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Loop Quantum Gravity

  1. Jan 11, 2004 #1
    I read about the Loop Quantum Gravity theory in some science magazine during my break at work. I wasn't reading attentively enough to make anything out of it. All I know is it is another theory to unite General Relativity and Quantum Mechanics, I think. Anyone care to share their knowledge on the subject for a physics laymen? Thanks.
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  3. Jan 11, 2004 #2


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    If you're wondering whether LQG is something worth spending your time on, the answer is that it really isn't. Hardly anyone in the physics community has ever taken it seriously and have always been and continue to be confident that the whole program is fundamentally flawed (the basic reason is that the assumption in LQG that GR should be valid as a basis of quantization all the way up to planck energies is wildly implausible given what we know about the other interactions and the likely behaviour and ultimate fate of quantum field theories at high energies).

    Pathetically, some PF members for their own questionable reasons continue attempts to convince other members (they sure wouldn't be able to do so with physicists) that there's real parity between LQG and strings, but really, all of the good ideas are being generated by string research and none by LQG. The twistor program recently rehabilitated within string theory is just the most recent example of how all roads appear to lead to strings and that the best hope for LQG is that it will ultimately share the same fate.

    Only a tiny, tiny fraction of papers on the subject of QG deal with LQG, and when compared to the thousands upon thousands of stringy papers submitted each year, are really of no consequence. All serious research in QG/TOE (not to mention a great deal of mathematical research) really is being driven by string theory and this will continue to be the case for a very, very long time to come.

    It's often said that string theory makes no predictions, but as is well-known, this is untrue. It turns out that the only self-consistent string theories necessarily contain GR and in this sense, string theory predicts spacetime! In fact for reasons related to this, string theory is the only bonafide quantum gravity theory we've ever had. LQG appears not to contain GR and is therefore not a QGT or even a physics theory but rather just some pretty but in the end vacant mathematics. This is not just my personal view, it's the view of the overwhelming majority of researchers in this field, though they don't argue about it since they choose not to deal with the misguided hobbiests in forums like these.

    One development likely to finally kill LQG off for good will be the generation in future accelerators of particles associated with the long predicted supersymmetries which have motivated so much important research in all aspects of physics (along with many aspects of mathematics as well) and required by strings for it's self-consistency.

    So, if you enjoy spending lots and lots of energy trying to understand a theory which few outside forums like this one take seriously, then go straight ahead andworry about LQG. If on the other hand you want to know about whats actually going on in the physics community, keep an eye on string theory.
  4. Jan 11, 2004 #3


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    ... and/or the discovery of such particles in astronomical research (e.g. cosmic ray detectors, GLAST).

    There are also a number of other astronomy projects that may provide solid support for - or refutations of - SST (SMT?) and/or LQG fairly soon, esp the neutrino telescopes and gravitational wave detectors.

    jeff -> is string theory at the point where it can account for neutrino oscillations yet? how about predicting the mass of any neutrino mixtures (with non-zero mass)?
    That's true, but isn't it a post-diction? What about predictions, in the sense of something specific and quantitative about things as yet undiscovered, such as the mass of the Higgs? How do SST/SMT and LQG compare in terms of their respective abilities to make specific, quantitative predictions (explicitly excluding post-dictions)?
  5. Jan 11, 2004 #4


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    The observation of supersymmetry, or the failure to find it (should that happen) is not a test of Loop Gravity since the theory can take it or leave it. Rovelli and Smolin have both made that point IIRC---anybody want a reference?

    It is sometimes said that string "requires" SUSY for its "consistency". So if LHC does not find SUSY that is certainly bad news for string (but it does not effect loop either way.)

    And if, on the other hand, SUSY is found, this also does not effect loop either way. The spin networks just have to carry more fields, more quantum numbers.

    Whether or not SUSY is found, string can still be wrong---supersymmetry is NOT in itself a final test of string theory.

