1、A. Einstein, Ann. Phys. 17, 132 1905Concerning an Heuristic Point of View Towardthe Emission and Transformation of LightA. EinsteinBern, 17 March 1905(Received March 18, 1905)Translation into EnglishAmerican Journal of Physics, v. 33, n. 5, May 1965 diamondmath diamondmath A profound formal distinct
2、ion exists between the theoretical conceptswhich physicists have formed regarding gases and other ponderable bodiesand the Maxwellian theory of electromagnetic processes in socalled emptyspace. While we consider the state of a body to be completely determinedby the positions and velocities of a very
3、 large, yet finite, number of atomsand electrons, we make use of continuous spatial functions to describe theelectromagnetic state of a given volume, and a finite number of parameterscannot be regarded as sufficient for the complete determination of such astate. According to the Maxwellian theory, e
4、nergy is to be considered a con-tinuous spatial function in the case of all purely electromagnetic phenomenaincluding light, while the energy of a ponderable object should, accordingto the present conceptions of physicists, be represented as a sum carriedover the atoms and electrons. The energy of a
5、 ponderable body cannot besubdivided into arbitrarily many or arbitrarily small parts, while the energyof a beam of light from a point source (according to the Maxwellian theoryof light or, more generally, according to any wave theory) is continuouslyspread an ever increasing volume.The wave theory
6、of light, which operates with continuous spatial func-tions, has worked well in the representation of purely optical phenomena1and will probably never be replaced by another theory. It should be kept inmind, however, that the optical observations refer to time averages ratherthan instantaneous value
7、s. In spite of the complete experimental confirma-tion of the theory as applied to diffraction, reflection, refraction, dispersion,etc., it is still conceivable that the theory of light which operates with con-tinuous spatial functions may lead to contradictions with experience whenit is applied to
8、the phenomena of emission and transformation of light.It seems to me that the observations associated with blackbody radia-tion, fluorescence, the production of cathode rays by ultraviolet light, andother related phenomena connected with the emission or transformation oflight are more readily unders
9、tood if one assumes that the energy of lightis discontinuously distributed in space. In accordance with the assumptionto be considered here, the energy of a light ray spreading out from a pointsource is not continuously distributed over an increasing space but consistsof a finite number of energy qu
10、anta which are localized at points in space,which move without dividing, and which can only be produced and absorbedas complete units.In the following I wish to present the line of thought and the facts whichhave led me to this point of view, hoping that this approach may be usefulto some investigat
11、ors in their research.1. Concerning a Difficulty with Regard to the The-ory of Blackbody RadiationWe start first with the point of view taken in the Maxwellian and the electrontheories and consider the following case. In a space enclosed by completelyreflecting walls, let there be a number of gas mo
12、lecules and electrons whichare free to move and which exert conservative forces on each other on closeapproach: i.e. they can collide with each other like molecules in the kinetictheory of gases.1Furthermore, let there be a number of electrons which arebound to widely separated points by forces prop
13、ortional to their distancesfrom these points. The bound electrons are also to participate in conserva-tive interactions with the free molecules and electrons when the latter come1This assumption is equivalent to the supposition that the average kinetic energies ofgas molecules and electrons are equa
14、l to each other at thermal equilibrium. It is wellknown that, with the help of this assumption, Herr Drude derived a theoretical expressionfor the ratio of thermal and electrical conductivities of metals.2very close. We call the bound electrons “oscillators”: they emit and absorbelectromagnetic wave
15、s of definite periods.According to the present view regarding the origin of light, the radiationin the space we are considering (radiation which is found for the case ofdynamic equilibrium in accordance with the Maxwellian theory) must beidentical with the blackbody radiation at least if oscillators
16、 of all therelevant frequencies are considered to be present.For the time being, we disregard the radiation emitted and absorbedby the oscillators and inquire into the condition of dynamical equilibriumassociated with the interaction (or collision) of molecules and electrons. Thekinetic theory of ga
17、ses asserts that the average kinetic energy of an oscillatorelectron must be equal to the average kinetic energy of a translating gasmolecule. If we separate the motion of an oscillator electron into threecomponents at angles to each other, we find for the average energy E of oneof these linear comp
18、onents the expressionE = (R/N) T,where R denotes the universal gas constant. N denotes the number of“real molecules” in a gram equivalent, and T the absolute temperature.The energy E is equal to two-thirds the kinetic energy of a free monatomicgas particle because of the equality the time average va
