DISCONNECTED SUGGESTIONS
Conditionality and Unconditionality of Physical Laws.--Conception of
Temperature.--Grain of Sand and Universe.--Are Laws
unalterable?--Paradoxes of Science.--Rejuvenation by Motion.--Gain of a
Second.--Deformed Worlds.--Atomic Model.--Researches of Rutherford and
Niels Bohr.--Microcosmos and Macrocosmos.--Brief Statement of the Principle
of Relativity.--Science with reduced Sense-Organs.--Eternal
Repetition.--Higher Types of Culture.
IN all branches of reasoning, no word and no conception has played a
more important part than that of _law_. Physical laws denote the barrier
that separates strictly chance and arbitrariness from necessity, and it
seems to us that the region of the latter must ever extend so that
finally nothing will be left of the former, which will have become
amalgamated with necessity. We shall be constrained to believe more and
more in a supreme law that will be a complete expression of all the
partial laws which science presents to us as more or less permanent
results of individual researches.
Our conversation was centred about these individual laws, such as those
that are taught in the theory of gases, optics, etc., and that are
associated with the names, Boyle, Gay-Lussac, Dalton, Marriotte,
Huyghens, Fresnel, Kirchhoff, Boltzmann, and others. In connexion with
these I asked Einstein whether he regarded the laws as things
unconditioned in themselves, and capable of proof under every set of
circumstances; and whether absolutely valid laws existed or could exist.
Einstein's answer was essentially in the negative. "A law cannot be
final, if only for the reason that the conceptions, which we use to
formulate it, show themselves to be imperfect or insufficient as science
progresses. Let us consider, for example, an elementary law such as
Newton's Law of Force. From our more recent point of view we find the
conception of direct action at a distance to be inexact in Nature. For
it has been shown that action at a distance is not an ultimate factor,
but must be resolved into a multiplicity of actions between immediately
neighbouring points (The Theory of Action by Contact or Contiguous
Action). Another example is provided by the conception _Temperature_.
This conception becomes meaningless if we endeavour to apply it to
molecules: it leads to no result if we try to impose it on the smallest
parts of matter as such. The reason is that the state, the velocity, and
the inner energy of the individual molecules fluctuates between very
wide limits. The conception 'temperature' is applicable only to a
configuration composed of many molecules, and even then it is not
applicable quite generally. For let us picture to ourselves an extremely
rarefied gas contained in a closed receiver. Two opposite walls are to
be at different temperatures, the one being cold and the other being hot
In a gas at such very low pressure the molecules come into collision so
seldom that, practically, we have to take into account only the
collisions of the molecules with the confining walls. The molecules that
rebound from the hot wall have greater velocities than those coming from
the colder wall, and hence the conception of temperature becomes
untenable for this gas."
"Would the temperature-scale on the thermometer then denote nothing?" I
asked. "The greater or lesser degree of warmth of a body, in this case
of the mass of gas, depends on the more rapid or less rapid motion of
its smallest parts. The motions are in any case present, so what would a
thermometer indicate?"
"It would betray only that it had nothing to indicate. If a thermometer
that is blackened on one side were inserted into the vessel containing
the gas, then _different_ temperatures would be recorded if the
thermometer were gradually turned about its own axis; and this signifies
that the conception of temperature has become meaningless for this
configuration of molecules. And passing beyond the quoted examples, I
should maintain that all our conceptions, however subtly they may have
been thought out, are shown in the course of progressive knowledge to be
too rough hewn, that is, too little differentiated."
* * * * * * * *
We spoke of the "Properties of Things," and of the degree to which these
properties could be investigated. As an extreme thought, the following
question was proposed:
Supposing it were possible to discover _all_ the properties of a _grain
of sand_, would we then have gained a complete knowledge of the _whole
universe_? Would there then remain no unsolved component of our
comprehension of the universe?
Einstein declared that this question was to be answered with an
unconditional affirmative. "For if we had completely and in a scientific
sense learned the processes in the grain of sand, this would have been
possible only on the basis of an exact knowledge of the laws of
mechanical events in time and space. These laws, differential equations,
would be the most general laws of the universe, from which the
quintessence of all other events would have to be deducible."
