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A clarification of LQG by Lubos Motl

  1. Jun 7, 2003 #1

    marcus

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    http://www.arxiv.org/abs/gr-qc/0212096

    Lubos Motl (at Harvard's Jefferson Phys. Lab.)

    this paper is pure gold for what it does on the side
    quite apart from what you might expect from the title,
    which sounds narrowly focused on a specialized technical issue.

    what Motl gives on the side is a *critical* overview of LQG
    that cuts thru the underbrush and distinguishes a short list of impressive results---you could say one impressive result

    Motl recognizes the landmark importance of Olaf Dreyer's
    2002 paper, which seems to have put LQG on a new footing.
    Dreyer's paper is less than 4 pages long and has
    potentially far-reaching effects on quantum gravity, which
    Motl provides perspective on. Here's Dreyer's 4 page paper:

    http://www.arxiv.org/abs/gr-qc/0211076
     
  2. jcsd
  3. Jun 7, 2003 #2

    marcus

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    One thing Motl does that seems very interesting to me at least is to use " good old-fashioned" methods to come up with a result suggesting that

    the quantum of area is 4 ln(3) times the conventional Planck area.

    By unexplained coincidence this is also what Dreyer came up with for the quantum of area---using LQG.

    But Motl's analysis is neither stringy nor loopy! It has a classical flavor----analysing the vibration frequencies of a vintage 1916 black hole based on the vintage 1916 Schwarzschild model of one! There is no quantum mechanics at all in the basic model. The classical GR model of hole supports vibrations, and the minimal steps in frequency which Motl finds (NOW planck's constant can come in) correspond to minimal steps in energy and therefore area. So there is a so-to-speak "classical" support for the quantum of area being 4 ln(3) planck.

    As Dreyer got by other (LQG) methods.

    Maybe it should be mentioned that Motl is analytically pinning down some results about the vibration frequency of black holes that were gotten four years earlier by (of all things!) a
    *computer simulation* of black hole vibrations.

    So this number was known to be equal to 4 ln(3) out to 5 decimal places---as far as the computer could get it---but until Motl one did not know that it was exactly 4 ln(3). The next decimal place could have been wrong:wink: I only mention this because this is not just the work of one person but a kind of convergence on the quantum of area by a computer simulation by a man named Sachar Hod and by classical analysis of Motl and by LQG of Dreyer and probably help from other people. It is no one person's thing.
    But Motl's account of the matter seems unusually clear-sighted to me.

    BTW for people like Instanton and Sauron who may already be somewhat familiar with LQG technicalities the corollary of this is that the LQG group changes to SO(3) and the Immirzi parameter becomes ln(3)/(2pi sqrt2) which is 1/8.088 or about 1/8. Motl explains the Immirzi parameter as giving the "bare" value of Newton's gravitational constant G. The bare value at planck scale is only about one eighth as big as the renormalized largerscale lower energy G that we know and love. For this interesting detail see middle of page 7 of Motl and also the explicit value of Immirzi at top of page 9. These developments may strike one as provocative and worth looking into---hope so anyway.
     
    Last edited: Jun 7, 2003
  4. Jun 7, 2003 #3

    jeff

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    Too many remarks that miss the mark marcus. To explain:

    To enforce agreement of the LQG result for black hole entropy with the accepted one, a dimensionless multiplicative factor - the "immirzi" parameter - was introduced without further justification. Later someone observed that the rounded off value of a number cropping up in a certain GR-based black hole related computation equaled the immirzi parameter value needed in a version of LQG previously argued to be more natural than the standard one.

    Lubos in his paper strengthened the view that this may not be mere coincidence by showing that the rounded off value was in fact the exact value, though the calculation itself shed little light on the ultimate significance of this result (but about which some speculation is offered anyway).

    This result added credence to the view that LQG may have something important to tell us about QG, even if LQG is wrong. Unfortunately, it could also be seen as doing the same for the view that the latter is the case, since it was already known that this alternative arguably more natural version of LQG is inconsistent with the existence of matter. In fact this inconsistency directly reflects the very naturality argument that "there is no reason why a man-made theory like LQG that is meant to reinterpret old physics should know about our desire to incorporate fermions" on which advocacy for this version of LQG was based.

