Relativity - Part 16-17 Einstein

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Correction for this chapter in mathematical formulaeinstead of I here one. This is
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information or to volunteer, please visitLibriVox dot org. Recording by Kelly Buscher.

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Relativity, The Special and General Theoryby Albert Einstein, continuing part one,
section sixteen and seventeen Section sixteen Experienceand the Special Theory of Relativity.
To what extent is the special theoryof relativity supported by experience? This question

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is not easily answered, for thereason already mentioned in connection with the fundamental
experiment of the Zeux. The specialtheory of relativity has crystallized out from the
Maxwell Lorentz theory of electromagnetic phenomena.Thus, all facts of experience which support
the electromagnetic theory also support the theoryof relativity, as being of particular importance.

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I mention here the fact that thetheory of relativity enables us to predict
the effects produced on the light reachingus from the fixed stars. These results
are obtained in an exceedingly simple manner, and the effects indicated, which are
due to the relative motion of theEarth with reference to those fixed stars are
found to be in accord with experience. We refer to the yearly movement of

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the apparent position of the fixed starsresulting from the motion of the Earth around
the Sun aberration, and to theinfluence of the radial components of the relative
motions of the fixed stars with respectto the Earth on the color of the
light reaching us from them. Thelatter effect manifests itself in a slight displacement
of the spectral lines of the lighttransmitted to us from a fixed star as

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compared with the position of them thesame spectral lines when they are produced by
a terrestrial source of light Doppler principle. The experimental arguments in favor of the
Maxwell Lorentz theory, which are atthe same time arguments in favor of the
theory of relativity, are too numerousto be set forth here. In reality,
they limit the theoretical possibilities to suchan extent that no other theory than

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that of Maxwell and Lorentz has beenable to hold its own when tested by
experience. But there are two classesof experimental facts hitherto obtained which can be
represented in the Maxwell Lurentz theory onlyby the introduction of an auxiliary hypothesis,
which in itself i e. Withoutmaking use of the theory of relativity,

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appears extraneous. It is known thatcathode rays, in the so called beta
rays emitted by radioactive substances, consistsof negatively electrified particles electrons of very small
inertia and large velocity. By examiningthe deflection of these rays under the influence
of electric and magnetic fields, wecan study the law of motion of these

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particles very exactly. In the theoreticaltreatment of these electrons, we are faced
with the difficulty that electrodynamic theory ofitself is unable to give an account of
their nature. For since electrical massesof one sign repel each other, the
negative electrical masses constituting the electron wouldnecessarily be scattered under the influence of their

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mutual repulsions, unless there are forcesof another kind operating between them, the
nature of which has hitherto remained obscureto us. Footnote. The general theory
of relativity renders it likely that electricalmasses of an electron are held together by
gravitational forces en footnote. If wenow assume that the relative distances between the

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electrical masses constituting the electron remain unchangedduring the motion of the electron rigid connection.
In the sense of classical mechanics,we arrive at a law of motion
of the electron which does not agreewith experience guided by purely formal points of
view. H. A. Lorenzwas the first to introduce the hypothesis that

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the particles constituting the electron experience acontraction in the direction of motion and consequence
of that motion, the amount ofthis contraction being proportional to the expression the
square root of the difference I minusthe fraction V squared over C squared.
This hypothesis, which is not justifiableby any electrodynamical facts, supplies us with

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that particular law of motion which hasbeen confirmed with great precision in recent years.
The theory of relativity leads to thesame law of motion without requiring any
special hypothesis whatsoever as to the structureand the behavior of the electron. We
arrived at a similar conclusion in sectionthirteen in connection with the experiment of the
zo, result of which is foretoldby the theory of relativity, without the

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necessity of drawing on hypotheses as tothe physical nature of the lud liquid.
The second class effects to which wehave alluded has referenced the question whether or
not the motion of the Earth inspace can be made perceptible in terrestrial experiments.
We have already remarked in section fivethat all attempts of this nature led
to a negative result. Before thetheory of relativity was put forward, it

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was difficult to become reconciled to thisnegative result. For reasons now to be
discussed. The inherited prejudices about timeand space did not allow any doubts to
arise as to the prime importance ofthe Galilei transformation for changing over from one
body of reference to another. Now, assuming that maxweller Run's equations hold for

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a reference body K, we thenfind that they do not hold for a
reference body K prime moving uniformly withrespect to K. If we assume that
the relations of the Galilean transformation existbetween the coordinates of K and K prime,
it thus appears that of all Galileancoordinate systems, one K, corresponding

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to our proteicular state of motion,is physically unique. This result was interpreted
physically by regarding K as at restwith respectable hypothetical ether of space. On
the other hand, all coordinate systemsk prime moving relatively to k or to
be regarded as in motion with respectto the ether. To this motion of
k prime against the ether, etherdrift relative to k prime were assigned the

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more complicated laws which were supposed tohold relative to kay prime. Strictly speaking,
such an ether drift ought also tobe assumed relative to the Earth,
and for a long time the effortsof physicists were devoted to attempts to detect
the existence of an ether drift atthe Earth's surface. In one of the
most notable of these attempts, Michaelsondevised a method which appears as though it

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must be decisive. Imagine two mirrorsso arranged on a rigid body that the
reflecting surfaces face each other. Aray of light requires a perfectly definite time
tea to pass from one mirror tothe other and back again, if the
whole see be at rest with respectto the ether. It is found by
calculation, however, that a slightdifferent time t prime is required for this

