Transcript Early Modern Theories of the Tides

Early Modern Theories of the
Tides
Nathan D. Smith
HCC Faculty Conference, 2012
Early Modern Philosophy and Science
• John Kepler, Francis Bacon, Galileo Galilei, and
Isaac Newton
– The Scientific Revolution
– The New Science
– Founders of Modern Science
Pre-modern  Modern
What happens at the ‘’?
Science in Fits and Starts
• Thomas Kuhn (1922-1996): scientific progress is
characterized by asymmetrical, non-linear shifts in
conceptual paradigms.
– Scientific truth is contextual: it refers to the background
assumptions and dominant theories of the time.
– The background theories and assumptions form a “paradigm”
that defines what is “normal” for science during a period.
– New discoveries in science will appear as “abnormal.” The new
paradigm will be a-scientific.
– On the boarders of two paradigms, you will find theories that do
not fit neatly into one or the other.
– It is a mistake to read our contemporary understanding “back
into” the scientists of the past.
– Scientific progress is non-linear, uneven, and unpredictable.
Resist the Cartoon Image
Isaac Newton and the
apple tree:
• Great Thinker is
pondering serious
matters.
• Something happens.
• Great Thinker has a
great thought.
• Voilá! Now Great
Thinker is just like us.
What does this mean for a theory of
tides?
• As anyone knows, high and low tides are caused by the
gravitational force of the moon (and sun) on oceans.
• Additionally, as anyone knows, Isaac Newton was the first
to provide a theory of universal gravitation.
• You may also know that Newton’s Principia Mathematica
(1697) contains a lengthy discussion of the nature of tides,
applying his theory of universal gravitation to explain tidal
flows as a result of the moon’s gravitational force.
• But if you know all of that, it would be easy to credit
Newton with a thoroughly modern theory of the tides.
• My goal today is to make trouble for that hasty conclusion.
THEORETICAL FRAMES, ANCIENT
AND MODERN
The Old Science
• Aristotelianism
– The dominant philosophy of the ancient and medieval world.
– Every natural being has a nature and purpose entirely determined
from within.
• The functional unity of every natural entity is determined by its substantial
form.
• Substantial forms were commonly identified with souls in living beings.
• For instance, all terrestrial bodies contain a quality inherent in them called
“gravity.” This is the reason why they tend to return to earth. By contrast,
heavenly bodies are made of an entirely different substance that causes them
to move in perfect (or nearly perfect) circular orbits around the earth.
• Atomism
– Several ancient philosophers (Democritus, Epicurus, et al.) believed
that the natural world is basically composed of atoms and the void.
– This view holds that particular atoms (indivisible material particles)
have inherent properties of shape and size that determine the way
they interact with other particles and give rise to all perceived
phenomena.
Astrology, Alchemy, and Magic
• Several ancient beliefs contributed to a prevalence of astrology, alchemy,
and magic even among serious philosophers and scientists in the late
medieval and renaissance periods (12th-16th centuries):
– Neoplatonic theories of knowledge: all of nature is one (God, nature,
existence) and our understanding of it facilitated by the fact that our intellect
participates in this divine nature.
– Empedocles (and Aristotle) held that all of nature was composed of four (or
five) basic elements: earth, air, fire, and water (with aether as a celestial
element).
– The stars and planets were thought to be gods, with perfect, unchanging
natures.
– There were many common, natural phenomena that were very difficult to
explain: magnetism, electricity, fermentation, spontaneous combustion, and
many issues related to health and medicine. The lack of an explanation of
these phenomena lead many serious philosophers to suppose that there were
hidden forces in nature.
• Together these beliefs supported the ideas that were labeled as occult at
the beginning of modern philosophy and science. (Raymond Llull,
Paracelsus, Agrippa, Alchemy)
The New Science
• Mathematical representation:
– Geometry, in particular, was taken to be the standard of scientific
certainty in the early modern period.
– A problem was taken to be solved if it could be demonstrated
geometrically. (This is why Newton’s Principia Mathematica, for
instance, has the structure of axioms, propositions, theorems, scholia,
etc.).