    As well, Lubos offers the following critique of LQG:

    "LQG has not been able to show that gravity at low energies behaves as it should and instead, it assumes some extremely unlikely conjectures about physics at high energies that we could not have tested: for example, LQG essentially claims that Einsteins equations are exact and uncorrected even at the Planck scale and the bad divergences in the Feynman diagrams only reflect our inappropriate choice of variables and the perturbative character of the calculations rather than new physics that we should learn. LQG formally agrees with Einstein in the regime where we have no reasons to believe that Einstein is correct; at the same moment, it most likely disagrees with Einstein at low energies where General Relativity has been successfully tested by many experiments. Since the LQG dynamics is pure Einstein at the Planck scale and the renormalization group flow is known to generate corrections, the physics at long distances probably does not exist. Many people believe that LQG, much like other discrete approaches to Quantum Gravity, does not contain large flat spacetime as a solution."

    Lubos has made it clear in his posts to sci.phys.research that he is no friend of LQG, and I think this paper reflects that to a significantly greater degree than marcus intimated above.

    Naturally, other immirzi parameter related ideas have been advanced since this paper. If your into LQG, take a look (even my always enthusiastic friend marcus :smile::smile: )
     
    Last edited: Jun 7, 2003
  5. Jun 7, 2003 #4

    marcus

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  6. Jun 8, 2003 #5
    >>Throughout this paper, we will neglect six or seven dimensions of >>the Universe and
    >>discuss four-dimensional Schwarzschild black holes

    Oh, what a lack of generality...

    Seriously, string theorist´s are bbecoming a bit crazy now adays. They expect for their theory the same respect that the standar model has.

    And by no means they deserve it. I could totally ignore string theory (it´s not the case) and still consider i am totally aware of high energy physics.


    I consider totally unbeliveable that somehting some exotic as M-theory is considered seriously and people like Myron Evans, who claims to have some experimntal evidence of new behaviours of electromagnetism -and a theory to explain the- would be totally ignored.
     
  7. Jun 8, 2003 #6
    BTW, a clarification about my knowledge of LQG, ii hve readed basicaly two intros, the Rovelli´s one in living reports and a a Thieman intro in pDF format of around 90 pages.

    I clarify it because i know there is another Thieman intro of 300+ pages wich i am begining to read now. Also i readed the Gambini-pullini book on the subjecto of gauge fields, knot theory and gravity. I have notices that Gambini has writen a more recent one, these time in collaboration wiith jonh Baez, but i am not sure aobut it.
     
  8. Jun 8, 2003 #7

    jeff

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    Has myron evans discussed his ideas with you?
     
  9. Jun 8, 2003 #8
    No, he hasn´t.

    But i colaborate from time to time with a friend in developing (extending into other areas, for example Yang-Mills) a theory of electromagnetic knots.

    And Myron Evans has sometimes cited these theory as favourable to his own work. Even, throught one of his collaborators hasmade to my friend the oportunity to publish the developments of the electromagnetics knot theory in his new incoming book.
     
  10. Jun 8, 2003 #9

    marcus

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    Hey Sauron,

    Motl is kind of outrageous in places----like at the end in the Unsolved Questions section he raises the question "could it be that LQG does not allow for the existence of fermions?"

    And his comic side comment you cited "thoughout this paper we neglect 6 or 7 dimensions!!!"

    But I still like his paper. He acknowledges a real advance in LQG even though he has often attacked LQG in the past.
    particularly around the issue of the Immirzi parameter.

    Now, while he talks critically about LQG, he has actually contributed a significant supporting result.


     
    Last edited: Jun 8, 2003
  11. Jun 8, 2003 #10

    marcus

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    Sauron,

    did you notice that steinitz said:

    " since it was already known that this alternative arguably more natural version of LQG is inconsistent with the existence of matter. "

    It is not what Motl said, either in his footnote (which speculates as to the original motive for using SU(2) instead of SO(3)) or in his "unanswered questions" at the end.

    Nobody else I know of says this either. Yet steinitz would
    have us think that this is "already known"
    .
     
