Mark,
Here is a comment from the same biologist in response to my amateur discussion of the
2nd Amendment, ...I mean the 2nd Law ( but not a jurisprudential one) of
thermodynamics.
I recall Engels discussing the sun burning out, but I hadn't realized he was not hip
to heat death for the whole universe. Engels does discuss Helmholz in notes that are
for unpublished book "Dialectics of Nature". (See prior post from me below which
begot the answer from the pro)
Charles
(((((((((
"Engels however had a hard time accepting the full implications of the 2nd law,
because of his belief in the inexhaustibility of motion in the universe. He postulated
there must be some mechanism to restore waste heat radiated into space to its original
higher quality (low entropy) state (see p.334, 561-563, Collected Works, vol.25, Intl
Publ., 1987, the annotated Dialectics of Nature). Hence his and later Marxist (and
Leninist) rejection of heat death of the universe. But heat death may be problematic
for other reasons; see my paper "Solar Communism", 1996, Science & Society 60, No.3:
307-331. Maybe ultimate heat death in our universe, but not in the multiverse! In any
case, ultimate heat death of course in no way preempts the emergence and continued
existence of self-organizing systems that export entropy ("disorder") to their
environment, while minimizing it within the system. Some even argue that these systems
emerge because of, not in spite of the 2nd law (Schneider, Swenson). They certainly
obey it."
Charles Brown wrote:
> Haines,
>
> Below is some justification for my claim that the 2nd Law of Thermodynamics was
>known to Engels , and that it was part of his conception of matter in motion .
>Evidently, Helmholz was important in developing thermodynamics, and we see Engels
>centers much discussion in the _Dialectics of Nature_ section below on Helmholz
>
> Charles
>
> ____________
>
> Charles B: I believe the 2nd Law of Thermodynamics was known to
> Engels and was part of the basis for his definition of motion as
> "the mode of existence of matter". So , Engels presumed a
> posteriori, after not only his experience , but the experience and
> observation of physical scientists.
>
>
A biologist on Marxism-and-Sciences .
Charles
>>> [EMAIL PROTECTED] 02/02/01 05:22PM >>>
> This statement is imprecise. Not a closed system, but an isolated one, to both
> matter and energy flows in and out. The confusion, deliberate or not, between
> closed and isolated systems led Georgescu-Roegen and his populizer Jeremy Rifkin
> to fallacious postulates regarding solar energy and economic growth. See my
> paper, "Solar Communism", 1996, Science & Society 60, No.3: 307-331 (heat death
> is also discussed).
Is this you who said this, Charles? What fallacious postulates?
mark
_______________________________________________
Entropy in the Physical Sciences
Original by Chris Hillman (Last modified by Chris Hillman 2 Feb 2001.)
--------------------------------------------------------------------------------
The thermodynamical notion of entropy was introduced in 1854 by Rudolph Clausius, who
built on the work of Carnot. His ideas were later extended and clarified by Helmholtz
and others. In the 1870's, Ludwig Boltzmann found a "statistical" definition of
entropy which, he claimed, reduced to the earlier notion of Clausius. Around the same
time, Josiah Willard Gibbs introduced a slightly different statistical notion of
entropy. Here are some pages discussing these ideas:
The Page of Entropy, by Dave Slaven (Physics,
((((((((
Engels'
Dialectics of Nature
--------------------------------------------------------------------------------
III. BASIC FORMS OF MOTION
Motion in the most general sense, conceived as the mode of existence, the inherent
attribute of matter, comprehends all changes and processes occurring in the universe,
from mere change of place right to thinking. The investigation of the nature of motion
had, as a matter of course, to start from the lowest, simplest forms of this motion
and to learn to grasp these before it could achieve anything in the way of explanation
of the higher and more complicated forms. Hence, in the historical evolution of the
natural sciences we see how first of all the theory of simplest change of place, the
mechanics of heavenly bodies and terrestrial masses, was developed; it was followed by
the theory of molecular motion, physics, and immediately afterwards, almost alongside
of it and in some places in advance of it, the science of the motion of atoms,
chemistry. Only after these different branches of the knowledge of the forms of motion
governing non-living nature had attained a high degree of development could the
explanation of the processes of motion represented by the life process be successfully
tackled. This advanced in proportion with the progress of mechanics, physics, and
chemistry. Consequently, while mechanics has for a fairly long time already been able
adequately to refer to the effects in the animal body of the bony levers set into
motion by muscular contraction and to the laws that prevail also in non-living nature,
the physico-chemical establishment of the other phenomena of life is still pretty much
at the beginning of its course. Hence, in investigating here the nature of motion, we
are compelled to leave the organic forms of motion out of account. We are compelled to
restrict ourselves * in accordance with the state of science * to the forms of motion
of non-living nature.
