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Can we transpose the Cambridge Handbook into natural units?

  1. Apr 1, 2005 #1


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    I am interested in a system of natural units that I see used more and more frequently in Quantum Gravity research papers so I like to try using them.

    the units are like conventional planck except |8piG| = 1

    I want to see if there is anything in the Cambridge Handbook of Physics Formulas which would be fun to transpose into natural units and see how it looks. Essentially to see how various formulas look if you
    set 8piG = c = hbar = k = e = 1
    (well not exactly but that's the idea)

    Richard has a copy of the handbook, I might have to get one or borrow a library copy.

    here is the publisher's page on it:

    here is the TOC:

    1. Units, constants and conversions;
    2. Mathematics;
    3. Dynamics and mechanics;
    4. Quantum physics;
    5. Thermodynamics;
    6. Solid state physics;
    7. Electromagnetism;
    8. Optics;
    9. Astrophysics;
  2. jcsd
  3. Apr 1, 2005 #2


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    well a new thing happened (something I hadnt experienced before)
    I went to Cambridge press and looked at the publisher's page on this
    and it offered to let me see a sample chapter and i clicked on that sample

    and it let me download a 20 page pdf file which basically is the detailed TOC plus Chapter 3, pages 63 -78 of the book.

    I have this file on my desktop now, but something prevents me from doing any "copy and paste" with it. If anyone happens to be interested, they could get Chapter 3 which is "Dynamics and Mechanics" and see if they can copy and paste. I can't

    It seems like a useful book, for a working physicist, but very expensive!
  4. Apr 1, 2005 #3


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    now I see, the PDF file of the sample Chapter 3 that you get to
    download is "password protected"
    so one can only view it.
    one cannot print it off, or copy and paste.

    that's fine. I am glad they let us view any sample of the book at all!

    I looked at the Dynamics and Mechanics chapter and the formulas area already very clean

    when he comes to General Relativity he switches to a system of units where c = G = 1
    so the formulas are very clean and streamlined
    So there is an 8pi in the einstein equation but we should not make a big deal. What he is doing is making things as neat as possible without doing anything the slightest unconventional. This is the right style for a handbook writer.

    It is a very nice book. Right now I dont see how we can make use of it but maybe something will turn up.
  5. Apr 1, 2005 #4


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    Last edited: Apr 1, 2005
  6. Apr 2, 2005 #5

    john baez

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    Yay! The main good thing about these units is that Einstein's
    equations become

    G = T

    instead of the annoying

    G = 8 pi T

    as they are in conventional Planck units, or the even sillier

    G = 8 pi G/c^2 T

    in SI units (where G means something completely different on the
    two sides of the equation, to make matters even more confusing).

    In Planck units, you get weird factors of pi all over the place.
    So, I've been using units with 8piG = 1 in my own work for years,
    despite some objections:

    J. J. Lodder Feb 15 2000, 12:00 am
    Newsgroups: sci.physics.research
    From: (J. J. Lodder)
    Date: 2000/02/15
    Subject: Re: Permittivity and Permeability Constants of Vacuum

    John Baez wrote:
    > Well... actually, like the particle physicists, I set c = hbar = 1.
    > And nowadays I also set 8 pi G = 1, to eliminate the disgusting factor
    > of 8 pi in Einstein's equation. This minimizes the amount of stuff I
    > need to remember, so I can go ahead and quantize gravity in peace instead
    > of pulling out my hair all the time trying to get the damned constants
    > straight.

    > Now, some people may complain that I should stick to SI units or else
    > bridges will start collapsing and satellites will start crashing... but
    > I promise not to build any bridges or satellites, so I don't think this
    > matters in my case. Any bridges I built would automatically fall down
    > anyway....

    Just curious:
    Are you going to mutilate Planck's units as well,
    or will you have an inconsistent Einstein/Newton versus Planck system,
    which will cause your black holes to fall down.

    (to the wrong radius :-)

    Last edited: Apr 2, 2005
  7. Apr 2, 2005 #6


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    If marcus had his way... I would weigh 1.33E28 GeV
  8. Apr 2, 2005 #7


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    I dont see the point of yr post, Chronos. It is not even close enough to be a parody, much less give any idea of what I've been trying out.

