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Physical Units
"... nearly a third of what you have to learn ..."

Richard P. Feynman

In Fond Memory of
Richard P. Feynman (Nobel 1965)
May 11, 1918 - February 15,1988

The Feynman's Lectures on Physics are based on a famous course of undergraduate lectures given at Caltech by Professor Richard Phillips Feynman in the early 1960's.  What Dick Feynman had to say to undergraduates about various physical units was considered too trivial by the editors and was not included in the published version of these lectures.  We resurrect it here, from the audio record, as a tribute to Richard P. Feynman.

See also: Feynman Online  |  There's Plenty of Room at the Bottom
A Life in Science (John & Mary Gribbin, 1997)

NOTICE: The text quoted below was transcribed by Dr. Gerard P. Michon from a copyrighted 6-hour audio record (© 1997 by the California Institute of Technology), published by Helix Books (Addison-Wesley, Reading, MA) with a printed collection of edited lectures by Richard P. Feynman, entitled "Six not-so-easy pieces".  Applicable copyright laws allow this short excerpt to appear here, but a formal permission from the California Institute of Technology and/or other parties may be required to reproduce any part of this text in a broader context.

For those who want some proof that physicists are human, the proof is in 
 the idiocy of all the different units which they use for measuring energy.
The Character of Physical Law (1967) R.P. Feynman   [ 1964-11-12 video ]

Before I begin the lecture [on spacetime], I wish to apologize for something that is not my responsibility: Physicists and scientists all over the world have been measuring things in different units, and causing an enormous amount of complexity.  As a matter of fact, nearly a third of what you have to learn 1 consists of different ways of measuring the same thing, and I apologize for it.  It's like having money in francs, and pounds, and dollars...  with the advantage over money that the ratios don't change, as time goes on.

For example, in the measurement of energy, the unit we use here is the joule (J), and a watt (W) is a joule per second.  But there are a lot of other systems to measure energy.  There are at least three different ones for engineers, which I have listed here.2

The physicists do something else when they want to talk about the energy of a single atom, instead of the energy of a gross amount of material.  The reason is, of course, that a single atom is such a small thing that to talk about its energy in joules would be inconvenient.  But instead of taking a definite unit in the same system (like 10-20 J), they have unfortunately chosen, arbitrarily, a funny unit called an electronvolt (eV), which is the energy needed to move an electron through a potential difference of one volt, and that turns out to be about 1.6 10-19 J.  I am sorry that we do that, but that's the way it is for the physicists.

Arms of Amedeo Avogadro The chemists also talk about the energy per atom.  Since they don't use the atoms individually but large blobs of them, in cans and barrels, they've chosen a certain number of atoms as a unit.  This number of things is called a mole (mol), and it is 6.023 1023  objects.  The more precise definition, which is now correct or soon 3 will be, is that one mole of carbon-12 atoms has a mass of exactly 12 grams.  A mole is just a certain number of things.  So, instead of giving the energy per atom, the chemists give the energy per mole.  It's good, therefore, to know how much energy is a mole of electronvolts.  In other words, if each atom had one electronvolt of energy, a large number of atoms would have a reasonable amount of joules, namely 96500 joules per mole.  Incidentally, a mole of electrons has a total charge of 96500 coulombs (C); these numbers are equal for a reason you have to figure out.4

Now, there is an additional unit that the physical chemists use, the kilocalorie per mole (kcal/mol), and 23 of those is an electronvolt per atom.   [23 kcal  =  96500 J]

Finally, unfortunately, you have another system for measuring masses.  The mass of an atom, from a chemist's point of view, is given by the mass of a mole of these atoms.  For example, the mass of carbon-12 is called 12 "atomic mass units" (u), because a mole of carbon-12 "weighs" 12 grams (or rather "has 12 grams of mass").  One atomic mass unit represents one gram for every mole of objects, one gram per mole.  We can measure that in electronvolts also.  "You can't measure mass in electron volts!" 5  Sure you can, because of the relation E = mc...  It is useful to know how much energy corresponds to the consumption of one atomic mass unit of material: That turns out to be about 931 million electronvolts (MeV).  Incidentally, the rest mass of a proton is 938 MeV, while the rest mass of an electron corresponds to 0.511 MeV.  The number 938 differs from 931, because a proton has a mass of about 1.008 amu.

