever towards Platonists, per se, and wouldn't "accuse" you of Platonism, either, using that verb. I sense we probably have different semantic fields for what "Platonist" means, in any case.<br /><br />And then, of course, I remember having (I thought, innocently) used the word "rebarbative" in a whimsical vein in describing Penrose's historical attack on classical AI, of which I was one of the early practitioners. Anyway, I certainly hadn't meant to convey either grumpiness or accusatoriness in either case (not, at the time, realizing that you were a particular admirer of Penrose and Plato, both). <br /><br />Bottom line: I also think it's perfectly fine (and conducive to interesting discussions) that we have somewhat disparate views. No "accusations" ever intended. :)<br /><br />Regards, PeterPKnoreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-62588056089822135102009-06-01T14:52:20.414+10:002009-06-01T14:52:20.414+10:00Thanks Peter,
You're entitled to accuse me of man...Thanks Peter,<br /><br />You're entitled to accuse me of many things. It's an area where we don't quite meet, along with a lot of others I expect - nothing wrong with that.<br /><br />I am a Platonist, at least mathematically speaking. In fact, the Platonic realm has a lot in common with the Chinese Tao (ref. prev. post).<br /><br />Having said that, I agree with Penrose, possibly the best known living Platonist, that you have to 'find' the 'right' mathematics (ref: <EM>The Road to Reality</EM>). I think he sympathises with Peter Woit's views on 'String Theory'; he's just more circumspect in expressing his opinions (he gives his endorsement on the cover). <br /><br />I admit to being an admirer of Penrose, as you would when you find someone who philosophically agrees with you in a number of areas, though not all, but then no one does that I believe. We don't live in the world of Gurus anymore - or, at least, I hope not.<br /><br />Or is that my 'Aussieness' showing through - we are traditionally a bit wary of Gurus of any persuasion.<br /><br />Regards, Paul.Paul P. Mealinghttps://www.blogger.com/profile/14573615711151742992noreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-14630018533226028412009-06-01T13:30:48.486+10:002009-06-01T13:30:48.486+10:00Hi Paul,
The comment about tensors wasn't intende...Hi Paul,<br /><br />The comment about tensors wasn't intended at all as an "accusation;" just a whimsical way of flailing my arms to differentiate between the mathematical representation and the thing represented. You're exactly right that the tensors *do* exist in our heads (or, at least, internal cognitive representations isomorphic to the external mathematical symbology that's isomorphic to the physical phenomena observable in the universe reside in our heads, insofar as we're capable of constructing yet some other neuronally-based model-theoretic interpretation thereof! :)) Actually, the more I think about it, the tensor I get! :)<br /><br />Regards, PeterPKnoreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-15921331537565368962009-05-29T12:40:00.868+10:002009-05-29T12:40:00.868+10:00Hi PK again,
Our comments passed in cyberspace, s...Hi PK again,<br /><br />Our comments passed in cyberspace, so my last comment is in response to your first comment.<br /><br />I confess to being a bit of a Pythagorean, so I may be guilty of your accusation. The tensors exist in our head, yet, wihout Reimann's geometry, we wouldn't know that the universe obeys said tensors to an inordinately accurate degree, as people like Penrose like to remind us. Penrose, by the way, is not a fan of string theories either.<br /><br />Regards, Paul.Paul P. Mealinghttps://www.blogger.com/profile/14573615711151742992noreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-36734868049775054912009-05-29T12:29:38.987+10:002009-05-29T12:29:38.987+10:00Hi PK,
Thanks for your generous comments.
