Relativity - Part 21-23 Einstein

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This is LibriVox recording. All LibriVoxrecordings are in the public domain. For
more information or to volunteer, pleasevisit LibriVox dot org. Recorded by Annie
Coleman www dot Annie Cooleman dot com. Relativity the Special and General Theory by

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Albert Einstein, Continuing Part two,sections twenty one through twenty three. Section
twenty one in what respects are thefoundations of classical mechanics and of the special
theory of relativity unsatisfactory? We havealready stated several times that classical mechanics starts

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out from the following law. Materialparticles sufficiently far removed from other material particles
continue to move uniformly in a straightline, or continue in a state of
rest. We have also repeatedly emphasizedthat this fundamental law can only be valid
for bodies of reference K, whichpossess certain unique states of motion, and

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which are in uniform translational motion relativeto each other. Relative to other reference
bodies K, the law is notvalid both in classical mechanics and in the
special theory of relativity. We thereforedifferentiate between reference bodies K relative to which

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the recognized laws of nature can besaid to hold and reference bodies k relative
to which these laws do not hold. But no person whose mode of thought
is logical can rest satisfied with thiscondition of things. He asks, how
does it come that certain reference bodiesor their states of motion are given priority

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over other reference bodies or their statesof motion? What is the reason for
this preference? In order to showclearly what I mean by this question,
I shall make use of a comparison. I am standing in front of a
gas range. Standing alongside of eachother. On the range are two pans

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so much alike that one may bemistaken for the other. Both are half
full of water. I notice thatsteam is being emitted continuously from one pan,
but not from the other. Iam surprised at this, even if
I have never seen either a gasrange or a pan before. But if
I now notice a luminous something ofbluish color under the first pan, but

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not under the other, I ceaseto be astonished, even if I have
never before seen a gas flame.For I can only say that this bluish
something will cause the emission of thesteam, or at least possibly it may
do so. If, however,I notice the bluish something in neither case,

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and if I observe that the onecontinuously emits steam whilst the other does
not, then I shall remain astonishedand dissatisfied until I have discovered some circumstance
to which I can attribute the differentbehavior of the two pans. Analogously,
I seek in vain for a realsomething in classical mechanics or in the special

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theory of relativity, to which Ican attribute the different behavior of bodies considered
with respect to the reference systems Kand K prime begin footnote. The objection
is of importance more especially when thestate of motion of the reference body is

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of such a nature that it doesnot require any external agency for its maintenance,
for example, in the case whenthe reference body is rotating uniformly.
End footnote. Newton saw this objectionand attempted to invalidate it, but without
success. But E. Mock recognizedit most clearly of all, and because

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of this objection he claimed that mechanicsmust be placed on a new basis.
It can only be got rid ofby means of a physics which is conformable
to the general principle of relativity.Since the equations of such a theory hold
for every body of reference, whatevermay be its state of motion. Section

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twenty two a few inferences from thegeneral principle of relativity. The considerations of
section twenty show that the general principleof relativity puts us in a position to
derive properties of the gravitational field ina purely theoretical manner. Let us suppose,

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for instance, that we know thespace time course for any natural process
whatsoever as regards the manner in whichit takes place in the Galilean domain relative
to a Galilean body of reference K, by means of purely theoretical operations i
e. Simply by calculation. Weare then able to find how this known

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natural process appears as seen from areference body K prime, which is accelerated
relatively to K. But since agravitational field exists with respect to this new
body of reference k prime, ourconsideration also teaches us how the gravitational field
influences the process studied. For example, we learn that a body which is

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in a state of uniform rectilinear motionwith respect to K, in accordance with
the law of Galilee, is executingan accelerated and in general curveline in the
year motion with respect to the acceleratedreference body k prime chest. This acceleration

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or curvature corresponds to the influence onthe moving body of the gravitational field prevailing
relatively to k prime. It isknown that a gravitational field influences the movement
of bodies in this way, sothat our consideration supplies us with nothing essentially
new. However, we obtain anew result of fundamental importance when we carry

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out the analogous consideration for a rayof light with respect to the Galilean reference
body K. Such a ray oflight is transmitted rectilinearly with the velocity c.
It can easily be shown that thepath of the same ray of light
is no longer a straight line whenwe consider it with reference to the accelerated

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chest reference body k prime. Fromthis we conclude that, in general,
rays of light are propagated curvilinearly ingravitational fields. In two respects, this
result is of great importance. Inthe first place, it can be compared
with the reality. Although a detailedexamination of the question shows that the curvature

