The Future of Mathematical Physics
The Principles and Experiment.— In the midst of so much ruin, what remains1 standing2? The principle of least action is hitherto intact, and Larmor appears to believe that it will long survive the others; in reality, it is still more vague and more general.
In presence of this general collapse3 of the principles, what attitude will mathematical physics take? And first, before too much excitement, it is proper to ask if all that is really true. All these derogations to the principles are encountered only among infinitesimals; the microscope is necessary to see the Brownian movement; electrons are very light; radium is very rare, and one never has more than some milligrams of it at a time. And, then, it may be asked whether, besides the infinitesimal seen, there was not another infinitesimal unseen counterpoise to the first.
So there is an interlocutory question, and, as it seems, only experiment can solve it. We shall, therefore, only have to hand over the matter to the experimenters, and, while waiting for them to finally decide the debate, not to preoccupy4 ourselves with these disquieting5 problems, and to tranquilly6 continue our work as if the principles were still uncontested. Certes, we have much to do without leaving the domain7 where they may be applied8 in all security; we have enough to employ our activity during this period of doubts.
The R?le of the Analyst9.— And as to these doubts, is it indeed true that we can do nothing to disembarrass science of them? It must indeed be said, it is not alone experimental physics that has given birth to them; mathematical physics has well contributed. It is the experimenters who have seen radium throw out energy, but it is the theorists who have put in evidence all the difficulties raised by the propagation of light across a medium in motion; but for these it is probable we should not have become conscious of them. Well, then, if they have done their best to put us into this embarrassment10, it is proper also that they help us to get out of it.
They must subject to critical examination all these new views I have just outlined before you, and abandon the principles only after having made a loyal effort to save them. What can they do in this sense? That is what I will try to explain.
It is a question before all of endeavoring to obtain a more satisfactory theory of the electrodynamics of bodies in motion. It is there especially, as I have sufficiently12 shown above, that difficulties accumulate. It is useless to heap up hypotheses, we can not satisfy all the principles at once; so far, one has succeeded in safeguarding some only on condition of sacrificing the others; but all hope of obtaining better results is not yet lost. Let us take, then, the theory of Lorentz, turn it in all senses, modify it little by little, and perhaps everything will arrange itself.
Thus in place of supposing that bodies in motion undergo a contraction13 in the sense of the motion, and that this contraction is the same whatever be the nature of these bodies and the forces to which they are otherwise subjected, could we not make a more simple and natural hypothesis? We might imagine, for example, that it is the ether which is modified when it is in relative motion in reference to the material medium which penetrates15 it, that, when it is thus modified, it no longer transmits perturbations with the same velocity16 in every direction. It might transmit more rapidly those which are propagated parallel to the motion of the medium, whether in the same sense or in the opposite sense, and less rapidly those which are propagated perpendicularly17. The wave surfaces would no longer be spheres, but ellipsoids, and we could dispense18 with that extraordinary contraction of all bodies.
I cite this only as an example, since the modifications19 that might be essayed would be evidently susceptible20 of infinite variation.
Aberration21 and Astronomy.— It is possible also that astronomy may some day furnish us data on this point; she it was in the main who raised the question in making us acquainted with the phenomenon of the aberration of light. If we make crudely the theory of aberration, we reach a very curious result. The apparent positions of the stars differ from their real positions because of the earth’s motion, and as this motion is variable, these apparent positions vary. The real position we can not ascertain22, but we can observe the variations of the apparent position. The observations of the aberration show us, therefore, not the earth’s motion, but the variations of this motion; they can not, therefore, give us information about the absolute motion of the earth.
At least this is true in first approximation, but the case would be no longer the same if we could appreciate the thousandths of a second. Then it would be seen that the amplitude23 of the oscillation depends not alone on the variation of the motion, a variation which is well known, since it is the motion of our globe on its elliptic orbit, but on the mean value of this motion, so that the constant of aberration would not be quite the same for all the stars, and the differences would tell us the absolute motion of the earth in space.
This, then, would be, under another form, the ruin of the principle of relativity. We are far, it is true, from appreciating the thousandth of a second, but, after all, say some, the earth’s total absolute velocity is perhaps much greater than its relative velocity with respect to the sun. If, for example, it were 300 kilometers per second in place of 30, this would suffice to make the phenomenon observable.
I believe that in reasoning thus one admits a too simple theory of aberration. Michelson has shown us, I have told you, that the physical procedures are powerless to put in evidence absolute motion; I am persuaded that the same will be true of the astronomic24 procedures, however far precision be carried.
However that may be, the data astronomy will furnish us in this regard will some day be precious to the physicist25. Meanwhile, I believe that the theorists, recalling the experience of Michelson, may anticipate a negative result, and that they would accomplish a useful work in constructing a theory of aberration which would explain this in advance.
