relativity by tying up together the findings of Chapter V. and those
of Chapters III. and IV. It represents more or less of a last-minute
change of plan; for while it had been the Editor's intent from the
beginning to place the material of Chapters II.-V. in its present
position, his preliminary impression would have been that the work
of the present Chapter VI. would be adequately done by the essayists
themselves. His reading of the essays, however, convinced him that it
had not so been done--that with the possible exception of Mr. Francis,
the essayists did not make either a serious or a successful effort to
show the organic connection between the Special Theory of Relativity
and the Minkowski space-time structure, or the utter futility of
trying to reconcile ourselves to the results of the former without
employing the ideas of the latter. So Chapter VI. was supplied to make
good this deficiency, and to complete the mental equipment which the
reader requires for his battle with the General Theory.
In laying down a set of general principles to govern the award of
the prize, one of the first things considered by the Judges was the
relative importance of the Special and the General Theories. It was
their opinion that no essay could possibly qualify for the prize which
did not very distinctly give to the General Theory the center of the
stage; and that in fact discussion of the Special Theory was pertinent
only so long as it contributed, in proportion to the space assigned
it, to the attack upon the main subject. The same principle has been
employed in selecting essays for complete or substantially complete
reproduction in this volume. Writers who dealt with the Special Theory
in any other sense than as a preliminary step toward the General Theory
have been relegated to the introductory chapters, where such excerpts
from their work have been used as were found usable. The distinction
of publication under name and title is reserved for those who wrote
consistently and specifically upon the larger subject--with the one
exception of Dr. Russell, whose exposition of the Special Theory is so
far the best of those submitted and at the same time so distinctive
that we have concluded it will appear to better advantage by itself
than as a part of Chapters III. and IV.
Following after Mr. Bolton's essay we have tried to arrange the various
contributions, not at all in any order of merit, but in the order
that will make connected reading of the book most nearly possible
and profitable. Each essay should be made easier of reading by the
examination of those preceding it; at the same time each, by the choice
of ground covered and by the emphasis on points not brought out sharply
by its predecessors, should throw new light upon these predecessors.
The reader will find that no two of the essays given thus in full
duplicate or even come close to duplicating one another. They have
of course been selected with this in view; each represents the best
of several essays of substantially the same character. Not all of
them require comment here, but concerning some of them a word may
well be said.
Mr. Francis, we believe, has succeeded in packing more substance
into his 3,000 words than any other competitor. Mr. Elliot has come
closer than anybody else to really explaining relativity in terms
familiar to everybody, without asking the reader to enlarge his
vocabulary and with a minimum demand so far as enlarging his mental
outlook is concerned. Were it not for certain conspicuous defects,
his essay would probably have taken the prize. In justice to the
Judges, we should state that we have taken the liberty of eliminating
Mr. Elliot's concluding paragraph, which was the most objectionable
feature of his essay.
Dr. Dushman chose for his title the one which we adopted for this
book. It became necessary, therefore, for us to find a new title for
his essay; aside from this instance, the main titles appearing at the
heads of the various complete essays are those of the authors. The
subtitles have in practically every instance been supplied editorially.
Dr. Pickering submitted two essays, one written from the viewpoint
of the physicist, the other from that of the astronomer. To make
each complete, he naturally found it necessary to duplicate between
them certain introductory and general material. We have run the two
essays together into a single narrative, with the elimination of this
duplicated material; aside from this blue-penciling no alteration
has been made in Dr. Pickering's text. This text however served as
the basis of blue-penciling that of several other contestants, as
indicated in the foot notes.
For the reader who is qualified or who can qualify to understand it,
Dr. Murnaghan's essay is perhaps the most illuminating of all. Even
the reader who does not understand it all will realize that its author
brings to the subject a freshness of viewpoint and an originality of
treatment which are rather lacking in some of the published essays,
and which it will readily be understood were conspicuously lacking
in a good many of the unpublished ones. Dr. Murnaghan of all the
competitors has come closest to making a contribution to science as
well as to the semi-popular literature of science.
In the composite chapters, the brackets followed by reference numbers
have been used as the most practicable means of identifying the
various individual contributions. We believe that this part of the
text can be read without allowing the frequent occurrence of these
symbols to distract the eye. As to the references themselves, the
asterisk marks the contributions of the Editor. The numbers are those
attached to the essays in order of and at the time of their receipt;
it has been more convenient to use these than to assign consecutive
numbers to the quoted essays. The several numbers identify passages
from the essays of the following contestants:
10: Frederick W. Shurlock, Derby, England.
18: L. L. Whyte, Cambridge, England.
24: Prof. Moritz Schlick, University of Rostock, Germany.
30: C. E. Rose, M.E., Little Rock, Ark.
33: H. Gartelmann, Bremen, Germany.
35: Prof. Joseph S. Ames, Johns Hopkins University, Baltimore.
47: James O. G. Gibbons, East Orange. N. J.
82: Charles H. Burr, Philadelphia.
101: L. F. H. de Miffonis. B.A., C.E., Ottawa, Canada.
102: Charles A. Brunn, Kansas City.
106: J. Elias Fries, Fellow A.I.E.E., Birmingham, Ala.
114: Dean W. P. Graham, Syracuse University, Syracuse, N. Y.
115: Rev. George Thomas Manley, London.
116: Prof. J. A. Schouten, Delft, Netherlands.
121: Elwyn F. Burrill, Berkeley, Cal.
125: Dorothy Burr, Bryn Mawr, Pa.
130: C. W. Kanolt, Bureau of Standards, Washington.
135: Robert Stevenson, New York.
139: Leopold Schorsch, New York.
141: Dr. M. C. Mott-Smith, Los Angeles, Calif.
147: Edward A. Clarke, Columbus, O.
149: Edward A. Partridge, Philadelphia.
150: Col. John Millis, U. S. A., Chicago.
152: George F. Marsteller, Detroit.
156: D. B. Hall, Cincinnati.
165: Francis Farquhar, York, Pa.
178: Dr. George de Bothezat, Dayton, O.
179: Professor A. E. Caswell, University of Oregon, Eugene, Ore.
182: C. E. Dimick, New London, Conn.
186: Earl R. Evans, Washington, D. C.
188: Norman E. Gilbert, Dartmouth College, Hanover, N. H.
192: A. d'Abro. New York.
194: L. M. Alexander, Cincinnati.
197: Kenneth W. Reed, East Cleveland, O.
198: Prof. E. N. da C. Andrade, Ordnance College, Woolwich, England.
216: Professor Andrew H. Patterson, University of North Carolina,
Chapel Hill, N. C.
220: Prof. Arthur Gordon Webster, Clark College, Worcester, Mass.
221: Walter van B. Roberts, Princeton University, N. J.
223: Paul M. Batchelder, Austin, Tex.
227: Prof. R. W. Wood, Johns Hopkins University, Baltimore.
229: E. P. Fairbairn, M.C., B.Sc., Glasgow.
231: R. F. Deimel, Hoboken, N. J.
232: Lieut. W. Mark Angus, U. S. N., Philadelphia.
235: Edward Adams Richardson, Kansas City.
263: Prof. William Benjamin Smith, Tulane University, New Orleans.
264: James Rice, University of London, London.
267: William Hemmenway Pratt, Lynn, Mass.
272: R. Bruce Lindsay, New Bedford, Mass.
283: Frank E. Law, Montclair, N. J.
In addition to the specific credit given by these references for
specifically quoted passages, the Editor feels that he ought to
acknowledge his general indebtedness to the competing essayists,
collectively, for the many ideas which he has taken away from their
text to clothe in his own words. This does not mean that the Editor has
undertaken generally to improve upon the language of the competitors,
but merely that the reading of all their essays has given him many
ideas of such complex origin that he could not assign credit if
he would.
TABLE OF CONTENTS
I.--The Einstein $5,000 Prize: How the Contest Came to be Held,
and Some of the Details of Its Conduct. By the Editor 1
II.--The World--And Us: An Introductory Discussion of the Philosophy
of Relativity, and of the Mechanism of our Contact with Time and
Space. By various contributors and the Editor 19
III.--The Relativity of Uniform Motion: Classical Ideas on the
Subject; the Ether and the Apparent Possibility of Absolute Motion;
the Michelson-Morley Experiment and the Final Negation of this
possibility. By various contributors and the Editor 47
IV.--The Special Theory of Relativity: What Einstein's Study of
Uniform Motion Tells Us About Time and Space and the Nature of the
External Reality. By various contributors and the Editor 76
V.--That Parallel Postulate: Modern Geometric Methods; the Dividing
Line Between Euclidean and Non-Euclidean; and the Significance of
the Latter. By the Editor 111
VI.--The Space-Time Continuum: Minkowski's World of Events, and the
Way in Which It Fits Into Einstein's Structure. By the Editor and a
few contributors 141
VII.--Relativity: The Winning Essay in the Contest for the Eugene
Higgins $5,000 Prize. By Lyndon Bolton, British Patent Office,
London 169
VIII.--The New Concepts of Time and Space: The Essay in Behalf of
Which the Greatest Number of Dissenting Opinions Have Been Recorded. By
Montgomery Francis, New York 181
IX.--The Principle of Relativity: A Statement of What it is All
About, in Ideas of One Syllable. By Hugh Elliot, Chislehurst, Kent,
England 195
X.--Space, Time and Gravitation: An Outline of Einstein's Theory of
General Relativity. By W. de Sitter, University of Leyden 206
XI.--The Principle of General Relativity: How Einstein, to a Degree
Never Before Equalled, Isolates the External Reality from the
Observer's Contribution. By E. T. Bell, University of Seattle 218
XII.--Force Vs. Geometry: How Einstein Has Substituted the Second
for the First in Connection with the Cause of Gravitation. By Saul
Dushman, Schenectady 230
XIII.--An Introduction to Relativity: A Treatment in which the
Mathematical Connections of Einstein's Work are Brought Out More
Strongly and More Successfully than Usual in a Popular Explanation. By
Harold T. Davis, University of Wisconsin 240
XIV.--New Concepts for Old: What the World Looks Like After Einstein
Has Had His Way with It. By John G. McHardy, Commander R. N.,
London 251
XV.--The New World: A Universe in Which Geometry Takes the Place of
Physics, and Curvature that of Force. By George Frederick Hemens,
M.C., B.Sc., London 265
XVI.--The Quest of the Absolute: Modern Developments in Theoretical
Physics, and the Climax Supplied by Einstein. By Dr. Francis
D. Murnaghan, Johns Hopkins University, Baltimore 276
XVII.--The Physical Side of Relativity: The Immediate Contacts between
Einstein's Theories and Current Physics and Astronomy. By Professor
William H. Pickering, Harvard College Observatory, Mandeville,
Jamaica 287
XVIII.--The Practical Significance of Relativity: The Best Discussion
of the Special Theory Among All the Competing Essays. By Prof. Henry
Norris Russell, Princeton University 306
XIX.--Einstein's Theory of Relativity: A Simple Explanation of His
Postulates and Their Consequences. By T. Royds, Kodaikanal Observatory,
India 318
XX.--Einstein's Theory of Gravitation: The Discussion of the
General Theory and Its Most Important Application, from the Essay by
Prof. W. F. G. Swann, University of Minnesota, Minneapolis 327
XXI.--The Equivalence Hypothesis: The Discussion of This, With Its
Difficulties and the Manner in Which Einstein Has Resolved Them, from
the Essay by Prof. E. N. da C. Andrade, Ordnance College, Woolwich,
England 334
XXII.--The General Theory: Fragments of Particular Merit on This
Phase of the Subject. By Various Contributors 338
I.