All motion is bound up with some change of place, whether it be change of place of
heavenly bodies, terrestrial masses, molecules, atoms, or ether particles. The higher
the form of motion, the smaller this change of place. It in no way exhausts the nature
of the motion concerned, but it is inseparable from the motion. It, therefore, has to
be investigated before anything else.
The whole of nature accessible to us forms a system, an interconnected totality of
bodies, and by bodies we understand here all material existence extending from stars
to atoms, indeed right to ether particles, in so far as one grants the existence of
the last named. In the fact that these bodies are interconnected is already included
that they react on one another, and it is precisely this mutual reaction that
constitutes motion. It already becomes evident here that matter is unthinkable without
motion. And if, in addition, matter confronts us as something given, equally
uncreatable as indestructible, it follows that motion also is as uncreatable as
indestructible. It became impossible to reject this conclusion as soon as it was
recognised that the universe is a system, an interconnection of bodies. And since this
recognition had been reached by philosophy long before it came into effective
operation in natural science, it is explicable why philosophy, fully two hundred years
before natural science, drew the conclusion of the uncreatability and
indestructibility of motion. Even the form in which it did so is still superior to the
present day formulation of natural science. Descartes' principle, that the amount of
motion present in the universe is always the same, has only the formal defect of
applying a finite expression to an infinite magnitude. On the other hand, two
expressions of the same law are at present current in natural science: Helmholtz's law
of the conservation of force, and the newer, more precise, one of the conservation of
energy. Of these, the one, as we shall see, says the exact opposite of the other, and
moreover each of them expresses only one side of the relation.
When two bodies act on each other so that a change of place of one or both of them
results, this change of place can consist only in an approach or a separation. They
either attract each other or they repel each other. Or, as mechanics expresses it, the
forces operating between them are central, acting along the line joining their
centres. That this happens, that it is the case throughout the universe without
exception, however complicated many movements may appear to be, is nowadays accepted
as a matter of course. It would seem nonsensical to us to assume, when two bodies act
on each other and their mutual interaction is not opposed by any obstacle or the
influence of a third body, that this action should be effected otherwise than along
the shortest and most direct path, i.e. along the straight line joining their centres.
It is well known, moreover, that Helmholtz (Erhaltung der Kraft [The Conservation of
Force], Berlin, 1847, Sections 1 and 2) has provided the mathematical proof that
central action and unalterability of the quantity of motion are reciprocally
conditioned and that the assumption of other than central actions leads to results in
which motion could be either created or destroyed. Hence the basic form of all motion
is approximation and separation, contraction and expansion * in short, the old polar
opposites of attraction and repulsion.
It is expressly to be noted that attraction and repulsion are not regarded here as
so-called "forces" but as simple forms of motion, just as Kant had already conceived
matter as the unity of attraction and repulsion. What is to be understood by the
conception of "forces" will be shown in due course.
All motion consists in the interplay of attraction and repulsion. Motion, however, is
only possible when each individual attraction is compensated by a corresponding
repulsion somewhere else. Otherwise in time one side would get the preponderance over
the other and then motion would finally cease. Hence all attractions and all
repulsions in the universe must mutually balance one another. Thus the law of the
indestructibility and uncreatibility of motion takes the form that each movement of
attraction in the universe must have as its complement an equivalent movement of
repulsion and vice versa; or, as ancient philosophy - long before the natural
scientific formulation of the law of conservation of force or energy - expressed it:
the sum of all attractions in the universe is equal to the sum of all repulsions.