[This thought may be spun out in yet another direction. Every piece of
research, however specialized it may appear and of whatever minor
importance it may be, retains a relationship with researches into the
universe, and may prove to be valuable for this latter task. If we
accept the view that science is capable of realizing perfection, then
every contribution to knowledge, even the most insignificant, is
essentially indispensable for attaining this goal.]
* * * * * * * *
Can a physical law alter with time? In more precise language, can time,
as such, enter explicitly into laws, so that, for example, an experiment
that is carried out at different times leads to different results? This
question has been treated several times, among others, by Poincaré, who
answered it with an emphatic "No!" but also by others to whom the
invariability of physical laws did not seem to hold for all eternity. If
my memory does not play me false, Helmholtz once expressed faint doubts
about the constancy of laws.
Einstein answered this question with a decided negative. "For a law of
physical nature is, by definition, a rule to which events conform
wherever and whenever they take place. Thus, if we were to be compelled
as a result of experience to make a law dependent on time, it would be a
necessary step to seek a law independent of time, which would include in
itself the law dependent on the time as a special case. The latter would
be excluded from the category of physical laws, and would henceforward
play the part only of a result deduced from the law which is independent
of the time."
* * * * * * * *
What attitude should we adopt if, in studying a scientific doctrine, we
encounter paradoxical results even though the inferences have been drawn
correctly--that is, if we meet with a deduction to which our reasoning
powers object, although no fallacy is discoverable in the argument?
Before we deal with cases which seem to me, personally, to be
interesting, let us hear what is Einstein's attitude in general. "As
soon as a paradox presents itself, we may, as a rule, infer that
inaccurate reasoning is the cause, and should thus examine in each
particular case whether an error of logic is discoverable, or whether
the paradoxical result denotes only a violent contrast with our present
views."
Let us first take examples from an entirely modern science, from the
_Theory of Aggregates_ founded by Georg Cantor of Halle. We shall follow
the argument by the only possible method for this book, namely, by rough
indications that will serve our purpose and do not claim to be accurate
in expression or in sense.
If we take an aggregate of three objects, for example, an apple, a pear,
and a plum, we may, by definition, form six partial aggregates, namely:
the apple
the pear
the plum
the apple and the pear
the apple and the plum
the pear and the plum.
The aggregate of the partial aggregates, which contains six elements, is
thus greater than (actually twice as great as) the original aggregate,
in which only three elements occur.
If the original aggregate contains an additional element, for example, a
nut, the following partial aggregates may be formed:
the apple
the pear
the plum
the nut
the apple and the pear
the apple and the plum
the apple and the nut
the pear and the plum
the pear and the nut
the plum and the nut
the apple, the pear, and the plum
the apple, the pear, and the nut
the apple, the plum, and the nut
the pear, the plum, and the nut.
Thus, in this case, the aggregate of the partial aggregates is already
considerably greater than the original aggregate. This numerical excess
increases rapidly with each successive increase in the original
aggregate, so that if we apply the same reasoning to an infinite
aggregate, the aggregate of partial aggregates becomes an infinity of a
_higher order_. This is expressed by saying that the infinite aggregate
of partial aggregates has a greater _potentiality_ than the infinity of
the elements of the original aggregate.
So we see that the one infinity is, in popular language, much more
comprehensive, more powerful than the other. Our minds do not find it
impossible to grasp this. But in a definite imaginary experiment it is
found that this theorem of progression not only fails in its
application, but leads to flagrant contradiction.
For if we start from the primary aggregate of "all conceivable things,"
its infinity can certainly not be transcended by any other infinity. But
according to the above theorem the "aggregate of all partial aggregates"
would have a greater potentiality, although it itself cannot extend
further than to the conception of the maximum of all conceivable things.
We thus arrive at an insoluble paradox, a typical example of how, in the
system of conceptions involved, something is insufficient or not in
conformity with logical thought. And this sceptical view receives
support from various remarks of Descartes, Locke, Leibniz, and
particularly Gauss, who, long before the advent of the Theory of
Aggregates, raised a protest against inexact definitions of infinity.