THE EINSTEIN $5,000 PRIZE
HOW THE CONTEST CAME TO BE HELD, AND SOME OF THE DETAILS OF ITS CONDUCT
BY THE EDITOR
In January, 1909, an anonymous donor who was interested in the spread
of correct scientific ideas offered through the Scientific American a
prize of $500 for the best essay explaining, in simple non-technical
language, that paradise of mathematicians and bugaboo of plain
ordinary folk--the fourth dimension. Many essays were submitted in
this competition, and in addition to that of the winner some twenty
were adjudged worthy of ultimate publication. It was felt that the
competition had added distinctly to the popular understanding of
this significant subject; that it had done much to clear up popular
misconception of just what the mathematician means when he talks
of four or even more dimensions; and that it had therefore been as
successful as it was unusual in character.
In November, 1919, the world was startled by the announcement from
London that examination of the photographs taken during the total
solar eclipse of May 29th had been concluded, and that predictions
based upon the Einstein theories of relativity had been verified. In
the reaction from the long surfeit of war news an item of this sort
was a thoroughly journalistic one. Long cable dispatches were carried
in the news columns all over the world; Einstein and his theories
were given a prominent place on the front pages day after day; leading
scientists in great number were called upon to tell the public through
the reportorial medium just what the excitement was all about, just
in what way the classical scientific structure had been overthrown.
Instead of being a mere nine days' wonder, the Einstein theories held
their place in the public mind. The more serious periodicals devoted
space to them. First and last, a very notable group of scientific men
attempted to explain to the general reader the scope and content of
Einstein's system. These efforts, well considered as they were, could
be no more than partially successful on account of the very radical
character of the revisions which the relativity doctrine demands in
our fundamental concepts. Such revisions cannot be made in a day;
the average person has not the viewpoint of the mathematician which
permits a sudden and complete exchange of one set of fundamentals
for another. But the whole subject had caught the popular attention
so strongly, that even complete initial failure to discover what it
was all about did not discourage the general reader from pursuing
the matter with determination to come to some understanding of what
had happened to Newton and Newtonian mechanics.
THE DONOR AND THE PRIZE
In May, 1920, Mr. Eugene Higgins, an American citizen long resident
in Paris, a liberal patron of the arts and sciences, and a lifelong
friend of the Scientific American and its proprietors, suggested that
the success of the Fourth Dimension Prize Contest of 1910 had been
so great that it might be desirable to offer another prize in similar
fashion for the best popular essay on the Einstein theories. He stated
that if in the opinion of the Scientific American these theories
were of sufficient importance, and the probability of getting a
good number of meritorious essays were sufficiently great, and the
public need and desire for enlightenment were sufficiently present,
he would feel inclined to offer such a prize, leaving the conduct
of the contest to the Scientific American as in the former event. It
was the judgment of the editors of the Scientific American that all
these provisos should be met with an affirmative, and that Mr. Higgins
accordingly could with propriety be encouraged to offer the prize.
In his preliminary letter Mr. Higgins had suggested that in view
of the apparent greater importance of the subject to be proposed
for discussion by the contestants of 1920, the prize offered should
probably be more liberal than in the former instance. This view met
with the approval of the editors as well; but they were totally
unprepared for the receipt, late in June, of a cablegram from
Mr. Higgins stating that he had decided to go ahead with the matter,
and that he was forwarding a draft for $5,000 to represent the amount
of the prize. Such a sum, exceeding any award open to a professional
man with the single exception of the Nobel Prize, for which he cannot
specifically compete, fairly took the breath of the Editors, and
made it immediately clear that the contest would attract the widest
attention, and that it should score the most conspicuous success. It
also made it clear that the handling of the contest would be a more
serious matter than had been anticipated.
In spite of the fact that it would not for some time be possible to
announce the identity of the Judges, it was felt that the prospective
contestants should have every opportunity for extensive preparation;
so the contest was announced, and the rules governing it printed
as far as they could be determined on such short shrift, in the
Scientific American for July 10, 1920. Several points of ambiguity
had to be cleared up after this initial publication. In particular,
it had been Mr. Higgins' suggestion that in the very probable event
of the Judges' inability to agree upon the winning essay, the prize
might, at their discretion, be divided between the contributors
of the best two essays. This condition was actually printed in the
first announcement, but the Post Office Department insisted upon its
withdrawal, on the ground that with it in force the contestant would
not know whether he were competing for $5,000 or for $2,500, and that
this would introduce the "element of chance" which alone was necessary,
under the Federal statutes, to make the contest a lottery. So this
provision was replaced by one to the effect that in the event the
Judges were not able to agree, the Einstein Editor should cast the
deciding vote between the essays respectively favored by them.
The announcement attracted the widest attention, and was copied in
newspapers and magazines all over the world. Inquiries poured in from
all quarters, and the Einstein Editor found it almost impossible to
keep himself supplied with proofs of the conditions and rules to mail
in response to these inquiries. It was immediately clear that there
was going to be a large number of essays submitted, and that many
distinguished names would be listed among the competitors.
THE JUDGES
In the Scientific American for September 18, announcement was carried
in the following words:
"We are assured with complete certainty that the competition for the
five-thousand-dollar prize will be very keen, and that many essays
will be submitted which, if they bore the names of their authors, would
pass anywhere as authoritative statements. The judges will confront a
task of extraordinary difficulty in the effort to determine which of
these efforts is the best; and we believe the difficulties are such
that multiplication of judges would merely multiply the obstacles to
an agreement. It is altogether likely that the initial impressions
of two or three or five judges would incline toward two or three
or five essays, and that any final decision would be attainable
only after much consultation and discussion. It seems to us that by
making the committee as small as possible while still preserving the
necessary feature that its decision represent a consensus, we shall
simplify both the mental and the physical problem of coming to an
agreement. We believe that the award should if possible represent
a unanimous decision, without any minority report, and that such a
requirement is far more likely to be met among two men than among
three or five. At the same time, the bringing together of two men and
the details of general administration of their work together are far
simpler than if there were three or five. So we have finally decided
to have but two judges, and in this we have the endorsement of all
the competent opinion that we have consulted.
"The gentlemen who have consented to act as Judges are Professors
Leigh Page and Edwin Plimpton Adams, of the departments of physics
of Yale and Princeton Universities, respectively. Both are of the
younger generation of physicists that has paid special attention to
those phases of mathematics and physics involved in the Einstein
theories, and both have paid special attention to these theories
themselves. We are gratified to be able to put forward as Judges
two men so eminently qualified to act. We feel that we may here
appropriately quote Professor Page, who says in his acceptance:
'As the large prize offers a great inducement, I had thought of
entering the contest. However I realize that not many people in
this country have made a considerable study of Einstein's theory,
and if all who have should enter the contest, it would be difficult
to secure suitable Judges.' Without any desire to put the gentleman
in the position of pleading for himself, we think this suggests very
well the extent to which the Scientific American, the contestants,
and the public at large, are indebted to Professors Page and Adams
for their willingness to serve in the difficult capacity of Judges."
It might appropriately have been added to this announcement that it
was altogether to the credit of science and the scientific spirit
that the first two gentlemen approached with the invitation to act
as Judges were willing to forego their prospects as contestants in
order thus to contribute to the success of the contest.
THREE THOUSAND WORDS
Of the conditions, the one which evoked most comment was that stating
the word limit. This limit was decided upon after the most careful
discussion of the possibilities of the situation. It was not imagined
for a moment that any contestant would succeed in getting within
3,000 words a complete discussion of all aspects of the Special
and the General Theories of Relativity. It was however felt that
for popular reading a single essay should not be much if any longer
than this. Moreover, I will say quite frankly that we should never
have encouraged Mr. Higgins to offer such a prize if we had supposed
that the winning essay was the only thing of value that would come
from the contest, or if we had not expected to find in many of the
other essays material which would be altogether deserving of the
light. From the beginning we had in view the present volume, and the
severe restriction in length was deliberately imposed for the purpose
of forcing every contestant to stick to what he considered the most
significant viewpoints, and to give his best skill to displaying the
theories of Einstein to the utmost advantage from these viewpoints. We
felt that divergent viewpoints would be more advantageously treated in
this manner than if we gave each contestant enough space to discuss
the subject from all sides; and that the award of the prize to the
essay which, among other requirements, seemed to the Judges to embody
the best choice of material, would greatly simplify the working of the
contest without effecting any injustice against those contestants who
displayed with equal skill less happily chosen material. Perhaps on
this point I may again quote with profit the editorial page of the
Scientific American:
"An essay of three thousand words is not long enough to lose a
reader more than once; if it does lose him it is a failure, and if
it doesn't it is a competitor that will go into the final elimination
trials for the prize. If we can present, as a result of the contest,
six or a dozen essays of this length that will not lose the lay reader
at all, we shall have produced something amply worth the expenditure
of Mr. Higgins' money and our time. For such a number of essays of
such character will of necessity present many different aspects of
the Einstein theories, and in many different ways, and in doing so
will contribute greatly to the popular enlightenment.
"Really the significant part of what has already appeared is
not the part that is intelligible, but rather the part that,
being unintelligible, casts the shadow of doubt and suspicion
on the whole. The successful competitor for the prize and
his close contestants will have written essays that, without
any claim to completeness, will emphasize what seems to each
author the big outstanding feature; and every one of them will be
intelligible. Together they will in all probability be reasonably
complete, and will retain the individual characteristic of
intelligibility. They will approach the various parts of the field
from various directions--we could fill this page with suggestions as
to how the one item of the four-dimensional character of Einstein's
time-space might be set forth for the general reader. And when a man
must say in three thousand words as much as he can of what eminent
scientists have said in whole volumes--well, the result in some cases
will be sheer failure, and in others a product of the first water. The
best of the essays will shine through intelligent selection of what
is to be said, and brilliant success in saying it. It is to get a
group of essays of this character, not to get the single essay which
will earn the palm, that the prize is offered."
