FURTHER EXPLANATIONS CONCERNING THE DENSITY AND ENERGY OF THE ETHER
A reader may suppose that in speaking of the immense density or
massiveness of ether, and the absurdly small density or specific
gravity of gross matter by comparison, I intend to signify that matter
is a _rarefaction_ of the ether. That, however, is not my intention.
The view I advocate is that the ether is a perfect _continuum_, an
absolute _plenum_, and that therefore no rarefaction is possible. The
ether inside matter is just as dense as the ether outside, and no
denser. A material unit--say an electron--is only a peculiarity or
singularity of some kind in the ether itself, which is of perfectly
uniform density everywhere. What we "sense" as matter is an aggregate
or grouping of an enormous number of such units.
How then can we say that matter is millions of times rarer or less
substantial than the ether of which it is essentially composed? Those
who feel any difficulty here, should bethink themselves of what they
mean by the average or aggregate density of any discontinuous system,
such as a powder, or a gas, or a precipitate, or a snowstorm, or a
cloud, or a milky way.
If it be urged that it is unfair to compare an obviously discrete
assemblage like the stars, with an apparently continuous substance
like air or lead,--the answer is that it is entirely and accurately
fair; since air, and every other known form of matter, is essentially
an aggregate of particles, and since it is always their average
density that we mean. We do not even know for certain their individual
atomic density.
The phrase "specific gravity or density of a powder" is ambiguous. It
may mean the specific gravity of the dry powder as it lies, like snow;
or it may mean the specific gravity of the particles of which it is
composed, like ice.
So also with regard to the density of matter, we might mean the
density of the fundamental material of which its units are made--which
would be ether; or we might, and in practice do, mean the density of
the aggregate lump which we can see and handle; that is to say, of
water or iron or lead, as the case may be.
In saying that the density of matter is small,--I mean, of course, in
the last, the usual, sense. In saying that the density of ether is
great,--I mean that the actual stuff of which these highly porous
aggregates are composed is of immense, of wellnigh incredible,
density. It is only another way of saying that the ultimate units of
matter are few and far between--i.e. that they are excessively small
as compared with the distances between them; just as the planets of
the solar system, or worlds in the sky, are few and far between,--the
intervening distances being enormous as compared with the portions of
space actually occupied by lumps of matter.
It may be noted that it is not unreasonable to argue that the density
of a _continuum_ is necessarily greater than the density of any
disconnected aggregate: certainly of any assemblage whose particles
are actually composed of the material of the _continuum_. Because the
former is "all there," everywhere, without break or intermittence of
any kind; while the latter has gaps in it,--it is here, and there, but
not everywhere.
Indeed, this very argument was used long ago by that notable genius
Robert Hooke, and I quote a passage which Professor Poynting has
discovered in his collected posthumous works and kindly copied out for
me:--
"As for _matter_, that I conceive in its essence to be
immutable, and its essence being expatiation determinate, it
cannot be altered in its quantity, either by condensation or
rarefaction; that is, there cannot be more or less of that
power or reality, whatever it be, within the same expatiation
or content; but every equal expatiation contains, is filled, or
is an equal quantity of _materia_; and the densest or
heaviest, or most powerful body in the world contains no more
materia than that which we conceive to be the rarest, thinnest,
lightest, or least powerful body of all; as gold for instance,
and _æther_, or the substance that fills the cavity of an
exhausted vessel, or cavity of the glass of a barometer above
the quicksilver. Nay, as I shall afterwards prove, this cavity
is more full, or a more dense body of æther, in the common
sense or acceptation of the word, than gold is of gold, bulk
for bulk; and that because the one, viz. the mass of æther, is
all æther: but the mass of gold, which we conceive, is not all
gold; but there is an intermixture, and that vastly more than
is commonly supposed, of æther with it; so that vacuity, as it
is commonly thought, or erroneously supposed, is a more dense
body than the gold as gold. But if we consider the whole
content of the one with that of the other, within the same or
equal quantity of expatiation, then are they both equally
containing the _materia_ or body."--[_From the Posthumous Works
of Robert Hooke, M.D., F.R.S., 1705, pp. 171-2_ (_as copied in
Memoir of Dalton, by Angus Smith_).]
