Dictionary of the History of Ideas Studies of Selected Pivotal Ideas |

2 |

3 |

9 |

2 | VI. |

V. |

VI. |

3 | I. |

VI. |

2 | V. |

2 | III. |

3 | III. |

2 | VI. |

1 | VI. |

6 | V. |

3 | V. |

1 | III. |

2 | VII. |

VI. |

1 | VI. |

1 | III. |

III. |

8 | II. |

3 | I. |

2 | I. |

1 | I. |

2 | V. |

1 | VII. |

2 | VI. |

4 | V. |

9 | III. |

4 | III. |

5 | III. |

16 | II. |

2 | I. |

9 | I. |

1 | I. |

1 | VI. |

VII. |

2 | III. |

1 | VII. |

3 | VII. |

2 | VII. |

2 | V. |

VI. |

1 | VI. |

1 | VI. |

2 | VI. |

2 | VI. |

1 | VII. |

III. |

IV. |

10 | VI. |

VI. |

1 | VI. |

1 | V. |

3 | V. |

4 | V. |

10 | III. |

6 | III. |

2 | VII. |

4 | III. |

I. |

7 | V. |

2 | V. |

2 | VII. |

1 | VI. |

5 | I. |

4 | I. |

7 | I. |

8 | I. |

1 | VI. |

12 | III. |

4 | IV. |

4 | III. |

2 | IV. |

1 | IV. |

1 | IV. |

VI. |

1 | VI. |

3 | VI. |

1 | V. |

2 | III. |

1 | VI. |

Dictionary of the History of Ideas | ||

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*II. DISCREPANCIES IN THE*

NEWTONIAN UNIVERSE

NEWTONIAN UNIVERSE

But even while this neat, orderly scheme of the

universe was being eagerly
incorporated into Victorian

philosophical and social concepts, its very
basis was

data, and by logical analysis in four different realms

of physics and astronomy: in the realm of optics, the

experiments of Michelson and Morley on the speed of

light were to destroy the Newtonian concepts of abso-

lute space and time and to replace them by the Ein-

steinian space-time concept (the special theory of rela-

tivity); in the realm of radiation, the discoveries of the

properties of the radiation emitted by hot bodies were

to upset the Maxwell wave-theory of light and to

introduce the quantum theory (the photon) with its

wave-particle dualism; in the realm of observational

astronomy, the discrepancy between the deductions

from Newtonian gravitational theory and the observed

motion of Mercury (the advance of its perihelion)

indicated the need for a new gravitational theory

which Einstein produced in 1914 (the general theory

of relativity); finally, in the realm of cosmology, var-

ious theoretical analyses showed that the nine-

teenth-century models of the universe, constructed

with Newtonian gravitational theory and space-time

concepts, were in serious contradiction with stellar

observations.

Although the investigation of each of these depar-

tures from classical physics is of extreme importance

and each
one has an important bearing on the most

recent cosmological theories, we
limit ourselves here

to the cosmological realm and, where necessary in
our

discussion, use the results of modern physics without

concern
about how they were obtained. However,

before we discuss the difficulties
inherent in Newtonian

cosmology, we must consider one other important

nineteenth-century discovery which, at the time,

seemed to have no bearing
on the structure of the

universe but which ultimately played a most
important

role in the development of cosmology. This was the

discovery
of the non-Euclidean geometries by Gauss,

Bolyai, Lobachevsky, Riemann, and
Klein. At the time

that these non-Euclidean geometries were
discovered,

and for many years following, scientists in general

considered them to be no more than mathematical

curiosities, with no
relevance to the structure of the

universe or to the nature of actual
space. Most mathe-

maticians and
scientists simply took it for granted

that the geometry of physical space
is Euclidean and

that the laws of physics must conform to Euclidean

geometry.

This attitude, however, was not universal and Gauss

himself, the spiritual
father of non-Euclidean geometry,

proposed a possible (but in practice,
unrealizable) test

of the flatness of space by measuring the interior
angles

of a large spatial triangle constructed in the neigh-

borhood of the earth. Also, the
mathematician W. K.

Clifford, in *The Common Sense of the
Exact Sciences*

(1870; reprint, New York, 1946), speculated that the

geometry of actual space might not be Euclidean. He

proposed
the following ideas: (1) that small portions

of space are, in fact, of a
nature analogous to little

hills on a surface which is, on the average,
flat—

namely, that the ordinary laws of geometry are not

valid in them; (2) that this property of being curved

or distorted is
continually being passed on from one

portion of space to another after the
manner of a wave;

(3) that this variation of the curvature of space is
what

really happens in that phenomenon which we call

motion of matter,
whether ponderable or ethereal; (4)

that in the physical world nothing else
takes place but

this variation, subject (possibly) to the laws of con-

tinuity.

Clifford summarized his opinion as follows:

The hypothesis that space is not homaloidal and, again, that

its
geometrical character may change with time may or may

not be destined
to play a great part in the physics of the

future; yet we cannot refuse
to consider them as possible

explanations of physical phenomena because
they may be

opposed to the popular dogmatic belief in the
universality

of certain geometrical axioms—belief which has
arisen from

centuries of indiscriminating worship of the genius of

Euclid.

These were, indeed, prophetic words, for, as we shall

see, in the hands of
Einstein the non-Euclidean geome-

tries
became the very foundation of modern cosmo-

logical theory. But let us first examine the flaws and

difficulties inherent in the Newtonian cosmology of the

nineteenth century.

Dictionary of the History of Ideas | ||