Time as the 4^{th} Dimension
"There is a fifth dimension beyond that which is known to man. It is a dimension as vast as space and as timeless as infinity. It is the middle ground between light and shadow, between science and superstition; and it lies between the pit of man's fears and the summit of his knowledge. This is the dimension of imagination. It is an area which we call, 'The Twilight Zone'. "  Rod Serling ( 1924  1975 )
Ok, so we now know about the Lorentz Transformation Equations. So why is time the 4^{th} dimension?
Here's a simple answer:
1). From the onset of John Harrison's H4 clock  watch [ 1761  62 and 1764 ] where
"Time of longitude, adjusted for latitude, and hence converted to longitudinal distance traveled " and " ... John Harrison's H4 clock  watch [ ... ] relates the idea of time with space  distance " already there had been made a direct connection between space  distance and time. [ see: "Distance and the John Harrison time clocks which measure it" ]
2). Also we know that
from before.
It's obvious that in order to describe the position of an event in spacetime that it essentially takes 4 coordinates, namely ( ).
So there you have it: time as the 4^{th} dimension. It's really just a mathematical physics thing.
But how do advanced mathematicians actually write all this down?
This then gives us the Lorentz Transformation Equations [ see above ] using some advanced matrix multiplication. Actually we are also verging upon Tensor Analysis which is an advanced form of matrix analysis whose usage Einstein made salient in Special Relativity mathematics.
In other words, all of the Lorentz Transformation Equations can be written as
which is always something to be admired for its mathematical elegance and simplicity!!
The World's Most Accurate Clock
source: "Topprecision optical atomic clock starts ticking",
Faculty of Physics, University of Warsaw, February 25, 2015
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