    Last edited: Jun 8, 2003
  12. Jun 8, 2003 #11

    marcus

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    Motl has been a staunch and vocal supporter of strings in the past and has attacked LQG. In this paper he uses a derogatory tone but makes several important contributions to LQG. It is revealing to see what has interested this one-time enemy but now partial collaborator. On page 7 he says:

    "The most interesting result of this controversial approach to quantization of gravity is the following area quantization law that results driectly from [the two basic defining equations]

    Area = 8piGnewton x Immirzi x Σ spin network terms

    ...Immirzi parameter, a pure number that can be interpreted as the finite renormalization of 8piGnewton between the Planck scale and low energies..."

    I cannot easily write this out. It is simple and elegant and I can understand Motl being intrigued by it. The minimal spin network term dominates the sum and is equal to the sqrt 2. The sum is over network links intersecting the surface whose area is to be measured.

    The newtonian gravitational constant occurs as 8piG in the main equation of GR, the Einstein equation. People have often taken 8piGnewton as the "real" gravitational constant.

    Motl (usually a foe of LQG) is telling us in effect that the constant in front of the sum of sqrt 2 terms (one for each crossing of the surface) is the *real, bare* gravitational constant.

    Motl is helping in this paper to establish the value of the Immirzi number as about 1/8.088 and in effect establish that the true gravitational constant (at Planck scale) is about 1/8 of our usual
    largescale low energy 8piGnewton

    And yes he certainly does his share of grudging quarreling and nit-picking while he is doing this!!! But Motl is making a substantial contribution and meanwhile recognizing (for all his critical-sounding talk) an impressive development.

    Wish I could write out the Σ sum of spin label terms
    as he has it in the paper. Very elegant formula for area.

    So this area formula is what impresses one of the most vocal critics of this new approach to modeling gravity. Its always important to notice what impresses the enemies of a theory
    and even temporarily brings them over to the other camp.
     
    Last edited: Jun 8, 2003
  13. Jun 8, 2003 #12

    jeff

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    Yep, I think you're right for bringing this up because looking at it again I clearly was cavalier, so thanks (and yes I really do mean that).

    But it's not that I was attributing that particular statement to motl or his paper. That statement was purely my own. Like any high energy theorist coming across this, I, and obviously the proponents of SO(3) LQG - of which I'm not one, as you know - immediately understood why - despite it's advantages purely in the context of the LQG program - coupling it to matter was impossible.

    What was wrong of me to do was make the unqualified remark that "In fact this inconsistency directly reflects the very naturality argument that "there is no reason why a man-made theory like LQG that is meant to reinterpret old physics should know about our desire to incorporate fermions" on which advocacy for this version of LQG was based." Btw, just in case there's any confusion - and I'm not suggesting there is - all matter is fermionic.

    Anyway, I appologize for this (sorry marcus).

    Btw, my name is jeff ("steinitz" is a reference to wilhelm steinitz, the father of modern chess)
     
    Last edited: Jun 8, 2003
  14. Jun 8, 2003 #13

    marcus

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    No problemo steinitz,

    BTW since you indicate that you are a "professional researcher" (in high energy particle theory one infers from context, or some related area) I would very much like to look over some of your published research. Please post some references so I can look them up----I have ready access to a large academic library of journals and it would be no trouble for me to find pretty much anything you have in print if it is peer-reviewed hard-copy.

     
  15. Jun 8, 2003 #14

    jeff

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    I think that revealing identities in online public forums is not necessarily the smartest move people can make. Sorry.
     
  16. Jun 8, 2003 #15

    marcus

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    For a contrast to your manner, check out this interesting website:

    http://www.geocities.com/jefferywinkler

    and the many posts by "Jeffery" on Usenet's

    sci.physics.research

    the guarded reserve of this Jeff (steinitz) sharply
    contrasts with the self-revelatory openness shown by
    Usenet's Mr. Winkler--a multifaceted
    and widely informed individual if there ever was one!

    No reflection on you but I think I may prefer the Jeff on Usenet.
     