Newton's contemporaries did not excel in power of clear expression, as
he himself did; but Professor Poynting interprets this singular
attempt at utterance thus:--"All space is filled with equally dense
_materia_. Gold fills only a small fraction of the space assigned to
it, and yet has a big mass. How much greater must be the total mass
filling that space."
The tacit assumption here made is that the particles of the aggregate
are all composed of one and the same continuous substance,
--practically that matter is made of ether; and that assumption, in
Hooke's day, must have been only a speculation. But it is the kind of
speculation which time is justifying, it is the kind of truth which we
all feel to be in process of establishment now.[6]
We do not depend on that sort of argument, however; what we depend on
is experimental measure of the mass, and mathematical estimate of the
volume, of the electron. For calculation shows that however the mass
be accounted for--whether electrostatically or magnetically, or
hydrodynamically--the estimate of ratio of mass to effective volume
can differ only in a numerical coefficient, and cannot differ as
regards order of magnitude. The only way out of this conclusion would
be the discovery that the negative electron is not the real or the
main matter-unit, but is only a subsidiary ingredient; whereas the
main mass is the more bulky positive charge. That last hypothesis
however is at present too vague to be useful. Moreover, the mass of
such a charge would in that case be unexplained, and would need a
further step; which would probably land us in much the same sort of
etherial density as is involved in the estimate which I have based on
the more familiar and tractable negative electron. (See Appendix 2.)
It may be said why assume any finite density for the ether at all? Why
not assume that, as it is infinitely continuous, so it is infinitely
dense--whatever that may mean--and that all its properties are
infinite? This might be possible were it not for the velocity of
light. By transmitting waves at a finite and measurable speed, the
ether has given itself away, and has let in all the possibilities of
calculation and numerical statement. Its properties are thereby
exhibited as essentially finite--however infinite the whole extent of
it may turn out to be. Parenthetically we may remark that
"gravitation" has not yet exhibited any similar kind of finite
property; and that is why we know so little about it.
ETHERIAL ENERGY.
Instead then of saying that the density of the ether is great, the
clearest mode of expression is to say that the density of matter is
small. Just as we can say that the density of the visible cosmos is
small, although in individual lumps its density is comparable to that
of iron or rock.
At the risk of repetition, I have explained this over again, because
it is a matter on which confusion may easily arise. The really
important thing about ether is not so much its density, considered in
itself, as the energy which that density necessarily involves, on any
kinetic theory of its elasticity. For it is not impossible--however
hopeless it may seem now--that a modicum of that energy may some day
be partially utilised.
Lord Kelvin's incipient kinetic theory of elasticity is a complicated
matter, and I will only briefly enter upon it. But before doing so, I
want to remove an objection which is sometimes felt, as to the fluid
and easily permeable character of a medium of this great
density,--that is to say, as to the absence of friction or
viscosity--the absence of resistance to bodies moving through it. As a
matter of fact there is no necessary connexion whatever between
density and viscosity.
'Density' and 'Viscosity' are entirely different things; and, if there
is no fluid friction, a fluid may have any density you please without
interposing any obstacle to constant velocity. To _acceleration_ it
does indeed oppose an obstacle, but that appears as essentially a part
of the inertia or massiveness of the moving body. It contributes to
its momentum; and, if the fluid is everywhere present, it is
impossible to discriminate between, or to treat separately, that part
of the inertia which belongs to the fluid displaced, and that part
which belongs to the body moving through it,--except by theory.
As for the elasticity of the ether, that is ascertainable at once from
the speed at which it transmits waves. That speed--the velocity of
light--is accurately known, 3 × 10¹⁰ centimetres per second. And
the ratio of the elasticity or rigidity to the density is equal to the
square of this speed;--that is to say, the elasticity must be 9 ×
10²⁰ times the density; or, in other words, 10³³ C.G.S. units.
That is an immediate consequence of the estimate of density and the
fact of the velocity of light; and if the density is admitted, the
other cannot be contested.