19、lues of the kineticand potential energies of the oscillator. If through any causein our casethrough radiation processesit should occur that the energy of an oscillatortakes on a time-average value greater or less than E, then the collisions withthe free electrons and molecules would lead to a gain o
20、r loss of energy bythe gas, different on the average from zero. Therefore, in the case we areconsidering, dynamic equilibrium is possible only when each oscillator hasthe average energy E.We shall now proceed to present a similar argument regarding the inter-action between the oscillators and the ra
21、diation present in the cavity. HerrPlanck has derived2the condition for the dynamics equilibrium in this caseunder the supposition that the radiation can be considered a completelyrandom process.3He found(E) = (L3/8pi2),2M. Planck, Ann. Phys. 1, 99 (1900).3This problem can be formulated in the follo
22、wing manner. We expand the Z componentof the electrical force (Z) at an arbitrary point during the time interval between t = 0and t = T in a Fourier series in which A 0 and 0 2pi: the time T is taken to3where (E) is the average energy (per degree of freedom) of an oscillatorwith eigenfrequency , L t
23、he velocity of light, the frequency, and dthe energy per unit volume of that portion of the radiation with frequencybetween and +d.If the radiation energy of frequency is not continually increasing ordecreasing, the following relations must obtain:(R/N) T = E = E = (L3/8pi2),= (R/N)(8pi2/L3) T.These
24、 relations, found to be the conditions of dynamic equilibrium, not onlyfail to coincide with experiment, but also state that in our model there canbe not talk of a definite energy distribution between ether and matter. Thewider the range of wave numbers of the oscillators, the greater will be therad
25、iation energy of the space, and in the limit we obtainintegraldisplay0d =RN8piL3Tintegraldisplay02d = .be very large relative to all the periods of oscillation that are present:Z =summationdisplay=1AsinparenleftBig2pitT+parenrightBig,If one imagines making this expansion arbitrary often at a given p
26、oint in space at randomlychosen instants of time, one will obtain various sets of values of Aand . There thenexist for the frequency of occurrence of different sets of values of Aand (statistical)probabilities dW of the form:dW = f(a1,A2,.,1,2,.)dA1dA2.d1d2.,The radiation is then as disordered as co
27、nceivable iff(A1,A2,.1,2,.) = F1(A1)F2(A2).f1(1)f2(2).,i.e., if the probability of a particular value of A or is independent of other values of A or. The more closely this condition is fulfilled (namely, that the individual pairs of valuesof Aand are dependent upon the emission and absorption proces
28、ses of specific groupsof oscillators) the more closely will radiation in the case being considered approximate aperfectly random state.42. Concerning Plancks Determination of the Fun-damental ConstantsWe wish to show in the following that Herr Plancks determination of thefundamental constants is, to
29、 a certain extent, independent of his theory ofblackbody radiation.Plancks formula,4which has proved adequate up to this point, gives for=3e/T1, = 6.101056, = 4.8661011.For large values of T/; i.e. for large wavelengths and radiation densities,this equation takes the form= (/) 2T.It is evident that
30、this equation is identical with the one obtained in Sec. 1from the Maxwellian and electron theories. By equating the coefficients ofboth formulas one obtains(R/N)(8pi/L3) = (/)orN = (/)(8piR/L3) = 6.171023.i.e., an atom of hydrogen weighs 1/N grams = 1.621024g. This is exactlythe value found by Herr
31、 Planck, which in turn agrees with values found byother methods.We therefore arrive at the conclusion: the greater the energy density andthe wavelength of a radiation, the more useful do the theoretical principleswe have employed turn out to be: for small wavelengths and small radiationdensities, ho
32、wever, these principles fail us completely.In the following we shall consider the experimental facts concerningblackbody radiation without invoking a model for the emission and propa-gation of the radiation itself.4M. Planck, Ann. Phys. 4, 561 (1901).53. Concerning the Entropy of RadiationThe follow
33、ing treatment is to be found in a famous work by Herr W. Wienand is introduced here only for the sake of completeness.Suppose we have radiation occupying a volume v. We assume that theobservable properties of the radiation are completely determined when theradiation density () is given for all frequ
34、encies.5Since radiation of differ-ent frequencies are to be considered independent of each other when there isno transfer of heat or work, the entropy of the radiation can be representedbyS = vintegraldisplay0(,) d,where is a function of the variables and . can be reduced to a function of a single v
35、ariable through formulation ofthe condition that the entropy of the radiation is unaltered during adiabaticcompression between reflecting walls. We shall not enter into this problem,however, but shall directly investigate the derivation of the function fromthe blackbody radiation law.In the case of
36、blackbody radiation, is such a function of that theentropy is maximum for a fixed value of energy; i.e.,integraldisplay0 (,) d = 0,providingintegraldisplay0d = 0.From this it follows that for every choice of as a function of integraldisplay0parenleftbiggparenrightbiggd = 0,where is independent of .