THE COMPETING ESSAYS
At all times after the first announcement the Einstein Editor had a
heavy correspondence; but the first real evidence that the contest was
under way came with the arrival of the first essay, which wandered
into our office in the middle of September. About a week later they
began to filter in at the rate of one or two per day--mostly from
foreign contestants who were taking no chances on the mails. Heavy
returns did not commence until about ten days before the closing
date. The great avalanche, however, was reserved for the morning of
Monday, November 1st. Here we had the benefit of three days' mail;
there were about 120 essays. Among those which were thrown out on
the ground of lateness the honors should no doubt go to the man who
mailed his offering in The Hague on October 31st.
Essays were received in greater quantity from Germany than from any
other foreign country, doubtless because of the staggering value of
$5,000 when converted into marks at late 1920 rates. England stood
next on the list; and one or more essays were received from Austria,
Czechoslovakia, Jugoslavia, France, Switzerland, the Netherlands,
Denmark, Italy, Chile, Cuba, Mexico, India, Jamaica, South Africa
and the Fiji Islands. Canada, of course, contributed her fair share;
and few of our own states were missing on the roll-call.
The general level of English composition among the essays from
non-English-speaking sources was about what might have been expected. A
man may have a thorough utilitarian knowledge of a foreign tongue,
but when he attempts intensive literary competition with a man who was
brought up in that tongue he is at a disadvantage. We read French and
German with ease and Spanish and Italian without too much difficulty,
ourselves; we should never undertake serious writing in any of these
languages. Not many of the foreign contributions, of course, were
as ludicrous as the one we quote to some extent in our concluding
chapter, but most of them were distinctly below par as literary
compositions. Drs. De Sitter and Schlick were the notable exceptions
to this; both showed the ability to compete on a footing of absolute
equality with the best of the native product.
We dare say it was a foregone conclusion that many essays should have
been over the limit, and that a few should have been over it to the
point of absurdity. The winning essay contains 2,919 words, plus or
minus a reasonable allowance for error in counting; that it should
come so far from being on the ragged edge should be sufficient answer
to those who protested against the severity of the limitation. One
inquirer, by the way, wanted to know if 3,000 words was not a misprint
for 30,000. Another contestant suggested that instead of disqualifying
any essay that was over the line, we amputate the superfluous words
at the end. This was a plausible enough suggestion, since any essay
able to compete after such amputation must necessarily have been one
of extreme worth; but fortunately we did not have to decide whether we
should follow the scheme. Perhaps twenty of the essays submitted were
so seriously in excess of the limit that it was not even necessary
to count their words in detail; most of these offenders ran to 3,500
words or thereabouts, and one--a good one, too, from which we use
a good deal of material in this volume--actually had 4,700. On the
other extreme were a few competitors who seemed to think that the
shortest essay was necessarily the best, and who tried to dismiss
the subject with 500 or 1,000 words.
By a curious trick of chance there were submitted in competition
for the prize exactly 300 essays. Of course a few of these did not
require serious consideration--this is inevitable in a contest of such
magnitude. But after excluding all the essays that were admittedly
not about the Einstein theories at all, and all those whose English
was so execrable as to make them quite out of the question, and all
those which took the subject so lightly as not to write reasonably
close to the limit of 3,000 words, and all those which were given
over to explanation of the manner in which Einstein's theories verify
those of the writer, and all those in which the writer attempted
to substitute his own cosmic scheme for Einstein's--after all this,
there remained some 275 essays which were serious efforts to explain
in simple terms the nature and content and consequences of Special
and General Relativity.
LOOKING FOR THE WINNER
The Einstein Editor was in sufficiently close touch with the details
of the adjudication of the essays to have every realization of
the difficulty of this work. The caliber of the essays submitted
was on the whole high. There were many which would have been well
worthy of the prize in the absence of others that were distinctly
better--many which it was not possible to eliminate on the ground of
specific faults, and which could only be adjudged "not the best" by
detailed comparison with specific other essays. It was this detailed
comparison which took time, and which so delayed the award that we
were not able to publish the winning essay any sooner than February
5th. Especially difficult was this process of elimination after the
number of surviving essays had been reduced to twenty or less. The
advantages of plan possessed by one essay had to be weighed against
those of execution exhibited in another. A certain essay had to be
critically compared with another so like it in plan that the two might
have been written from a common outline, and at the same time with
a third as unlike it in scope and content as day and night. And all
the time there was present in the background the consciousness that
a prize of $5,000 hung upon the decision to be reached. For anyone
who regards this as an easy task we have no worse wish than that he
may some day have to attack a similar one.
We had anticipated that the bulk of the superior essays would be
among those received during the last day or two of the contest;
for we felt that the men best equipped to attack the subject would
be the most impressed with its seriousness. Here we were quite off
the track. The seventeen essays which withstood most stubbornly the
Judges' efforts at elimination were, in order of receipt, numbers 8,
18, 28, 40, 41, 43, 92, 95, 97, 130, 181, 194, 198, 223, 267, 270, 275:
a fairly even distribution. The winner was the 92nd essay received.
The Judges held their final meeting in the editorial office on
January 18, 1921. The four essays which were before the committee
at the start of the session were speedily cut to three, and then
to two; and after an all-day session the Judges found themselves
conscientiously able to agree on one of these as the best. This
unanimity was especially gratifying, the more so since it by no
means was to be confidently expected, on a priori grounds, that it
would be possible of attainment. Even the Einstein Editor, who might
have been called upon for a final decision but wasn't, can hardly be
classed as a dissenter; for with some slight mental reservations in
favor of the essay by Mr. Francis which did not enter the Judges'
final discussion at all, and which he rather suspects appeals more
to his personal taste than to his soundest judgment, he is entirely
in accord with the verdict rendered.
The fact that the prize went to England was no surprise to those
acquainted with the history of Einstein's theories. The Special Theory,
promulgated fifteen years ago, received its fair share of attention
from mathematicians all over the world, and is doubtless as well
known and as fully appreciated here as elsewhere. But it has never
been elevated to a position of any great importance in mathematical
theory, simply because of itself, in the absence of its extension
to the general case, it deserves little importance. It is merely an
interesting bit of abstract speculation.
The General Theory was put out by Einstein in finished form during
the war. Owing to the scientific moratorium, his paper, and hence a
clear understanding of the new methods and results and of the sweeping
consequences if the General Theory should prevail, did not attain
general circulation outside Germany until some time in 1918 or even
later. Had it not been for Eddington it is doubtful that the British
astronomers would have realized that the eclipse expeditions were of
particular consequence. Therefore at the time of these expeditions,
and even as late as the November announcement of the findings, the
general body of scientific men in America had not adequately realized
the immense distinction between the Special and the General Theories,
had not adequately appreciated that the latter led to distinctive
consequences of any import, and we fear in many cases had not even
realized explicitly that the deflection of light and the behavior of
Mercury were matters strictly of the General and in no sense of the
Special Theory. Certainly when the American newspapers were searching
frantically for somebody to interpret to their public the great stir
made by the British announcement that Einstein's predictions had
been verified, they found no one to do this decently; nor were our
magazines much more successful in spite of the greater time they had
to devote to the search. In a word, there is not the slightest room
for doubt that American science was in large measure caught asleep
at the switch--perhaps for no reason within its control; and that
American writers were in no such favorable case to write convincingly
on the subject as were their British and continental contemporaries.
So it was quite in accord with what might have been expected to find,
on opening the identifying envelopes, that not alone the winning essay,
but its two most immediate rivals, come from members of that school of
British thought which had been in contact with the Einstein theories
in their entirety for two years longer than the average American of
equal competence. This riper familiarity with the subject was bound
to yield riper fruit. Indeed, had it not been for the handicap of
writing in a strange language, it is reasonable to assume that the
scientists of Germany would have made a showing superior to that of
either Americans or British--and for the same reason that Britain
showed to better advantage than America.
THE WINNER OF THE PRIZE
Mr. Bolton, the winner of the big prize, we suppose may fairly be
referred to as unknown in a strict scientific sense. Indeed, at
the time of the publication of his essay in the Scientific American
nothing could be learned about him on the American side of the water
beyond the bare facts that he was not a young man, and that he had
for a good many years occupied a position of rank in the British
Patent Office. (It will be recalled that Einstein himself was in the
Swiss Patent Office for some time.) In response to the request of the
Scientific American for a brief biographical sketch that would serve
to introduce him better to our readers, Mr. Bolton supplied such a
concise and apparently such a characteristic statement that we can
do no better than quote it verbatim.
"I was born in Dublin in 1860, but I have lived in England since
1869. My family belonged to the landed gentry class, but I owe nothing
to wealth or position. I was in fact put through school and college
on an income which a workman would despise nowadays. After attending
sundry small schools, I entered Clifton College in 1873. My career
there was checkered, but it ended well. I was always fairly good at
natural science and very fond of all sorts of mechanical things. I
was an honest worker but no use at classics, and as I did practically
nothing else for the first four years at Clifton, I came to consider
myself something of a dunce. But a big public school is a little
world. Everyone gets an opportunity, often seemingly by accident,
and it is up to him to take it. Mine did not come till I was nearly
17. As I was intended for the engineering profession, I was sent to
the military side of the school in order to learn some mathematics,
at which subject I was then considered very weak. This was certainly
true, as at that time I barely knew how to solve a quadratic, I was
only about halfway through the third book of Euclid, and I knew no
trigonometry. But the teaching was inspiring, and I took readily
to mathematics. One day it came out that I had been making quite a
good start with the differential calculus on my own without telling
anybody. After that all was well. I left Clifton in 1880 with a School
Exhibition and a mathematical scholarship at Clare College, Cambridge.
"After taking my degree in 1883 as a Wrangler, I taught science and
mathematics at Wellington College, but I was attracted by what I had
heard of the Patent Office and I entered it through open competition in
1885. During my official career I have been one of the Comptroller's
private secretaries and I am now a Senior Examiner. During the
war I was attached to the Inventions Department of the Ministry of
Munitions, where my work related mainly to anti-aircraft gunnery. I
have contributed, and am still contributing to official publications
on the subject.