    Either one or the other or both of the two theories, Loop and String, can be wrong---gotta keep an open mind, the proof is in the empirical pudding:smile:
  6. Jan 11, 2004 #5


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    I very much appreciate that you responded marcus. Thankyou.
  7. Jan 11, 2004 #6


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    hello Nibles, yeah I guess we might refrain from squabbles and get around to answering your question which basically was "what is Loop Gravity?" The way the term is used it includes several recently developed research lines---still small in terms of the number of people working them, but definitely experiencing an upswing, and getting results and gaining visibility.

    The first hardcopy book on the subject will be published this year
    or next---Rovelli's "Quantum Gravity", about 350 pages, Cambridge University Press.
    Also hardcopy textbook by Thiemann "Lecture Notes on Quantum Gravity" or some such title will be published by Springer Verlag, Berlin.

    Before this everything was online, or in scholarly journals. You did not have Loop books. So the field is getting established.

    this year there are already more Loop conferences scheduled than last.
    I listed some in the "Intuitive Loop---Rovelli's Program" thread
    in the LQG String Brane Forum here at PF. I try to keep that
    thread up to date on study resources and current events. So the
    upcoming conference links should be near the end of the thread.

    Also there was that Scientific American article by Lee Smolin, and the hardcopy magazine Physics World had its November issue devoted to Quantum Gravity and gave equal billing to Rovelli about Loop and Susskind about String. Loop has far fewer people than String but is nevertheless gaining parity in certain respects.

    The main names are Rovelli, Smolin, Bojowald, Thiemann, Freidel, Livine, Ashtekar, Corichi, Perez, Roche, Noui... I am leaving too many out. The main centers are Marseille, Berlin, Mexico City, Penn State, Waterloo, again it is hard to be complete.

    Experimental tests of Loop Gravity are expected soon---especially with GLAST starting 2006----and "Quantum Gravity Phenomenology" has become a hot topic with collaboration going on between LQG people and leading phenomenologists like Kowalski-Glikman and Amelino-Camelia.
    Phenomenology basically just means figuring out how to check theories against reality--how to get testable predictions from theory. Ted Jacobson, one of the founders of LQG with Smolin and Rovelli, is working primarily in phenomenology now---using astronomical data to narrow down and guide theory.

    I have some discussion of developments in that area in recent posts in the "Intuitive LQG--Rovelli's program" thread.

    So that is a birds-eye view of the research activity called Loop Gravity. There are links to plenty to read at that other thread.
    Now I'll try to give a sketch of the various lines of theoretical development that come under this heading----quantizing General Relativity, spin networks, spin foams (the 4D version of spin networks), the hardcore principles that characterize all these approaches.

    Actually Smolin's January 2004 SciAm article did that so well it is a shame to repeat it---I take it you read Smolin's article, which was the "cover story" of that SciAm issue.
    Last edited: Jan 11, 2004
  8. Jan 12, 2004 #7
    Yes, I believe it was Smolin's article that I read. Anyways, thanks for the replies, I suppose if LQG is a rediculous theory, as most seem to think, then there is no need to bother with it. It's not something I need to know, just something I was curious about since it was in the magazine .
  9. Jan 12, 2004 #8


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    Since strings contain QFT, it can accomodate all of these ideas.

    The point is that strings must contain GR.

    The only way to get LQG to make any kind of conventional QFT prediction is to somehow put the requisite structure in by hand. On the other hand, string theory is unavoidably a theory of everything and so automatically contains all the requisite machinery. The problem for string theory is then how to break the symmetries needed to produce low energy phenomenology consistent with observation.

    Suppose that while deciding between becoming a christian (string theory proponent) or a jew (LQG proponent) christ (supersymmetry) showed up. How persuasive would you find claims advanced by jews that this doesn't matter since they've no need of him and besides, it's possible that his 2nd coming could be incorporated into judiasm if necessary? My guess is not very.

    My basic point is that although this may be true, it's important to be honest and clear with PF members that only a handful of researchers have ever taken LQG seriously and that really strings dominate. It's not fair to take advantage of the lack of sophistication and knowledge of layman to coax them into spending enormous amounts of valuable energy learning ideas that have little bearing on what's currently driving high energy research.