In another case, however, the same theory seems to arise by perfectly
logical processes, although it again leads to a statement that does not
seem correct to "common sense." For it shows by a very subtle and
ingenious method that all the surface-points of a surface infinitely
extended in all directions may be brought to correspond in a reversible
single manner to the linear points of a line, however small; so that to
every point of the unlimited plane there corresponds a definite point of
the line, and vice versa. The same theorem may be extended to
three-dimensional space, with the result that we have to reconcile
ourselves with the incredible fact that, expressed in popular language,
a straight line of however small length exhibits the same potentiality
with regard to the number of its points, as all the points in the
universe.
For my own part, I must confess that no means suggests itself to me to
make this paradox intelligible. But the _sacrificium intellectus_ comes
within dangerous proximity. Einstein, who values and marvels at the
theory of aggregates as a science, or perhaps more as a work of art
built up from the materials of science, gives whole-hearted support to
the proof. He refuses to accept the notion of a paradox--that is, he
recognizes a contradiction not in our process of reasoning, but only in
a habit of thought that is open to correction. I should give much to
discover the means of correction!
* * * * * * * *
A third example arises out of the special theory of relativity. It has a
mysterious paradoxical character that vanishes when a clear view of the
relationships involved has been obtained.
According to this theory the rate at which events happen alters
according to the state of motion of the system under consideration. Let
us now consider two twins A and B, that, although born at one place on
the earth, are immediately separated, B remaining at rest, whilst A
rushes out into space at an enormous rate, describing what, viewed from
the earth, is an inconceivably great circle. In this way the rate of
happening of all events is reduced very considerably for A in a manner
that may be calculated. If A then returns to B, it may happen that the
twin who stayed at home is now sixty years old, whereas the wanderer is
only fifteen years of age, or is perhaps only an infant still.
The first introduction to this flight of imagination naturally causes
profound perplexity. Nevertheless, we are dealing not with a realm of
miracles, but with something that is within the range of comprehension.
"In the case of these two twins," Einstein declared, "we have merely a
paradox of _feeling_. It would be a paradox of thought only if no
sufficient ground could be suggested for the behaviour of these two
creatures. This ground, which accounts for the comparative youth of A,
is given, from the point of view of the special theory of relativity, by
the fact that the creature in question, and only this creature, has been
subject to accelerations. A proper grasp of the reason is furnished only
when we adopt the _general_ theory of relativity, which tell us that,
from the point of view of A, a centrifugal field exists, whereas it is
absent from the point of view of B. This field exerts an influence on
the relative rate of happening of the events of life."
It certainly requires a prodigious mechanism to allow the moving twin to
gain even only one second of time. If he were to spend a year in a
merry-go-round whose circumference were about 19 milliard miles in
length, he would have to travel in it at the rate of over 600 miles per
second if he is to gain a second on his brother.
This inevitable result that is immediately apparent to a trained
scientific mind throws light on the nature of "common sense," the
validity of which, as an ultimate criterion, Kant too has refused to
recognize, in so far as this "common sense" is incapable of passing
beyond the examples offered in its own experience. It circulates, as
Einstein says, in the "realms of feeling and analogy." It finds no
analogy for a phenomenon like that described above, and since it can
apply rules only concretely, many things appear to it paradoxical that,
in the light of intensified abstraction, appear logical and necessary.
* * * * * * * *
Let us speculate on the following question. If all things in the
universe should increase or decrease enormously in dimensions, and if,
at the same time, in a manner totally concealed from us, certain
physical conditions should become changed, we should lack all means of
discovering the difference between things before and after the change.
For since all measuring-rods, including those furnished by our senses,
would have become changed in the same proportion, the two conditions
could not be differentiated from one another. It may easily be shown
that this would necessarily occur, if an extramundane power were
non-uniformly to displace, deform, compress, or bend all things in the
universe, provided that our instruments and senses participated in this
transformation. Accordingly it is permissible also to regard the
universe known to us as one that is deformed, and one that is derived
from another, the original form of which will ever remain a secret to
us.
Is there any connexion between this grotesque speculation and the theory
of relativity?