37、In the case of blackbody radiation, therefore,/ is independent of .5This assumption is an arbitrary one. One will naturally cling to this simplest assump-tion as long as it is not controverted experiment.6The following equation applies when the temperature of a unit volumeof blackbody radiation incr
38、eases by dTdS =integraldisplay=0parenleftbiggparenrightbiggdd,or, since / is independent of .dS = (/) dE.Since dE is equal to the heat added and since the process is reversible, thefollowing statement also appliesdS = (1/T) dE.By comparison one obtains/ = 1/T.This is the law of blackbody radiation.
39、Therefore one can derive the lawof blackbody radiation from the function , and, inversely, one can derivethe function by integration, keeping in mind the fact that vanishes when = 0.4. Asymptotic from for the Entropy of Monochro-matic Radiation at Low Radiation DensityFrom existing observations of t
40、he blackbody radiation, it is clear that thelaw originally postulated by Herr W. Wien, = 3e/T,is not exactly valid. It is, however, well confirmed experimentally for largevalues of /T. We shall base our analysis on this formula, keeping in mindthat our results are only valid within certain limits.Th
41、is formula gives immediately(1/T) = (1/) ln (/3)7and then, by using the relation obtained in the preceeding section,(,) = bracketleftbigglnparenleftbigg3parenrightbigg1bracketrightbigg.Suppose that we have radiation of energy E, with frequency between and +d, enclosed in volume v. The entropy of thi
42、s radiation is:S = v(,)d = EbracketleftbigglnparenleftbiggEv3dparenrightbigg1bracketrightbigg.If we confine ourselves to investigating the dependence of the entropy onthe volume occupied by the radiation, and if we denote by S0the entropyof the radiation at volume v0, we obtainS S0= (E/) ln (v/v0).T
43、his equation shows that the entropy of a monochromatic radiation ofsufficiently low density varies with the volume in the same manner as theentropy of an ideal gas or a dilute solution. In the following, this equationwill be interpreted in accordance with the principle introduced into physicsby Herr
44、 Boltzmann, namely that the entropy of a system is a function ofthe probability its state.5. MolecularTheoretic Investigation of the De-pendence of the Entropy of Gases and Dilute solu-tions on the volumeIn the calculation of entropy by moleculartheoretic methods we frequentlyuse the word “probabili
45、ty” in a sense differing from that employed in thecalculus of probabilities. In particular “gases of equal probability” have fre-quently been hypothetically established when one theoretical models beingutilized are definite enough to permit a deduction rather than a conjecture.I will show in a separ
46、ate paper that the so-called “statistical probability” isfully adequate for the treatment of thermal phenomena, and I hope that bydoing so I will eliminate a logical difficulty that obstructs the applicationof Boltzmann s Principle. here, however, only a general formulation andapplication to very sp
47、ecial cases will be given.8If it is reasonable to speak of the probability of the state of a system, andfuthermore if every entropy increase can be understood as a transition to astate of higher probability, then the entropy S1of a system is a function ofW1, the probability of its instantaneous stat
48、e. If we have two noninteractingsystems S1and S2, we can writeS1= 1(W1),S2= 2(W2).If one considers these two systems as a single system of entropy S andprobability W, it follows thatS = S1+S2= (W)andW = W1W2.The last equation says that the states of the two systems are independentof each other.From
49、these equation it follows that(W1W2) = 1(W1)+2(W2)and finally1(W1) = C ln(W1)+const,2(W2) = C ln(W2)+const,(W) = C ln(W)+const.The quantity C is therefore a universal constant; the kinetic theory of gasesshows its value to be R/N, where the constants R and N have been definedabove. If S0denotes the entropy of a system in some initial state and Wde