    But not within the physics community.
  10. Jan 12, 2004 #9


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    I dont think this thread has any further purpose now that Nibles is satisfied that he doesnt have to know any more about Loop Gravity.
    After all, it began with him asking about LQG---we never got around to saying anything very real about the subject but regardless of whatever curiosity he had is finished.

    But I'll take the opportunity to give some of my own reasons (which others may share or not as they choose) why I am interested in Loop Gravity. I dont normally do this---I dont think anyone here should have to justify their physics interests. And I dont think I need to explain or justify liking to discuss LQG and report on recent papers etc.

    Loop Gravity is interesting for me because it says something about the fundamental texture of space and time---even about their very existence---and because some strands of the theory are surprisingly close to being testable (contrary to what was expected a few years back)----and because as a research field it is still small, each person's contribution counts----and because it is just now "coming of age" with its first hardcopy books (having been mostly online till now)---and because the researchers themselves are obviously excited.

    And because of a couple of notions that make Loop special.

    ----here's a footnote----
    I take for granted you know that classical 1915 Relativity itself is BI and DI----no fixed background geometry, no absolute space, time and space coordinates have no physical meaning. No absolute time or any notion of an ideal clock: since relativistic mechanics is about relations between observables (not about evolution in time, though one of the possible observables can be a reading from some particular real-world material clock).

    BI, background independence, says you have no prearranged background geometry---the shape of space is freely variable and dynamic.
    DI, diffeo-invariance, says any smooth deformation of a solution is still a solution. If the shape of space and the distribution of energy in it are related according to the theory, and if you then re-map the shape and the energy, they stay in the right relation. Solutions--like silly-putty--can be stretched and squeezed and bent around at will.

    BI and DI are the core principles of classical 1915 Relativity and they are what makes Loop Gravity different from stringy theories for example.
    -------end of footnote---------

    One suspicion I have about these things is that if GR is a large-scale limit of some more fundamental theory or class of theories, then those theories must also be BI AND DI.

    A major stumbling block for string theory has been that by not being Background Independent it fails to really reproduce GR---only a kind of fake version that is not BI (sorry if the abbreviation bothers you because also used in the classified sex ads but it is needed here too).

    A corollary of this is that string theory has not produced a candidate model of gravity that has GR as a large-scale limit. Since GR is BI and DI, you need some candidate which is itself also BI and DI, and because of string's basic limitations, such is not forthcoming.

    Incidentally this central failure of string theory (Tom Banks mentioned it when he said the long hoped-for goal of Background Independence in string theory was a "chimera"---I think he meant an elusive will o' the wisp) is why evidence of supersymmetry wouldn't make me more interested in string theory. SUSY is a liability for string, not an asset----predicted in an earlier theoretical context but something the theory cannot do without.

    ------now to get to the heart of why I'm interested----
    BTW remember YOU don't have to be interested in LQG. I dont care if you are or arent. I like to report on it and discuss it with others who share my interest. Some people may feel threatened by an open discussion of LQG but that's their problem.

    What I see happening in recent physics is Relativity taking initiative and driving progress. A large fraction of current theoretical and observational developments is about extremely curved spacetime situations or those with dynamic geometry----quasars, gammaray bursts, neutron star mergers, black holes, inflation, big bang, singularity removal, ripples in the CMB, the integrated Sachs-Wolfe effect, dark energy, accelerated expansion, cosmological constant. All these things are born out of GR. The interesting things in the news (physics-wise) are increasingly turning out to be General Relativity-type things.

    HEP physics is based on static geometry, it is built on fixed backgrounds which are NOT highly curved as a rule and not dynamic.
    Minor perturbations of geometry can be considered, but the underlying space is not freely-evolving. A fixed space either can't even expand or at best does so in a rigid artificial fashion.

    Fixed space theories can't cope gracefully what is increasingly of central interest. So HEP is out and GR is in---its that simple. What represents the leading edge of new understanding has started to be mainly in the precincts of Relativity (and I dont mean 1905 "special", which is not BI and DI and shouldnt even count as relativity).