We can establish only one that is negative and that arises _e
contrario_. "These deformations," said Einstein, "are in themselves
abstractions that are physically meaningless. Only _relations between
bodies_ have a physical meaning, for example, the relation between
measuring-rods and the objects they measure. Therefore, it is reasonable
to talk of deformations only when we are dealing with the deformations
of two or more bodies with respect to one another, whereas the
conception of deformation has no sense, unless a real object is
specified, to which it is referred. The philosophical merit of the
general theory of relativity, as compared with previous views of
physics, consists in the fact that the former avoids entirely these
meaningless abstractions with respect to space and time."
[According to this, it is not purposeless to enter on these grotesque
trains of thought, even if they are untenable physically. For since the
new physics teaches us to avoid these false tracks, it seems of value to
know what it is that is to be avoided. Just as we must study scholastic
thought if we wish to grasp thoroughly the philosophy which sprang up
after the scholastic fetters were burst. Moreover, these reflections on
concealed universes are not without a certain attraction, reminiscent of
the sorcerer's wand, if they pursued any other goal than that of making
universes distorted. It is true that they hold out latent temptations
that may in some cases lead us on to dangerous ground, in encouraging us
to venture on analogies beyond the scope of geometry and physics. Would
it be possible to enter suddenly into a world that is distorted and
deformed with respect to its ethics, its culture, and its reasoning
intellects, without our observing the difference? Are we ourselves
perhaps living under such deranged conditions, of which we cannot become
aware, because our perceptual organs have likewise become deformed? I
must frankly confess that I do not regard it as quite inconceivable that
this argument of deformation may be spun out in this direction, but I
must add that Einstein rejects absolutely all such extensions, since,
as he emphasizes, they lead to regions that are merely fields for the
exhibition of "verbal gymnastics."]
* * * * * * * *
The question whether Nature makes leaps or not is very old. In the
theory of descent it forms the foundation of the difference between
revolutionists and the evolutionists, who uphold the axiom _natura non
facit saltus_, with all its consequences. Recently attempts have been
made, particularly by psychologists, to propound and justify a natural
principle of discontinuity. They assert that our own perceptions and
sensations are discontinuous in themselves, and that the mechanism of
every perception is akin to that of a cinematograph with its extremely
rapid interruptions. If this should actually be the case, we should
scarcely have a means of solving definitely the question whether
continuity reigns, or not, in Nature.
Einstein does not recognize the possibility of this alternative for a
moment. If a doubt had ever arisen, the researches of Maxwell would in
themselves have been sufficient to dispel it. Our universe that is to be
described in terms of differential equations is absolutely continuous.
"But," I interjected, "does not modern physics offer a certain support
to the assumption of a discontinuity? Does not the Quantum Theory point
to an atomistic structure of energy, and hence also of events that are
to be imagined as happening in jerks and as involving relations
expressible in whole numbers?"
Einstein gave an answer of epigrammatic brevity and flavour. "The fact
that these phenomena are expressible in whole numbers must not be
construed into an argument against continuous happening. Just imagine to
yourself for a moment that beer is sold only in whole litres; would you
then infer that beer, as such, is discontinuous?"
* * * * * * * *
What achievements are to be expected of astronomy in the present era?
This question would have a special meaning if it were assumed that the
astronomer who works in observatories is surrounded by solved problems,
and can no longer hope to solve problems having the universal
significance of those of Copernicus or Kepler. This assumption, however,
would not be in agreement with the actual state of affairs.
Einstein indicated to me a number of fundamental problems that present
themselves to modern astronomy, and the solution of which he expected of
future times.
Above all, the geometrical and physical constitution of the stellar
systems will, in the main, become revealed.
At present we do not yet know whether Newton's Law of Attraction holds,
at least approximately, for configurations of the type of the Milky Way
and of the spherical clusters of stars--that is, in extents of space in
which the influence of space-curvature would become appreciable. The
rapid progress of recent astronomy justifies our great hopes that the
solution of this universal problem will be found within the coming
decades.