However it appears that there are still two possibilities for all motion to cease at
some time or other, either by repulsion and attraction finally cancelling each other
out in actual fact, or by the total repulsion finally taking possession of one part of
matter and the total attraction of the other part. For the dialectical conception,
these possibilities are excluded from the outset. Dialectics has proved from the
results of our experience of nature so far that all polar opposites in general are
determined by the mutual action of the two opposite poles on one another, that the
separation and opposition of these poles exists only within their unity and
inter-connection, and, conversely, that their inter-connection exists only in their
separation and their unity only in their opposition. This once established, there can
be no question of a final cancelling out of repulsion and attraction, or of a final
partition between the one form of motion in one half of matter and the other form in
the other half, consequently there can be no question of mutual penetration or of
absolute separation of the two poles. It would be equivalent to demanding in the first
case that the north and south poles of a magnet should mutually cancel themselves out
or, in the second case, that dividing a magnet in the middle between the two poles
should produce on one side a north half without a south pole, and on the other side a
south half without a north pole. Although, however, the impermissibility of such
assumptions follows at once from the dialectical nature of polar opposites,
nevertheless, thanks to the prevailing metaphysical mode of thought of natural
scientists, the second assumption at least plays a certain part in physical theory.
This will be dealt with in its place.
How does motion present itself in the interaction of attraction and repulsion? We can
best investigate this in the separate forms of motion itself. At the end, the general
aspect of the matter will show itself.
Let us take the motion of a planet about its central body. The ordinary school
textbook of astronomy follows Newton in explaining the ellipse described as the result
of the joint action of two forces, the attraction of the central body and a tangential
force driving the planet along the normal to the direction of this attraction. Thus it
assumes, besides the form of motion directed centrally, also another direction of
motion or so-called "force" perpendicular to the line joining the central points.
Thereby it contradicts the above-mentioned basic law according to which all motion in
our universe can only take place along the line joining the central points of the
bodies acting on one another, or, as one says, is caused only by centrally acting
forces. Equally, it introduces into the theory an element of motion which, as we have
likewise seen, necessarily leads to the creation and destruction of motion, and
therefore presupposes a creator. What had to be done, therefore, was to reduce this
mysterious tangential force to a form of motion acting centrally, and this the
Kant-Laplace theory of cosmogony accomplished. As is well known, according to this
conception the whole solar system arose from a rotating, extremely tenuous, gaseous
mass by gradual contraction. The rotational motion is obviously strongest at the
equator of this gaseous sphere, and individual gaseous rings separate themselves from
the mass and clump themselves together into planets, planetoids, etc., which revolve
round the central body in the direction of the original rotation. This rotation itself
is usually explained from the motion characteristic of the individual particles of
gas. This motion takes place in all directions, hut finally an excess in one
particular direction makes itself evident and so causes the rotating motion, which is
bound to become stronger and stronger with the progressive contraction of the gaseous
sphere. But whatever hypothesis is assumed of the origin of the rotation, it abolishes
the tangential force, dissolving it in a special form of the phenomena of centrally
acting motion. If the one element of planetary motion, the directly central one, is
represented by gravitation, the attraction between the planet and the central body,
then the other tangential element appears as a relic, in a derivative or altered form,
of the original repulsion of the individual particles of the gaseous sphere. Then the
life process of a solar system presents itself as an interplay of attraction and
repulsion, in which attraction gradually more and more gets the upper hand owing to
repulsion being radiated into space in the form of heat and thus more and more
becoming lost to the system.
One sees at a glance that the form of motion here conceived as repulsion is the same
as that which modern physics terms "energy." By the contraction of the system and the
resulting detachment of the individual bodies of which it consists to-day, the system
has lost "energy," and indeed this loss, according to Helmholtz's well-known
calculation, already amounts to 453/454 of the total quantity of motion originally
present in the form of repulsion.
Let us take now a mass in the shape of a body on our earth itself. It is connected
with the earth by gravitation, as the earth in turn is with the sun; but unlike the
earth it is incapable of a free planetary motion. It can be set in motion only by an
impulse from outside, and even then, as soon as the impulse ceases, its movement
speedily comes to a standstill, whether by the effect of gravity alone or by the
latter in combination with the resistance of the medium in which it moves. This
resistance also is in the last resort an effect of gravity, in the absence of which
the earth would not have on its surface any resistant medium, any atmosphere. Hence in
pure mechanical motion on the earth's surface we are concerned with a situation in
which gravitation, attraction, decisively predominates, where therefore the production
of the motion shows both phases: first counteracting gravity and then allowing gravity
to act * in a word, production of rising and falling.