    What I am saying here is an observation about the history of science and in particular physics. The HEP (high energy physics) paradigm with its fixed absolute space was in charge for a while and did great things. And now the GR paradigm has taken the initiative and is calling the important shots.

    People with a heavy investment in HEP-style thinking may sometimes feel envy or resentment---their sense of priority or privilege is somehow threatened---or they're in denial. Whatever. It does not concern me personally and it doesn't really have much to do with Loop Gravity.

    Loop Gravity is just the most direct way to quantize classic 1915 BI and DI General Relativity. In the process of doing that it may come up with an explanation of the cosmological constant---there are hints of that in the Girelli/Livine paper (link in the other thread).
    And it may come up with some non-commutative geometry or some quantum groups---like in the Noui/Roche paper (link in the same place).
    Or with high-energy, planck scale modifications of GR, of which classic GR is the large-scale limit. Or a modification of Lorentz symmetry that makes both the speed of light the same for all observers and other planck quantities the same as well (like in DSR
    and work by Kowalski-Glikman, Smolin and several others)

    Links to all those papers are posted here
    in the "Rovelli's program" thread

    In other words there are possibilities for interesting development stemming from insisting on really quantizing GR---preserving the core ideas of Background Indep and Diffeo-Invariance---and not giving up and falling back on some Absolute-Space-with-Gravitons substitute for GR.

    So there are some reasons I'm interested.

    Also I am not looking for something to believe in.
    Physical theories arent religions. The idea of setting out to choose one to believe in---to decide whether to be a this-proponent or a that-proponent---seems ridiculous. I can happily contemplate the possibility that all theories in sight are wrong.
    The question for me is where are the new concepts of space and time
    coming from that will allow quantum mechanics to be put together
    with general relativity. Rovelli discusses this in his book. From their birth early last century, QM and GR have had an incompatibility at the foundations level--they've been like oil and water.
    Uniting them will cause a basic re-thinking of space and time. I guess I'd like to be on hand as more of nature gets to be understood and able to watch the deeper ideas as they emerge.
    Last edited: Jan 13, 2004
  11. Jan 17, 2004 #10


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    I really enjoy reading your posts. Thanks.
  12. Jan 18, 2004 #11


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    I appreciate the compliment because I can return it,
    I enjoy yours----largely because of the gift for one-liners,
    the elements of humor and surprise.

    the Joan Crawford's daughter inset caused some discomfort
    but that may merely have been an idiosyncratic reaction
    Last edited: Jan 18, 2004
  13. Jan 18, 2004 #12


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    following the development of Loop Gravity means sharing
    in a common conjecture that the planck scale (which is different
    from the string scale) is fundamental and intrinsic to nature.

    That means there is a fundamental length and a fundamental frequency in the universe.

    The length is almost exactly (within half a percent) of
    E-38 of a mile

    the frequency is almost exactly (within a tenth of a percent or so) of E40 times middle D on a conventionally tuned piano.

    So if you know what a mile is, imagine 10-38 of it and that is Planck length.

    And if you know what middle D sounds like, imagine a frequency which is imagine 1040 times higher and that is Planck frequency, the reciprocal of planck time, one event per planck time unit, one radian of phase or turn per planck unit, whatever.

    The conjecture which is a semiconscious assumption in the minds of people involved with this kind of quantum gravity is that this frequency is "universe frequency" and this length also a universal---a threshold scale for new physics. Or a limit of some kind, the way the speed of light is a speed limit.

    It is not yet clear HOW these new scales are built into nature but the suspicion is that they are built into her as deep proportions.
    We think we understand fairly well how the speed of light is built in--thru all those special relativity formulas and thru the (lorentz) group of symmetries. But how, in what symmetries or formulas are these other scales present.

    An early hint was when Rovelli and Smolin calculated the Loop Gravity area and volume operator's spectrum and found that all the possible eigenvalues (in a quantum theory, the outcomes of measuring some observable thing like a volume or area) were order-one multiples of the planck area and the planck volume.

