"The Big Bang was not the beginning...In some sense the light cones or the null cones are more fundamental than the metric. This means that if you like the geometry determined by massless objects or photons, things which don't have any mass, is more basic then geometry where you have distances and times. One tends to think of distances and times as the metrics of structures, but think of that as a secondary notion.
It's a quite useful way of thinking about it, because the metric is a quantity which has ten numbers defining a point. So every point in spacetime, you have four dimensions of spacetime, and every point you have four numbers which tells you what the metric is. That's the usual ...and it has ten numbers to define. Now nine of those numbers define just where the light cone is. Now when I say nine I really mean independent ratios of those ten numbers. I'm not interested in overall scaling, I'm just interested in independent ratios which are nine independent ratios. That tells you the light cone or the null cone. It tells you how photons go in spacetime.
In spacetime you have this cone thing and you have the history of the photon that goes along these cones. ...the tenth component is determined by mass. And that is the two most fundamental equations of 20th century physics.. one is a of course Einstein's equation...energy and mass are equivalent....
Plank's Constant and Mu (energy and frequency are equivalent. Energy and Mass are equivalent. Mass and frequency are equivalent!).
If you have mass then you have a clock........ mass is where you get the one extra thing, scale comes from mass.
In the very remote future it's pretty much photons...so you have conformal cosmology. You don't have the 10 full components. You have the nine, which tell you the null cones.
At the Big Bang they are massless for a different reason. So at the two ends you have the geometry of conformal geometry, scale has got lost.
So it's not so outrageous to say...that the Big Bang... stretch it out...The Remote Future, squash it down....I'm not affecting the Conformal geometry....
So you can represent infinity as a nice boundary - that's one trick. Stretching out the Big Bang can also be a nice boundary....
https://www.youtube.com/watch?v=xlDNh5WYGbU
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