Thus we have again mutual action between attraction on the one hand and a form of
motion taking place in the opposite direction to it, hence a repelling form of motion,
on the other hand. But within the sphere of terrestrial pure mechanics (which deals
with masses of given states of aggregation and cohesion taken by it as unalterable)
this repelling form of motion does not occur in nature. The physical and chemical
conditions under which a lump of rock becomes separated from a mountain top, or a fall
of water becomes possible, lie outside our sphere. Therefore, in terrestrial pure
mechanics, the repelling, raising motion must be produced artificially: by human
force, animal force, water or steam power, etc. And this circumstance, this necessity
to combat the natural attraction artificially, causes the mechanicians to adopt the
view that attraction, gravitation, or, as they say, the force of gravity, is the most
important, indeed the basic, form of motion in nature.
When, for instance, a weight is raised and communicates motion to other bodies by
falling directly or indirectly, then according to the usual view of mechanics it is
not the raising of the weight which communicates this motion but the force of gravity.
Thus Helmholtz, for instance, makes "the force which is the simplest and the one with
which we are best acquainted, viz. gravity, act as the driving force... for instance
in grandfather clocks that are actuated by a weight. The weight... cannot comply with
the pull of gravity without setting the whole clockwork in motion." But it cannot set
the clockwork in motion without itself sinking and it goes on sinking until the string
from which it hangs is completely unwound:
"Then the clock comes to a stop, for the operative capacity of the weight is exhausted
for the time being. Its weight is not lost or diminished, it remains attracted to the
same extent by the earth, but the capacity of this weight to produce movements has
been lost.... We can, however, wind up the clock by the power of the human arm,
whereby the weight is once more raised up. As soon as this has happened, it regains
its previous operative capacity and can again keep the clock in motion." (Helmholtz,
Popular Lectures, German Edition, II. pp. 144 * 5.)
According to Helmholtz, therefore, it is not the active communication of motion, the
raising of the weight, that sets the clock into motion, but the passive heaviness of
the weight, although this same heaviness is only withdrawn from its passivity by the
raising, and once again returns to passivity after the string of the weight has
unwound. If then according to the modern conception, as we saw above, energy is only
another expression for repulsion, here in the older Helmholtz conception force appears
as another expression for the opposite of repulsion, for attraction. For the time
being we shall simply put this on record.
When this process, as far as terrestrial mechanics is concerned, has reached its end,
when the heavy mass has first of all been raised and then again let fall through the
same height, what becomes of the motion that constituted it? For pure mechanics, it
has disappeared. But we know now that it has by no means been destroyed. To a lesser
extent it has been conveyed into the air as oscillations of sound waves, to a much
greater extent into heat * which has been communicated in part to the resisting
atmosphere, in part to the falling body itself, and finally in part to the floor, on
which the weight comes to rest. The clock weight has also gradually given up its
motion in the form of frictional heat to the separate driving wheels of the clockwork.
But, although usually expressed in this way, it is not the falling motion, i.e.. the
attraction, that has passed into heat, and therefore into a form of repulsion. On the
contrary, as Helmholtz correctly remarks, the attraction, the heaviness, remains what
it previously was and, accurately speaking, becomes even greater. Rather it is the
repulsion communicated to the raised body by rising that is mechanically destroyed by
falling and reappears as heat. The repulsion of masses is transformed into molecular
repulsion.
Heat, as already stated, is a form of repulsion. It sets the molecules of solid bodies
into oscillation, thereby loosening the connections of the separate molecules until
finally the transition to the liquid state takes place. In the liquid state also, on
continued addition of heat, it increases the motion of the molecules until a degree is
reached at which the latter split off altogether from the mass and, at a definite
velocity determined for each molecule by its chemical constitution, they move away
individually in the free state. With a still further addition of heat, this velocity
is further increased, and so the molecules are more and more repelled from one
another.
But heat is a form of so-called "energy "; here once again the latter proves to be
identical with repulsion.
In the phenomena of static electricity and magnetism, we have a polar division of
attraction and repulsion. Whatever hypothesis may be adopted of the modus operandi of
these two forms of motion, in view of the facts no one has any doubt that attraction
and repulsion, in so far as they are produced by static electricity or magnetism and
are able to develop unhindered, completely compensate one another, as in fact
necessarily follows from the very nature of the polar division. Two poles whose
activities did not completely compensate each other would indeed not be poles, and
also have so far not been discovered in nature. For the time being we will leave
galvanism out of account, because in its case the process is determined by chemical
reactions, which makes it more complicated. Therefore, let us investigate rather the
chemical processes of motion themselves.