• Mechanical explanation:
– Instead of substantial forms or occult forces, almost all philosophers
and scientists of the early modern period insisted that natural events
had to be explained by underlying mechanisms.
– Kinematics vs. dynamics: the 17th century sees an important
development in what we think of as classical mechanics. This is the
move from kinematics—the study and explanation of the motion
alone—to dynamics—the study of motion as the result of forces.
Kepler and Galileo remain strictly kinematic in their physics, while
Newtonian mechanics are dynamic.
KEPLER’S THEORY OF THE TIDES
Tides are the Result of the Attractive
Force of the Moon
• Kepler advances a theory of tides very briefly in the introduction to
his New Astronomy (1609)
• There, he suggests that the tides are the result of the attractive
force of the moon.
• This has lead some to suggest that Kepler’s foray into the tides was
more insightful than Galileo’s or Desartes’ (Cunningham, 9).
• But we should not be too hasty in making this conclusion:
– Kepler’s “attractive force” is described as a kind of magnetism.
– Kepler imagines an opposing force that resists the magnetic
compulsion of planets to unit, calling this “an animate force or
something equivalent to it.”
– Both of these forces invoke “occult” qualities without the theoretical
framework of dynamics to explain them. Thus, Kepler’s explanation is
not an explanation at all.
Gravity is a Kind of Magnetism
In the Introduction to the New Astronomy, Kepler writes,
“The true theory of gravity rests upon the following axioms.
(1) Every corporeal substance, to the extent that it is corporeal has been so made as
to be suited to rest in every place in which it is put by itself, outside the sphere
of influence of a kindred body.
(2) Gravity is a mutual corporeal disposition among kindred bodies to unite or join
together; thus, the earth attracts a stone much more than the stone seeks the
earth. (The magnetic faculty is another example of this sort)… [3]
If the moon and the earth were not each held back in its own circuit by an animate
force or something else equivalent to it, the earth would ascend toward the
moon by one fifty-fourth part of the interval [since the moon was taken to be
1/54 the size of the earth], and there they would be joined together; provided,
that is, that the substance of each is of the same density.
If the earth should cease to attract its waters to itself, all the seawater would be lifted
up, and would flow onto the body of the moon.
The sphere of influence of the attractive power in the moon is extended all the way to
the earth, and in the torrid zone calls the waters forth, particularly when it
comes to be overhead in one or another of its passages. This is imperceptible in
enclosed seas, but noticeable where the beds of the ocean are widest and there
is much free space for the waters’ reciprocation. (55-6)
GALILEO’S THEORY OF THE TIDES
Tides as Proof of Copernicanism
Galileo’s theory disregards the effects of the
moon. His explanation is based on the nonuniform acceleration of water particles on
the surface of the earth. In that figure on the
left, E is the sun, A the earth’s axis of
rotation, and the circle AFGI, its orbit around
the sun. The idea is that for any water
particle, P, on the surface of the earth, the
circular acceleration due to the earth’s
rotation, when added to the orbital
acceleration, results in a greater acceleration
at B and a lesser acceleration at D.
“So far, then, we can see that any body of water
(be it a sea, a lake, or a pond) has a
continuous but nonuniform motion, since it is
retardated during some hours of the day and
much accelerated during others; we also
have the principles and the cause why the
water contained in it, being fluid and not
firmly attached to the container, flows and
moves now in this and now in the opposite
direction. And we can invoke this as the
primary cause of the effect, without which it
would not occur at all.” (quoted in Palmeri,
231-2)
Can Galileo Explain the Diurnal Cycle
of the Tides?
•
•
•
At first, it may seem that Galileo cannot account for the presence of a high tide
twice a day. In fact, the slightly extra acceleration at B and deceleration at D would
suggest one high and one low tide per day.
However, Galileo recognized that in an enclosed container an oscillating effect on
water could result in doubling the presence of high and low tides.