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process. If the body, togetherwith the mirrors, be moving relatively to
the ether and yet another point.It is shown by calculation that for a
given velocity v with reference to theether, this time t prime is different
when the body is moving perpendicularly tothe planes of the mirrors, from that
resulting when the motion is parallel tothese planes. Although the estimated difference between

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these two times is exceedingly small,Michaelson and Morley performed in an experiment involving
interference in which this result should havebeen clearly detectable, but the experiment gave
a negative result, a fact veryperplexing to physicists. Lorentz and Fitzgerald rescued
this theory from this difficulty by assumingthat the motion of the body relative to

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the ether produces a contraction of thebody in the direction of motion, the
amount of contract being just sufficient tocompensate for the difference in time mentioned above.
Comparison with the discussion in section twelveshows us that from the standpoint also
the theory of relativity, this solutionof the difficulty was the right one,
but on the basis of the theoryof relativity, the method of interpretation is

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incomparably more satisfactory. According to thistheory, there is no such thing as
especially favored unique coordinate system to occasionthe introduction of the ether idea, and
hence there can be no either driftnor any experiment with which to demonstrate it.
Here, the contraction of moving bodiesfollows from the two fundamental principles of

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the theory, without the introduction ofparticular hypotheses. And as the prime factor
involved in this contraction, we findnot the motion in itself, to which
we cannot attach any meaning, butthe motion with respect to the body of
reference chosen in the particular case inpoint. Thus, for a coordinate system
moving with the Earth, the mirrorsystem of Michaelson and Morley is not shortened,

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and it is shortened for a coordinatesystem which is at rest relatively to
the Sun. End of Section sixteen, Section seventeen. Minkowski's four dimensional space.
The non mathematician is seized by mysteriousshuddering when he hears of four dimensional

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things, by feeling not unlike thatawakened by thoughts of the occult. And
yet there is no more commonplace statementthan that the world in which we live
is a four dimensional space time continuumspace is a three dimensional continuum. By
this we mean that it is possibleto describe the position of a point at
rest by means of three numbers,where coordinates x y z, and that

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there is an indefinite number of pointsin the neighborhood of this one, the
position of which can be described bycoordinates such as x of one, y
one z some one, which maybe as near as we choose the respective
values of the coordinate x y zof the first point. In virtue of
the latter property, we speak ofa continuum, and owing to the fact
that there are three coordinates, wespeak of it as being three dimensional.

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Similarly, the world of physical phenomena, which was briefly called world by Minkowski,
is naturally four dimensional in the spacetime sense, for it is composed
of individual events, each of whichis described by four numbers, namely three
space coordinates x, y z anda time coordinate the time value T.
The world is in this sense alsoa continuum, for to every event there

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are as many neighboring events realize orat least thinkable as we care to choose
the coordinates x of one and whysub one zs and onae tis of one,
of which differ by an indefinitely smallamount from those of the events x,
y z T. Originally considered thatwe have not been accustomed to regard
the world in this sense as afour dimensional continuum is due to the fact

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that in physics, before the adventof the theory of relativity, time played
a different and more independent role ascompared with the space coordinates. It is
for this reason that we have beenin the habit of treating time as an
independent continuum. As a matter offact, according to classical mechanics, time
is absolute, i e. Itis independent of the position and the condition

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of the motion of the system ofcoordinates. We see this expressed in the
last equation of the Galilean transformation tprime equals t. The four dimensional mode
of consideration of the world is naturalon the theory of relativity, since according
to this theory, time is robbedof its independence. This is shown by

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the fourth equation of the Lorentz transformationT prime equals the fraction, in which
the enumerator is t minus the fractionvx over C squared and the denominator is
the square root of the difference iusthe fraction v squared over C squared.
Moreover, according to this equation,the time difference deals to t prime of

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two events with respect to k primedoes not, in general vanish, even
when the time difference of delta Tof the same events with reference to k
vanishes. Pure space distance of twoevents with respect to k results in time
distance of the same events with respectto k prime. But the discovery of
Minkowski, which was of importance inthe formal development of the theory of relativity,

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does not lie here. It isto be found rather in the fact
of his recognition that the four dimensionalspace time continuum of the theory of relativity,
in its most essential formal properties,shows a pronounced relationship to the three
dimensional continuum of Euclidean geometrical space.Begin footnote. Compare the somewhat more detailed

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discussion in Appendix two end footnote.In order to give due prominence to this
relationship, however, we must replacethe usual time coordinate te why in imaginary
magnitude square root of negative eye ct proportional to it. Under these conditions,
the natural laws satisfying the demands ofthe special theory of relativity assume mathematical

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forms in which the time coordinate playsexactly the same role as the three space
coordinates. Formerly, these four coordinatescorrespond exactly to the three space coordinates in
Euclidean geometry. It must be cleareven to the non mathematician that as a
consequence of this purely formal addition toour knowledge, the theory propores gained clearless.

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In no mean measure, these inadequateremarks can give the reader only a
vague notion of the important idea contributedby Minkowski. Without it, the general
theory of relativity, of which thefundamental ideas are developed in the following pages,
would perhaps have got no farther thanits long clothes. Minkowski's work is
doubtless difficult of access to anyone inexperiencedin mathematics. But since it is not

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necessary to have a very exact graspof this work in order to understand the
fundamental life ideas of either the specialor the general theory of relativity, I
shall at present leave it here,and shall revert to it only towards the
end of Part two, end ofsection seventeen, end of Part one,