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Consider now two events which occur at the same place in frame S′ at different times, These events are said to be timelike separated. (The four-dimensional space flash-of-light surface is not so easy to visualize, but is clearly the higher-dimensional analog: the plane surface corresponding to time Possible causal connections are as follows: an event at the origin (0, 0, 0, 0) could cause an event inside or on the forward light cone: so that is the “future”, as seen from the origin.Events in the backward light cone—the “past”—could cause an event at the origin.The point P with coordinates We say the two events are spacelike separated.
It should be mentioned that this lack of synchronization as viewed from another frame only occurs for clocks separated in the direction of relative motion.
Consider two clocks some distance apart on the axis of S′.
In other words, we shall derive the Lorentz transformations—which are just the equations giving the four coordinates of an event in one inertial frame in terms of the coordinates of the same event in another inertial frame.
We take ) O′ flashes a bright light, which she observes to create an expanding spherical shell of light, centered on herself (imagine it’ s a slightly foggy day, so she can see how the ripple of light travels outwards).
How can O′ and O, as they move further apart, possibly both be right in maintaining that at any given instant the outward moving light pulse has a spherical shape, each saying it is centered on herself or himself?
Imagine the light shell as O′ sees it—at the instant !“I want to get everything sorted out in my mind before I start writing or I’ll just end up wasting my time re-writing”.The process of having to describe your study in detail, in a logical sequence of written words, will inevitably highlight where more thought is needed, and it may lead to new insight into connections, implications, rationale, relevance, and may lead to new ideas for further research.“I know I’m not good at writing so I keep putting it off”.“I know I’m good at writing so I can leave it to later”.However, these transformations presuppose that time is a well-defined universal concept, that is to say, it’s the same time everywhere, and all observers can agree on what time it is.Once we accept the basic postulate of special relativity, however, that the laws of physics, including Maxwell’s equations, are the same in all inertial frames of reference, and consequently the speed of light has the same value in all inertial frames, then as we have seen, observers in different frames do not agree on whether clocks some distance apart are synchronized.(This is just the old story of synchronizing the two clocks at the front and back of the train one more time.) That is why O does not see O′’s sphere: the arrival of the light at the sphere of radius is said to be a Lorentz invariant: it doesn’t vary on going from one frame to another.A simple two-dimensional analogy to this invariant is given by considering two sets of axes, Oxy and Ox′ y′ having the same origin O, but the axis Ox′ is at an angle to Ox, so one set of axes is the same as the other set but rotated.Please report examples to be edited or not to be displayed.Rude or colloquial translations are usually marked in red or orange.