To explain the obvious six hour period of tides in the Mediterranean Galileo
appeals to “secondary causes” in addition to the primary acceleration and
deceleration noted above:
The secondary cause must be introduced for it; that is the greater or lesser the length of the vessel and the
greater or lesser the depth of the water … These causes, although they do not operate to move the
water … are nevertheless the principal factors in limiting the duration of the reciprocants. (Quoted in
Palmieri, 269)
•
•
Palmieri (1998) has shown that diurnal periods can be reproduced because
oscillation effects in the water produce waves that compound the ebb and flow of
the water on shore.
Galileo likely came to this realization by performing experiments with buckets of
water. Palmieri (1998) has reproduced some of those experiments.
NEWTON’S THEORY OF THE TIDES
Newton’s Laws
• Newton’s three laws:
1. Inertia: an object in motion stays in motion, an
object at rest stays at rest.
2. Force F = ma
3. For every action there is an equal and opposite
reaction.
• Universal gravitation: the force of acceleration
due to gravity between two objects is inversely
proportional to the square of the distance
between them and directly proportional to the
product of the two masses.
Gravity is “Action at a Distance”
• Newton would be repeatedly accused of invoking the occult,
especially by Cartesians up through the 18th century.
• He spent a great deal of intellectual energy combating this notion.
• “Hypotheses non fingo”:
I have not as yet been able to deduce from phenomena the reason for
these properties of gravity, and I do not feign hypotheses. For whatever
is not deduced from the phenomena must be called a hypothesis; and
hypotheses, whether metaphysical or physical, or based on occult
qualities, or mechanical, have no place in experimental philosophy. In
this experimental philosophy, propositions are deduced from the
phenomena and are made general by induction. The impenetrability,
mobility, and impetus of bodies, and the laws of motion and law of
gravity have been found by this method. And it is enough that gravity
should really exist and should act according to the laws that we have
set forth and should suffice for all the motions of the heavenly bodies
and of our sea. (Newton 943)
Newton’s Explanation of Tides
•
This is a depiction of the earth. L is
taken to be the Moon. AQE is the
equator. And the area between fF and
Dd is taken to a be a channel of deep
waters.
Newton was aware that most coasts on earth
experience two tidal floods (high tide) and
two tidal depressions (low tide) a day. He
was also aware that these generally
happened an interval of 6 hours after the
passing of the moon.
The force of the sun or moon in raising the sea is
greatest in the appulse of the luminary to the
meridian of the place; but the force
impressed upon the sea at that time
continues a little while after the impression,
and is afterwards increased by a new though
less force still acting upon it. This makes the
sea rise higher and higher, till this new force
becoming too weak to raise it any more, the
sea rises to its greatest height. And this will
come to pass, perhaps, in one or two hours,
but more frequently near the shores in about
three hours, or even more, where the sea is
shallow. (Newton 415)
Diurnal Cycle
•
•
•
•
•
How does Newton explain two high tides a
day with only one moon?
First, Newton predicted a slight perturbation
in the orbit of the earth because the center
of gravity for the earth-moon system is not
the same as the center of gravity for the
earth, resulting in a slight “wobble” around
the earth’s axis. (This would results in a slight
variation of the centrifugal force of matter on
the surface of the earth.)
Second, Newton realized that the effect of
the moon’s gravity on water facing the moon
would be greater than its effect on water
away from the earth.
So, when the total gravitational effects are
combined, the earth effectively “pulls away”
from the water on the side of the earth
facing away from the moon.
Semidiurnal and daily tides are explained by
the combined effects of two different tidal
floods so that sometimes they interfere with
each other to create two high tides and
sometimes they “balance one another,”
reducing the effect to one high tide and one
low tide.
Spring Tides and Neap Tides
•
Newton realized that both the sun and the
moon have an effect on the tides.
