Harry Bateman

“ If we could represent an event by a point on a line, the idea of simultaneity would be quite simple, for two events could be regarded as simultaneous when their representative points were coincident. In reality such a representation is not valid, there is no sensation of such a simple nature that it can be represented by a point on a line. If we adopt a representation by means of an interval on a line, we obtain what is probably a truer representation of an event as regards its duration ”

“ During recent years mathematicians and philosophers have been much occupied in analysing the fundamental conceptions on which the different sciences are based, with the result that many things which were formerly regarded as quite simple and axiomatic can no longer be regarded as such. The tendency has, of course, been to make definitions as precise as possible, and to make descriptions of phenomena approximate to reality as we know it, and not to a preconceived idea of what the description ought to be. ”

“ The description of any series of phenomena is thus qualitatively the same in the two series of coordinates.
It is interesting to compare the result just obtained with some ideas with regard to the way in which experience is interpreted by the mind.
If we suppose that some physical process taking place in the brain is the physical adjunct of a sensation in the mind, such as visual perception, we may regard the mind's interpretation of the sensation as a transformation of the actual physical process as it would be described by external observers if observed directly by them. ”

“ Let us suppose that a large number of observers find that their observations of one another's experiences give a consistent universal time as far as they are concerned; they can then regard themselves as being at constant distances from one another, the distance between two observers , being defined as , where is the time light takes to travel from to , and C is a constant called the velocity of light. ”

“ In the case of time, for instance, it is found that we have to examine the connection between time as it is known to us by the mind's experience, i.e., psychological time, and time as it is measured by the course of physical phenomena, i.e., physical time. ”

“ The advantage of using the age of a particle in forming the equations of motion is that there is a gain in simplicity. The analytical methods based upon the use of the age of a particle may be compared with Lagrange's method of dealing with problems in hydrodynamics, while the methods based on the use of a standard time may be compared with the Eulerian method. ”

“ Many difficulties arise, however, in a careful examination of the fundamental concepts of any science, and this is soon found to be the case when we commence to examine the ideas of space and time which are fundamental in all physical and metaphysical enquiries. ”

“ Systems of non-Newtonian mechanics and kinematics of a rigid electron have been based upon the theory of relativity for the case of uniform motion, but they can hardly be regarded as satisfactory, and difficulties arise as soon as a uniform motion of rotation about an axis is considered. [14]
If mechanics is to be based on the science of electromagnetism, we must make a complete study of the transformations connected with the fundamental equations of electromagnetism. ”

“ It is possible that when the mind is concentrated on a subject the type of transformation is practically constant, and so our interpretations of sensations become clearer as they become more of a quantitative nature, but it is dangerous to speculate and so I shall leave the subject at this point. ”

“ An observer situated at a point A observes at time t an event which has taken place at another point B. If τ is the time which light takes to travel from B to A, the universal time to be associated with the event at B according to A's measurements is . ”

“ These observers may then form a standard system for the measurement of time and distances at other points of space. The measurements of four standard observers should suffice to determine the position and time of any occurrence, if space is of three dimensions. If there are more than four observers in the standard system the relations between all the different observations of an event will depend upon the nature of space, and will take a comparatively simple form if the space is Euclidean. ”

“ At present the theory is being widely used as a working hypothesis, and is of great theoretical importance, as it enables us to pass from the known analytical specification of a phenomenon for a medium at rest to the corresponding case of a medium in motion. ”

“ Since the flow of energy depends upon the state of the electromagnetic field, the formulæ of transformation will depend upon the character of the electromagnetic field, but it can be shown that if the above equations are invariant, the fundamental equations which describe the sequence of electromagnetic disturbances are also invariant. ”