I am sorry about the confusion produced by all these systems of units.  I left out, obviously, a large number of different things.  For example, when measuring luminous 6 energy, the lumen (lm) is used, which corresponds to about 1.5 mW of power in the "most visible" light, around 5500 Å (ångströms).  It's all very annoying, but don't worry about it now.  When you need to measure light, just look up in a book what a lumen is.

That's an unfortunate fact that we measure things in a whole series of different kinds of units.  This causes a lot of confusion.

It's too bad, but I have already apologized, and there is nothing else I can do...

Richard P. Feynman (1961)

Notes :
1  Feynman may well be overstating the case, but the opposing understatement is so widespread that we decided to feature this statement as a subtitle for this web page...  
2  Consistent "engineering" systems of mechanical units are listed below.  The units of energy and power advocated by Feynman for use at CalTech, the joule (J) and the watt (W), are metric (SI) units.  The other systems are now obsolete, or are being deprecated:
  • Metric system (SI) for mechanical units (MKS = meter-kilogram-second).
    The unit of force is the newton (N).  The unit of energy is the joule [J].
  • CGS system (centimeter-gram-second).
    The unit of force is the dyne (dyn).  The unit of energy is the erg [erg].
  • British [absolute] system (foot-pound-second).
    The unit of force is the poundal [pdl].  The unit of energy is denoted ft-pdl.
  • Metric-technical system, or "gravitational MKS" (meter-hyl-second).
    The unit of force is the kilogram-force [kgf].  The unit of energy is denoted kgm.
  • British engineering system, or "English gravitational system" (foot-slug-second).
    The unit of force is the pound-force [lbf].  The unit of energy is denoted ft-lb. 
3  The CGPM finally adopted this definition of the mole in 1971.  It is based on the "unified" definition of the "atomic mass unit" as 1/12 the mass of a Carbon-12 atom, which was adopted at the 10th General Assembly of the International Union of Pure and Applied Physics (Ottawa, 1960) and subsequently by the International Union of Pure and Applied Chemistry in 1961.  The unified unit (symbol "u") replaced two earlier competing definitions, both using the symbol "amu", which were based on different aspects of oxygen:  The physical amu was defined to be 1/16 of the mass of the Oxygen-16 atom, while the larger chemical amu was 1/16 of the average mass of an atom of natural oxygen, with the isotopic composition found on Earth (99.759% O-16, 0.037% O-17, 0.204% O-18).  The unified amu (u) is only 0.004% more than this chemical amu.  Thus, the chemists got to keep the value of their amu, while the physicists got their wish in having the atomic mass unit defined in terms of a given nucleus, not an isotopic mixture.  The symbol for the unified amu is "u".  A chemical amu was 0.999958 u, a physical amu was 0.999687 u.   [See sizes.com].  The unified atomic mass unit (u) is increasingly referred to as a "dalton" (symbol Da) in honor of  John Dalton (1766-1844).  That name was adopted by the IUPAC in 1993, by the CIPM in 2003, by the IUPAP in 2005 and by ISO in 2009. 
4  Moving a mole of electrons through a potential of one volt involves an energy equal to a mole of electronvolts.  Expressed in joules, this equals one volt multiplied by the charge of a mole of electrons, expressed in coulombs  (Faraday's constant). 
5  To remove this objection, the "Mev of mass" is now best abbreviated  Mev/c2.  Similar notations are used for other mass units obtained from various energy units. 
6  In the spoken lecture, Feynman wrongly used the qualifier "radiant", instead of the term "luminous" which properly qualifies electromagnetic radiation measured with the spectral sensitivity of the human eye under normal "photopic" conditions (when the eye adapts to darkness, it has a different spectral response, which is called "scotopic").  Luminous power --often called "luminous flux"-- is expressed in lumens, whereas the corresponding radiant power would simply be measured in watts.  The qualifier "bolometric" may be used for radiant power, to insist that radiant measurements are meant to include all energies at all frequencies with the same weight, which is not the case for luminous measurements.
Current  (CODATA-2010)  recommended values for the fundamental
constants and the conversion factors quoted by Richard Feynman:

 Electronvolt (ev) 1.602 176 565(35)  10-19 J
 - Thermochemical (1 kcal º 4184 J)a 23.060 548 88(51)   kcal/mol
 - International Steam Tables (IT, IST)b 23.045 126 71(51)   kcal/mol
 Avogadro Constant 6.022 141 29(27) 1023/mol
 Faraday Constant 96 485.3365(21)  C/mol
 Atomic Mass Unit (u) 931.494 061(21)  Mev/c2
 Mass of the Proton 938.272 046(21)  Mev/c2
1.007 276 466 812(90)  u
 Mass of the Electron 0.510 998 928(11)  Mev/c2
 Mechanical Equivalent of Light
 (1/683 watt per lumen at 540 THz)c
1.464 128 843 338 21...  mW/lm
 Wavelength of Light at 540 THz
 (c = 299792458 m/s)d
5551.712 185 185 185...  Å
 Precision is indicated by the estimated standard deviation (between
 parentheses), expressed in units of the least significant digit shown.
  1. In 1935, the thermochemical calorie was defined as exactly equal to 4.184 J.  No other conversion factor is acceptable for modern chemists  (or nutrionists).
  2. The fifth  International Conference on the Properties of Steam  (London, July 1956)  adopted the most authoritative version of the  British thermal unit  (Btu)  by equating  1 Btu/lb  to exactly  2326 J/kg.  Conversion factors derived from this equivalence are identified by the abbreviation IT or IST (International [Steam] Tables).  When the avoirdupois pound was finally defined in metric terms as exactly 0.45359237 kg  (effective January 1, 1959), the  IT Btu  became equal to exactly 1055.05585262 J (namely, 2326 J  multiplied into the ratio of the pound to the kilogram).
    To this official Btu corresponds, unfortunately, a widespread (bogus) "IST kilocalorie" obtained by equating a kilocalorie per kilogram to 1.8 times the above ratio of  2326 J/kg  (since 1.8°F is 1°C).  This makes an "IT calorie"  exactly  4.1868 J.  However, this wasn't a reason to revise thermochemical data that had been published for decades with the firm 1935 equivalence of  4.184 J  to the calorie.  Most authors were wise enough to hold on to that established equivalence but the  bogus  conversion factor of  4.1868 J/cal  has infected computers, handheld calculators and... the above table  (sort of).
  3. Since 1979  (16th CGPM)  the  candela  is defined so that the "Mechanical Equivalent of Light" is  exactly  one watt per 683 lumens  (at 540 THz).
  4. The speed of light in a vacuum (c) is Einstein's constant (the name was advocated by Kenneth Brecher of Boston University, in April 2000).  Because of the (fifth and final) definition of the meter adopted by the 17th CGPM in 1983, Einstein's constant is now exactly equal to 299792458 m/s.
          In 1948, the definition of the ampere by the 9th CGPM equated the magnetic constant mo  (the permeability of the vacuum)  to  4p 10-7 H/m  (one henry per meter  is the same as one  newton per square ampere ).
          The second has been defined in absolute terms since the 13th CGPM, in 1967.  (The previous astronomical definitions are obsolete.)
          The final fundamental step in the construction of the SI system would be to redefine the kilogram by giving yet another fundamental constant an exact value.  For this transition to happen seamlessly, current precision on the known value of such a constant should be about as good as the precision of comparisons with the international prototype of the kilogram.  We are almost there:  A large device (2 stories high) called a watt-balance compares a mechanical watt (proportional to a calibrated mass) to an electric watt, known in terms of the Planck constant.  The best watt-balances have already determined Planck's constant [namely 6.626 069 57(29) 10-34 J/Hz] to an accuracy (1 s) of about 0.044 ppm, which is within a factor of 2 from the best mass comparisons.  The end is in sight.