  17. Jun 8, 2003 #16

    marcus

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    Jeff Winkler's online (mostly science) resource

    Good gracious!

    http://www.geocities.com/jefferywinkler/Aristotles_Lyceum_in_Cyberspace.html

    Index page for Winkler's online (mostly) Science resource. All these things are links including the "idea for a Shakespearean comedy". A great many science essays on diverse topics. I will quote the page to show the remarkable and wideranging breadth. Some posters may wish to refer to some of these essays
    as tutorials or whatnot. At your own risk however, I cannot vouch for them.
    --------------------------------------------------------------------------------

    Greetings Lifeform. Welcome to my humble page. I'm Jeffery Winkler. I live in Hanford, CA. Here are some things that I've written.

    Physics
    The Big Bang
    Quantum Physics
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    Tensors
    Lagrangian
    The Standard Model
    Beyond The Standard Model
    Particle Physics
    Brane World Cosmology
    Special Relativity
    Black Holes
    Superconductivity
    Historical and Current Cosmology
    Mach's Principle
    Alternative Histories
    UFO's
    Religion
    Cults
    Early British History
    Stonehenge
    Art
    Halloween
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    Computers
    IBM and the first computers
    Political Terminology
    Earth's Core
    Reproduction
    NVFRAM's
    CGI
    Human Cloning
    Martial Arts
    Environmentalism
    Egyptian Hieroglyphics
    Greek Myth Triplets
    The Soviet Union
    Humor
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    Sports
    I maintain a Physics Website.

    You can also read my posts on a Vietnam board.

    I wrote a chart of the ups and downs of Bill Clinton. Read my article explaining why Clinton should have been impeached.

    Read my interactive novel.

    I wrote a screenplay.

    Here is a short story I wrote. Here you can read my idea for a Shakespearean comedy.

    I wrote haiku and a sonnet.

    Please visit my other homepage.

    Here I have yet another homepage.

    I draw fantasy art.

    Finally, here you can look at various other stuff.
    ------------------------------------------------------------------------
     
  18. Jun 8, 2003 #17

    jeff

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    Electromagnetic knots?
     
  19. Jun 8, 2003 #18

    jeff

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    marcus - and I do feel this is a fair question - do you not see the basis for this remark and why lubos ended the paper with it?
     
    Last edited: Jun 8, 2003
  20. Jun 8, 2003 #19
    I don´t know where the claim aobut LQG unability to incorprate fermionic matter comes from. In fact it surprises me.

    In the Thieman paper i readed he has no problem to talk about matter. I guess that if fermionic matter is not allowed he would clarify it.

    Also i readed Smollin paper comparing Strings and LQG and his claim is htat LQG can include the standard model without any problem.



    And at first glance i don´t see areason for it. The Asthekar forumulation is based in the vielvein wich allows the introduction of fermions in gravity, is is in fact the way to include fermions.

    I was not criticizing the contribution these article means for LQG at all. It is just that recently i am getting the impression that string theoriests try to convince people his theory is as good as standar model physics althought it has no experimental support. And aalso that they are THE WAY to do things.

    And i find that a bit stupid. I recognize the erits of string theory, and also i like some of their achievemnts.But to be honest i don´t find it as elegant as some people say. The days in which the use of XX century maths (topology mainly) could givve shine to a theory by themselves are gne.

    Electormagnetic knots is a reformulation of classical e-m first created by Antonio Rañeda, and developed by a friend in his doctoral thesis. Ateending a sugestion by Michael Berry they applied it to ball rays (hope the back traslation from spanish to english would be right).

    It has no relatiion with LQG, nor even with the application of LQG thecniques to classical e-m.

    It is based in a change of variables of the electromagnetic field. Instead of E an dB you use a fields wich are related to them by a nonliear relation. These fields permit the use of topological thecniques to find solutions of the Maxwell equations. The can be interpreted as maps from S^3^->S^2 (I use the ^ to indicate supraindice).


    These solutions can be classified according the hopf index of the map that the fields represnt. These index is conserved by time evolution. And it can be related to a classical quantities, the electric and magnetic helicities.

    A more extensive description of these theory would lead us far from the topic i guess.
     