Electrons and Spectra26.— This dynamics11 of electrons can be approached from many sides, but among the ways leading thither27 is one which has been somewhat neglected, and yet this is one of those which promise us the most surprises. It is movements of electrons which produce the lines of the emission28 spectra; this is proved by the Zeeman effect; in an incandescent29 body what vibrates is sensitive to the magnet, therefore electrified30. This is a very important first point, but no one has gone farther. Why are the lines of the spectrum31 distributed in accordance with a regular law? These laws have been studied by the experimenters in their least details; they are very precise and comparatively simple. A first study of these distributions recalls the harmonics encountered in acoustics32; but the difference is great. Not only are the numbers of vibrations33 not the successive multiples of a single number, but we do not even find anything analogous34 to the roots of those transcendental equations to which we are led by so many problems of mathematical physics: that of the vibrations of an elastic35 body of any form, that of the Hertzian oscillations in a generator36 of any form, the problem of Fourier for the cooling of a solid body.
The laws are simpler, but they are of wholly other nature, and to cite only one of these differences, for the harmonics of high order, the number of vibrations tends toward a finite limit, instead of increasing indefinitely.
That has not yet been accounted for, and I believe that there we have one of the most important secrets of nature. A Japanese physicist, M. Nagaoka, has recently proposed an explanation; according to him, atoms are composed of a large positive electron surrounded by a ring formed of a great number of very small negative electrons. Such is the planet Saturn37 with its rings. This is a very interesting attempt, but not yet wholly satisfactory; this attempt should be renewed. We will penetrate14, so to speak, into the inmost recess38 of matter. And from the particular point of view which we to-day occupy, when we know why the vibrations of incandescent bodies differ thus from ordinary elastic vibrations, why the electrons do not behave like the matter which is familiar to us, we shall better comprehend the dynamics of electrons and it will be perhaps more easy for us to reconcile it with the principles.
Conventions Preceding Experiment.— Suppose, now, that all these efforts fail, and, after all, I do not believe they will, what must be done? Will it be necessary to seek to mend the broken principles by giving what we French call a coup39 de pouce? That evidently is always possible, and I retract40 nothing of what I have said above.
Have you not written, you might say if you wished to seek a quarrel with me — have you not written that the principles, though of experimental origin, are now unassailable by experiment because they have become conventions? And now you have just told us that the most recent conquests of experiment put these principles in danger.
Well, formerly41 I was right and to-day I am not wrong. Formerly I was right, and what is now happening is a new proof of it. Take, for example, the calorimetric experiment of Curie on radium. Is it possible to reconcile it with the principle of the conservation of energy? This has been attempted in many ways. But there is among them one I should like you to notice; this is not the explanation which tends to-day to prevail, but it is one of those which have been proposed. It has been conjectured42 that radium was only an intermediary, that it only stored radiations of unknown nature which flashed through space in every direction, traversing all bodies, save radium, without being altered by this passage and without exercising any action upon them. Radium alone took from them a little of their energy and afterward43 gave it out to us in various forms.
What an advantageous44 explanation, and how convenient! First, it is unverifiable and thus irrefutable. Then again it will serve to account for any derogation whatever to Mayer’s principle; it answers in advance not only the objection of Curie, but all the objections that future experimenters might accumulate. This new and unknown energy would serve for everything.
This is just what I said, and therewith we are shown that our principle is unassailable by experiment.
But then, what have we gained by this stroke? The principle is intact, but thenceforth of what use is it? It enabled us to foresee that in such or such circumstance we could count on such a total quantity of energy; it limited us; but now that this indefinite provision of new energy is placed at our disposal, we are no longer limited by anything; and, as I have written in ‘Science and Hypothesis,’ if a principle ceases to be fecund46, experiment without contradicting it directly will nevertheless have condemned47 it.
Future Mathematical Physics.— This, therefore, is not what would have to be done; it would be necessary to rebuild anew. If we were reduced to this necessity; we could moreover console ourselves. It would not be necessary thence to conclude that science can weave only a Penelope’s web, that it can raise only ephemeral structures, which it is soon forced to demolish48 from top to bottom with its own hands.
As I have said, we have already passed through a like crisis. I have shown you that in the second mathematical physics, that of the principles, we find traces of the first, that of central forces; it will be just the same if we must know a third. Just so with the animal that exuviates, that breaks its too narrow carapace49 and makes itself a fresh one; under the new envelope one will recognize the essential traits of the organism which have persisted.
We can not foresee in what way we are about to expand; perhaps it is the kinetic50 theory of gases which is about to undergo development and serve as model to the others. Then the facts which first appeared to us as simple thereafter would be merely resultants of a very great number of elementary facts which only the laws of chance would make cooperate for a common end. Physical law would then assume an entirely51 new aspect; it would no longer be solely52 a differential equation, it would take the character of a statistical53 law.