In distant connexion with this we also touched on the question of the
habitability of other worlds. This theme of Fontenelle, "la pluralité
des mondes habités," which has again become a centre of public
interest, owing to investigations of Mars, has evoked a storm of
discussion. We hear the noisy war-cries of geocentric scientists who
wish to regain for the earth her shattered supremacy in astronomy, and
who claim the existence of organic forms as the sole prerogative of our
planet. It is scarcely necessary to mention that Einstein rejects the
motives of these human and all-too-human individuals as small-minded and
short-sighted. Creatures in distant worlds are derived from, and are
subject to, conditions of organic nature, of which we can form no idea
by deductions from the world which we inhabit. But to deny their
existence on numberless constellations, or to demand an ocular proof of
their presence, is no better than to assume the point of view of an
infusoria to whom there is no life other than that in a dirty drop of
ditch-water.
* * * * * * * *
The idea of the atom as the ultimate structural element involves a
philological as well as a conceptual contradiction. For _atomos_
signifies the indivisible, the no-further-divisible, whereas the idea of
a body, however small, an element of structure differing from zero,
demands, at least geometrically, further divisibility. Even the original
founders of the theory of atoms, Leukippus, Epicurus, and Democritus,
assigned definite forms to the ultimate components, and we may read in
the splendid work of Lucretius how he infers from the nature of
substance that the ultimate particles are smooth, round, or rough, or
have the shapes of hooks and eyes. The further analysis pressed forward,
the more the simplicity of the original idea vanished. Microcosms came
to be regarded as copies of macrocosms, and the atoms of present-day
science actually exact from us that we should regard them as worlds in
themselves.
Einstein acceded to my request that he might give a sketch of the latest
achievements of science sufficient to provide an approximate idea of the
_atomic model_. According to the researches of Rutherford and Niels
Bohr, we are to picture it as a planetary system.
The central body of this system is represented by a positively charged
nucleus, which constitutes almost the whole mass of the atom, surrounded
by a certain number of electrons, negative charges, that move in uniform
circular or elliptic orbits about the nucleus. There is thus a certain
analogy that allows us to regard the nucleus as the sun, and the
electrons as the planets of this system.
The number of these electrons varies between the limits 1 and 92,
according to the chemical constitution of the element. The smallest
number occurs in the case of helium (in which there are two), and of the
hydrogen atom, in which only one electron-planet describes its circular
path about the nucleus. In other atoms there are probably more
complicated orbits, although they are more or less approximately
circular. According to this still very new theory, which is supported by
very convincing facts, the electrons are to be imagined as arranged in
concentric shells (like the layers of an onion), among which the
innermost shell plays a distinctive part inasmuch as the number of the
electrons arranged in it decides the chemical character of the atom in
question. It sometimes occurs that electrons spring, under external
influence, from one orbit to another; when the electron jumps back to
the original orbit, light is emitted. An essential fact is to be noted:
Whereas any arbitrary orbits of any arbitrary radius may occur in a
planetary system of the celestial regions, the manifold of these orbits
in the case of the electrons is restricted, in that only certain orbits
are possible, namely, those that are determined mathematically by the
quantum condition.
"Perhaps," I interrupted, "the whole analogy may be inverted. If the
atom is considered analogous to a planetary system in the model, it
should be admissible to regard our true planetary system as a cosmic
atom. And then, long after we have become accustomed to regard our earth
as playing the part of a grain of sand, the sovereignty of the sun, too,
would be past. The whole majesty of the solar system as far as the orbit
of Neptune would then shrink to a configuration compared with which the
world of a grain of sand would be infinitely complex."
"This fantastic inversion is permissible up to a certain extent," said
Einstein, "but we must not lose sight of the fact that there is a
cardinal difference. If we disregard the enormous disparity in
dimensions, the analogy is far from exact owing to the circumstance that
the atom is only an element of structure, whereas the true planetary
system is an extraordinarily complex structure in itself. Thus the
difference between a simple thing and one that is very highly complex
still remains."
"But, Professor, may not a similar complexity yet be discovered in the
atom? It may be merely a difference of philosophical view from the
primary idea to that of regarding the electrons as circulating like
planets. May we not conjecture that in each successive step we are
merely carrying out a true _regressus in infinitum_?"
"That seems highly improbable," he replied, "although, of course,
structural investigations can never cease. At first they are directed at
the more remote object of finding out why certain atoms are radioactive,
that is, exhibit a tendency to disintegrate. It has already been
established that this tendency is a property of the positive nucleus, of
which little is as yet known. This means that the nucleus is not simple,
yet it does not open up the possibility of an unending regression. Our
aim must be to get a clear insight into the constitution of the nucleus,
as regards the positive and negative charges, and it is my opinion," he
concluded, "that beyond this there will be no further subdivision of
matter."