    If you use the Planck-variant units Baez is talking about then E8 mass units comes to about a pound (434 grams if you have to know more precisely for some reason)

    so think of E8 as a pound, and if your mass is OOM 200 pound conventional, then it is 200E8 natural.

    I guess if I had my way (which aint very likely) you would just quietly be aware that in natural units your mass is 2E10
    and wouldnt need to talk about it :smile:
  9. Apr 2, 2005 #8


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    I hope you meant

    [tex] \hat{G}=\frac{8\pi G}{\displaystyle{c^{4}}} \hat{T} [/tex]...

  10. Apr 2, 2005 #9


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    Professor Baez, the answer to your question is here. Marcus not only uses the "deformed" Planck units, he justifies doing so by reference to existing practice in the LQG program.
  11. Apr 2, 2005 #10


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    If you read Baez post he confirms the existing practice saying that he uses the |8piG| = 1 units in his own work.

    what your post identifies as "your [Baez] question" was a sarcastic question posed by Jan Lodder to Baez after Baez had defended (on SPR) the practice of using modified Planck units with |8piG| = 1.

    Since then it looks to me as if Planck units with |8piG| = 1 have become much more common and I wonder if JJ Lodder would be so vehemently opposed to them now. Things that seem offensively newfangled at one time can begin looking pretty usual a couple of years later.
  12. Apr 2, 2005 #11


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    I take exception to calling this variant of Planck units "deformed" (dont know who is being quoted). I think that adjusting by giving 8piG unit value is a slight improvement.

    Also the link you gave, selfAdjoint, to the other thread needs to be supplemented, since a reader could easily get lost in non-essential and miss the gist. the thread you linked to contains physics problems couched in natural units terms.

    Exercises to get familiar with the natural units or, for those already familiar with them, to keep in practice using the units:

    Robin Hood and the giant chickens (I.)

    Robin Hood and the giant chickens (II.)

    Robin Hood and the giant chickens (III.)

    Robin Hood challenges the giant chickens

    Robin Hood and the giant chickens (episode IV)

    Batman in zero gee

    Batman at bedtime

    Batman and his aircushion vehicle

    Frog and Toad at the merrygoround

    Henry Cavendish

    Frog and Toad visit the ladies

    Frog drives his sportscar (and Toad almost gives him a ticket)

    Short people and static electricity

    How the gypsies stole the moon

    Rimbaud and Verlaine in Brussels

    The angle of deflection of the cat

    Count Rumford and the Genii

    The cat engines of the ships of Ornish

    Invasion of the Junk Food Snatchers

    The au pair girls go to the planet of the giant air-breathing squid

    How the giant squid heat their hot tubs

    The Ornish battle cruiser punishes Trenton New Jersey with lightning

    An Ornish scout ship avoids hitting Atlantic City

    The ballerina on the asteroid

    A traditional rollercoaster problem

    The Akamatsu Incident

    The King who needed soldiers

    The Prince and the Diva

    The sage and his boombox

    Dog and Goat go for a balloon ride

    The vegetarian pirate gets airconditioning

    Dog and Goat reckon the fuel needed for liftoff

    Goat weighs the family car

    Goat measures the height of the clouds using gin-and-tonics

    The cyclotron frequency of the proton

    The cyclotron frequency of the cat

    Measuring a 1 Tesla field with stirrup gauge

    Terminal coasting speed for cyclist going down a hill

    Bohr magneton and magnetic moment of the electron

    Speed of solar wind particle

    Length of organ pipe

    A sentimental keepsake black hole

    Orbiting a small planet at tree-top level

    Airplane flying over the north magnetic pole

    Convection and temperature gradient on Titan

    Rough sizes of nat. units and some useful constants (may be a duplicate of a more recent post)
    How to get metric equivalents if you like them
  13. Apr 2, 2005 #12


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    Sorry about the mixup, Marcus. I was distracted (infected foot).
  14. Apr 2, 2005 #13