When two parts by weight of hydrogen combine with 15.96 parts by weight of oxygen to
form water vapour, an amount of heat of 68,924 heat units is developed during the
process. Conversely, if 17.96 parts by weight of water vapour are to be decomposed
into 2 parts by weight of hydrogen and 15.96 parts by weight of oxygen, this is only
possible on condition that the water vapour has communicated to it an amount of motion
equivalent to 68,924 heat units * whether in the form of heat itself or of electrical
motion. The same thing holds for all other chemical processes. In the overwhelming
majority of cases, motion is given off on combination and must be supplied on
decomposition. Here, too, as a rule, repulsion is the active side of the process more
endowed with motion or requiring the addition of motion, while attraction is the
passive side producing a surplus of motion and giving off motion. On this account, the
modern theory also declares that, on the whole, energy is set free on the combination
of elements and is bound up on decomposition. And Helmholtz declares:
"This force (chemical affinity) can be conceived as a force of attraction.... This
force of attraction between the atoms of carbon and oxygen performs work quite as much
as that exerted on a raised weight by the earth in the form of gravitation.... When
carbon and oxygen atoms rush at one another and combine to form carbonic acid, the
newly-formed particles of carbonic acid must be in very violent molecular motion, i.e.
in heat motion.... When after they have given up their heat to the environment, we
still have in the carbonic acid all the carbon, all the oxygen, and in addition the
affinity of both continuing to exist just as powerfully as before. But this affinity
now expresses itself solely in the fact that the atoms of carbon and oxygen stick fast
to one another, and do not allow of their being separated" (Helmholtz, loc. cit., p.
169).
It is just as before: Helmholtz insists that in chemistry as in mechanics force
consists only in attraction, and therefore is the exact opposite of what other
physicists call energy and which is identical with repulsion.
Hence we have now no longer the two simple basic forms of attraction and repulsion,
but a whole series of sub-forms in which the winding up and running down process of
universal motion goes on in opposition to both attraction and repulsion. It is,
however, by no means merely in our mind that these manifold forms of appearance are
comprehended under the single expression of motion. On the contrary, they themselves
prove in action that they are forms of one and the same motion by passing into one
another under given conditions. Mechanical motion of masses passes into heat, into
electricity, into magnetism; heat and electricity pass into chemical decomposition;
chemical combination in turn develops heat and electricity and, by means of the
latter, magnetism; and finally, heat and electricity produce once more mechanical
movement of masses. Moreover, these changes take place in such a way that a given
quantity of motion of one form always has corresponding to it an exactly fixed
quantity of another form. Further, it is a matter of indifference which form of motion
provides the unit by which the amount of motion is measured, whether it serves for
measuring mass motion, heat, so-called electromotive force, or the motion undergoing
transformation in chemical processes.
We base ourselves here on the theory of the "conservation of energy" established by J.
R. Mayer [1] in 1842 and afterwards worked out internationally with such brilliant
success, and we have now to investigate the fundamental concepts nowadays made use of
by this theory. These are the concepts of "force," "energy," and " work."
It has been shown above that according to the modern view, now fairly generally
accepted, energy is the term used for repulsion, while Helmholtz generally uses the
word force to express attraction. One could regard this as a mere distinction of form,
inasmuch as attraction and repulsion compensate each other in the universe, and
accordingly it would appear a matter of indifference which side of the relation is
taken as positive and which as negative, just as it is of no importance in itself
whether the positive abscissae are counted to the right or the left of a point in a
given line. Nevertheless, this is not absolutely so.