When Goethe writes of the immovable pole in the flux of phenomena, we
recognize that his beautiful remark pronounces an elegy to the
possibility of attaining ultimate simplicity. Einstein's utterance, if I
understand him aright, converts this elegy into a song of hope. If the
subdivision of matter actually has an end somewhere, then we are now on
the threshold of ultimate things, we are near the immovable pole, which
we are capable of reaching.
* * * * * * * *
"Every new truth of science must be such that, in ordinary writing, it
may be communicated completely within the space of a quarto leaf."
Kirchhoff made this remark, and gave a sufficient, if not literal,
demonstration of its truth. When Bunsen and he published the first
notice about spectral analysis, they compressed their publication into
the small space of three printed pages.
But what is to happen if the new truth should be built up of very
comprehensive materials, when it requires many links, of which none can
be omitted if the truth is to be made intelligible? Would Kirchhoffs
quarto page still be sufficient?
"Certainly," said Einstein, "provided, of course, that it is addressed
to a reader who has already mastered what went before--that is, to one
who is so far acquainted with the older facts that he has to learn only
the really new part of the new truth."
"That sounds very hopeful," I remarked, "for then it should also be
possible to describe very briefly the theory of relativity."
"Let us rather say its essentials--the heart of the matter. Well, then,
get your Kirchhoff page ready. We shall see whether we can set out on it
the special theory of relativity."
The totality of our experience compels us to assume that light travels
with a constant velocity in empty space. Likewise, our whole experience
in optics compels us to recognize that all inertial systems are
equivalent; these are systems that are produced from an allowable one by
means of a uniform translation. An allowable system is one in which
Galilei's and Newton's Law of Inertia holds. (This law states that a
moving body that is left to itself retains its direction and velocity
permanently.)
Now, the law of the constancy of light propagation seems to conflict
with the classical principle of relativity, according to which the
velocity of a ray of light assumes different values in the moving system
according to the direction of the ray.
This apparent incompatibility arises from the following unproved
assumptions:
(_a_) If two events are simultaneous with regard to one inertial system,
they are also simultaneous with regard to any other inertial system.
(_b_) The length of a measuring-rod, the shape and size of a rigid body,
and the rate of a clock are independent of their motion with respect to
the system of reference used, provided this motion is rectilinear and
non-rotational.
These assumptions must be discarded if this disagreement is to be
eliminated. If we substitute for them the assumption that all inertial
systems are equivalent and that the velocity of light _in vacuo_ is
constant, we get:
(1) That the dimensions of bodies and the rate of clocks have a
functional relation to the motion.
(2) That the equations of motion of Newton require to be modified; this
modification leads to results that, for rapid motions, differ
appreciably from those of Newton.
This is, in a very compressed form, the meaning of the special theory of
relativity.
As there is still some space left on our quarto page, we may add a
remark that, it is hoped, will make a little clearer the above-mentioned
discrepancy.
Let us choose as our system of reference an express train 18 miles long.
There are two passengers--Mr. Front, right at the front of the train,
and Mr. Back, at the extreme end of the train, so that a rigid distance
of 18 miles separates the two passengers. The carriages are transparent,
so that the two passengers can signal to one another. They are,
moreover, furnished with ideal clocks that run at exactly the same rate.
First, suppose that the train is at rest. Back is just opposite
milestone 100, whilst Front is opposite milestone 118. By means of a
flash, Back signals to Front his time, exactly 12 o'clock. It takes
light very nearly ¹⁄₁₀₀₀₀ second to traverse the length of
the train--18 miles; hence the flash will reach Front at 12 o'clock
¹⁄₁₀₀₀₀ second. Exactly the same result would have come
about if Front had signalled his time to Back. Light makes no difference
in travelling forwards and backwards. If the train moves at a great
speed, the two travellers can conduct the same experiment as when the
train was at rest. They will then set the time that light takes to
travel from Back to Front equal to the time that it takes to traverse
the same way in the reverse direction. But this phenomenon will assume a
different aspect if viewed from the railway embankment. An observer on
the latter would affirm that light does not take the same time in
travelling the length of the train in one direction as it does when
travelling in the opposite direction.
