The Minkowski space-time continuum

What would happen if the rotes of the two systems were interchanged Tb this end let us express x, t by x/, t. By inversion of the transformation matrix we ob- 

Now let us cuiiie back to Einstein s luurning uaiu meditationabout what he would see on the tramstop clock if the tram had the velocity of light. Now we have the tools to solve the problem. It concerns the two events - two ticks of the clock observed in the coordinate system associated with the tramstop, i.e. x =X2 = x, but happening at two different times and t2 (differing by, say, one second, i.e. t2 — h = 1, this is associated with the corresponding movement of the clock hand). 

What will Einstein see when his tram leaves the stop with velocity v with respect to the stop, or in other words when the tramstop moves with respect to him with velocity —v He will see the same two events, but in his coordinate system they will happen at 

when the tram ran through the streets of Bern with velocity v = c, the hands on the tramstop clock when seen from the tram would not move at all, and this second would be equivalent to eternity. 

This is known as time dilation. Of course, for the passengers waiting at the tramstop (for the next tram) and watching the clock, its two ticks would be separated by exactly one second. If Einstein took his watch out of his waistcoat pocket and showed it to them through the window they would be amazed. The seconds will pass at the tramstop, while Einstein s watch would seem to be stopped. The effect we are describing has been double checked experimentally many times. For example, the meson lives such a short time (in the coordinate system associated with it), that when created by cosmic rays in the stratosphere, it would have no chance of reaching a surface laboratory before decaying. Nevertheless, as seen from the laboratory coordinate system, the meson s clock ticks very slowly and mesons are observable. 

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The Vanishing of Apparent Forces The Galilean Transformation The Michelson-Morley Experiment The Galilean Transformation Crashes The Lorentz Transformation New Law of Adding Velocities The Minkowski Space-Time Continuum How do we Gel E =... 

Hermann Minkowski introduced the seminal concept of the four-dimensional space-time continuum (jc, y, z, ct). In our one-dimensional space, the elements of the Minkowski space-time continuum are events, i.e. vectors (x,ct), something happens at space coordinate x at time t, when the event is observed from coordinate system O. When the same event is observed in two coordinate tys-... 

Hermann Minkowski introduced the seminal concept of the four-dimensional space-time continuum (jc, y, z, ctY. ... 

We may remind ourselves that according to conventional wisdom, Poincare failed to derive an early relativity theory mainly as a result of his stubborn adherence to the nineteenth century concept of the ether as an utter void while Einstein, just few years later, succeeded because he stayed behind the assertion of a new kind of ether that was the superfluous space-time substratum. His relativity postulate was called an absolute world by Minkowski. Fifteen years later, however, Einstein used Mach s ideas on rational movement in order to cancel the action-at-a-distance and refreshed the idea of the ether because his relativity space is endowed with physical qualities. The ether should be regarded as a primary thing (similarly to the prematurely Aristotelian plenum) assuming that matter is derived from it [40], citing the metrical qualities of the continuum of space-time differ in the environment of different points of space-time being conditioned by the matter existing outside of the territory under consideration . 

The background Minkowski space can be identified now with an absolute space-time, perhaps unobservable as we are immersed in the deformable continuum in which there is no absolute space-time. It then follows that we could treat the index p and a in the... 

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