© 2001 American Institute of Physics, S-0031-9228-0111-220-2 PHYSICS TODAY 15

Walking the PlanckLength through History

Frank Wilczek’s Reference Framearticle in the June 2001 issue of

PHYSICS TODAY (page 12) shows how simple dimensional analysis, together with a few elementary facts,can lead to profound conclusions.

I would like to comment from per-sonal experience on one historicalpoint. Speaking of Planck’s proposalthat the Planck mass (M), length (L),and time (T) should form a funda-mental system of units, Wilczeknotes that the proposal was at firstmerely formally correct, but that“over the course of the 20th century,however, his proposal became com-pelling.” But I can testify that it wasstill considered heretical well intothe 1960s.

In 1959, I submitted a paper pro-posing that the Planck length L andtime T should play a fundamentalrole in physics. In the case of L, theidea was based on an analysis ofWerner Heisenberg’s microscopeexperiment, taking account of thegravitational field of the photon usedto measure the position of the parti-cle. For T, the analysis involved theproblem of keeping clocks synchro-nized in view of both the uncertaintyrelation between the reading of aclock and its energy, and the influ-ence of gravitational energy on therate of the clock. In both cases, I found that one runs into troublewhen trying to obtain a positionmeasurement (clock synchronization)with error less than L (T). At thetime, I knew nothing of Planck’s pro-posal. Eventually this paper, and afollow-up, were published.1 While mypaper was suffering referee trouble,a similar idea was proposed byAsher Peres and Nathan Rosen.2

I don’t claim that my papersdeserved any better fate than theyreceived: years of referee trouble,

eventual publication, a cold shoulderfrom the physics community. Butsome of the reasons for this coldshoulder are worth noting. At thetime, I read many referee reports onmy papers and discussed the matterwith every theoretical physicist whowas willing to listen; nobody that Icontacted recognized the connectionwith the Planck proposal, and fewtook seriously the idea of L as a pos-sible fundamental length. The viewwas nearly unanimous, not just thatI had failed to prove my result, butthat the Planck length could neverplay a fundamental role in physics. A minority held that there could beno fundamental length at all, butmost were then convinced that a fun-damental length L!, of the order ofthe proton Compton wavelength, wasthe wave of the future. Moreover, thepeople I contacted seemed to treatthis much longer fundamental lengthas established fact, not speculation,despite the lack of actual evidence forit. Of the people I contacted, the onlyones I can recall who had a positiveattitude to the idea of L as a funda-mental length were Henry Primakoff,David Bohm, and Roger Penrose.

I don’t know when or how thetransition of the Planck proposalfrom heresy to conventional wisdomtook place, but I can attest that ithad not even begun in the mid-1960s. I suspect that it did not reallybegin to take hold until at least themid-1970s, but perhaps others canenlighten me on this.

References1. C. A. Mead, Phys. Rev. 135, B849

(1964); Phys. Rev. 143, 990 (1966).2. A. Peres, N. Rosen, Phys. Rev. 118,

335 (1960).C. ALDEN MEAD

(camead@compuserve.com)Savannah, Georgia

WILCZEK REPLIES: It is true andsignificant that the Planck

length arises naturally when oneconsiders the ultimate limits tomeasurement. Crudely, it happensbecause refined length measurementrequires large momentum, accordingto Heisenberg’s uncertainty princi-ple, but when the momentumbecomes too large, its gravitationaleffect becomes strong, curving space-time and distorting the interval oneseeks to measure. Thus a fundamen-

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PHYSICS TODAY 81

tal difficulty arises in resolvinglengths below the Planck scale. Thispoint has been “rediscovered” manytimes, but C. Alden Mead’s discussionis the earliest I’m aware of. It nicelysupplements the article, in which thePlanck length was introduced in asomewhat different way.

One can understand the source ofthe bias Mead encountered, and inthe process highlight an importantprinciple: What quantities one choosesto regard as fundamental can dependon what domain one seeks to describe.A good approximate description ofmuch of chemistry and molecularbiology can be obtained by takingonly the electron mass and charge asinputs, using Planck’s constant \ asthe unit of action, and regardingatomic nuclei as infinitely massivepoint-particles. In this system, theBohr radius \2/e2m appears as thefundamental unit of length; indeedthis sets the scale for atomic andmolecular sizes. A good approximatedescription of strong-interactionphysics can be obtained by takingonly the quantum chromodynamicsmass scale L as input, using Planck’sconstant and the speed of light c asunits of action and velocity. In thissystem the fundamental unit oflength is L/\c; and indeed this setsthe scale for proton and nuclear sizes.In the 1960s and early 1970s, strong-interaction physics was the primaryfocus of fundamental physics, andthis system (implicitly) seemed most natural.

FRANK WILCZEKwilczek@mit.edu

Massachusetts Institute of TechnologyCambridge

On Keeping ChineseScience Students

I’d like to add to the story by LynleyHargreaves (PHYSICS TODAY, May

2001, page 24) on the dropout rateamong Chinese physics PhD stu-dents. I am the chair of the graduateadmissions committee in chemistryat Colorado State University. Since1991, I have noticed similar trendsamong our chemistry students fromthe People’s Republic of China. Likemany state schools, CSU has signifi-cantly different tuition for residentversus nonresident graduate stu-dents. This is a cost that the depart-ment or the research advisor’s grants

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