As I'v...Hi PK,<br /><br />Thanks for your generous comments.<br /><br />As I've said in previous posts, that I know you've read, mathematics is one the most efficacious mediums we have for bridging our inner and outer worlds.<br /><br />To paraphrase Robyn Arionrhod from <EM>Einstein's Heroes</EM>, mathematics is really about the relationships between numbers rather than the numbers themselves. In response to the age-old philosophical question: is mathematics invented or discovered? Well, I would say the 'symbols' (numbers) are invented, but the relationships are not. <br /><br />The fact that nature seems to obey some of these relationships (if not all of them) is one of the reasons that we are 'privileged' to be able to comprehend the very universe that created us, as I say in my post.<br /><br />Regards, Paul.Paul P. Mealinghttps://www.blogger.com/profile/14573615711151742992noreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-53377193007270397862009-05-29T12:25:07.156+10:002009-05-29T12:25:07.156+10:00Hi Larry,
Oh, I'd never asseverate that none exis...Hi Larry,<br /><br />Oh, I'd never asseverate that none exists. On the contrary, if there's one theory that more-or-less adequately predicts the behavior of the universe, to the extent that we're able currently to observe that behavior, then there're provably an <I>infinitude</I> of such theories. How you'd choose among them I'd guess would be on the basis of theoretical economy, if you had no other. And I'm not even saying that we'll never find one: only that, if we do, it'll be a mathematical construct, and not the same thing as reality itself. And also that there's no reason <I>a priori</I> to believe that one <I>has to</I> exist (God seems neither inclined to "play dice," nor necessarily everywhere to adhere to principles of maximal semantic economy).<br /><br />I do tend instinctively to embrace Paul's view that a GUT may not be found because multiple, disparate and non-unifiable explanatory mechanisms may actually be necessary to account for the observable phenomenon, but that's just an instinct, akin to Paul's: it's really not possible to know. I was just focussing more on a pet peeve of mine: the failure to distinguish between mathematical constructs and the physical universe whose properties they seek to characterize. If you look out your window, you won't see any tensors zooming around through space. Anyway, no cause for "horror" just yet. (Though I *am* reminded of Rilke's observation: "Jeder Engel ist Schrecklich.") :) :)PKnoreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-74610162190652608322009-05-29T12:12:16.749+10:002009-05-29T12:12:16.749+10:00Hi Larry,
Well, I certainly don't think we've com...Hi Larry,<br /><br />Well, I certainly don't think we've come to the end of science. <br /><br />The history of science, in the last century, has revealed that as we go to smaller and smaller scales by using bigger and better particle accelerators, we uncover new mathematical relationships, or laws of physics, that we didn't even know existed.<br /><br />GUT requires looking at the energy or scale at the big bang, when all the 4 gauge theories we currently know about: electromagnetic, electroweak, strong and gravity; all meet. Approximately 10exp.16 to 10exp.20 GeV. But, as Woit points out, the physics at this level may not be the same as the physics we already know, and history suggests it almost certainly won't be.<br /><br />Woit argues a very strong case that 20 years of string theories hasn't even produced a proper 'scientific' theory. But, string theory aside, it may be that the extremities of scale of the laws of physics are not unified in a way we expect to find. I think it's quite possible that nature follows different laws at different levels (or scales) and the belief in finding one 'law' or GUT, that mathematically combines them all together, may be a chimera.<br /><br />As I like to say: only future generations know how ignorant the current generation is. And, of course, the current generation includes me.<br /><br />Regards, Paul.Paul P. Mealinghttps://www.blogger.com/profile/14573615711151742992noreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-82825357354554182422009-05-29T11:50:48.596+10:002009-05-29T11:50:48.596+10:00Well, but is this a feature of reality or of us? I...Well, but is this a feature of reality or of us? It's one thing to say that we'll never find a theory of everything and quite another to say that none exists: the former would be merely annoying whereas the latter would be sort of horrifying, in a way.Elihttps://www.blogger.com/profile/03543293341085230171noreply@blogger.comtag:blogger.com,1999:blog-3427479692989285926.post-5745609327766006612009-05-29T10:57:36.699+10:002009-05-29T10:57:36.699+10:00Mathematics does "allow us to go conceptually wher...Mathematics <I>does</I> "allow us to go conceptually where we can't physically." I'm not a Ph.D. physicist, nor do I play one on television, but I did marry one, so I'm absorbed a certain amount of physics osmotically, on top of what I'd acquired in the same manner as you (autodidactically), and can find not a thing in your post that you haven't presented both correctly and with extraordinary lucidity, so let me express my admiration for your exposition before going on to the one point that has always seemed (to me) not consciously to be recognized by theorists (and which tends to support both Feynman's cry of "nonsense," and your own skepticism about the ultimate realizability of a GUT). It's simply this:<br /><br />A mathematical theory is just a predictive isomorphism, strings of symbols that, when manipulated, yield other strings of symbols. Now all these symbols can stand for things (time and space and mass and temperature and so forth), and the system *can* be explanatory in the sense that it produces results that accord with our observations of physical reality. But they're still just mathematical systems that <I>represent</I> aspects of reality, not the reality itself, and historically, we've kept discovering that our systems needed tweaking to account for hitherto unobserved anomalies, hence the development of new conceptualizations embodied mathematically in the form of new systems of symbols. But nor are these <I>new</I> mathematical systems anything other than mathematical systems with a certain apparent explanatory adequacy. They're not the same thing as the reality. Even if string theory, to take an example, is shown conclusively to work at a predictive level, that doesn't mean that real strings exist, only that the math exists.<br /><br />Which sort of recapitulates in a different way something you've perhaps already expressed more cogently, but shorter version: I tend to agree with you about the "GUT" issues. :)PKnoreply@blogger.com