Posted: 06.10.2014

Einstein had assumed that the total mass of the matter contained in the universe is finite, and therefore, in the model of the universe suggested by him, the universe was regarded as finite. In this model, the four-dimensional continuum was conceived to be identical with the surface of the sphere. Famous physicist Sir James Jeans has tried to explain the model of Einstein’s universe by the illustration of a soap-bubble. He writes: “A soap-bubble with irregularities and corrugations on its surface is perhaps the best representation, in terms of simple and familiar materials, of the new universe revealed to us by the theory of relativity. The universe is not the interior of the soap-bubble but its surface, and we must always remember that, while the surface of the soap- bubble has only two dimensions, the universe-bubble has four- three dimensions of space and one of time. And the substance out of which this bubble is blown, the soap-film, is empty space welded on to empty time.”^{[1]}

Other scientists have also tried to describe Einsteinian model of the universe in simple language. Sir A. S. Eddington has observed: “I suppose that everyone has at some time plagued his imagination with the question, `Is there an end to space?` If space comes to end what is beyond the end? On the other hand, the idea that there is no end, but space beyond space for ever, is inconceivable. And so the imagination is tossed to and fro in dilemma. Prior to the relativity theory, the orthodox view was that space is infinite. No one can conceive infinite space; we had to be content to admit in the physical world an inconceivable conception disquieting but not necessarily illogical. Einstein`s theory now offers a way out of the dilemma. Is space infinite or does it comes to an end? Neither. Space is finite but it has no end; `finite but unbounded` is the usual phrase.”^{[2]}

Another eminent scientist Werner Heisenberg expounds the concept of finite but endless universe thus: “It may be that the space filled by the universe is finite. This would not mean that there is an end of the universe at some place. It would only mean that by proceeding farther and farther in one direction in the universe, one would finally come back to the point from which one had started. The situation would be similar as in the two- dimensional geometry on the surface of the earth where we, when starting from a point in in an eastward direction, finally come back to this point from the west.”^{[3]}

Sir Edmund Whittaker explain the Einstein`s model thus: “The idea of a finite universe has ever been a great stumbling block. A distinguished writer- not a man of science-objected to it some time ago on the ground that, as he puts it, ‘the mental concept of a limit with nothing beyond it is self-contradictory’. Here he confused two totally different notions, that of being finite and that of having a boundary. The space of non-Euclidean geometry of positive curvature is finite, that is it contains only a definite number of cubic miles, but it has no boundary or frontiers-there is no place where it comes to an end, so as to have something that is not itself across the boundary. This obvious to a mathematician, but seems to be very difficult for everybody else.”^{[4]}

The model of Einsteinian universe may become more simplified in the words of some popular authors. For instance, Henshaw Ward remarks: “Strangely enough the mathematicians reckon that the total amount of matter which exists is limited, and that the total extent of the universe is finite. They do not conceive that there is a limit beyond which no space exists but that the totality of space is so `curved` that a ray of light, after travelling in direct line for a long enough time, would come back to its starting point.”^{[5]}

Prof. N. R. Sen, the famous exponent of the theory of relativity, quoting the view of Prof. Einstein writes: “Einstein himself asserts that the universe consisting of large and small masses hanging apparently in infinite space is not in fact infinite. One suggestion from his theory is that the universe of four dimensions is finite in spatial direction and infinite in the direction of time. It is like a cylinder whose surface is bounded in some direction viz., across the lines which generate the cylinder. This finite dimension corresponds to the three spatial dimensions of our world of perception. But the cylinder is also infinite in two other directions, so is also our universe which is infinite in the dimension of time running from the infinite past into the infinite future.”^{[6]}

A similar view has been expressed by Prof. A. C. Banerji: “According to Einstein’s original theory of relativity, dimensions of space are determined by the amount the mater it contains. Space, if there be matter inside, bends round until it closes up. The more matter there is, the smaller space there must be, and space could only be of literally infinite extent if it contained no matter at all. So matter is responsible for the curvature of space dimensions. So in Einstein’s space containing matter, if one goes right on in one direction, one does not get to infinity, but gets back to his starting point again. Closed space differs from an open infinite in the same way that the surface of a sphere differs from the infinite plane. We say that the surface of a sphere is (1) a curved surface and (2) a closed surface, enclosing a three dimensional volume. Similarly we can say that our three-dimensional space is (1) a curved space and (2) a closed space, enclosing a four-dimensional continuum. In Einstein’s world the time dimensions is uncurved and so may extend to infinity. It is what is called Einstein’s cylindrical world.”^{[7]}

The fundamental basis of the finiteness of the Universe appears to be that the total mass of the matter contained in it is finite.^{[8]} In other words, matter is responsible for the curvature of the space which bends round until it closes up. Closed space differs from an open infinite in the same way that the surface of a cylinder differs from the infinite plane.

Thus many famous scientists and thinkers have succeeded in making the concept of the Einsteinian model of the Universe comprehensible to a great extent. Nevertheless, as Lincoln Barnett has remarked, “Like most of the concepts of modern science, Einstein’s finite, spherical universe cannot be visualized any more than a photon or electron can be visualized.”^{[9]}

Footnotes: | |

[1] | The Mysterious Universe, p.100. |

[2] | The Nature of the Physical World, p. 80. |

[3] | Physics and Philosophy, p.111. |

[4] | From Euclid to Eddington, p.187.. |

[5] | Exploring the Universe, p. 16 |

[6] | Dr. Sen’s article on ‘Relativity’ published in the Proceedings of the Physics Seminar, Allahabad University, July, 1925. |

[7] | From the lecture delivered by Prof. Banerji on The Expanding Universe at the Science Congress, Bombay, 1933 |

[8] | Sir A.S. Eddington has calculated that if the number of protons and electrons existing in the universe were equal, this number would be 1.19x1079. --The Expanding Universe, p. 68. Also see, The New Pathways in Science, p 221. |

[9] | The Universe and Dr. Einstein, p.106. |