"I have written a fair number of essays on various subjects, even
on literature, but my only extra-official publications relate to
stereoscopic photography. I read a paper on this subject before the
Royal Photographic Society in 1903 which was favorably noticed by
Dr. von Rohr of Messrs. Zeiss of Jena. I have also written in the
Amateur Photographer.
"I have been fairly successful at athletics, and I am a member of
the Leander Club."
That Mr. Bolton did not take the prize through default of serious
competition should be plain to any reader who examines the text from
competing essays which is to be found in this volume. The reference
list of these competitors, too, supplemented by the names that appear
at the heads of complete essays, shows a notable array of distinguished
personalities, and I could mention perhaps a dozen more very well
known men of science whose excellent essays have seemed a trifle too
advanced for our immediate use, but to whom I am under a good deal
of obligation for some of the ideas which I have attempted to clothe
in my own language.
Before leaving the subject, we wish to say here a word of appreciation
for the manner in which the Judges have discharged their duties. The
reader will have difficulty in realizing what it means to read such
a number of essays on such a subject. We were fortunate beyond all
expectation in finding Judges who combined a thorough scientific
grasp of the mathematical and physical and philosophical aspects
of the matter with an extremely human viewpoint which precluded any
possibility of an award to an essay that was not properly a popular
discussion, and with a willingness to go to meet each other's opinions
that is rare, even among those with less ground for confidence in
their own views than is possessed by Drs. Page and Adams.
II.
THE WORLD--AND US
An Introductory Discussion of the Philosophy of Relativity, and of
the Mechanism of Our Contact with Time and Space
BY VARIOUS CONTRIBUTORS AND THE EDITOR
From a time beyond the dawn of history, mankind has been seeking
to explain the universe. At first the effort did not concern itself
further probably than to make a supposition as to what were the causes
of the various phenomena presented to the senses. As knowledge
increased, first by observation and later by experiment also,
the ideas as to these causes passed progressively through three
stages--the theological (the causes were thought to be spirits or
gods); the metaphysical (the causes were thought in this secondary
or intermediate stage to be some inherent, animating, energizing
principles); and the scientific (the causes were finally thought of
as simply mechanical, chemical, and magneto-electrical attractions
and repulsions, qualities or characteristics of matter itself, or of
the thing of which matter is itself composed.)
With increase of knowledge, and along with the inquiry as to the nature
of causes, there arose an inquiry also as to what reality was. What was
the essential nature of the stuff of which the universe was made, what
was matter, what were things in themselves, what were the noumena (the
realities), lying back of the phenomena (the appearances)? Gradually
ideas explaining motion, force, and energy were developed. At the
same time inquiry was made as to the nature of man, the working
of his mind, the nature of thought, the relation of his concepts
(ideas) to his perceptions (knowledge gained through the sense)
and the relations of both to the noumena (realities).]283
[The general direction taken by this inquiry has been that of a
conflict between two schools of thought which we may characterize
as those of absolutism and of relativism.]* [The ancient Greek
philosophers believed that they could tap a source of knowledge
pure and absolute by sitting down in a chair and reasoning about the
nature of time and space, and the mechanism of the physical world.]221
[They maintained that the mind holds in its own right certain concepts
than which nothing is more fundamental. They considered it proper to
conceive of time and space and matter and the other things presented
to their senses by the world as having a real existence in the mind,
regardless of whether any external reality could be identified
with the concept as ultimately put forth. They could even dispute
with significance the qualities which were to be ascribed to this
abstract conceptual time and space and matter. All this was done
without reference to the external reality, often in defiance of that
reality. The mind could picture the world as it ought to be; if the
recalcitrant facts refused to fit into the picture, so much the worse
for them. We all have heard the tale of how generation after generation
of Greek philosophers disputed learnedly why and how it was that a live
fish could be added to a brimming pail of water without raising the
level of the fluid or increasing the weight; until one day some common
person conceived the troublesome idea of trying it out experimentally
to learn whether it were so--and found that it was not. True or false,
the anecdote admirably illustrates the subordinate place which the
externals held in the absolutist system of Greek thought.]*
[Under this system a single observer is competent to examine a
single phenomenon, and to write down the absolute law of nature
by referring the results to his innate ideas of absolute qualities
and states. The root of the word absolute signifies "taking away,"
and in its philosophical sense the word implies the ability of the
mind to subtract away the properties or qualities from things, and
to consider these abstract qualities detached from the things; for
example, to take away the coldness from ice, and to consider pure or
abstract coldness apart from anything that is cold; or to take away
motion from a moving body, and to consider pure motion apart from
anything that moves. This assumed power is based upon the Socratic
theory of innate ideas. According to this theory the mind is endowed
by nature with the absolute ideas of hardness, coldness, roundness,
equality, motion, and all other absolute qualities and states, and
so does not have to learn them. Thus a Socratic philosopher could
discuss pure or absolute being, absolute space and absolute time.]121
GETTING AWAY FROM THE GREEK IDEAS
[This Greek mode of thought persisted into the late Middle Ages,
at which time it was still altogether in order to dispose of a
troublesome fact of the external world by quoting Aristotle against
it. During the Renaissance, which intellectually at least marks the
transition from ancient to modern, there came into being another
type of absolutism, equally extreme, equally arbitrary, equally
unjustified. The revolt against the mental slavery to Greek ideas
carried the pendulum too far to the other side, and early modern
science as a consequence is disfigured by what we must now recognize
as gross materialism. The human mind was relegated to the position
of a mere innocent bystander. The external reality was everything,
and aside from his function as a recorder the observer did not in the
least matter. The whole aim of science was to isolate and classify the
elusive external fact. The rôle of the observer was in every possible
way minimized. It was of course his duty to get the facts right,
but so far as any contribution to these was concerned he did not
count--he was definitely disqualified. He really played the part of
an intruder; from his position outside the phenomena he was searching
for the absolute truth about these phenomena. The only difference
between his viewpoint and that of Aristotle was that the latter looked
entirely inside himself for the elusive "truth," while the "classical"
scientist, as we call him now, looked for it entirely outside himself.
Let me illustrate the difference between the two viewpoints which
I have discussed, and the third one which I am about to outline,
by another concrete instance. The Greeks, and the medievals as well,
were fond of discussing a question which embodies the whole of what
I have been saying. This question involved, on the part of one who
attempted to answer it, a choice between the observer and the external
world as the seat of reality. It was put in many forms; a familiar
one is the following: "If the wind blew down a great tree at a time
and place where there was no conscious being to hear, would there
be any noise?" The Greek had to answer this question in the negative
because to him the noise was entirely a phenomenon of the listener. The
classical scientist had to answer it in the affirmative because to him
the noise was entirely a phenomenon of the tree and the air and the
ground. Today we answer it in the negative, but for a very different
reason from that which swayed the Greek. We believe that the noise is
a joint phenomenon of the observer and the externals, so that in the
absence of either it must fail to take existence. We believe there are
sound waves produced, and all that; but what of it? There is no noise
in the presence of the falling tree and the absence of the observer,
any more than there would be in the presence of the observer and the
absence of the tree and the wind; the noise, a joint phenomenon of
the observer and the externals, exists only in their joint presence.
RELATIVISM AND REALITY
This is the viewpoint of relativism. The statue is golden for
one observer and silver to the other. The sun is rising here and
setting in another part of the world. It is raining here and clear in
Chicago. The observer in Delft hears the bombardment of Antwerp and
the observer in London does not. If they were to be consistent, both
the Greek and the medieval-modern absolutist would have to dispute
whether the statue were "really" golden or silver, whether the sun
were "really" rising or setting, whether the weather were "really"
fair or foul, whether the bombardment were "really" accompanied by
loud noises or not; and on each of these questions they would have to
come to an agreement or confess their methods inadequate. But to the
relativist the answer is simple--whether this or that be true depends
upon the observer. In simple cases we understand this full well, as
we have always realized it. In less simple cases we recognize it less
easily or not at all, so that some of our thought is absolutist in
its tendencies while the rest is relativistic. Einstein is the first
ever to realize this fully--or if not this, then the first ever to
realize it so fully as to be moved toward a studied effort to free
human thought from the mixture of relativism and absolutism and make
it consistently the one or the other.
This brings it about that the observed fact occupies a position of
unexpected significance. For when we discuss matters of physical
science under a strictly relativistic philosophy, we must put away as
metaphysical everything that smacks of a "reality" partly concealed
behind our observations. We must focus attention upon the reports
of our senses and of the instruments that supplement them. These
observations, which join our perceptions to their external objects,
afford us our only objective manifestations; them we must accept as
final--subject always to such correction as more refined observations
may suggest. The question whether a "true" length or area or mass
or velocity or duration or temperature exists back of the numerical
determination, or in the presence of a determination that is subject
to correction, or in the absence of any determination at all, is a
metaphysical one and one that the physicist must not ask. Length,
area, mass, velocity, duration, temperature--none of these has any
meaning other than the number obtained by measurement.]* [If several
different determinations are checked over and no error can be found
in any of them, the fault must lie not with the observers but with
the object, which we must conclude presents different values to
different observers.]33
[We are after all accustomed to this viewpoint; we do not demand that
Pittsburgh shall present the same distance from New York and from
Philadelphia, or that the New Yorker and the Philadelphian come to
any agreement as to the "real" distance of Pittsburgh. The distance
of Pittsburgh depends upon the position of the observer. Nor do we
demand that the man who locates the magnetic pole in one spot in 1900
and in another in 1921 come to a decision as to where it "really"
is; we accept his statement that its position depends upon the time
of the observation.
What this really means is that the distance to Pittsburgh and the
position of the magnetic pole are joint properties of the observer
and the observed--relations between them, as we might put it. This
is obvious enough in the case of the distance of Pittsburgh; it is
hardly so obvious in the case of the position of the magnetic pole,
varying with the lapse of time. But if we reflect that the observation
of 1900 and that of 1921 were both valid, and both represented the
true position of the pole for the observer of the date in question, we
must see that this is the only explanation that shows us the way out.
I do not wish to speak too definitely of the Einstein theories in
these introductory remarks, and so shall refrain from mentioning
explicitly in this place the situation which they bring up and upon
which what I have just said has direct bearing. It will be recognized
when it arises. What must be pointed out here, however, is that we
are putting the thing which the scientist calls the "observed value"
on a footing of vastly greater consequence than we should have been
willing offhand to concede to it. So far as any single observer is
concerned, his own best observed values are themselves the external
world; he cannot properly go behind the conditions surrounding
his observations and speak of a real external world beyond these
observations. Any world which he may think of as so existing is purely
a conceptual world, one which for some reason he infers to exist
behind the deceptive observations. Provided he makes this reservation
he is quite privileged to speculate about this concealed world, to
bestow upon it any characteristics that he pleases; but it can have
no real existence for him until he becomes able to observe it. The
only reality he knows is the one he can directly observe.
