Please, by all means, keep going. I'm feeling a bit like Johnny-5 this morning and I'm hungry for more input!
Documentaries often leave something to be desired. They are like books on various aspects of science. A science book can be chock full of advanced mathematics or none at all. I read that some publishers will not accept a book for general readership if it has even only one simple mathematical formula in it.
There is a lot of very interesting aspects to the various advanced topics in science that any high school grad can understand if only a little math is involved, but nobody publishes at that level.
This is something I have only seen once somewhere. It is very simple, but it gave a much deeper understanding of Relativity. Bare with me.
The Pythagorean theorem to find the distance along a diagonal is:
D = sqrt( x^2 + y ^2)
Suppose I told you the the dimensions were x =3 and y = 4. What is D. You would say 5? I fooled you because x is in inches and y is in centimeters. In order to solve it now, you need to have a conversion factor for the units of measurement. It would be
D = sqrt( (2 in)^2 + ( 3 cm * (1 in / 2.54 cm))^2 )
To simplify it lets just rename the conversion factor:
c = (1 in / 2.54 cm)
The Pyth theorem for that case is now
D^2 = sqrt( x^2 + (y*c)^2 )
That version is the distance between two points
Suppose we are told that time is a fourth dimension. The Pyth theorem for that case is
S^2 = sqrt( x^2 + y^2+ + z^2 + t^2 ), ... where t is time.
Oops I forgot we need a conversion factor. Suppose x, y, and z are in miles, the conversion factor for time must be some constant, c, in units of distance/time. Those units are a velocity which happens to be 186000 miles/hour, the speed of light.
So it turns out that when we think of the velocity of light as the maximum that any object can travel, we are missing the very important fact that it is really a conversion factor to make the Pyth theorm work. However that's not quite all of it. The conversion is also multiplied by an imaginary number i, where i^2 = -1.
That gives an unusual distinction between space and time. So the result is
S = sqrt( x^2 + y^2 + z^2 - (t*c)^2 ) ... the t term has a minus sign.
This version is the distance between two events.
The thing that struck me about that analysis is that the velocity of light is just a conversion factor. And it was shown that anything with a zero mass (photon) is obligated to travel at the speed of that conversion factor. Variable S is no longer a distance because it involves time. S is an event (a point in space and time), separated by another event.
Maybe tomorrow I will show why I think quantum entanglement isn't as bizarre as some might think.