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By Harrison D.M.

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Suppose Sue stands at one end of her train car and emits a pulse of light (event q), which travels across the car and some short time later hits the far wall (event p). Since it travels in the x-direction, its speed will be Δxpq/Δtpq. Under a Galilean transformation Δx will be changed while Δt remains invariant, so the speed must also change. For Δxpq/Δtpq to remain unchanged under a coordinate transformation either Δt and Δx must both be unchanged or they must both change in the same proportion.

Acceleration of a body is nothing more than the curvature of its trajectory through space-time. A corollary of Newton’s first Law, then, is that we can legitimately demand that the time axis of our coordinate system be a straight line in space-time. Indeed, we can demand that every spatial coordinate sweep out a straight trajectory. Coordinate systems which satisfy this constraint are precisely the inertial frames of classical physics. The postulation of global inertial frames is a bold and risky hypothesis.

Classical gravitational and electrical forces were described as being determined by the contemporaneous global distributions of matter or of electric charge. Any change in that global distribution would therefore immediately have effects on the forces felt everywhere. Although instantaneousness was a feature of the first theories of gravitation and electricity, it was not an essential feature. Newton thought that gravitation must be the effect of some subtle particles, about which he famously framed no hypotheses.

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