    Maybe they were wrong! The wheel is still turning.
    But they may in fact be right and, in any case, even if the result eventually needs to be revised it seems likely that area and volume will still turn out to be a discrete set of order-one multiples of the planck units. That is these units of area and volume are basic to nature and to nature's space. It is a space that can only have areas and volumes chosen from that discrete set.

    And then last year Girelli and Livine (part of a generation 20 or more years younger than Rovelli and Smolin) posted this exquisite 4-page paper that SPEED was quantized in little speed-steps too, in a way that incorporates the cosmological constant or vacuum energy density or "dark energy" density---something that can be incorporated as a small positive quantity rather easily in the theory, that "fits" in Loop Gravity without much trouble. Great that speed is quantized, but even better that determining the steps involves the density of dark energy.

    So that is the suspicion, the conjecture----that the basic stuffs of geometry are quantized----that nature is constructed that way: dyed-in-the-wool so it wont wash out.

    You can find the Girelli/Livine article link, if you want it,
    in this post of useful Loop links:


    For links to the National Institute of Standards and Technology page that gives values for the planck length, timescale, temperature scale and such:

    Last edited: Jan 18, 2004
  14. Jan 18, 2004 #13


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    Why, thank you very much!! :wink:

    Yes, I agree. That's why I posted it. I hate being alone in my discomfort zone.
  15. Jan 18, 2004 #14


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    Totally fascinating stuff, but, being the non-nerd that I am, it certainly gives me the worst twisty-face!!! But keep it comin'!
  16. Jan 19, 2004 #15


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    tutorial on natural units

    a distinctive thing about quantum gravity is that the planck scale of area and volume come out as a result---not something put in by hand.
    starting from very general principles like background independence and diffeomorphism invariance (Einstein called it "general covariance") rovelli and smolin were able to derive the area and volume spectra and they turned out to be a discret set of multiples of the planck area and volume units---the natural units (at least up to order-one factors) of area and volume.

    how to say this? It had been suspected on general theoretical grounds for more than half a century that a new picture of spacetime would emerge at planck scale. But when LQG came along it pointed like a compass-needle at that scale, without having been told by its inventors to do that. (smolin, rovelli 1995)

    so if someone wants to follow the ongoing development of quantum gravity they would do well to get a comfortable familiarity with the planck units, hence this informal introduction.

    down at the end of this post I will just directly define them in the immediate hard-ass algebraic way, as is usually done, without a serious attempt at motivation. So if you want to avoid the gradual step-by-step introduction, just scroll down and there will be the usual formulas.

    -------gradualist treatment of planck units------

    one way to get a handle on them is to take a fresh look at one of the most basic equations in science, the 1915 Einstein equation, the central equation in our model of how gravity works: General Relativity. this equation relates the density of energy in a region ("joules per cubic meter", "footpounds per cubic foot") to the curvature in that region. It says the two are proportional!

    Except for a factor of [tex]8\pi[/tex] which is no big deal, and the fact that they use special symbols for curvature and energy density, this equation is customarily laid out this way:

    [tex]curvature = \frac{G}{c^4}energy density[/tex]

    Curvature in this context is measured in units of reciprocal area ("per square meter", "per square foot").

    Now just suppose that we deviate a tiny bit from the customary layout and write the Einstein equation this way:

    [tex]\frac{c^4}{G}curvature = energy density[/tex]

    This quantity c^4/G is the planck unit of force, that is, the force unit which belongs to a system of units that Max Plack discovered in 1899 and presented to his contemporaries as a natural (rather than artificial or man-made) system of units.

    So in 1915 Einstein discovered that nature knows about the force
    c^4/G. It is the force that connects the amount of curvature in a region to the energy density there.