LAWS OF NATURE
The observations which we have been discussing, and which we have
been trying to endow with characteristics of "reality" which they are
frequently not realized to possess, are the raw material of physical
science. The finished product is the result of bringing together a
large number of these observations.]* [The whole underlying thought
behind the making of observations, in fact, is to correlate as many
as possible of them, to obtain some generalization, and finally to
express this in some simple mathematical form. This formulation is
then called a "law of nature."]35
[Much confusion exists because of a misunderstanding in the lay mind
of what is meant by a "law of nature." It is perhaps not a well chosen
term. One is accustomed to associate the word law with the idea of
necessity or compulsion. In the realm of nature the term carries
no such meaning. The laws of nature are man's imperfect attempts to
explain natural phenomena; they are not inherent in matter and the
universe, not an iron bar of necessity running through worlds, systems
and suns. Laws of nature are little more than working hypotheses,
subject to change or alteration or enlargement or even abandonment,
as man's vision widens and deepens. No sanctity attaches to them,
and if any one, or all, of them fail to account for any part, or all,
of the phenomena of the universe, then it or they must be supplemented
or abandoned.]102
[The test of one of these laws is that it can be shown to include
all the related phenomena hitherto known and that it enables us to
predict new phenomena which can then be verified. If new facts are
discovered that are not in agreement with one of these generalized
statements, the assumptions on which the latter is based are examined,
those which are not in accordance with the new facts are given up,
and the statement is modified so as to include the new facts.]10
[And if one remembers that the laws of physics were formerly based
on a range of observations much narrower than at present available,
it seems natural that in the light of this widening knowledge one law
or another may be seen to be narrow and insufficient. New theories
and laws do not necessarily disprove old ones, but explain certain
discrepancies in them and penetrate more deeply into their underlying
principles, thereby broadening our ideas of the universe. To follow the
new reasoning we must rid ourselves of the prejudice behind the old,
not because it is wrong but because it is insufficient. The universe
will not be distorted to fit our rules, but will teach us the rules
of existence.]125
[Always, however, we must guard against the too easy error of
attributing to these rules anything like absolute truth.]* [The
modern scientist has attained a very business-like point of view
toward his "laws of nature." To him a law is fundamentally nothing
but a short-hand way of expressing the results of a large number of
experiments in a single statement. And it is important to remember that
this mere shortening of the description of a lot of diverse occurrences
is by no means any real explanation of how and why they happened. In
other words, the aim of science is not ultimately to explain but only
to discover the relations that hold good among physical quantities and
to embody all these relations in as few and as simple physical laws
as possible.]221 [This is inherently the method of relativism.]*
[Under it a set of phenomena is observed. There are two or many
observers, and they write down their several findings. These are
reviewed by a final observer or judge, who strains out the bias due
to the different viewpoints of the original observers. He then writes
down, not any absolute law of nature governing the observed phenomena,
but a law as general as possible expressing their interrelations.]121
[And through this procedure modern science and philosophy reveal
with increasing emphasis that we superimpose our human qualities
on external nature to such an extent that]106 [we have at once the
strongest practical justification, in addition to the arguments
of reason, for our insistence that the contact between objective
and subjective represented by the observation is the only thing
which we shall ever be able to recognize as real. We may indulge in
abstract metaphysical speculation to our heart's content, if we be
metaphysically inclined; we may not attempt to impose the dicta of
metaphysics upon the physical scientist.]*
CONCEPTS AND REALITIES
[From the inquiry and criticism which have gone on for centuries has
emerged the following present-day attitude of mind toward the sum
total of our knowledge. The conceptual universe in our minds in some
mysterious way parallels the real universe, but is totally unlike
it. Our conceptions (ideas) of matter, molecules, atoms, corpuscles,
electrons, the ether, motion, force, energy, space, and time stand
in the same or similar relation to reality as the x's and y's of the
mathematician do to the entities of his problem. Matter, molecules,
atoms, corpuscles, electrons, the ether, motion, force, energy, space,
and time do not exist actually and really as we conceive them, nor do
they have actually and really the qualities and characteristics with
which we endow them. The concepts are simply representations of things
outside ourselves; things which, while real, have an essential nature
not known to us. Matter, molecules, atoms, corpuscles, electrons,
the ether, motion, force, energy, space and time are merely devices,
symbols, which enable us to reason about reality. They are parts of
a conceptual mechanism in our minds which operates, or enables our
minds to operate, in the same sequence of events as the sequence of
phenomena in the external universe, so that when we perceive by our
senses a group of phenomena in the external universe, we can reason
out what result will flow from the interaction of the realities
involved, and thus predict what the situation will be at a given
stage in the sequence.
But while our conceptual universe has thus a mechanical aspect,
we do not regard the real universe as mechanical in its nature.]283
[This may be illustrated by a little story. Entering his friend's
house, a gentleman is seized unawares from behind. He turns his
head but sees nothing. His hat and coat are removed and deposited
in their proper places by some invisible agent, seats and tables and
refreshments appear in due time where they are required, all without
any apparent cause. The visitor shivers with horror and asks his
host for an explanation. He is then told that the ideas "order" and
"regularity" are at work, and that it is they who acquit themselves so
well of their tasks. These ideas cannot be seen nor felt nor seized
nor weighed; they reveal their existence only by their thoughtful
care for the welfare of mankind. I think the guest, coming home,
will relate that his friend's house is haunted. The ghosts may be
kind, benevolent, even useful; yet ghosts they are. Now in Newtonian
mechanics, absolute space and absolute time and force and inertia and
all the other apparatus, altogether imperceptible, appearing only at
the proper time to make possible a proper building up of the theory,
play the same mysterious part as the ideas "order" and "regularity"
in my story. Classical mechanics is haunted.]116
[As a matter of fact, we realize this and do not allow ourselves to
be imposed upon with regard to the true nature of these agencies.]*
[We use a mechanistic terminology and a mechanistic mode of reasoning
only because we have found by experience that they facilitate our
reasoning. They are the tools which we find produce results. They
are adapted to our minds, but perhaps it would be better to say that
our minds are so constructed as to render our conceptual universe
necessarily mechanical in its aspect in order that our minds may reason
at all. Two things antithetic are involved--subject (our perceiving
mind which builds up concepts) and object (the external reality); and
having neither complete nor absolute knowledge of either, we cannot
affirm which is more truly to be said to be mechanistic in its nature,
though we may suspect that really neither is. We no longer think
of cause and effect as dictated by inherent necessity, we simply
regard them as sequences in the routine of our sense-impressions of
phenomena. In a word, we have at length grasped the idea that our
notions of reality, at present at least, whatever they may become
ultimately, are not absolute, but simply relative. We see, too, that
we do not explain the universe, but only describe our perceptions of
its contents.
The so-called laws of nature are simply statements of formulæ which
resume or sum up the relationships and sequences of phenomena. Our
effort is constantly to find formulæ which will describe the widest
possible range of phenomena. As our knowledge increases, that is,
as we perceive new phenomena, our laws or formulæ break down,
that is, they fail to afford a description in brief terms of all
of our perceptions. It is not that the old laws are untrue, but
simply that they are not comprehensive enough to include all of our
perceptions. The old laws are often particular or limiting instances
of the new laws.]283
[From what we have said of the reality of observations it follows that
we must support that school of psychology, and the parallel school
of philosophy, which hold that concepts originate in perceptions. But
this does not impose so strong a restriction upon conceptions as might
appear. The elements of all our concepts do come to us from outside;
we manufacture nothing out of whole cloth. But when perception
has supplied a sufficient volume of raw material, we may group its
elements in ways foreign to actual occurrence in the perceptual world,
and in so doing get conceptual results so entirely different from
what we have consciously perceived that we are strongly tempted to
look upon them as having certainly been manufactured in our minds
without reference to the externals. Of even more significance is our
ability to abstract from concrete objects and concrete incidents the
essential features which make them alike and different. But unlike
the Greeks, we see that our concept of coldness is not something with
which we were endowed from the beginning, but merely an abstraction
from concrete experiences with concrete objects that have been cold.
THE CONCEPTS OF SPACE AND TIME
When we have formed the abstract ideas of coldness and warmth, and
have had experience indicating that the occurrence of these properties
varies in degree, we are in a position to form the secondary abstract
notion covered by the word "temperature." When we have formed the
abstract ideas of size and position and separation, we are similarly
in a position to form a secondary abstraction to which we give the name
"space." Not quite so easy to trace to its definite source but none the
less clearly an abstraction based on experience, is our idea of what
we call "time." None of us are deceived as to the reality of these
abstractions.]* [We do not regard space as real in the sense that
we regard a chair as real; it is merely an abstract idea convenient
for the location of material objects like the chair.]198 [Nor do we
regard time as real in this sense. Things occupy space, events occupy
time; space and time themselves we realize are immaterial and unreal;
space does not exist and time does not happen in the same sense that
material objects exist and events occur. But we find it absolutely
necessary to have, among the mental machinery mentioned above as
the apparatus by aid of which we keep track of the external world,
these vessels for that world to exist in and move in.
Space and time, then, are concepts.]* [It is not strange, however,
that when confronted with the vast and bewildering complexity of
the universe and the difficulty of keeping separate and distinct in
our minds our perceptions and conceptions, we should at times and as
respects certain things project our conceptions illegitimately into the
perpetual universe and mistake them for perceptions. The most notable
example perhaps of this projection has occurred in the very case of
space and time, most fundamental of all of our concepts. We got to
think of these as absolute, as independent of each other and of all
other things, and as always existing and continuing to exist whether
or not we or anything else existed--space as a three-dimensional,
uniform continuum, having the same properties in all directions;
time as a one-dimensional, irreversible continuum, flowing in one
direction. It is difficult to get back to the idea that space and
time so described and defined are concepts merely, for the idea of
their absolute existence is ingrained in us as the result probably
of long ancestral experience.]283
[Newton's definitions of course represent the classical idea of time
and space. He tells us that "absolute, true and mathematical time
flows in virtue of its own nature, uniformly and without reference to
any external object;" and that "absolute space, by virtue of its own
nature and without reference to any external object, always remains
the same and is immovable." Of course from modern standpoints it is
absurd to call either of these pronouncements a definition; but they
represent about as well as any words can the ideas which Newton had
about time and space, and they make it clear enough that he regarded
both as having real existence in the external world.