But we must go on to ask, To what is this rigidity due? If the ether
does not consist of parts, and if it is fluid, how can it possess the
rigidity appropriate to a solid, so as to transmit transverse waves?
To answer this we must fall back upon Lord Kelvin's kinetic theory of
elasticity:--that it must be due to rotational motion--intimate
fine-grained motion throughout the whole etherial region--motion not
of the nature of locomotion, but circulation in closed curves,
returning upon itself,--vortex motion of a kind far more finely
grained than any waves of light or any atomic or even electronic
structure.
Now if the elasticity of any medium is to be thus explained
kinetically, it follows, as a necessary consequence, that the speed
of this internal motion must be comparable to the speed of wave
propagation;--that is to say that the internal squirming circulation,
to which every part of the ether is subject, must be carried on with a
velocity of the same order of magnitude as the velocity of light.
This is the theory then,--this theory of elasticity as dependent on
motion,--which, in combination with the estimate of density, makes the
internal energy of the ether so gigantic. For in every cubic
millimetre of space we have, according to this view, a mass equivalent
to what, if it were matter, we should call a thousand tons,
circulating internally, every part of it, with a velocity comparable
to the velocity of light, and therefore containing--stored away in
that small region of space--an amount of energy of the order 10²⁹
ergs, or, what is the same thing, 3 × 10¹¹ kilowatt centuries;
which is otherwise expressible as equal to the energy of a million
horse-power station working continuously for forty million years.
SUMMARISED BRIEF STATEMENTS CONCERNING THE ETHER
_(As communicated by the author to the British Association at
Leicester, 1907)._
1. The theory that an electric charge must possess the equivalent of
inertia was clearly established by J.J. Thomson in the _Philosophical
Magazine_ for April, 1881.
2. The discovery of masses smaller than atoms was made experimentally
by J.J. Thomson, and communicated to Section A at Dover in 1899.
3. The thesis that the corpuscles so discovered consisted wholly of
electric charges was sustained by many people, and was clinched by the
experiments of Kaufmann in 1902.
4. The concentration of the ionic charge, required to give the
observed corpuscular inertia, can be easily calculated; and
consequently the size of the electric nucleus, or electron, is known.
5. The old perception that a magnetic field is kinetic has been
developed by Kelvin, Heaviside, FitzGerald, Hicks, and Larmor, most of
whom have treated it as a flow along magnetic lines; though it may
also, perhaps equally well, be regarded as a flow perpendicular to
them and along the Poynting vector. The former doctrine is sustained
by Larmor, as in accordance with the principle of Least Action, and
with the absolutely stationary character of the ether as a whole; the
latter view appears to be more consistent with the theories of J.J.
Thomson.
6. A charge in motion is well known to be surrounded by a magnetic
field; and the energy of the motion can be expressed in terms of the
energy of this concomitant field,--which again must be accounted as
the kinetic energy of ethereous flow.
7. Putting these things together, and considering the ether as
essentially incompressible--on the strength of the Cavendish electric
experiment, the facts of gravitation, and the general idea of a
connecting continuous medium--the author reckons that to deal with the
ether dynamically it must be treated as having a density of the order
10¹² grammes per cubic centimetre. (See Appendix 2.)
8. The existence of transverse waves in the interior of a fluid can
only be explained on gyrostatic principles, i.e. by the kinetic or
rotational elasticity of Lord Kelvin. And the internal circulatory
speed of the intrinsic motion of such a fluid must be comparable with
the velocity with which such waves are transmitted.
9. Putting these things together, it follows that the intrinsic or
constitutional vortex energy of the ether must be of the order 10³³
ergs per cubic centimetre.
_Conclusion._--Thus every cubic millimetre of the universal ether of
space must possess the equivalent of a thousand tons, and every part
of it must be squirming internally with the velocity of light.
FOOTNOTE:
[6] It does not seem to have been noticed that in Query 22, quoted in
the Introduction to the present book, Newton seems to throw out a
curious hint in this same direction,--though he immediately abandons
it again. He does not appear to have carefully _edited_ his queries;
probably they were published posthumously.