For we are concerned here, first of all, not with the universe, but with phenomena
occurring on the earth and conditioned by the exact position of the earth in the solar
system, and of the solar system in the universe. At every moment, however, our solar
system gives out enormous quantities of motion into space, and motion of a very
definite quality, viz. the sun's heat, i.e. repulsion. But our earth itself allows of
the existence of life on it only owing to the sun's heat, and it in turn finally
radiates into space the sun's heat received, after it has converted a portion of this
heat into other forms of motion. Consequently, in the solar system and above all on
the earth, attraction already considerably preponderates over repulsion. Without the
repulsive motion radiated to us from the sun, all motion on the earth would cease. If
to-morrow the sun were to become cold, the attraction on the earth would still, other
circumstances remaining the same, be what it is to-day. As before, a stone of 100
kilogrammes, wherever situated, would weigh 100 kilogrammes. But the motion, both of
masses and of molecules and atoms, would come to what we would regard as an absolute
standstill. Therefore it is clear that for processes occurring on the earth to-day it
is by no means a matter of indifference whether attraction or repulsion is conceived
as the active side of motion, hence as "force" or "energy." On the contrary, on the
earth to-day attraction has already become altogether passive owing to its decisive
preponderance over repulsion; we owe all active motion to the supply of repulsion from
the sun. Therefore, the modern school * even if it remains unclear about the nature of
the relation constituting motion * nevertheless, in point of fact and for terrestrial
processes, indeed for the whole solar system, is absolutely right in conceiving energy
as repulsion.
The expression "energy" by no means correctly expresses all the relationships of
motion, for it comprehends only one aspect, the action but not the reaction. It still
makes it appear as if "energy" was something external to matter, something implanted
in it. But in all circumstances it is to be preferred to the expression " force."
As conceded on all hands (from Hegel to Helmholtz), the notion of force is derived
from the activity of the human organism within its environment. We speak of muscular
force, of the lifting force of the arm, of the leaping power of the legs, of the
digestive force of the stomach and intestinal canal, of the sensory force of the
nerves, of the secretory force of the glands, etc. In other words, in order to save
having to give the real cause of a change brought about by a function of our organism,
we fabricate a fictitious cause, a so-called force corresponding to the change. Then
we carry this convenient method over to the external world also, and so invent as many
forces as there are diverse phenomena.
In Hegel's time natural science (with the exception perhaps of heavenly and
terrestrial mechanics) was still in this naive state, and Hegel quite correctly
attacks the prevailing way of denoting forces (passage to be quoted).[2] Similarly in
another passage:
"It is better (to say) that a magnet has a Soul (as Thales expresses it) than that it
has an attracting force; force is a kind of property which is separable from matter
and put forward as a predicate * while soul, on the other hand, is its movement,
identical with the nature of matter." (Geschichte der Philosophie [History of
Philosophy], I, p. 208.)
To-day we no longer make it so easy for ourselves in regard to forces. Let us listen
to Helmholtz:
"If we are fully acquainted with a natural law, we must also demand that it should
operate without exception.... Thus the law confronts us as an objective power, and
accordingly we term it a force. For instance, we objectivise the law of the refraction
of light as a refractive power of transparent substances, the law of chemical
affinities as a force of affinity of the various substances for one another. Thus we
speak of the electrical force of contact of metals, of the force of adhesion,
capillary force, and so on. These names objectivise laws which in the first place
embrace only a limited series of natural processes, the conditions for which are still
rather complicated.... Force is only the objectivised law of action.... The abstract
idea of force introduced by us only makes the addition that we have not arbitrarily
invented this law but that it is a compulsory law of phenomena. Hence our demand to
understand the phenomena of nature, i.e. to find out their laws, takes on another form
of expression, viz. that we have to seek out the forces which are the causes of the
phenomena." (Loc. chit., pp. 189 * 191. Innsbruck lecture of 1869.)
Firstly, it is certainly a peculiar manner of "objectivising" if the purely subjective
notion of force is introduced into a natural law that has already been established as
independent of our subjectivity and therefore completely objective. At most an
Old-Hegelian of the strictest type might permit himself such a thing, but not a
Neo-Kantian like Helmholtz. Neither the law, when once established, nor its
objectivity, nor that of its action, acquires the slightest new objectivity by our
interpolating a force into it; what is added is our subjective assertion that it acts
in virtue of some so far entirely unknown force. The secret meaning, however, of this
interpolating is seen as soon as Helmholtz gives us examples: refraction of light,
chemical affinity, contact electricity, adhesion, capillarity, and confers on the laws
that govern these phenomena the "objective" honorary rank of forces. "These names
objectivise laws which in the first place embrace only a limited series of natural
processes, the conditions for which are still rather complicated." And it is just here
that the "objectivising," which is rather subjectivising, gets its meaning; not
because we have become fully acquainted with the law, hut just because this is not the
case. Just because we are not yet clear about the "rather complicated conditions" of
these phenomena, we often resort here to the word force. We express thereby not our
scientific knowledge, but our lack of scientific knowledge of the nature of the law
and its mode of action. In this sense, as a short expression for a causal connection
that has not yet been explained, as a makeshift expression, it may pass for current
usage. Anything more than that is bad. With just as much right as Helmholtz explains
physical phenomena from so-called refractive force, electrical force of contact, etc.,
the medieval scholastics explained temperature changes by means of a vis calorifica
and a vis frigifaciens and thus saved themselves all further investigation of heat
phenomena.