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of light rays required by the generaltheory of relativity is only exceedingly small for
the gravitational fields at our disposal.In practice, its estimated magnitude for light
rays passing the Sun at grazing incidentsis nevertheless one point seven seconds of arc.
This ought to manifest itself in thefollowing way. As seen from the

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Earth, certain fixed stars appear tobe in the neighbourhood of the Sun,
and are thus capable of observation duringa total eclipse of the Sun. At
such times, these stars ought toappear to be displaced outwards from the Sun
by an amount indicated above, ascompared with their apparent position in the sky

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when the Sun is situated at anotherpart of the heavens. The examination of
the correctness or otherwise of this deductionis a problem of the greatest importance,
the early solution of which is tobe expected of astronomers. Begin footnote.
By means of the star photographs oftwo expeditions equipped by a joint committee of

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the Royal and Royal Astronomical Societies.The existence of the deflection of light demanded
by theory was first confirmed during thesolar eclipse of twenty ninth May nineteen nineteen.
End footnote. In the second place, our result shows that, according
to the general theory of relativity.The law of the constancy of the velocity

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of light in vacuo, which constitutesone of the two fundamental assumptions in the
special theory of relativity, and towhich we have all already frequently referred,
cannot claim any unlimited validity. Acurvature of rays of light can only take
place when the velocity of propagation oflight varies with position. Now, we

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might think that as a consequence ofthis, the special theory of relativity,
and with it the whole theory ofrelativity, would be laid in the dust.
But in reality this is not thecase. We can only conclude that
the special theory of relativity cannot claiman unlimited domain of validity. Its results

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hold only so long as we areable to disregard the influences of gravitational fields
on the phenomena, for example,of light. Since it has often been
contended by opponents of the theory ofrelativity that the special theory of relativity is
overthrown by the general theory of relativity, it is perhaps advisable to make the

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facts of the case clearer by meansof an appropriate comparison. Before the development
of electrodynamics, the laws of electrostaticswere looked upon as the laws of electricity.
At the present time. We knowthat electric fields can be derived correctly
from electrostatic considerations only for the casewhich is never strictly realized, in which

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the electrical masses are quite at restrelatively to each other and to the coordinate
system. Should we be justified insaying that for this reason electrostatics is overthrown
by the field equations of Maxwell inelectrodynamics. Not in the least electrostatics is
contained in electrodynamics as a limiting case. The laws of the latter lead directly

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to those of the former. Forthe case in which the fields are invariable
with regard to time, No fairerdestiny could be allotted to any physical theory
than that it should of itself pointout the way to the introduction of a
more comprehensive theory in which it liveson as a limiting case. In the
example of the transmission of light justdealt with, we have seen that the

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general theory of relativity enables us toderive theoretically the influence of a gravitational field
on the course of natural processes.The laws of which are already known when
a gravitational field is absent. Butthe most attractive problem to the solution of
which the general theory of relativity suppliesthe key, concerns the investigation of the

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laws satisfied by the gravitational field itself. Let us consider this for a moment.
We are acquainted with spacetime domains whichbehave approximately in a Galilean fashion under
suitable choice of reference body i e. Domains in which gravitational fields are absent.

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If we now refer such a domainto a reference body k prime possessing
any kind of motion, then relativeto k prime, there exists a gravitational
field which is variable with respect tospace and time. Begin footnote. This
follows from a generalization of the discussionin section twenty end footnote. The character

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of this field will, of coursedepend on the motion chosen for k prime.
According to the general theory of relativity, the general law of the gravitational
field must be satisfied for all gravitationalfields obtainable in this way. Even though
by no means all gravitational fields canbe produced in this way, Yet we

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may entertain the hope that the generallaw of gravitation will be derivable from such
gravitational fields of a special kind.This hope has been realized in the most
beautiful manner. But between the clearvision of this goal and its actual realization
it was necessary to surmount a seriousdifficulty. And as this lies deep at

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the root of things, I darenot withhold it from the reader. We
require to extend our ideas of thespace time continuum still farther section twenty three
behavior of clocks and measuring rods ona rotating body of reference. Hitherto,
I have purposely refrained from speaking aboutthe physical interpretation of space and time data

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in the case of this general theoryof relativity. As a consequence, I
am guilty of a certain slovenliness oftreatment, which, as we know from
the special theory of relativity, isfar from being unimportant and pardonable. It
is now high time that we remedythis defect. But I would mention at
the outset that this matter lays nosmall claims on the patients and on the

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power of abstraction of the reader.We start off again from quite special cases
which we have frequently used before.Let us consider a space time domain in
which no gravitational field exists relative toa reference body K, whose state of
motion has been suitably chosen. Kis then a Galilean reference body as regards