  21. Jun 9, 2003 #20

    jeff

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  22. Jun 9, 2003 #21

    jeff

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    Okay guys, briefly - as all children learn in kindergarten (maybe you guys skipped?) - particles are defined in terms of their mass and spin which label - and this reflects their deeper significance - the representations of the inhomogeneous lorentz group under which their states must transform to respect invariances related to the geometry of spacetime that give rise by noether's theorem to conservation of mass-energy-momentum. In particular, spin specifies the representation of the rotational subgroup SO(3) of the homogeneous lorentz group SO(3,1). For even and odd spin particles - i.e. bosons and fermions - the reps are tensorial and spinorial respectively. For instance, in the case of spin-1 particles - the photon is an example - the rep is SO(3) itself. On the other hand, states of the spin-1/2 particles out of which all matter in our universe is composed transform under the double cover SU(2) of SO(3).

    We'll marcus, you now have the answer to the question "why SU(2)?" I challenged you to answer a while back, which is that the LQG gauge group G is some representation of the rotational subgroup SO(3) of the lorentz group, with the observed existence of matter requiring G=SU(2), the double cover of SO(3), with G=SO(3) being by itself insufficient to incorporate this basic empirical fact.

    But cheer-up guys because recently it's been argued - though inconclusively - that restoring SU(2) without invalidating lubos's basic result is possible.

    We don't.

    We think of string theory very much more as beautiful and deep than elegant. I think the reason that hobbiests gravitate towards LQG is their realization that the string theory program is for a whole host of reasons simply too monumentally difficult for them to ever really assimilate.
     
    Last edited: Jun 9, 2003
  23. Jun 9, 2003 #22

    marcus

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    Sauron,

    your back-translation is understandable but I could possibly edit parts of the post, if you wish me to try, to make it communicate more immediately in English.

    I think "ball rays" may mean spherical wave-fronts----not sure about this.


    I have mentioned the double cover of SO(3) by SU(2) several times in recent posts-----Steinitz pretends that I ignored his request out of ignorance, which is insulting. I see nothing wrong with his brief exposition here, however.

    Steinitz' problem comes when he says it is "already known" that using SO(3) makes LQG inconsistent with the existence of fermionic matter. Not every part of nature has to use the same group of symmetries. If quantum gravity turns out to use SO(3) fine, we can still have spin 1/2 particles. This is not my personal opinion but evident from the main references----as Sauron points out----such as Thiemann, Rovelli etc.

    BTW Sauron you also have been reading Smolin's March 2003 side by side comparison of String and LQG. "How far are we from the quantum theory of gravity"

    this seems valuable because it is an up-to-date comparison of what remains unsolved in the two theories, and takes account of the fixing of the Immirzi parameter----which earlier surveys do not since Dreyer's result is so recent.

    I am glad someone else here has been looking at that paper!

    I am appending a copy of the previous "rant" for I know not what reason----enjoyment?

     
  24. Jun 9, 2003 #23

    jeff

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    When you post a response, be sure to quote the most recent version of my posts because I try to give answers that are precise and detailed, and that requires an editing process.

    As you can see by the log, I edited my response long before you posted it, in part because I decided to look through the literature to see if any progress had been made on overcoming the problem crystallized in lubos's paper. It turns out there has been as I was delighted (at the time) to indicate in my post. I didn't do that for my benefit because I don't work on LQG. I did it out of deference to your interest in LQG which I've absolutely no problem with, I mean, why on earth would I? Now I feel like a complete chump for even wasting my time.

    Anyway, what you've written here is utter nonsense; it's wrong period; you simply don't know what you're talking about. Please ask one of the "mentors" to go over yours and my posts with you.

    The thing is that we're not talking about any old gauge theory of interactions in which who knows what symmetries might be involved. We're talking about gravity, and like all QG theories, in order to work, LQG - and strings - must be consistent with lorentz invariance. There's simply no escaping this. The limitations of SO(3) LQG are not a matter of conjecture or opinion. No matter what the correct theory looks like, there's simply no escaping the fact that they're low energy effective theories will have to obey the standard invariances of GR, and in the case of LQG this constrains it, as I've with great care indicated.

