What if we could prove that “time is space”?

This post is a spontaneous contribution from Christian Walter, an actuary, a consultant and author of the (French language) book The B Virus (“Le Virus B”).  Christian contributed in 2009 with the post French language post: “What if we gave

chance a chance?” (Et si on donnait sa chance à la chance?).  If the old adage tells us that “Time is money”, for Christian Walter, “time is space”, and he has the means to prove it!

It is known that speed accumulates: if you shoot a gun while running the bullet’s impact speed will be the firearm’s plus your running speed.  So, if you’re running at 20 km/hour and your firearm triggers the bullet forward at 600 km/hour, it will obtain its target (if you’re a good shoot) at 620 km/hr.  If, on the other hand, you decide to shoot from behind while you run (Western style), the impact speed will be 580 km/hour (and the chances of hitting your mark are even slimmer, unless you’re in an actual Western!)  This is the law of inertia of Galilean Referential: this law implies that speeds accumulate algebraically.  Time and space are two absolutes, as beautifully explained by Newton in 1687 in Principia.

Lets imagine that our running shooter, now is armed with a light saber (Star Wars style) that advances at the speed of 1,079,280,000 km/hour (approximately 300,000 km/second!).  At this speed, which is the speed of light, something phenomenal starts happening: the speed no longer accumulates—in the year 1894, it was observed that this speed stays the same, violating the law of inertia of Galilean Referentials.  This brought into question the validity of a Galilean-Newtonian conception of time and space: what if time was space?  This was found to be true.

In 1904, the Dutch physicist Hendrik Lorentz invented transformation equations that allowed for a resolution of the contradiction of non-addition to the speed of light.  Lorentz posited that light was invariant and nothing could overtake it.  In 1905, the French mathematician Henri Poincaré took this one step further by introducing an appropriate mathematical formalism.  In 1908, Hermann Minkowski resolved this problem by incorporating time into space.  In between, Einstein created a new theory of time and space, taken by light.  Finally; time was space.  Velocity does not accumulate and the measure of time and space depend on the movement of the person who measures them.  This is why, for a given observer, a clock with a pendulum appears to move slower than a clock without a pendulum.  The more these speeds approach the speed of light, the more they slow down.  Oh time suspend your flight: at the very limit (the speed of light) the clocks stops ticking.  Time is stopped.

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