For the ray of light moving in the forward direction has to traverse not
only the distance between Back and Front, but also the very short
distance that Front has moved forward during the interval that the light
has been moving; whereas, inversely, the flash sent out by Front to Back
will traverse a distance that is correspondingly less than that between
the passengers, since Back is moving towards the signal.
Thus the duration of the two phenomena of light propagation is the same
or different, respectively, according as it is judged from the train or
from the embankment. In other words, _the judgment of the length of time
depends on the state of motion of the observer_.
All further pronouncements of the special theory of relativity are based
on the preceding arguments of the relativity of time.
* * * * * * * *
Would Man be able to construct a Science if he possessed one sense less
than at present--for example, if he were deprived of sight? Let us apply
this to a definite case. In the new physics the velocity of light plays
a decisive part as a world-constant. At first sight it would appear
impossible for us to determine it and recognize its importance, if we
had not at our disposal some organ which enabled us to become aware of
optical phenomena.
But, as Einstein explained to me, even under such difficult
circumstances, it would be possible to build up a science, for the
reason that phenomena, as far as they are perceptible, may be
transformed so that they become manifest to other senses if one sense
should be absent. For example, the electrical conductivity of selenium
is strongly influenced by the amount of illumination that falls on it.
Thus light acts on a selenium cell, causing changes of current
intensity, which in their turn may be perceived by feeling, or by
chemical action on the mucous fluid of the tongue. Ultimately we are
concerned only with a differentiation that enables us to refer identical
experiences to identical events. We should certainly encounter enormous
difficulties in endeavouring to form a physical picture of our
surrounding world if the number of our senses should become less than
the organs with which we actually operate. Yet, in principle, we should
be able to overcome all difficulties by means of much lengthened and
complicated lines of research, even if we should have only a single
sense left, or if we had only one at the very outset. The construction
of a Science would then be possible, and would give the same results,
although it might be propounded only after a delay of perhaps millions
of years.
[It is naturally assumed that the intellect is retained, as this is the
necessary condition for all scientific research. Since the degree of
understanding depends on the senses--_nihil est in intellectu, quod non
prius fuerit in sensu_--we may conjecture that a human being with only
one sense organ would work with a minimum degree of understanding, which
would be insufficient for the acquirement of any knowledge whatsoever.
This transcendental question, which lies almost beyond the bounds of
discussion, was not touched on in our conversation, as the subject was
restricted so that it should not drift into metaphysical regions.
Nevertheless, I should like to mention that a speculation of this kind
is recorded in the history of science. Condillac, in a study teeming
with ideas, investigates the behaviour of a "Statue," that he represents
as a human being, with the assumption that there is at first no idea in
the soul of this statue-person. This living creature is enclosed in a
marble envelope, the sole exterior organ of which is at first the organ
of smell. He then shows that by means of this single sense all manner of
sensations and expressions of will may develop in his "statue."
Condillac does not, however, undertake to give a convincing proof that
this creature, restricted to the organ of smell, would be able to
discover physically the relationships that hold in physical nature, and
thus to build up a scientific system. Thus Einstein, in his discussion,
goes considerably further than the author of this statue.]
* * * * * * * *
Has the "eternal repetition," as outlined by Nietzsche, any meaning?
The sage of Sils-Maria tells us that this revelation came to him midway
between tears and ecstasy, as a fantasy with a real meaning. The crux of
his idea is a finite world built up of a finite number of atoms. From
the fact that the present state emerges out of the immediately preceding
one, the latter from the one just before, and so on, he concludes that
the present state exhibits repetition both forwards and backwards. All
becoming recurs and moves in a multiple cycle of absolutely identical
states.
Let us discard for the moment all philosophical objections, above all
this, that the recurrence of the same disposition of atoms may not
necessarily entail the recurrence of the same psychical states.
Furthermore, let us suppress the cynical thought that in the return to
the same state the world would have reason to enjoy extreme happiness
only for moments, but to lament for aeons. Then we are left with the
comparatively simple question: Is this repetition, from the point of
view of physics, conceivable and possible?
