Wow talk about alot of useless space!
HTRC
NO SUCH THING AS USELESS SPACE HATE, READ THIS!
NUFF' SAID!
XXVI. The Space-Time Continuum of the Special Theory of Relativity Considered as a Euclidean Continuum
WE are now in a position to formulate more exactly the idea of Minkowski, which was only vaguely indicated in Section XVII. In accordance with the special theory of relativity, certain co-ordinate systems are given preference for the description of the four-dimensional, space-time continuum. We called these “Galileian co-ordinate systems.” For these systems, the four co-ordinates x, y, z, t, which determine an event or—in other words—a point of the four-dimensional continuum, are defined physically in a simple manner, as set forth in detail in the first part of this book. For the transition from one Galileian system to another, which is moving uniformly with reference to the first, the equations of the Lorentz transformation are valid. These last form the basis for the derivation of deductions from the special theory of relativity, and in themselves they are nothing more than the expression of the universal validity of the law of transmission of light for all Galileian systems of reference. 1
Minkowski found that the Lorentz transformations satisfy the following simple conditions. Let us consider two neighbouring events, the relative position of which in the four-dimensional continuum is given with respect to a Galileian reference-body K by the space co-ordinate differences dx, dy, dz and the time-difference dt. With reference to a second Galileian system we shall suppose that the corresponding differences for these two events are dx', dy', dz', dt'. Then these magnitudes always fulfil the condition. 1
2
The validity of the Lorentz transformation follows from this condition. We can express this as follows: The magnitude ds2=dx2+dy2+dz2-c2dt2
which belongs to two adjacent points of the four-dimensional space-time continuum, has the same value for all selected (Galileian) reference-bodies. If we replace x, y, z,
ct, by x1, x2, x3, x4, we also obtain the result that
is independent of the choice of the body of reference. We call the magnitude ds the “distance” apart of the two events or four-dimensional points. 3
Thus, if we choose as time-variable the imaginary variable
ct instead of the real quantity t, we can regard the space-time continuum—in accordance with the special theory of relativity—as a “Euclidean” four-dimensional continuum, a result which follows from the considerations of the preceding section. 4
[This message was edited by Patrick McIrish on October 17, 2003 at 3:07PM.]
WHAT HAPPENED TO FREE SPEECH MCPUPPET, LET THE GUYS POST STAND!
ANYONE WHO DOESN'T THINK THERE IS RACISM IN THE WORLD, IF YOUR DAUGHTER WAS DATING FORUM OWNERS MAJOR,PEEP AND SHRINK, WHO WOULD YOU WELCOME INTO YOUR HOUSE?
[This message was edited by BEANTOWNJIM on October 17, 2003 at 3:10PM.]
