the relation between energy and mass in the works of

The relation between energy and

mass in the works of Einstein,

Landau and FeynmanThe talk at the Memorial Meetingdedicated to the 100th birthday of

L.D.Landau,Moscow, June 19, 2008

L.B. Okun

ITEP, Moscow

No2PPT - Prosper – p. 1/17

Personal gratitude

First of all I want to express my deep gratitude toLev Davidovich Landau (Dau). He predeterminedthe direction of my worldline in many ways. First,through his influence on my professor and teacherIsaak Yakovlevich Pomeranchuk (Chuk). Second,through the Course of theoretical physics publishedby him and by Evgenii Mikhailovich Lifshitz. Third,through personal contacts.


Pomeranchuk advised me in 1950 to attendLandau’s seminars on Thursdays at the KapizaInstitute of Physical Problems (IPP). In 1954 Ibecame Pomeranchuk’s graduate student atTermo-Technical Laboratory, TTL, where Dau hada part-time position. (TTL was later renamed intoInstitute of Theoretical and Experimental Physics,ITEP). Now I was able to see Dau not only onThursdays at IPP, but also on Wednesdays – thedays of A .I. Alikhanov’s seminar at ITEP.


Dau at ITEPThis was a remarkable experience!. During theseminar, which was mainly experimental, Dau wassitting in the first row together with Alikhanov andmaking sharp remarks. After the seminar he wouldmove to the office number 9, just behind the lecturehall, to chat with theorists. Sitting in a deeparmchair and stretching his long legs, Dau withvirtuosity discussed questions posed to him byChuk and his team: V.B. Berestetsky, A.D.Galanin, A.P. Rudik, V.V. Sudakov, B.L. Ioffe,I.Yu.Kobzarev, and myself.


The hottest subjects under discussion were the socalled “theta-tau puzzle"and “nullificanion ofcharge”. Theta and tau were the names of decays ofkaons into two and three pions correspondingly.They started to look as decays of the same particle,which meant that parity P is violated. Dauconsidered violation of parity – of symmetrybetween left and right – in nature as aesteticallyugly. First he tried to deny the possibility of Pviolation, but finally gave up and put forward theidea of exact conservation of combined CP parity. Abeautiful realization of CP symmetry was the ideaof longitudinally polarized massless neutrinos andantineutrinos.


These ideas were accepted enthusiastically byphysicists. Though later minor effects of CPviolation in weak decays and tiny neutrino masseswere discovered, still CP and longitudinalpolarization are “the reference concepts” of modernfundamental physics. The importance of CPviolation for the baryonic asymmetry of theUniverse and hence for our existence was stressed in1967 by Andrei Dmitrievich Sakharov. But theorigin of this violation in cosmology is stillunknown.


The “nullification of charge” turned out to be no lessdeep. The growth of electric charge of the electronwith the increase of momentum transfer seemed toimply that any finite charge at the shortest distancewould result in a zero observable charge at largedistances. The solution of this paradox came laterwith the discovery of the asymptotic freedom in thenon-Abelian gauge theories.

Unfortunately, a recurrent administrative reformprohibited scientists to combine jobs. Dau wasoffended and ceased his weekly visits to ITEP. Thencame the tragic January 7 1961.


Teaching the theory of relativity

“Teoria polya” by Landau and Lifshitz was the bookfrom which most of us, Russian theoreticalphysicists, learned relativity. The mass in this bookis expressed through energy and momentum by therelativistically invariant equation

E2− p

2c2= m2c4 .

(If the speed of light c is used as the unit ofvelocity, then E2

− p2

= m2.) The book by Landauand Lifshitz served as a vaccination against thevirus of relativistic mass, defined by the famous butmisleading formula E = mc2.


Only a few years ago did I realize that “Teoriapolya”, which appeared in 1941, was the firstmonograph on relativity in the world that did notuse the concept of mass depending on velocity. Andonly a few months ago had I discovered that in noneof his writings on mass and energy did Einstein usethe equation E2

− p2

= m2. Though quite often heused the equation E0 = mc2, which defines the restenergy E0, he nevertheless insistently spoke aboutcomplete equivalence of mass and energy.

Listen to Einstein:


Movie“It follows from the Special Theory of Relativitythat mass and energy are but differentmanifestations of the same thing – a somewhatunfamiliar conception for the average man.Furthermore the equation E = mc2 in which energyis put equal to mass multiplied with the square ofthe velocity of light showed that very small amountof mass may be converted into a very large amountof energy and vice versa. The mass and energy werein fact equivalent according to the formulamentioned above. This was demonstrated byCockcroft and Walton in 1932 experimentally.”


Einstein and LandauIn 1929 Landau, who was 21 years old, met Einsteinin Berlin. They discussed quantum mechanics.According to recollections of Rumer, Landaucommented a seminar given by von Laue. Not muchis known to me about their meeting.The somewhat blurred views of Einstein concerningenergy and mass seem to be at the heart of thecentury - long confusion which could be called“Does mass depend on velocity?” The famous bookby Born, as well as dozens of other textbooks said“yes!”. This “yes” was dogmatized in hundreds ofarticles and books popularizing the relativitytheory. Even Landau in a brochure “What isrelativity?” coauthored with Rumer had chosen tojoin the popular bandwagon.


Landau and Feynman

Landau and Feynman never met.

In a sense Landau and Rumer were followed byRichard Feynman, Robert Leighton and MatthewSands in the famous “Feynman Lectures onPhysics”, though the velocity-independent mass isthe cornerstone of the method of Feynmandiagrams.

Last year I exchanged a few emails with M. Sands –the man who initiated “The Feynman Lectures”.


On January 12, 2007 he wrote:

“I agree with you that it would be preferable toreserve the symbol m as the invariant magnitude ofthe energy - momentum four-vector. I am surprisedthat Feynman did not take this view in Volume 1.I never discussed this with him at the time –Leighton was in charge of preparing that volume.”

On January 19, referring to Landau and Feynman,he characterized them as “two of the great teachersof physics in the last 50 years”.


Momentum versus velocity

It seems to me that the standard courses onrelativity are too biased towards velocity, which atrelativistic energies is “frozen” in the vicinity of c.Momentum is a “live” and hence a better variable todescribe relativistic processes. Understandingexperiments in terms of momentum is simpler thanin terms of velocity. Starting the course onrelativity with velocity reminds me lessons ofswimming in a dry pool without water.It is muchbetter to start with t,x and E,p and withrelativistic version of Hamilton - Jacobi equation.


Spin

Another concept that deserves more attention inteaching relativity is spin. The spin ofelectromagnetic field and hence of photon is 1.That’s why it is called vector field. The spin of thegravitational field is 2. This is a tensor field. Spinsof photon and of graviton determine the mostimportant features of electromagnetic andgravitational interactions. In a certain sense, thesespins preceded the spin of the electron in thehistory of physics.


ConclusionThe introduction of only one mass – the Lorentzinvariant mass m, as Landau and Lifshitz taught us,is the most adequate way of teaching relativity. Norelativistic mass, no rest mass. Mass is equivalentnot to energy E, but to the rest energy E0. The adof baby-food with E0 = mc2 was given to me by mygrand-daughter Katya.See the ad.

The ad looks more scientific than many of physicstextbooks which advertise E = mc2.


the relation between energy and mass in the works of

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