If space and time are to be the vessels of our universe, and if the
only thing that really matters is measured results, it is plain enough
that we must have, from the very beginning, means of measuring space
and time. Whether we believe space and time to have real existence or
not, it is obvious that we can measure neither directly. We shall have
to measure space by measuring from one material object to another;
we shall have to measure time by some similar convention based
on events. We shall later have something further to say about the
measurement of time; for the present we need only point out that]*
[Newtonian time is measured independently of space; and the existence
is presupposed of a suitable timekeeper.]10
[The space of Galileo and Newton was conceived of as empty, except in
so far as certain parts of it were occupied by matter. Positions of
bodies in this space were in general determined by reference to]283
[a "coordinate system" of some kind. This is again something that
demands a certain amount of discussion.
THE REFERENCE FRAME FOR SPACE
The mathematician, following the lead of the great French all-around
genius, Descartes, shows us very clearly how to set up, for the
measurement of space, the framework known as the Cartesian coordinate
system. The person of most ordinary mathematical attainments
will realize that to locate a point in a plane we must have two
measurements; and we could probably show this person, without too
serious difficulty, that we can locate a point in any surface by
two measurements. An example of this is the location of points on the
earth's surface by means of their latitude and longitude. It is equally
clear that if we add a third dimension and attempt to locate points
in space, we must add a third measurement. In the case of points on
the earth's surface, this might be the elevation above sea level,
which would define the point not as part of the spherical surface
of the earth but as part of the solid sphere. Or we may fall back
on Dr. Slosson's suggestion that in order to define completely the
position of his laboratory, we must make a statement about Broadway,
and one about 116th Street, and one telling how many flights of stairs
there are to climb. In any event, it should be clear enough that the
complete definition of a point in space calls for three measurements.
The mathematician formulates all this with the utmost precision. He
asks us to]* [pick out any point whatever in space and call it $O$. We
then draw or conceive to be drawn through this point three mutually
perpendicular lines called coordinate axes, which we may designate
$OX$, $OY$ and $OZ$, respectively. Finally, we consider the three
planes also mutually perpendicular like the two walls and the floor of
a room that meet in one common corner, which are formed by the lines
$OX$ and $OY$, $OY$ and $OZ$, and $OZ$ and $OX$, respectively. These
three planes are called coordinate planes. And then any other point $P$
in space can be represented with respect to $O$ by its perpendicular
distances from each of the three coordinate planes--the distances $x$,
$y$, $z$ in the figure. These quantities are called the coordinates
of the point.]272
[To the layman there seems something altogether naive in this notion
of the scientist's setting up the three sides of a box in space and
using them as the basis of all his work. The layman somehow feels
that while it is perfectly all right for him to tell us that he
lives at 1065 (one coordinate) 156th Street (two coordinates) on
the third floor (three coordinates), it is rather trivial business
for the serious-minded scientist to consider the up-and-down, the
forward-and-back, the right-and-left of every point with which he has
occasion to deal. There seems to the layman something particularly
inane and foolish and altogether puerile about a set of coordinate
axes, and you simply can't make him believe that the serious-minded
scientist has to monkey with any such funny business. He can't be
induced to take this coordinate-axis business seriously. Nevertheless,
the fact is that the scientist takes it with the utmost seriousness. It
is necessary for him to define the positions of points; and he does
do it by means of a set of coordinate axes.
The scientist, however, is not interested in points of empty space. The
point is to him merely part again of the conceptual machinery which
he uses in his effort to run along with the external world. He knows
there are no real points, but it suits his convenience to keep track
of certain things that are real by representing them as points. But
these things are in practically every instance material bodies; and
in practically every instance, instead of staying put in one spot,
they insist upon moving about through space. The scientist has to use
his coordinate system, not merely to define a single position of such
a "point," but to keep track of the path over which it moves and to
define its position in that path at given moments.
TIME AND THE COORDINATE SYSTEM
This introduces the concept of time into intimate relationship with
the spatial coordinate system. And at once we feel the lack of a
concrete, visualized fourth dimension.]* [If we want to fix objects
in the floor alone, the edge of the room running toward the ceiling
would become unnecessary and could be dropped from our coordinate
system. That is, we need only two coordinates to fix the position of a
point in a plane. Suppose instead of discarding the third coordinate,
we use it to represent units of time. It then enables us to record
the time it took a moving point in the floor to pass from position
to position. Certain points in the room would be vertically above
the corresponding points occupied by the moving point in its path
across the floor; and the vertical height above the floor of such
points corresponds to a value of the time-coordinate which indicates
the time it took the point to move from position to position.]152
[Just as the path of the point across the floor is a continuous curve
(for the mathematician, it should be understood, this term "curve"
includes the straight line, as a special case in which the curvature
happens to be zero); so the series of points above these in the room
forms a continuous curve which records for us, not merely the path of
the point across the floor, but in addition the time of its arrival
at each of its successive positions. In the algebraic work connected
with such a problem, the third coordinate behaves exactly the same,
regardless of whether we consider it to represent time or a third
spatial dimension; we cannot even tell from the algebra what it
does represent.
When we come to the more general case of a point moving freely through
space, we have but three coordinates at our disposal; there is not
a fourth one by aid of which we can actually diagram its time-space
record. Nevertheless, we can write down the numerical and algebraic
relations between its three space-coordinates and the time which it
takes to pass from one position to another; and by this means we can
make all necessary calculations. Its motion is completely defined
with regard both to space and to time. We are very apt to call
attention to the fact that if we did have at our disposal a fourth,
space-coordinate, we could use it to represent the time graphically,
as before, and actually construct a geometric picture of the path of
our moving point with regard to space and time. And on this account
we are very apt to speak as though the time measurements constituted
a fourth coordinate, regardless of any question of our ability to
construct a picture of this coordinate. The arrival of a point in
a given position constitutes an event; and this event is completely
defined by means of four coordinates--three in space, which we can
picture on our coordinate axes, and one in time which we cannot.
The set of coordinate axes in space, together with the zero point from
which we measure time, constitute what we call a frame of reference. If
we are not going to pay any attention to time, we can think of the
space coordinate system alone as constituting our reference frame. This
expression appears freely throughout the subsequent text, and always
with one or the other of these interpretations.
We see, then, how we can keep track of a moving point by keeping track
of the successive positions which it occupies in our reference frame.]*
[Now we have implied that these coordinate axes are fixed in space;
but there is nothing to prevent us from supposing that they move.]272
[If they do, they carry with them all their points; and any motion
of these points which we may speak about will be merely motion with
reference to the coordinate system. If we find something outside
our coordinate system that is not moving, the motion of points in
our system with regard to those outside it will be a combination of
their motion with regard to our coordinate axes and that of these axes
with regard to the external points. This will be a great nuisance;
and it represents a state of affairs which we shall try to avoid. We
shall avoid it, if at all, by selecting a coordinate system with
reference to which we, ourselves, are not moving; one which partakes
of any motion which we may have. Or perhaps we shall sometimes wish to
reverse the process, in studying the behavior of some group of bodies,
and seek a set of axes which is at rest with respect to these bodies;
one which partakes of any motion they may have.
THE CHOICE OF A COORDINATE FRAME
All this emphasizes the fact that our coordinate axes are not
picked out for us in advance by nature, and set down in some one
particular spot. We select them for ourselves, and we select them in
the most convenient way. But different observers, or perhaps the same
observer studying different problems, will find it advantageous to
utilize different coordinate systems.]* [The astronomer has found it
possible, and highly convenient, to select a coordinate frame such
that the great majority of the stars have, on the whole, no motion
with respect to it.]283 [Such a system would be most unsuited for
investigations confined to the earth; for these we naturally select
a framework attached to the earth, with its origin O at the earth's
center if our investigation covers the entire globe and at some more
convenient point if it does not, and in either event accompanying the
earth in its rotation and revolution. But such a framework, as well
as the one attached to the fixed stars, would be highly inconvenient
for an investigator of the motions of the planets; he would doubtless
attach his reference frame to the sun.]101
[In this connection a vital question suggests itself. Is the
expression of natural law independent of or dependent upon the choice
of a system of coordinates? And to what extent shall we be able to
reconcile the results of one observer using one reference frame, and
a second observer using a different one? The answer to the second
question is obvious.]* [True, if any series of events is described
using two different sets of axes, the descriptions will be different,
depending upon the time system adopted and the relative motion of the
axes. But if the connection between the reference systems is known,
it is possible by mathematical processes to deduce the quantities
observed in one system if those observed in the other are known.]35
[This process of translating the results of one observer into those of
another is known as a transformation; and the mathematical statement
of the rule governing the transformation is called the equation or the
equations (there are usually several of them) of the transformation.]*
[Transformations of this character constitute a well-developed branch
of mathematics.]35
[When we inquire about the invariance of natural law it is necessary to
be rather sure of just what we mean by this expression. The statement
that a given body is moving with a velocity of 75 miles per hour is of
course not a natural law; it is a mere numerical observation. But aside
from such numerical results, we have a large number of mathematical
relations which give us a more or less general statement of the
relations that exist between velocities, accelerations, masses,
forces, times, lengths, temperatures, pressures, etc., etc. There
are some of these which we would be prepared to state at once as
universally valid--distance travelled equals velocity multiplied by
time, for instance. We do not believe that any conceivable change of
reference systems could bring about a condition in which the product
of velocity and time, as measured from a certain framework, would
fail to equal distance as measured from this same framework. There
are other relations more or less of the same sort which we probably
believe to be in the same invariant category; there are others,
perhaps, of which we might be doubtful; and presumably there are
still others which we should suspect of restricted validity, holding
in certain reference systems only and not in others.
The question of invariance of natural law, then, may turn out to
be one which may be answered in the large by a single statement;
it may equally turn out to be one that has to be answered in the
small, by considering particular laws in connection with particular
transformations between particular reference systems. Or, perhaps,
we may find ourselves justified in taking the stand that an alleged
"law of nature" is truly such a law only in the event that it is
independent of the change from one reference system to another. In
any event, the question may be formulated as follows:
Observer A, using the reference system R, measures certain quantities
$t$, $w$, $x$, $y$, $z$. Observer B, using the reference system S,
measures the same items and gets the values $t'$, $w'$, $x'$, $y'$,
$z'$. The appropriate transformation equations for calculating the
one set of values from the other is found. If a mathematical relation
of any sort is found to exist between the values $t$, $w$, $x$, $y$,
$z$, will the same relation exist between the values $t'$, $w'$,
$x'$, $y'$, $z'$? If it does not, are we justified in still calling
it a law of nature? And if it does not, and we refrain from calling
it such a law, may we expect in every case to find some relation that
will be invariant under the transformation, and that may therefore
be recognized as the natural law connecting $t$, $w$, $x$, $y$ and $z$?