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the domain considered, and the resultsof the special theory of relativity hold relative
to K. Let Us suppose thesame domain referred to a second body of
reference K prime, which is rotatinguniformly with respect to K. In order
to fix our ideas, we shallimagine K prime to be in the form

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of a plane circular disc which rotatesuniformly in its own plane about its center.
An observer who is sitting eccentrically onthe disc k prime is sensible of
a force which acts outward in aradial direction, and which would be interpreted
as an effect of inertia centrifugal forceby an observer who was at rest with

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respect to the original reference body K. But the observer on the disc may
regard his disc as a res whichis at rest on the basis of the
general principle of relativity. He isjustified in doing this. The force acting
on himself and in fact on allother bodies which are at rest relative to

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the disc he regards as the effectof a gravitational field. Nevertheless, the
space distribution of this gravitational field isof a kind that would not be possible
on Newton's theory of gravitation. Beginfootnote. The field disappears at the center
of the disc and increases proportionally tothe distance from the center as we proceed

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outwards and footnote. But since theobserver believes in the general theory of relativity,
this does not disturb him. Heis quite in the right when he
believes that a general law of gravitationcan be formulated, a law which not
only explains the motion of the starscorrectly, but also the field of force

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experience himself. The observer performs experimentson his circular disc with clocks and measuring
rods. In doing so, itis his intention to arrive at exact definitions
for the significance of time and spacedata with reference to the circular disc k
prime, these definitions being based onhis observations, what will be his experience

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in the enterprise? To start with, he places one of two identically constructed
clocks at the center of the circulardisc and the other on the edge of
the disc, so that they areat rest relative to it. We now
ask ourselves whether both clocks go atthe same rate from the standpoint of the

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non rotating Galilean reference body K.As judged from this body, the clock
at the center of the disc hasno velocity, whereas the clock at the
edge of the disc is in motionrelative to K in consequence of the rotation.
According to a result obtained in sectiontwelve, it follows that the latter

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clock goes at a rate permanently slowerthan that of the clock at the center
of the circular disc i e.As observed from K. It is obvious
that the same effect would be notedby an observer, whom we will imagine
sitting alongside his clock at the centerof the circular disc. Thus, on

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our circular disc, or, tomake the case more general, in every
gravitational field, a clock will gomore quickly or less quickly according to the
position in which the clock is situatedat rest. For this reason, it
is not possible to obtain a reasonabledefinition of time with the aid of clocks

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which are arranged at rest with respectto the body of reference. A similar
difficulty presents itself when we attempt toapply our earlier definition of simultaneity in such
a case. But I do notwish to go any farther into this question.
Moreover, at this stage, thedefinition of the space coordinates also presents

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insurmountable difficulties. If the observer applieshis standard measuring rod a rod which is
short as compared with the radius ofthe disc tangentially to the edge of the
disc, then, as judge fromthe Galilean system, the length of this
rod will be less than I,since, according to section twelve, moving

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bodies suffer a shortening in the directionof the motion. On the other hand,
the measuring rod will not experience ashortening in length, as judge from
K, if it is applied tothe disc in the direction of the radius.
If then the observer first measures thecircumference of the disc with his measuring
rod, and then the diameter ofthe disk on dividing the one by the

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other, he will not obtain asquotient the familiar number Pi equals three point
one four, et cetera, buta larger number begin footnote. Throughout this
consideration we have to use the Galileannon rotating system K as reference body.
Since we may only assume the validityof the results of the special theory of

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relativity relative to k. Relative tok prime a gravitational field prevails end footnote,
but a larger number, whereas,of course, for a disk which
is at rest with respect to k, this operation would yield pi exactly.
This proves that the propositions of Euclideangeometry cannot hold exactly on the rotating disc,

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nor in general in a gravitational field, at least if we attribute the
length i to the rod in allpositions in every orientation. Hence the idea
of a straight line also loses itsmeaning. We are therefore not in a
position to define exactly the coordinates x, y z relative to the disc by

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means of the method used in discussingthe special theory, And as long as
the coordinates and times of events havenot been defined, we cannot assign an
exact meaning to the natural laws inwhich these occur. Thus, all our
previous conclusions based on general relativity wouldappear to be called in question. In

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reality, we must make a subtledetour in order to be able to apply
the postulate of general relativity exactly.I shall prepare the reader for this in
the following paragraphs end of sections twentyone to twenty three. Read by Annie
Coleman in Saint Louis, Missouri,on August thirteen, two thousand six,