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    drat. what a shame!
    are you soaking in strong warm epsom salt solution?
    no problem about mixup!

    what did you do to get an infected foot?
    my son always drops things on his feet while he moves to a different house, my wife goes barefoot in the garden. they both suffer the consequences.
    Man is a shoe wearing animal with vestigial toes that he would be better off without.
    Last edited: Apr 2, 2005
  15. Apr 2, 2005 #14
    Hi all

    The CHOP formula book uses SI units, choosing to reduce pretty much everything to units of length, mass, time interval, electric current, thermodynamic temperature, amount of substance, and luminous intensity. This would be the SI metre, kilogram, second, ampere, kelvin, mole, candela scale, I guess. They point out that the choice of base units is somewhat arbitrary.

    Force is derived as the Newton, m kg s^-2. A few others: illuminance, lux, lx, cd sr m^-2. Luminous flux, lumin, lm, cd sr. Radient flux (power) watt, W, Js^-1.

    I would have been confused by cd and sr in the notation, but they are mostly pretty thorough and define everything. A cd is a candela, and sr is stereoradian, a three dimensional version of plane angle, dimensionless at m^2 m^-2.

    They also recognise some non-SI units. Area, barn, b, 10^-28 m^2. Energy, eV, 1.60218 x10^-19 Joules. Under mass, they like the unified atomic mass unit, u, 1.66054 x10^-27 kg. Then follows some pages of constants, followed by more pages of conversions, and finally two pages of dimensions. I was looking at these when I had the brilliant idea of adding a column for values in force constant units.
    Last edited by a moderator: Apr 2, 2005
  16. Apr 2, 2005 #15
    I once had a cat named Micawber. One evening he astonished me by running full speed across the yard, then lept to a height above the level of my head, where he intercepted and caught a bat in mid-flight. If anyone had told me a cat had done that, I would have said it is impossible. But who knows? Maybe something will turn up.

    Meanwhile I am having lots of educational fun with the CHOP. My creaky old head doesn't churn through formulas as fast as yours, does, Marcus. By the time I have figured out what one thing is, I have forgotten what the other thing was, or even why I wanted to know how they stood in relationship. Drat! But I am working on it.

  17. Apr 2, 2005 #16

    john baez

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    It just goes to prove my point: this beautiful equation gets awfully cluttered if you use the wrong units!

    (You could even be bluffing, and I wouldn't know unless I did some dimensional analysis.)
  18. Apr 2, 2005 #17


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    a literary gem anecdote
    what makes it good is the last sentence
    surprise LOL throwaway quote unostentatiously completing the idea of the impossible being possible AND the Dickens connection
    not one word can be changed. congratulations

    as for the CHOP and your idea of "adding a column" to the list of fundamental physical constants. that is a good idea
    if you supply a list of constants----I would say just choice ones, perhaps not more than 20, perhaps even fewer----in a table form where I can edit, then I would be happy to supply numbers for a natural units column.

    footnote for whoever hasnt read Dickens: there is a Dickens character Mr Micawber whose favorite thing to say is "Maybe something will turn up."
    Richard the nightcleaner and selfAdjoint the supermentor know this. that's the high level that prevails at PF, so be advised
    Last edited: Apr 2, 2005
  19. Apr 2, 2005 #18


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    dexter is right (he never bluffs on purpose) and it does prove the point.

    when a fundamental equation gets so cluttered that one has to memorize whether 2 or 3 or 4 in the exponent of something that shouldnt be there in the first place then it is time to reduce the knobs on it
  20. Apr 2, 2005 #19


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    Just to spoil everybody's fun and literal-mindedly identify the source, it's David Copperfield, and the improvident, cheerful Micawber, who notably comes through in the clinch, is supposed to be based on Dicken's own father.
  21. Apr 5, 2005 #20


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    Drat, marcus caught my glaring mathematical error. I recalculated the conversion and agree I am am either 8 years old, or emaciated. I forgot to square the 3 in c = 3E09 m/s. :redface: Oops, marcus doesn't miss much.
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