I have found it advisable to discuss this point in such detail because
here more than in any other single place the competing essayists
betray uncertainty of thought and sloppiness of expression. It doesn't
amount to much to talk about the invariance of natural laws and
their persistence as we pass from one coordinate system to another,
unless we are fairly well fortified with respect to just what we mean
by invariance and by natural law. We don't expect the velocity of a
train to be 60 miles per hour alike when we measure it with respect
to a signal tower along the line and with respect to a moving train
on the other track. We don't expect the angular displacement of
Mars to change as rapidly when he is on the other side of the sun
as when he is on our side. But we do, I think, rather expect that
in any phenomenon which we may observe, we shall find a natural law
of some sort which is dependent for its validity neither upon the
units we employ, nor the place from which we make our measurements,
nor anything else external to the phenomenon itself. We shall see,
later, whether this expectation is justified, or whether it will have
to be discarded in the final unravelling of the absolutist from the
relativistic philosophy which, with Einstein, we are to undertake.]*
III
THE RELATIVITY OF UNIFORM MOTION
Classical Ideas on the Subject; the Ether and the Apparent Possibility
of Absolute Motion; the Michelson-Morley Experiment and the Final
Negation of This Possibility
BY VARIOUS CONTRIBUTORS AND THE EDITOR
When we speak of a body as being "in motion," we mean that this
body is changing its position "in space." Now it is clear that the
position of an object can only be determined with reference to other
objects: in order to describe the place of a material thing we must,
for example, state its distances from other things. If there were no
such bodies of reference, the words "position in space" would have
no definite meaning for us.]24 [The number of such external bodies of
reference which it is necessary to cite in order to define completely
the position of a given body in space depends upon the character
of the space dealt with. We have seen that when we visualize the
space of our experience as a surface of any character, two citations
are sufficient; and that when we conceive of it as surrounding us
in three dimensions we require three. It will be realized that the
mathematician is merely meeting this requirement when he sets up his
system of coordinate axes to serve as a reference frame.]*
[What is true of "place" must be true also of "motion," since the
latter is nothing but change of place. In fact, it would be impossible
to ascribe a state of motion or of rest to a body poised all alone
in empty space. Whether a body is to be regarded as resting or as
moving, and if the latter at what speed, depends entirely upon the
objects to which we refer its positions in space.]24 [As Einstein
sits at his desk he appears to us to be at rest; but we know that
he is moving with the rotation of the earth on its axis, with the
earth in its orbit about the sun, and with the solar system in its
path through space--a complex motion of which the parts or the whole
can be detected only by reference to appropriately chosen ones of the
heavenly bodies. No mechanical test has ever been devised which will
detect this motion,]182 [if we reserve for discussion in its proper
place the Foucault pendulum experiment which will reveal the axial
rotation of our globe.]* [No savage, if he were to "stand still,"
could be convinced that he was moving with a very high velocity
or in fact that he was moving at all.]30 [You drop a coin straight
down a ship's side: from the land its path appears parabolic; to a
polar onlooker it whirls circle-wise; to dwellers on Mars it darts
spirally about the sun; to a stellar observer it gyrates through
the sky]263 [in a path of many complications. To you it drops in a
straight line from the deck to the sea.]* [Yet its various tracks
in ship-space, sea-space, earth-space, sun-space, star-space, are
all equally real,]263 [and the one which will be singled out for
attention depends entirely upon the observer, and the objects to
which he refers the motion.]* [The earth moves in the solar system,
which is itself approaching a distant star-cluster. But we cannot say
whether we are moving toward the cluster, or the cluster toward us,]18
[or both, or whether we are conducting a successful stern chase of it,
or it of us,]* [unless we have in mind some third body with reference
to which the motions of earth and star-cluster are measured.]18 [And
if we have this, the measurements made with reference to it are of
significance with regard to it, rather than with regard to the earth
and the star-cluster alone.]*
[We can express all this by saying "All motions are relative; there
is no such thing as absolute motion." This line of argument has in
fact been followed by many natural philosophers. But is its result
in agreement with actual experience? Is it really impossible to
distinguish between rest and motion of a body if we do not take into
consideration its relations to other objects? In fact it can easily
be seen that, at least in many cases, no such distinction is possible.
WHO IS MOVING?
Imagine yourself sitting in a railroad car with veiled windows and
running on a perfectly straight track with unchanging velocity: you
would find it absolutely impossible to ascertain by any mechanical
means whether the car were moving or not. All mechanical instruments
behave exactly the same, whether the car be standing still or in
motion.]24 [If you drop a ball you will see it fall to the floor in
a straight line, just as though you had dropped it while standing on
the station platform. Furthermore, if you drop the ball from the same
height in the two cases, and measure the velocities with which it
strikes the car floor and the station platform, or the times which
it requires for the descent, you will find these identical in the
two cases.]182
[Any changes of speed or of direction (as when the car speeds up
or slows down or rounds a curve) can be detected by observing the
behavior of bodies in the car, without apparent reference to any
outside objects. This becomes particularly obvious with sudden
irregularities of motion, which manifest themselves by shaking
everything in the car. But a uniform motion in a straight line does
not reveal itself by any phenomenon within the vehicle.]24
[Moreover, if we remove the veil from our window to the extent that
we may observe the train on the adjoining track, we shall be able to
make no decision as to whether we or it be moving. This is indeed an
experience which we have all had.]* [Often when seated in a train
about to leave the station, we have thought ourselves under way,
only to perceive as the motion becomes no longer uniform that another
train has been backing into the station on the adjoining track. Again,
as we were hurried on our journey, we have, raising suddenly our eyes,
been puzzled to say whether the passing train were moving with us or
against us or indeed standing still; or more rarely we have had the
impression that both it and we seemed to be at rest, when in truth
both were moving rapidly with the same speed.]82 [Even this phrase "in
truth" is a relative one, for it arises through using the earth as an
absolute reference body. We are indeed naive if we cannot appreciate
that there is no reason for doing this beyond convenience, and that
to an observer detached from the earth it were just as reasonable
to say that the rails are sliding under the train as that the train
is advancing along the rails. One of my own most vivid childhood
recollections is of the terror with which, riding on a train that
passed through a narrow cut, I hid my head in the maternal lap to shut
out the horrid sight of the earth rushing past my window. The absence
of a background in relatively slow retrograde motion was sufficient
to prevent my consciousness from drawing the accustomed conclusion
that after all it was really the train that was moving.]*
MECHANICAL RELATIVITY
[So we can enunciate the following principle: When a body is in
uniform rectilinear motion relatively to a second body, then all
phenomena take place on the first in exactly the same manner as on
the second; the physical laws for the happenings on both bodies are
identical.]24 [And between a system of bodies, nothing but relative
motion may be detected by any mechanical means whatever; any attempt
to discuss absolute motion presupposes a super-observer on some body
external to the system. Even then, the "absolute" motion is nothing
but motion relative to this super-observer. By no mechanical means
is uniform straight-line motion of any other than relative character
to be detected. This is the Principle of Mechanical Relativity.
There is nothing new in this. It was known to Galileo, it was known
to Newton, it has been known ever since. But the curious persistence
of the human mind in habits of thought which confuse relativity with
absolutism brought about a state of affairs where we attempted to
know this and to ignore it at the same time. We shall have to return
to the mathematical mode of reasoning to see how this happened. The
mathematician has a way all his own of putting the statement of
relativity which we have made. He recalls, what we have already seen,
that the observer on the earth who is measuring his "absolute" motion
with respect to the earth has merely attached his reference framework
to the earth; that the passenger in the train who measures all motion
naively with respect to his train is merely carrying his coordinate
axes along with his baggage, instead of leaving them on the solid
ground; that the astronomer who deals with the motion of the earth
about the sun, or with that of the "fixed" stars against one another,
does so simply by the artifice of hitching his frame of reference to
the sun or to one of the fixed stars. So the mathematician points out
that dispute as to which of two bodies is in motion comes right down
to dispute as to which of two sets of coordinate axes is the better
one, the more nearly "natural" or "absolute." He therefore phrases
the mechanical principle of relativity as follows:
Among all coordinate systems that are merely in uniform straight-line
motion to one another, no one occupies any position of unique natural
advantage; all such systems are equivalent for the investigation of
natural laws; all systems lead to the same laws and the same results.
The mathematician has thus removed the statement of relativity
from its intimate association with the external observed phenomena,
and transferred it to the observer and his reference frame. We must
either accept the principle of relativity, or seek a set of coordinate
axes that have been singled out by nature as an absolute reference
frame. These axes must be in some way unique, so that when we refer
phenomena to them, the laws of nature take a form of exceptional
simplicity not attained through reference to ordinary axes. Where
shall we look for such a preferred coordinate system?]*
THE SEARCH FOR THE ABSOLUTE
[Older theory clung to the belief that there was such a thing as
absolute motion in space.]197 [As the body of scientific law developed
from the sixteenth century onward, the not unnatural hypothesis crept
in, that these laws (that is to say, their mathematical formulations
rather than their verbal statements) would reveal themselves in
especially simple forms, were it possible for experimenters to make
their observations from some absolute standpoint; from an absolutely
fixed position in space rather than from the moving earth.]264
[Somewhere a set of coordinate axes incapable of motion was to be
found,]197 [a fixed set of axes for measuring absolute motion; and
for two hundred years the world of science strove to find it,]147 [in
spite of what should have been assurance that it did not exist. But
the search failed, and gradually the universal applicability of the
principle of relativity, so far as it concerned mechanical phenomena,
grew into general acceptance.]* [And after the development, by the
great mathematicians of the eighteenth century, of Newton's laws of
motion into their most complete mathematical form, it was seen that so
far as these laws are concerned the absolutist hypothesis mentioned is
quite unsupported. No complication is introduced into Newton's laws
if the observer has to make his measurements in a frame of reference
moving uniformly through space; and for measurements in a frame like
the earth, which moves with changing speed and direction about the
sun and rotates on its axis at the same time, the complication is
not of so decisive a nature as to give us any clue to the earth's
absolute motion in space.
