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Proving the Schwartz Inequality and Heisenberg's Uncertainty Principle

In this post we once again derive the Heisenberg uncertainty principle, but this time we make use of the Schwartz inequality and the posit...

Thursday, May 18, 2017

Derive the Big Bang From Einstein's Field Equations

Was the universe once a singularity? If so, did it have infinite gravity? What forces overcame infinite gravity so our universe could expand to its current size? We can get some answers from Einstein's field equations.

Equation 1 below is the typical textbook rendition of the field equations. At equation 2, on the left side, I changed a plus sign to a minus sign. The third term contains the cosmological constant and shall represent spacetime expansion which is the opposite of gravity, so a minus sign is placed in front of it. We shall treat gravity as positive and expansion as negative.

Normally the first two terms on left side are huge compared to the third term, so the left side of the equation has a positive value. Albeit, something surprising happens if we reduce the universe's radius (r) and hold all other values constant. To make this more obvious, let's change up the variables a bit:

We now reduce the radius to zero:

Equation 13 above shows we derive infinite negative pressure or expansion pressure--and no gravity to hold it back! How is that possible? Well, if we start with the assumption that there was infinite gravity, we are stuck trying to find a force that overcame it. On the other hand, if there was infinite outward pressure and no gravity, it's pretty obvious why the universe grew to its present size.

Gravity must have emerged from the rapid expansion that resulted from so much pressure. To have gravity, there needs to be more than just a point of spacetime. The first two terms of the field equations show that there must be a difference of spacetime curvature between two points in space. In other words, there needs to be more than one reference frame. If the universe was just a single point, there was only one reference frame. Because they represent the same point of spacetime, the first term has a value of infinity, the second term also has a value of infinity. Infinity - infinity = zero spacetime curvature. As soon as there was some distance between, say, point A and point B, gravity emerged.

But then the question becomes, "What caused the infinite pressure at a single point?" The answer is nothing. If the infinite pressure was the beginning, nothing happened before it; there was no time or space. A "cause" is an event, and an event is a function of time and space. So, in the beginning there was infinite outward pressure from a single point ...