    As I've done with every sensible question I've responded to in this forum, I've given prompt, thoughtful and detailed answers to every single question you've put to me. All you've done is justify your refusals to answer my questions by claiming they're somehow insulting. Unlike some around here, I'm perfectly happy to let the quality of my physics explanations speak for me, and I've had every right to ask you the questions I have, and expect an answer, even if it's that you're not quite sure, in which case I'd just explain it.

    Now, is it not part of an explainers role to do what they can to identify where there may be confusion? You do it all the time. In fact you're virtually the only guy here who seems to need to start his own threads to lecture on something you just taught yourself. What's that about? And have you noticed that there really isn't alot of "hey, how ya doin" going on around here? Your dainty style of explanation doesn't mean a damn thing, only the physics does which is why in the long run continuing this can only be to you're great great disadvantage. If you want to critique my posts, have the decency to address me directly.

    When you say you mentioned that SU(2) is the double cover of SO(3), I have no problem believing that whatsoever. But that well known fact can be stated without being understood. Do you understand the physical significance of SU(2) doubly covering SO(3)?
     
    Last edited: Jun 9, 2003
  25. Jun 9, 2003 #24

    marcus

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    Not sure what you are talking about.
    I took your most recent, pressed "quote" which gives a reply with quote.

    My post was dated 10:28 and your self-revision was dated
    10:36.

    As far as I know I used the most recent. But I would be happy to go back to earlier versions of your posts if I wanted to make a point about the author which was essential to the discussion.

    You appear to be self-taught, which if fine unless you claim to be a "professional researcher" or to be professionally qualified. PF posters would be deceived if they read you as an authority. But I like the fact that you are obviously intelligent and widely read.

    You appear to be a bright "hobbyist" to use your word. I have great respect for talented and even brilliant amateurs. But some of your posts SUGGEST by innuendo (as if to say: I Jeff post on sci.physics.research Usenet which is for professional researchers and we string-theorists or high energy whatnots believe such and such) that you fancy yourself as a member of a professional research community.

    And even something of an authority!!! :wink:

    Your occasional mistakes belie this. Besides I think in this kind of unstructured environment it may be best to have no rigid idea of an "Explainer" role----your word, which I find a bit confusing. Everybody feels free to explain as best he or she can to anybody else! At least I hope this is the case!!!

    It may be best not to claim or suggest that one has professional qualifications, but to leave all that stuff behind and jump into the swimming pool devoid of status. And one certainly should not try to impose ones pretensions on others and imply non-existent professional standing.

    No rancour on my part---despite your frequently insulting tone.

    I think you can contribute lot to a board like this as long as you dont think of yourself as God's gift to it----and cut out the professional pretensions.

    Regards
     
  26. Jun 9, 2003 #25

    jeff

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    Check again. My final edit was made at 11:14a.m. your post was tagged 2hrs and 14 mins later at 1:28p.m.

    Again you're making assumptions about things you don't know. In this case how theorists learn. I do not know of a single high energy theorist that was not completely self-taught.

    I've made no mistakes. And even if I had, you wouldn't know it. In particular, take another look at that apology I made earlier in this thread. It should be easy to remember given it's (purposefully, he he) unequivocal and gracious tone. But what did I actually do wrong? Nothing! It was a test of your character, and you flunked. You fell for it because you don't understand the physics well enough to realize I had in fact done nothing wrong. That horribly "unqualified statement" required no qualification whatsoever! But if someone had made an apology like that to me, I'd be doubled over with new respect. Instead, I got a "no problemo steinitz" and you proceeded to insult me in this really bizarre way and then talk right past me in an unbelievable display of pure pettiness and disrespect.

    I felt that way as well, but only briefly as experience with people who don't understand that they don't understand quickly disabused me of that notion altogether. Letting them have it right from the start is in the long run far more time-efficient for me, and the other guy too. Of course, not everyone reacts well to this, but usually they do. But in the end what do I care, I'm not here to make friends. I'm here to answer the kind of basic questions that keep minds in the right gear for being creative.

    Still, I don't want to fight with you. You annoy me, but you clearly love physics. If you can agree with me that we both made mistakes - and we both did - and leave it behind us, I think we can have some good uncritical exchanges. Anyway that's my olive branch. Take it or leave it.
     
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