Richard P. Feynman The Feynman Webring

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We are proud to have this page belong to the Feynman Webring, which connects a number of fine pages which perpetuate the legacy of Richard Feynman in various ways.  Some are more controversial than others:

At this writing, the next site in this ring happens to feature an essay where James G. Gilson presents his own formula (involving two integer parameters) for the value of the so-called Fine-Structure Constant  a = 0.007297352533(27) [whose reciprocal is 1/a = 137.035 999 76(50)].  This dimensionless fundamental constant of Nature was apparently first introduced in 1915 or 1916, by Arnold Sommerfeld (1868-1951).

alpha = mu0 c e^2 / 2h

Sommerfeld's Fine-Structure Constant  may be viewed as the only free parameter in QED, the relativistic quantum theory of the interactions between electrons and photons (for which Feynman, Schwinger and Tomonaga shared the 1965 Nobel Prize).  In QED, the coupling constant's effective limit is simply the square root of a, and Feynman was understandably annoyed that QED was thus based on an unexplained numerical value.  He expressed the wish that a deeper understanding of Nature would eventually explain that value and/or allow it to be expressed in terms of known constants, like p or e.

Before and after Feynman, others have tried to guess such a relation, possibly hoping that it could be a clue to whatever more general theory may underly our current understanding of the laws of Nature.  Around 1923, Sir Arthur Eddington (1882-1944) "proved" a to be 1/136, in agreement with early rough estimates.  When subsequently faced with incompatible experimental data, he amended the "proof" to show that the value had to be 1/137, so that Punch magazine dubbed him Sir Arthur Adding-One.  See 137 by Charles C. Mann, or look up the description by Robert Munafo of the so-called Eddington number [the outrageously asserted total number of electrons in the Universe, as the inverse of the fine structure constant multiplied by a power of two].

The two integers in Dr. Gilson's dubious formula may be tuned to accurately reflect modern experimental data only up to a point:  The pair (137,25) was the best match for the midrange of the previous (1986) CODATA value of a [namely 0.00729735308(33)] and (137,29) is a good match for the current one (CODATA 1998, as of 2002).
Interestingly, Gilson quotes Michael Wales, who had argued that the cube of a should be the reciprocal of some integer (namely 2573380).  The 1986 CODATA value of a placed Wales' number at 2573379.99(35), which encouraged the conjecture.  However, the more precise 1998 CODATA update gives 2573380.571(29), which does not stand any reasonable chance of being an integer!  Even more so with  2573380.5325(25)  the value derived from CODATA 2010.
Likewise, for the pair  (137,x)  to match the value  137.036999076(44)  with Gibson's formula, the parameter  x  ought to be  28.645(23).  Not an integer!

Gilson's formula and its justifications are pseudoscientific.  Gilson is [at best] guilty of wishful thinking when he presents his formula as a generally accepted  fait accompli.  This is simply  not so.  You've been warned; you may proceed  (http://www.fine-structure-constant.org/page5A.html).

Feynman's Legacy also Includes:

Wheeler-Feynman Absorber Theory   |   Hellmann-Feynman Theorem
Sum over Histories   |   Feynman Diagrams   |   Superfluidity (1953)   |   "V-A"
Quantum Computing.   |   Challenger Space Shuttle Accident   |   etc.

 2005 US Stamp Honoring 
Richard Feynman (1918-1988)

Photos from ESVA (AIP)   |   UMD photos   |   Dissertation   |   Wikipedia

Videos :

Clips   |   BBC Interviews:   Uncertainty   |   Flower   |   Honors   |   Inertia   |   Chess
BBC Horizon Interviews:  1   |   2   |   3   |   4   |   5       "Atom" (BBC):  1   |   2   |   3
Messenger Lectures (Cornell University, November 1964) "The Character of Physical Law" :
1-Gravitation   |   2-Mathematics   |   3-Conservation   |   4-Symmetry   |   5-Past & Future   |   6-Quantum
Strangeness Minus Three (BBC Horizon, 1964)   1   |   2   |   3
Take the world from another point of view (1972)   1   |   2   |   3   |   4
QED made simple (1979 Conference)   |   Horizon - "The pleasure of finding things out" (1983)
"Fun to Imagine" (1983)  Jiggling | Fire | Rubber | Why? | Electricity | Mirror | Train | Seeing | Stuff | Stars | Think | Imagine
Connection between Spin and Statistics (1986 Dirac Memorial Lecture, about the spin-statistics theorem)
The Reason for Antiparticles, Part II, Part III, Part IV, Part V
Testimonies :   John Wheeler   |   Hans Bethe   |   Freeman Dyson   |   Murray Gell-Mann   |   Leonard Susskind
Remembering Richard Feynman  (Caltech, 2015-05-14).
visits since Dec. 25, 2001
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