And even in this sense it is one-sided, for it expresses everything in a one-sided
manner. All natural processes are two-sided, they rest on the relation of at least two
effective parts, action and reaction. The notion of force, however, owing to its
origin from the action of the human organism on the external world, and further
because of terrestrial mechanics, implies that only one part is active, effective, the
other part being passive, receptive; hence it lays down a not yet demonstrable
extension of the difference between the sexes to non-living objects. The reaction of
the second part, on which the force works, appears at most as a passive reaction, as a
resistance. This mode of conception is permissible in a number of fields even outside
pure mechanics, namely where it is a matter of the simple transference of motion and
its quantitative calculation. But already in the more complicated physical processes
it is no longer adequate, as Helmholtz's own examples prove. The refractive force lies
just as much in the light itself as in the transparent bodies. In the case of adhesion
and capillarity, it is certain that the "force " is just as much situated in the
surface of the solid as in the liquid. In contact electricity, at any rate, it is
certain that both metals contribute to it, and " chemical affinity " also is situated,
if anywhere, in both the parts entering into combination. But a force which consists
of separated forces, an action which does not evoke its reaction, but which exists
solely by itself, is no force in the sense of terrestrial mechanics, the only science
in which one really knows what is meant by a force. For the basic conditions of
terrestrial mechanics are, firstly, refusal to investigate the causes of the impulse,
i.e. the nature of the particular force, and, secondly, the view of the one-sidedness
of the force, it being everywhere opposed by au identical gravitational force, such
that in comparison with any terrestrial distance of fall the earth's radius =
(infinity).
But let us see further how Helmholtz, " objectivises " his " forces " into natural
laws.
In a lecture of 1854 (loc. cit.., p. 119) he examines the "store of working force "
originally contained in the nebular sphere from which our solar system was formed. "
In point of fact it received an enormously large legacy in this respect, if only in
the form of the general force of attraction of all its parts for one another." This
indubitably is so. But it is equally indubitable that the whole of this legacy of
gravitation is present undiminished in the solar system to-day, apart perhaps from the
minute quantity that was lost together with the matter ' We should now call this
potential energy. which was flung out, possibly irrevocably, into space. Further, "The
chemical forces too must have been already present and ready to act; but as these
forces could become effective only on intimate contact of the various kinds of masses,
condensation had to take place before they came into play." If, as Hclmholtz does
above, we regard these chemical forces as forces of affinity, hence as attraction,
then again we are bound to say that the sum-total of these chemical forces of
attraction still exists undiminished within the solar system.
But on the same page Helmholtz gives us the results of his calculations "that perhaps
only the 454th part of the original mechanical force exists as such "* that is to say,
in the solar system. How is one to make sense of that? The force of attraction,
general as well as chemical, is still present unimpaired in the solar system.
Helmholtz does not mention any other certain source of force. In any case, according
to Helmholtz, these forces have performed tremendous work. But they have neither
increased nor diminished on that account. As it is with the clock weight mentioned
above, so it is with every molecule in the solar system and with the solar system
itself. "Its gravitation is neither lost nor diminished." What happens to carbon and
oxygen as previously mentioned holds good for all chemical elements: the total given
quantity of each one remains, and "the total force of affinity continues to exist just
as powerfully as before." What have we lost then? And what "force" has performed the
tremendous work which is 453 times as big as that which, according to his calculation,
the solar system is still able to perform? Up to this point Helmholtz has given no
answer. But further on he says:
" Whether a further reserve of force in the shape of heat was present, we do not
know." * But, if we may be allowed to mention it, heat is a repulsive "force," it acts
therefore against the direction of both gravitation and chemical attraction, being
minus if these are put as plus. Hence if, according to Helmholtz, the original store
of force is composed of general and chemical attraction, an extra reserve of heat
would have to be, not added to that reserve of force, but subtracted from it.