Therefore the greatest tides fall out in those
syzygies, and the least in those quadratures,
which happen about the time of both
equinoxes: and the greatest tide in the
syzygies is always succeeeded by the least
tide in the quadratures, as we find by
experience. (Newton 416)
•
He expected the spring tide to occur at the
syzygy (when the moon, sun, and earth are
aligned) and the neap tide to occur in the
quadrature (when the moon is perpendicular
to the gravitational effect of the sun). This is
not quite right, however. The spring and
neap tides actually follow these locations
slightly. Again, Newton is unable to explain
this delay.
Newton’s Apparent Mathematical
Precision
• One of the aims of the Principia was to establish Newtonian physics (and
the three laws of motion) on the most solid, scientific basis.
• In so doing, Newton effectively established a new standard and theoretical
frame for science: mathematical precision in natural scientific.
• However, Westfall (1973) carefully catalogues three instances in the
Principia where Newton masks discrepancies in his data to reinforce
theoretical projections. These examples include the centripetal
acceleration of the moon toward the earth, the velocity of sound, and
axial precession (precession of the equinox).
…[W]as the compelling demonstration a cloud of exquisitely powdered fudge
factor blown in the eyes of his scientific opponents? I have chose the three
examples because all of them underwent significant modifications in the
second edition of the Principia… The second edition … introduced major
changes … that signally increased the level of apparent precision by the mere
numerical manipulation of the same basic body of data. (753)
Later, Westfall is less charitable, calling Newton’s presentation “nothing short of
deliberate fraud” (753). He also quotes Newton’s editor, Roger Cotes, “If you
can mend the numbers … so as to make ye precession of the Equinox about
50” or 51”, it is sufficient” (757)
Laplace’s Dynamical Solution to Tides
•
•
The truly modern explanation of tides belongs primarily to Pierre Simon, Marquis
de Laplace (1749-1827)
Laplace provides a dynamic model of tides based on the interaction of a number
of forces:
– Gravitational force of the moon and sun.
– Rotational friction from the earth.
– Wave propagation from surrounding water
•
•
•
This dynamic model suggests (correctly) that the primary forces resulting in
changes in the tides are not perpendicular to the surface of the earth (a result of
acceleration toward the moon and sun), but horizontal to the surface of the earth
(a result of compounding forces).
Today, tides are recognized to be extremely complex mechanical processes. The
interaction of various forces (especially the contours of the ocean floor) introduce
so many variables, that supercomputers were required before accurate
calculations could be made.
By attributing success to Newton in terms of explaining the nature of the tides, we
deny the great mathematical and scientific achievement of Laplace (and others) in
the 18th century as well as the incredible complexity of our modern understanding
of tidal phenomena.
Conclusions
• Early Modern theories of the tides reveal the messy and drawn out
progression of science. On the one hand, Kepler is exceedingly close
to a true, Newtonian theory of the tides. On the other hand, even
Newton fails in some key respects to attain a complete theory of
the tides.
– Kepler continues to invoke occult theories to explain the attractive
force of the moon and the countervailing force that keeps celestial
objects in motion.
– Galileo’s purely kinematic explanation hits upon the importance of the
wave-like oscillation of water in the production of various tides.
– Newton’s theory is incomplete. It assumes that water moves directly
outward toward the moon as a result of the moon’s gravitational
force. But this can’t explain the delay between the passing of the
moon and the appearance of high tide. It also suggests that tides are
“lifted” from the sea floor, when in fact tidal forces result in a myriad
of swirling motions, but primarily a horizontal thrust toward the shore.
References
Cartwright, D. E. 1999. Tides: A Scientific History. Cambridge
University Press.
Cunningham, C. J. 2007. Galileo Versus Kepler: Two Minds on
Tides. Mercury 36 (1), 9.
Griffin, A. 2008. Tides, as Explained by Newton. Phys. Ed. 43,
129-31.
Newton, I. 1846. Principia. New York.
Palmeri, P. 1998. Re-examining Galileo’s Theory of Tides.
Communicated by C. Wilson. Arch. Hist. Exact Sci. 53 (1998)
223-375.
Westfall, R. S. 1973. Newton and the Fudge-Factor. Science
179, 751-8.