The Primeval Atom

THE PRiMEVAL ATOM hypothesis is a cosmogonic hypothesis which pictures the present universe as the result of the radioactive disintegration of an atom.

I formulated this hypothesis 15 years ago from thermodynamic considerations while trying to interpret the law of degradation of energy in the frame of quantum theory.

Since then, the discovery of the universality of radioactivity shown by artificially provoked disintegrations, as well as the establishment of the corpuscular nature of cosmic rays, manifested by the force which the Earth’s magnetic field exercises on these rays, made more plausible an hypothesis which assigned a radioactive origin to these rays, as well as to all existing matter.

Therefore, I think that the moment has come to present the theory in deductive form.i shall first show how easily it avoids several major objections which would tend to disqualify it from the start.

Then I shall strive to deduce its results far enough to account, not only for cosmic rays, but also for the present stmcture of the universe, formed of stars and gaseous clouds, organized into spiral or elliptical nebulae, sometimes grouped in large clusters of several thousand nebulae which, more often, are composed of isolated nebulae, receding from one another according to the mechanism known by the name of the expanding universe.

My hypothesis uses several elementary geometric conceptions:

• the closed space of Riemann which led to that of space with a variable radius
• the theory of relativity as the cosmological constant and of the cosmic repulsion which is the result of it.

Closed Space

All partial space is open space. It is comprised in the interior of a surface, its boundary, beyond which there is an exterior region.

Our habit of thought about such open regions impels us to think that this is necessarily so, however large the regions being considered may be. it is to Riemann that we are indebted for having demonstrated that total space can be closed.

To explain this concept of closed space, the most simple method is to make a small-scale model of it in an open space. Let us imagine, in such a space, a ball in which we are going to represent the whole of closed space.

On the spherical surface of the ball, each point of closed space will be supposed to be represented twice, by two points, A and A’, which, for example, will be two antipodal points, that is, two extremities of the same diameter. if we join these two points A and A’ by a line located in the interior of the ball, this line must be considered as a closed line, since the two extremities A and A’ are two distinct representations of the same, single point.

The situation is altogether analogous to that which occurs with the Mercator projection, where the points on the 180th meridian are represented twice, at the eastern and western edges of the map. One can thus circulate indefinitely in this space without ever having to leave it.

It is important to notice that the points represented by the outer surface of the ball, in which we have represented all space, are not distinguished by any properties from the other points of space, any more than is the 180th meridian for the geographic map. in order to account for that, let us imagine that we displace the sphere in such a manner that point A is superposed on B, and the antipodal point A’ on B'.

We shall then suppose that the entire segment AB and the entire segment A’B’ are two representations of a similar segment in closed space.

Thus we shall have a portion of space which has already been represented in the interior of the initial sphere which is now represented a second time at the extirior of this sphere. Let us disregard the interior representation as useless; a complete representation of the space in the interior of the new sphere will remain.

In this representation, the closed contours will be soldered into a point which is twice represented, namely, by the points B and B’, mentioned above, instead of being welded, as they were formerly, to points A and A’. Threefore, these latter are not distinguished by an essential property.

Elliptical Space

That is the essential of the topology of closed space.

It is possible to complete these topological ideas by introducing, as is done in a geographical map, scales which vary from one point to another and from one direction to another. That can be done in such a manner that all the points of space and all the directions in it may be perfectly equivalent. Thus, Riemann’s homogeneous space, or elliptical space, is obtained.

The straight line is an odd contour of minimum length. Any two points divide it into two segments, the sum of which has a length which is the same for all straight lines and which is called the tour of space.

All elliptical spaces are similar to one another. They can be described by comparison with one among them.

The one in which the tour of the straight line is equal to ‘iT = 3.i4i6 is chosen as the standard elliptical space. in every elliptical space, the distances between two points are equal to the corresponding distances in standard space, multiplied by the number R which is called the radius of elliptical space under consideration.

The distances in standard space, called space of unit radius, are termed angular distances. Therefore, the true distances, or linear distances, are the product of the radius of space times the angular distances.

Space Of Variable Radius

When the radius of space varies with time, space of variable radius is obtained.

One can imagine that material points are distributed evenly in it, and that spatio-temporal observations are made on these points. The angular distance of the various observers remains invariant, therefore the linear distances vary proportionally to the radius of space. All the points in space are perfectly equivalent.

A displacement can bring any point into the center of the representation. The measurements made by the observers are thus also equivalent, each one of them makes the same map of the universe.

If the radius increases with time, each observer sees all points which surround him receding from him, and that occurs at velocities which become greater as they recede further. it is this which has. been observed for the extra-galactic nebulae that surround us. The constant ratio between distance and velocity has been determined by Hubble and Humason. it is equal to TH=2x10(9) years.

If one makes a graph, plotting as abscissa the values of time and as ordinate the value of radius, one obtains a curve, the sub-tangent of which at the point representing the present instant is precisely equal to T H’.

The Primeval Atom

The entire universe existed in the form of an atomic nucleus which filled elliptical space of convenient radius in a uniform manner.

When the universe had a density of 10 (27) gram per cubic centimeter, the radius of space was about a billion light-years, that is, 10 (27) centimeters. Thus the mass of the universe is 10(54) grams.

If the universe formerly had a density equal to that of water, its radius was then reduced to 10 (18) centimeters, say, one light-year.

In it, each proton occupied a sphere of one angstrom, say, 10 (8) centimeter.

In an atomic nucleus, the protons are contiguous and their radius is 10 (13), thus about 100,000 times smaller. Therefore, the radius of the corresponding universe is 10 (13) centimeters, that is to say, an astronomical unit.

This description of the primeval atom will have to be modified when our knowledge of atomic nuclei is more perfect.

Cosmogonic theories propose to seek out initial conditions which are ideally simple, from which the present world, in all its complexity, might have resulted, through the natural interplay of known forces.

It seems difficult to conceive of conditions which are simpler than those which obtained when all matter was unified in an atomic nucleus.

The future of atomic theories will perhaps tell us, some day, how far the atomic nucleus must be considered as a system in which associated particles still retain some individuality of their own.

The fact that particles can issue from a nucleus during radioactive transformations certainly does not prove that these particles pre-existed as such.

Photons issue from an atom of which they were not constituent parts; electrons appear where they were not previously, and the theoreticians deny them an individual existence in the nucleus. Still more protons or alpha particles exist there, without doubt.

When they issue forth, their existence becomes more independent, nevertheless, and their degrees of freedom more numerous.

Also, their emergence in the course of radioactive transformations, is a typical example of the degradation of energy, with an increase in the number of independent quanta or increase in entropy.

That entropy increases with the number of quanta is evident in the case of electromagnetic radiation in thermodynamic equilibrium. in fact, in black body radiation, the entropy and the total number of photons are both proportional to the third power of the temperature.

Therefore, when one mixes radiations of different temperatures. and one allows a new statistical equilibrium to be established, the total number of photons has increased. The degradation of energy is manifested as a pulverization of energy.

The total quantity of energy is maintained, but it is distributed in an ever larger number of quanta, it becomes broken into fragments which are ever more numerous.

If, therefore, by means of thought, one wishes to attempt to retrace the course of time, one must search in the past for energy concentrated in a lesser number of quanta.

The initial condition must be a state of maximum concentration. it was in trying to formulate this condition that the idea of the primeval atom was germinated.

Who knows if the evolution of theories of the nucleus will not, some day, permit the consideration of the primeval atom as a single quantum?