Otherwise the sun's heat would have had to strengthen the force of attraction of the
earth when it causes water to evaporate in direct opposition to this attraction, and
the water vapour to rise; or the heat of an incandescent iron tube through which steam
is passed would strengthen the chemical attraction of oxygen and water, whereas it
puts it out of action. Or, to make the same thing clear in another form: let us assume
that the nebular sphere with radius r, and therefore with volume 4/3(pi)r³ has a
temperature t. Let us further assume a second nebular sphere of equal mass having at
the higher temperature T the larger radius R and volume 4/3(pi)R³. Now it is obvious
that in the second nebular sphere the attraction, mechanical as well as physical and
chemical, can act with the same force as in the first only when it has shrunk from
radius R to radius r, i.e. when it has radiated into world space heat corresponding to
the temperature difference T * t. A hotter nebular sphere will therefore condense
later than a colder one; consequently the heat, considered from Helmholtz's standpoint
as an obstacle to condensation, is no plus but a minus of the " reserve of force."
Helmholtz, by pre-supposing the possibility of a quantum of repulsive motion in the
form of heat becoming added to the attractive forms of motion and increasing the total
of these latter, commits a definite error of calculation.
Let us now bring the whole of this " reserve of force," possible as well as
demonstrable, under the same mathematical sign so that an addition is possible. Since
for the time being we cannot reverse the heat and replace its repulsion by the
equivalent attraction, we shall have to perform this reversal with the two forms of
attraction. Then, instead of the general force of attraction, instead of the chemical
affinity, and instead of the heat, which moreover possibly already exists as such at
the outset, we have simply to put * the sum of the repulsive motion or so-called
energy present in the gaseous sphere at the moment when it becomes independent. And by
so doing Helmholtz's calculation will also hold, in which he wants to calculate "the
heating that must arise from the assumed initial condensation of the heavenly bodies
of our system from nebulously scattered matter." By thus reducing the whole " reserve
of force " to heat, repulsion, he also makes it possible to add on the assumed "heat
reserve force." The calculation then asserts that 453/454 of all the energy, i.e.
repulsion, originally present in the gaseous sphere has been radiated into space in
the form of heat, or, to put it accurately, that the sum of all attraction in the
present solar system is to the sum of all repulsion, still present in the same, as
453: 1. But then it directly contradicts the text of the lecture to which it is added
as proof.
If then the notion of force, even in the case of a physicist like Helmholtz, gives
rise to such confusion of ideas, this is the best proof that it is in general not
susceptible of scientific use in all branches of investigation which go beyond the
calculations of mechanics. In mechanics the causes of motion are taken as given and
their origin is disregarded, only their effects being taken into account. Hence if a
cause of motion is termed a force, this does no damage to mechanics as such; but it
becomes the custom to transfer this term also to physics, chemistry, and biology, and
then confusion is inevitable. We have already seen this and shall frequently see it
again.
For the concept of work, see the next chapter.
NOTES
1. Helmholtz, in his Pop. Vorlesungen [Popular Lectures], II, p. 113, appears to
ascribe a certain share in the natural scientific proof of Descartes' principle of the
quantitative immutability of motion to himself as well as to Mayer, Joule, and
Colding. "I myself, without knowing anything of Mayer and Codling, and only becoming
acquainted with Joule's experiments at the end of my work, proceeded along the same
path; I occupied myself especially with searching out all the relations between the
various processes of nature that could be deduced from the given mode of
consideration, and I published my investigations in 1847 in a little work entitled
Uber die Erhaltung der Kraft [On the Conservation of Force]." * But in this work there
is to be found nothing new for the position in 1847 beyond the above-mentioned,
mathematically very valuable, development that "conservation of force" and central
action of the forces active between the various bodies of a system are only two
different expressions for the same thing, and further a more accurate formulation of
the law that the sum of the live and tensional forces in a given mechanical system is
constant. In every other respect, it was already superseded since Mayer's second paper
of 1845. Already in 1842 Mayer maintained the "indestructibility of force," and from
his new standpoint in 1845 he had much more brilliant things to say about the
"relations between the various processes of nature " than Helmholtz had in 1847.
2. See Appendix II, p. 881.
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