    For dimensional reasons a force is the only type of quantity that can do that. Multiplying a curvature ("per sq. foot") by a force ("pounds") gives a pressure ("pounds per square foot") and that is dimensionally the same type of quantity as an energy density
    ("footpounds per cubic foot"). Or say the same thing substituting metric newtons for pounds and meters for feet. Newtons per sq. meter is the same as joules per cubic meter. The longandshort is that if you multiply a curvature by a force you get an energy density and the only thing you CAN multiply a curvature by to get an energy density is a force. Einstein found that the force that works in this context
    is the unit force c^4/G in planck's 1899 system of units


    we can get all the planck units from this force, and stuff you already know like the speed of light

    People COULD have realized that planck units were basic as early as 1915, but they did not and it was still a bit surprising in 1995 when the area and volume spectra were found to be multiples of planck area and volume units. Our species is not quick to catch on, sometimes.

    To summarize
    around 1900 Planck discovered that nature knows about a certain ratio of energy to frequency called hbar. (when using hbar you need to express frequency in angular format, radians per unit time, but that is a technicality involving a factor of 2pi and I wont belabor it)

    in 1905 Einstein reminded everybody that nature knows about c the speed of light, in fact you could almost say nature is obsessed with the speed of light. that was the year he expounded the universal speed limit and E = mc^2 and a bunch of other things involving c.

    in 1915 Einstein showed that nature knows about a certain force
    c^4/G which is the force unit belonging to Planck's system of natural units. It turns up as the central constant in General Relativity: the thing that relates the lefthand side to the righthand side in the main GR equation. If you have a book where you can look up the metric values of G and c, or if you just know them, then you can easily calculate what the planck force unit is---just follow the formula c^4/G. You will get the answer in terms of the metric force unit, the so-called "newton" which is about a tenth the weight of a kilogram in normal gravity.

    all the other planck quantities come from these three that were already immanent and obvious in 1900, 1905, 1915.

    in any system of units the unit power is always equal to the unit force multiplied by the unit speed (in our case c^4/G multiplied by c)
    If you work out c^5/G with a calculator you get planck power unit is
    3.6E52 watts. Lots of watts.

    In the planck system, hbar is the ratio of unit energy to unit frequency. So unit power divided by hbar gives the square of unit frequency, namely c^5/hbarG

    [tex]unit frequency = \omega = \sqrt{\frac{c^5}{Ghbar}}[/tex]

    this is a frequency expressed in angular format, so the convention is to use the symbol omega for it, instead of the letter f.
    Anybody who wants can immediately find out what the planck unit energy is at this point because it is [tex]hbar\omega[/tex]
    in a consistent system of units the unit length is equal to the unit speed divided by the unit frequency
    so in our case
    [tex]unit length = \frac{c}{\omega} = \sqrt{\frac{Ghbar}{c^3}}[/tex]

    that's about it for the definitions, now we have unit force, power, frequency, time (the reciprocal of frequency), and length----the rest derive in familiar ways from these. the mass unit, for instance, is equal to the energy unit divided by the square of the unit speed (the square of the speed of light) and so on like that.
    now the question is: what sizes are these units. Of course now you have the formulas for many of them so you could calculate them out in metric terms. But to save you the bother, the best way I know is just look them up at the NIST website.

    BTW the NIST "fundamental constants" website has the planck temperature unit too---which is the planck energy unit divided by boltzmann's constant.

    Beyond just always looking them up, there are some facts about them that are not too hard to remember. Like 2E-30 planck temp is a reasonably good reference temperature to remember---it's about 10 Celsius or 50 Fahrenheit. And E38 planck length is a mile.