Perhaps, too, we shall have to construct an entirely new mechanics that we only succeed in catching54 a glimpse of, where, inertia55 increasing with the velocity, the velocity of light would become an impassable limit. The ordinary mechanics, more simple, would remain a first approximation, since it would be true for velocities56 not too great, so that the old dynamics would still be found under the new. We should not have to regret having believed in the principles, and even, since velocities too great for the old formulas would always be only exceptional, the surest way in practise would be still to act as if we continued to believe in them. They are so useful, it would be necessary to keep a place for them. To determine to exclude them altogether would be to deprive oneself of a precious weapon. I hasten to say in conclusion that we are not yet there, and as yet nothing proves that the principles will not come forth45 from out the fray57 victorious58 and intact.
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1
remains
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| n.剩余物，残留物；遗体，遗迹 | |
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standing
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| n.持续，地位；adj.永久的，不动的，直立的，不流动的 | |
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collapse
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| vi.累倒；昏倒；倒塌；塌陷 | |
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preoccupy
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| vt.使全神贯注，使入神 | |
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disquieting
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| adj.令人不安的，令人不平静的v.使不安，使忧虑，使烦恼( disquiet的现在分词 ) | |
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tranquilly
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| adv. 宁静地 | |
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domain
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| n.(活动等)领域，范围；领地，势力范围 | |
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applied
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| adj.应用的；v.应用，适用 | |
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analyst
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| n.分析家，化验员；心理分析学家 | |
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embarrassment
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| n.尴尬；使人为难的人(事物)；障碍；窘迫 | |
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dynamics
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| n.力学，动力学，动力，原动力；动态 | |
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sufficiently
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| adv.足够地，充分地 | |
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contraction
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| n.缩略词，缩写式，害病 | |
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penetrate
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| v.透(渗)入；刺入，刺穿；洞察，了解 | |
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penetrates
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| v.穿过( penetrate的第三人称单数 )；刺入；了解；渗透 | |
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velocity
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| n.速度，速率 | |
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perpendicularly
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| adv. 垂直地, 笔直地, 纵向地 | |
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dispense
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| vt.分配，分发；配(药)，发(药)；实施 | |
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modifications
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| n.缓和( modification的名词复数 )；限制；更改；改变 | |
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susceptible
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| adj.过敏的，敏感的；易动感情的，易受感动的 | |
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aberration
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| n.离开正路，脱离常规，色差 | |
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ascertain
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| vt.发现，确定，查明，弄清 | |
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amplitude
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| n.广大；充足；振幅 | |
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astronomic
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| 天文学的，星学的 | |
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physicist
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| n.物理学家，研究物理学的人 | |
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spectra
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| n.光谱 | |
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thither
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| adv.向那里；adj.在那边的，对岸的 | |
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emission
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| n.发出物，散发物；发出，散发 | |
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incandescent
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| adj.遇热发光的， 白炽的，感情强烈的 | |
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electrified
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| v.使电气化( electrify的过去式和过去分词 )；使兴奋 | |
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spectrum
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| n.谱，光谱，频谱；范围，幅度，系列 | |
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acoustics
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| n.声学，(复)音响效果，音响装置 | |
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vibrations
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| n.摆动( vibration的名词复数 )；震动；感受；（偏离平衡位置的）一次性往复振动 | |
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analogous
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| adj.相似的；类似的 | |
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elastic
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| n.橡皮圈，松紧带；adj.有弹性的；灵活的 | |
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generator
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| n.发电机，发生器 | |
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Saturn
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| n.农神，土星 | |
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recess
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| n.短期休息，壁凹（墙上装架子，柜子等凹处） | |
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coup
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| n.政变；突然而成功的行动 | |
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retract
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| vt.缩回，撤回收回，取消 | |
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formerly
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| adv.从前，以前 | |
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conjectured
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| 推测，猜测，猜想( conjecture的过去式和过去分词 ) | |
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afterward
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| adv.后来；以后 | |
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advantageous
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| adj.有利的；有帮助的 | |
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forth
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| adv.向前；向外，往外 | |
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fecund
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| adj.多产的，丰饶的，肥沃的 | |
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condemned
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| adj. 被责难的, 被宣告有罪的 动词condemn的过去式和过去分词 | |
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demolish
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| v.拆毁(建筑物等)，推翻(计划、制度等) | |
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carapace
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| n.（蟹或龟的）甲壳 | |
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kinetic
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| adj.运动的；动力学的 | |
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entirely
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| ad.全部地，完整地；完全地，彻底地 | |
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solely
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| adv.仅仅，唯一地 | |
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statistical
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| adj.统计的，统计学的 | |
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catching
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| adj.易传染的，有魅力的，迷人的，接住 | |
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inertia
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| adj.惰性，惯性，懒惰，迟钝 | |
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velocities
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| n.速度( velocity的名词复数 )；高速，快速 | |
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fray
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| v.争吵；打斗；磨损，磨破；n.吵架；打斗 | |
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victorious
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| adj.胜利的，得胜的 | |
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