It would be the death-knell of Nietzsche's idea if the answer of a great
physical research scientist were entirely in the negative. But Einstein
still allows it a small measure of life. "Eternal repetition," so he
expressed himself, "cannot be denied by science with absolute
certainty." The disciples of Nietzsche will have to rest satisfied with
this very small concession. For what, in Nietzsche's eyes, is a logical
necessity becomes transformed by Einstein's supplementary remark into a
vague assumption, the product of fantasy. From the point of view of
physics the recurrence of the same condition is to be regarded as
"enormously improbable." This statement is founded chiefly on the famous
second Law of Thermodynamics, according to which the processes of Nature
are in the main irreversible, so that a one-sided tendency is expressed
in natural phenomena. The fact that the course of phenomena is in only
one sense or direction speaks in favour of the view that the events of
the world are to be regarded as occurring only once.
So that when Nietzsche, in contradistinction to this, vigorously
supported the doctrine of repetition, he contradicted at least one
important recognized theorem of physics. The fact that he did not become
conscious of this contradiction, but that, on the contrary, he regarded
his idea as the most important event in the development of his
intellect, may be regarded as an example of a _docta ignorantia_. But it
is allowable, too, that philosophic fantasies that complete the poetical
picture of the universe should be given expression. And Nietzsche would
presumably have been deprived of a degree of pleasure if he had been
aware of this second law.
"Truth is the most expedient error"; this statement may be traced back
to a sequence of thought developed by Nietzsche. But the Eternal
Repetition is shattered by just this remark, for judged by its
consequences it would be a very inexpedient error.
* * * * * * * *
Supposing we should succeed in exchanging thoughts with the inhabitants
of distant worlds and should, through them, acquire the elements of a
civilization _superior to our own_, would this knowledge prove a
blessing to us or the reverse?
The word "superior" must, of course, be treated circumspectly. It is to
denote only that, relatively, this distant civilization bears somewhat
the same relation to our civilization of to-day as our own bears to that
of an Australasian negro or an anthropoid ape. There are fanatics of
progress whose wishes plunge headlong and without restraint into the
future, and to whom nothing could be more desirable than the sudden
appearance of a civilization that, as they opine, would at one stroke
carry us "forward" many thousands of years.
But the view of these magicians with their seven-league boots is
untenable. Let me cite a mere outline of the many opposing arguments in
a few words of Einstein. "Every sudden change in the conditions of
existence, even if it occurred in the form of a higher development,
would come upon us like a doom, and would probably annihilate us, just
as the Indians succumb to the civilization that has outstripped them.
The tragedy of our own highly civilized times is that we cannot create
the social organizations that have become necessary as a consequence of
the technical advances of the last century. This has given rise to the
crises, impasses, and senseless competition between nations, and to the
impoverishment of defenceless individuals. These deplorable conditions
would become inconceivably accentuated if we were to be invaded by
extra-mundane technical sciences of a higher order."
* * * * * * * *
Nevertheless, there is still a possibility that the "superior
civilization" might contain indications of the organizations which we
lack. Instead of entering on the question of this Utopia, we confined
ourselves to comparing past conditions in our world with present ones.
Did we not have the most promising preliminaries for an organization
that was devoid of friction and tended to reduce the competition between
nations in the numerous international institutions that drew together a
great section of the intellectual world to work in co-operation? Are
there hopes that this international coalition will be resumed?
Einstein expressed himself optimistically, not to do homage to an
organization artificially formed, but to extol the world-wide mastery of
intellect. "Even if international congresses were to be swept away," he
said, "international co-operation would not be abolished, as it effects
itself automatically." I should venture to assert that if all these
congresses were to cease, we should not even have cause to fear that
there would be an appreciable diminution in the combined effort of
research. If certain developments are hindered by political conditions,
it is only due to the resulting economic hardships affecting individuals
in their work and robbing them of their intellectual freedom. The real
friends of Truth have always clung together, and do so actually now;
indeed, many feel the tie to be closer than that connecting them to
their own country. In spite of all obstacles and boundaries they will
never cease to find contact with one another!