    -----direct no-nonsense definitions----

    [tex]unit time = t_P = \sqrt{\frac{Ghbar}{c^5}}[/tex]

    [tex]unit length = l_P = \sqrt{\frac{Ghbar}{c^3}}[/tex]

    [tex]unit energy = E_P = \sqrt{\frac{c^5hbar}{G}}[/tex]

    [tex]unit temperature = T_P = \frac{\sqrt{\frac{c^5hbar}{G}}}{k}[/tex]

    -------direct no-nonsense explanation---------

    the only way that it is possible to cook up a quantity with the dimension of time using the quantities G, hbar, c is this definition written here and simple constant multiples of it, but why bother to scale the thing by an extra number?

    since c is going to be unit speed in the system, it must be unit length divided by unit time
    so to get unit length simply multiply tP by c (unit time by unit speed)

    since hbar is the product of energy with time, and since it is going to be a unit quantity in the system, it must be equal to the unit energy multiplied by the unit time
    so to get the unit energy simply divide hbar by the unit time

    the boltzmann k is a ratio of energy to temperature and it is a unitary ratio (like c and hbar) in the system
    so to get the unit temperature, divide the unit energy by k

    I'm trying to remember how to spell the original titles of the two basic references. Planck's 1899 paper is little-known but lays out the system and gives essentially the same values for the basic natural units that we use today

    Planck (1899). "Ueber irreversible Strahlungsvorgaenge. Fuenfte Mitteilung." Koeniglich Preussische Akademie der Wissenschaften (Berlin). Sitzungsberichte: 440-480.

    Einstein (1916) "Grundlage der allgemeinen Relativitaetstheorie"
    Last edited: Jan 19, 2004
  17. Jan 19, 2004 #16

    Ivan Seeking

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    After reading the last post, Tsunami looked at me and said that her face is now permanently stuck in the twisted position. Thanks a lot Marcus!
  18. Jan 19, 2004 #17


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    well Ivan you know I never have a sure notion of who, if anyone,
    reads these posts. Or for whom, and at what level, to write

    Did you ever read from the 3 article series "Scaling Mount Planck"
    in Physics Today, by Frank Wilczek.
    Wilczek is one of todays great (senior) theoretical physicists, at least in my view, and he gave one of best explanations Ive seen for why one ought to try to understand Planck scale and think about things from Planck scale perspective.
    It is hard tho because the natural units are so extreme, many of them.
    But they seem more and more to be a part of nature.

    Tell Tsunami to smile enigmatically (as if she were nature) instead of looking puzzled

    the calm enigmatic smile is the other side of the twistyface and much easier on the eyes
  19. Jan 19, 2004 #18

    Ivan Seeking

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    If not I will...I don't recall reading the series.

    Really don't worry. She has looked twisted and pain ridden since the day we got married.

    I am goint to say diffeomorphism invariance a lot for awhile just to annoy her. By the way, she wanted to know if this - diffeomorphism invariance - has anything to do with Michael Jackson?
  20. Jan 19, 2004 #19


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  21. Jan 19, 2004 #20


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    Wilczek gives a way to understand why the planck time is so brief and the planck length so tiny

    he starts by considering the question of why gravity is so weak
    compared to other forces, and defines a number N as a measure or indicator of its weakiness, and about halfway thru the first paper he says:

    "...Thus hbar and c appear directly as primary units of measurement in the basic laws of these two great theories. Finally, in general relativity theory, spacetime curvature is proportional to the density of energy--and G (actually c^4/G) is the conversion factor.

    If we accept that G is a primary quantity, together with hbar and c, then the enigma of N's smallness looks quite different. We see that the question it poses is not, "Why is gravity so feeble?" but rather, "Why is the proton's mass so small?" For in natural (Planck) units, the strength of gravity simply is what it is, a primary quantity, while the proton's mass is the tiny number sqrt N.

    That's a provocative and fruitful way to invert the question, because..."

    The tiny number sqrt N that he is talking about is one over the rather large number 13.01 quintillion. It is one of a small bunch of mysterious numbers that are really fundamental constants, like 137 or 1/137. It is easiest to remember it as 13E18 or 13 quintillion.

    What Wilczek says is that our theory is being challenged to explain this number 13 quintillion, and (surprisingly enough) according to him it is making some progress towards explaining it!

    Remember Feynmann saying something like this about the number 137, that in his opinion every physicist worth his salt should have that number pasted up on the wall to remind him to try to figure out why it was that----why it was 137 instead of something else.
    (I dont always distinguish between numbers and their reciprocals as you see :wink:)
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