On the foundations of dynamics

Abstract

1— Observations of red-shifts in the spectra of the extra-galactic nebulae are compatible with the view that the nebulae are receding from one another, and the theory incorporating this phenomenon makes it appear probable that the universe had a definite beginning about 2 x 10 9 years ago. There is thus a natural origin for the reckoning of time, and a definite epoch can be assigned to any given event. Further, at each point in space, at any given epoch, there is a characteristic velocity relative to any chosen observer, and this defines a standard of local rest. This absolute time and characteristic velocity may possibly be involved in the description of the fundamental laws of nature, for example the laws of dynamics and gravitation. It is the object of the present paper tentatively to examine what, if any, modifications in certain laws of nature are to be anticipated in this way. The guiding principle will be to retain the forms of Newtonian dynamics and gravitation as far as possible unchanged. Mach’s Principle 2— It was held by Mach that the property of matter we call inertia is due to the presence of other matter in the universe. Mach’s view was that since (in addition to a temporal experience for the observer) we can describe the motion of a particle only by reference to other particles, these other particles are essential to the description of the motion and so to the possibility of observations which could disclose the possession of inertia. For example, “When we say that a body preserves unchanged its direction and velocity in space , our assertion is nothing more or less than an abbreviated reference to the entire universe.”Again:“ We see that even in the simplest case, in which we deal with the mutual action of only two masses, the neglecting of the rest of the world is impossible.”Lastly:“ In all the dynamical propositions that we have discussed, velocity plays a prominent role. The reason of this, in our view, is that, accurately considered, every single body in the universe stands in some definite relation with every other body in the universe, that any one body, consequently also any several bodies, cannot be regarded as wholly isolated.