But mechanics, albeit the oldest, is yet only one of the physical
sciences. The great advance made in the mathematical formulation
of optical and electromagnetic theory during the nineteenth century
revived the hope of discovering absolute motion in space by means of
the laws derived from this theory.]264 [Newton had supposed light
to be a material emanation, and if it were so, its passage across
"empty space" from sun and stars to the earth raised no problem. But
against Newton's theory Huyghens, the Dutch astronomer, advanced the
idea that light was a wave motion of some sort. During the Newtonian
period and for many years after, the corpuscular theory prevailed;
but eventually the tables were turned.]* [Men made rays of light
interfere, producing darkness (see page 61). From this, and from
other phenomena like polarization, they had deduced that light was a
form of wave motion similar to water ripples; for these interfere,
producing level surfaces, or reinforce each other, producing waves
of abnormal height. But if light were to be regarded as a form of
wave motion--and the phenomena could apparently be explained on no
other basis--then there must be some medium capable of undergoing
this form of motion.]135 [Transmission of waves across empty space
without the aid of an intermediary material medium would be "action
at a distance," an idea repugnant to us. Trammeled by our tactual,
wire-pulling conceptions of a material universe, we could not accustom
ourselves to the idea of something--even so immaterial a something
as a wave--being transmitted by nothing. We needed a word--ether--to
carry light if not to shed it; just as we need a word--inertia--to
carry a projectile in its flight.]231 [It was necessary to invest this
medium with properties to account for the observed facts. On the whole
it was regarded as the perfect fluid.]235 [The ether was imagined as
an all-pervading, imponderable substance filling the vast emptiness
through which light reaches us, and as well the intermolecular spaces
of all matter. Nothing more was known definitely, yet this much served
as a good working hypothesis on the basis of which Maxwell was enabled
to predict the possibility of radio communication. By its fruits the
ether hypothesis justified itself; but does the ether exist?]231
THE ETHER AND ABSOLUTE MOTION
[If it does exist, it seems quite necessary, on mere philosophical
grounds, that it shall be eligible to serve as the long-sought
reference frame for absolute motion. Surely it does not make sense to
speak of a homogeneous medium filling all space, sufficiently material
to serve as a means of communication between remote worlds, and in
the next breath to deny that motion with respect to this medium is a
concept of significance.]* [Such a system of reference as was offered
by the ether, coextensive with the entire known region of the universe,
must necessarily serve for all motions within our perceptions.]186
[The conclusion seems inescapable that motion with respect to the
ether ought to be of a sufficiently unique character to stand out
above all other motion. In particular, we ought to be able to use the
ether to define, somewhere, a system of axes fixed with respect to
the ether, the use of which would lead to natural laws of a uniquely
simply description.
Maxwell's work added fuel to this hope.]* [During the last century,
after the units of electricity had been defined, one set for static
electrical calculations and one for electromagnetic calculations, it
was found that the ratio of the metric units of capacity for the two
systems was numerically equal to what had already been found as the
velocity with which light is transmitted through the hypothetical
ether. One definition refers to electricity at rest, the other
to electricity in motion. Maxwell, with little more working basis
than this, undertook to prove that electrical and optical phenomena
were merely two aspects of a common cause,]235 [to which the general
designation of "electromagnetic waves" was applied. Maxwell treated
this topic in great fullness and with complete success. In particular,
he derived certain equations giving the relations between the various
electrical quantities involved in a given phenomenon. But it was
found, extraordinarily enough, that these relations were of such
character that, when we subject the quantities involved to a change
of coordinate axes, the transformed quantities did not preserve these
relations if the new axes happened to be in motion with respect to
the original ones. This, of course, was taken to indicate that motion
really is absolute when we come to deal with electromagnetic phenomena,
and that the ether which carries the electromagnetic waves really may
be looked to to display the properties of an absolute reference frame.
Reference to the phenomenon of aberration, which Dr. Pickering has
discussed adequately in his essay and which I need therefore mention
here only by name, indicated that the ether was not dragged along
by material bodies over and through which it might pass. It seemed
that it must filter through such bodies, presumably via the molecular
interstices, without appreciable opposition. Were this not the case,
we should be in some doubt as to the possibility of observing the
velocity through the ether of material bodies; if the ether adjacent
to such bodies is not dragged along or thrown into eddies, but "stands
still" while the bodies pass, there seems no imaginable reason for
anything other than the complete success of such observations. And
of course these are of the utmost importance, the moment we assign
to the ether the rôle of absolute reference frame.
THE EARTH AND THE ETHER
One body in motion with respect to the ether is our earth itself. We
do not know in advance in what direction to expect this motion or what
magnitude to anticipate that it will have. But one thing is clear.]*
[In its motion around the sun, the earth has, at opposite points on its
orbit, a difference in velocity with respect to the surrounding medium
which is double its orbital velocity with respect to the sun. This
difference comes to 37 miles per second. The earth should therefore,
at some time in the year, show a velocity equal to or greater than
18 1/2 miles per second, with reference to the universal medium. The
famous Michelson-Morley experiment of 1887 was carried out with the
expectation of observing this velocity.]267
[The ether, of course, and hence velocities through it, cannot be
observed directly. But it acts as the medium for the transmission of
light.]* [If the velocity of light through the ether is $C$ and that
of the earth through the ether is $v$, then the velocity of light
past the earth, so the argument runs, must vary from $C-v$ to $C+v$,
according as the light is moving exactly in the same direction as the
earth, or in the opposite direction,]182 [or diagonally across the
earth's path so as to get the influence only of a part of the earth's
motion. This of course assumes that $C$ has always the same value;
an assumption that impresses one as inherently probable, and one that
is at the same time in accord with ordinary astronomical observation.
It is not possible to measure directly the velocity of light (186,330
miles per second, more or less) with sufficient accuracy to give any
meaning to the variation in this velocity which might be effected by
adding or subtracting that of the earth in its orbit (a mere 18 1/2
miles per second). It is, however, possible to play a trick on the
light by sending it back and forth over several paths, and comparing
(not measuring absolutely, but merely comparing) with great minuteness
the times consumed in these several round trips.
A JOURNEY UPSTREAM AND BACK
The number of letters the Scientific American has received questioning
the Michelson-Morley experiment indicates that many people are not
acquainted with the fundamental principle on which it is based. So
let us look at a simple analogous case. Suppose a swimmer or a rower
make a return trip upstream and down, contending with the current
as he goes up and getting its benefit when he comes down. Obviously,
says snap judgment, since the two legs of the journey are equal, he
derives exactly as much benefit from the current when he goes with it
as he suffers handicap from it when he goes against it; so the round
trip must take exactly the same time as a journey of the same length
in still water, the argument applying equally in the case where the
"swimmer" is a wave of light in the ether stream.
But let us look now at a numerical case. A man can row in still water
at four miles per hour. He rows twelve miles upstream and back, in a
current of two miles per hour. At a net speed of two miles per hour
he arrives at his turning point in six hours. At a net speed of six
miles per hour he makes the down-stream leg in two hours. The elapsed
time for the journey is eight hours; in still water he would row the
twenty-four miles in six hours.
If we were to attempt an explanation of this result in words we should
say that by virtue of the very fact that it does delay him, the adverse
current prolongs the time during which it operates; while by virtue of
the very fact that it accelerates his progress, the favoring current
shortens its venue. The careless observer realizes that distances are
equal between the two legs of the journey, and unconsciously assumes
that times are equal.
If the journey be made directly with and directly against the stream
of water or ether or what not, retardation is effected to its fullest
extent. If the course be a diagonal one, retardation is felt to an
extent measurable as a component, and depending for its exact value
upon the exact angle of the path. Felt, however, it must always be.
Here is where we begin to get a grip on the problem of the earth
and the ether. In any problem involving the return-trip principle,
there will enter two velocities--that of the swimmer and that of the
medium; and the time of retardation. If we know any two of these items
we can calculate the third. When the swimmer is a ray of light and the
velocity of the medium is that of the ether as it flows past the earth,
we know the first of these two; we hope to observe the retardation
so that we may calculate the second velocity. The apparatus for the
experiment is ingenious and demands description.
THE MICHELSON-MORLEY EXPERIMENT
The machine is of structural steel, weighing 1,900 pounds. It has two
arms which form a Greek cross. Each arm is 14 feet in length. The whole
apparatus is floated in a trough containing 800 pounds of mercury.
Four mirrors are arranged on the end of each arm, sixteen in all,
with a seventeenth mirror, M, set at one of the inside corners of the
cross, as diagrammed. A source of light (in this case a calcium flame)
is provided, and its rays directed by a lens toward the mirror M. Part
of the light is allowed to pass straight through M to the opposite
arm of the cross, where it strikes mirror 1. It is reflected back
across the arm to mirror 2, thence to 3, and so on until it reaches
mirror 8. Thence it is reflected back to mirror 7, to 6, and so on,
retracing its former path, and finally is caught by the reverse side
of the mirror M and is sent to an observer at O. In retracing its
path the light sets up an interference phenomenon (see below) and the
interference bands are visible to the observer, who is provided with
a telescope to magnify the results.
A second part of the original light-beam is reflected off at right
angles by the mirror M, and is passed to and fro on the adjacent arms
of the machine, in exactly the same manner and over a similar path,
by means of the mirrors I, II, III, ... VIII. This light finally
reaches the observer at the telescope, setting up a second set of
interference bands, parallel to the first.
A word now about this business of light interference. Light is a wave
motion. The length of a wave is but a few millionths of an inch,
and the amplitude is correspondingly minute; but none the less,
these waves behave in a thoroughly wave-like manner. In particular,
if the crests of two waves are superposed, there is a double effect;
while if a crest of one wave falls with a trough of another, there
is a killing-off or "interference".
Under ordinary circumstances interference of light waves does not
occur. This is simply because under ordinary circumstances light waves
are not piled up on one another. But sometimes this piling up occurs;
and then, just so sure as the piled-up waves are in the same phase
they reinforce one another, while if they are in opposite phase they
interfere. And the conditions which we have outlined above, with the
telescope and the mirrors and the ray of light retracing the path
over which it went out, are conditions under which interference does
occur. If the returning wave is in exact phase with the outgoing one,
the effect is that of uniform double illumination; if it is in exactly
opposite phase the effect is that of complete extinguishing of the
light, the reversed wave exactly cancelling out the original one. If
the two rays are partly in phase, there is partial reinforcement or
partial cancelling out, according to whether they are nearly in phase
or nearly out of phase. Finally, if the mirrors are not set absolutely
parallel--as must in practice be the case when we attempt to measure
their parallelism in terms of the wave-length of light--adjacent
parts of the light ray will vary in the extent to which they are out
of phase, since they will have travelled a fraction of a wave-length
further to get to and from this, that or the other mirror. There
will then appear in the telescope alternate bands of illumination
and darkness, whose width and spacing depend upon all the factors
entering into the problem.