strontium

What the field equations are telling us, is that the answer has been right in front of our face this whole time, but it is not a discrete finite answer. The question "what happened at the beginning?" is an understandable but illegitimate question. All matter and energy in the Universe emanates from the source, and because the source is infinite and not finite, matter and energy never "began" they simply are. As matter and energy move away from a singular point of infinite energy and towards zero energy, the Universal energy disperses in relative terms and therefore the Universe appears to expand. This is why light redshifts as it moves through space, even though it doesn't slow down. Because the Universe "originates" (again to be clear, not in a sense of the discrete finite understanding of cause and effect, but rather in terms of reference) from infinite energy, the Universe expands forever.

Planck units are also a consequence of the fundamental assumption that there are universal constants that can be described with objective accuracy in discrete finite terms. Of course, no matter how accurate your measurements are in relative terms, your calculations will break down at a certain point. You can't describe infinity mathematically in discrete finite terms, obviously. So the question becomes, how do we make our measurements more accurate and modify our equations? In order to use Pi in Einstein's field equations, you must approximate it. The more accurate your approximation is, the more precise your calculations will be. But your approximation of Pi is not just dependent on how many significant digits you choose to use, but the precision of the measurements you use to calculate Pi. The same goes for the speed of light. Because all units are arbitrary in complexity and infinitely divisible, it is always possible to improve the precision of your measurements and your resulting conclusions. Our measurements of the speed of light are more accurate than previous generations, but they are still an approximation, and the same goes for Pi. Future generations will be able to make more precise measurements, and in turn more precise calculations.

You are right that I got that backwards. The astronaut ages .007 seconds less for every second his counterpart on Earth's surface ages. The point I was making, however, is that revolutions of the Earth around the Sun don't correlate to a precise passage of time. So a year in orbit on the ISS is 31,315,248 seconds, while a year on the surface is 31,536,000 seconds (if I did the math right). The point being, it is meaningless in terms of time to claim the Universe is 13.8 billion years old. From the surface dweller's perspective, that would mean the Universe is approximately 4.351968×10^16 seconds old, but from the astronaut's perspective, 4.321504224×10^16 seconds old. There are an infinite variety of perspectives, each of which will lead to a unique conclusion regarding the age of the Earth, or of the Universe, depending on how you measure it.

Right, but there is no valid reason to reject the conception of a singularity defined by infinite density. "Infinite density" is a bit of a misnomer, as I explained, it is an infinite progression of physics. If you try to treat a point of infinite density like you would any other apparently discrete object of course it doesn't make sense. The laws of physics break down at the singularity precisely because physicists have stubbornly assumed that there are universal constants that can be described with objective accuracy in discrete finite terms, which is an errant assumption.

Let's say hypothetically two people on Earth are born on the same day at the same time down to the second, and one of them becomes an astronaut. He leaves Earth and launches into space. He lives in orbit on the ISS for one revolution of the Earth around the Sun, while his counterpart remains on the surface of the Earth. Upon returning to the Earth, the astronaut is now older than his surface-dwelling counterpart, even though they were born on the same day at the same time and have experienced the same number of revolutions of the Earth around the Sun. In fact, it is not just the astronaut who is older. If we assume that when he launched into space the Universe was 13.8 billion years old, when he returns to Earth, his very Universe itself is now older than his Earthly counterpart's, even though they reside on the same planet at the same time. So the question is, what does it mean in terms of time to say one year has passed? In terms of time, it means nothing. There is no way to objectively quantify the passage of time, because time is relative. Therefore to claim the Universe is 13.8 billion years old is meaningless, because there is no such thing as an objectively valid standardized year in terms of time.

Einstein viewed the Singularity merely as a mathematical curiosity and believed black holes would not occur in nature. He should have seen the Singularity as the heart of his theory. While some physicists view each occurrence of singularities in the context of Relativity as distinct and individualized phenomena, each instance of the Singularity should be understood as a manifestation of a singular, Universal phenomenon. The Singularity at the heart of the Big Bang is essentially all the matter and energy in the Universe condensed into what can be described as a singular mathematical "point". The Singularity at the heart of a black hole is essentially localized matter and energy stretched towards a singular mathematical "point" of infinite density (in other words, the thermodynamic arrow of time can be described as expansion from infinite blueshift to infinite redshift. The Universe can be described as a spectrum from infinite energy to zero energy, observable in terms of Cosmic expansion from a singular point of infinite density. There is no discernible beginning or end of the Universe in discrete finite terms, rather this spectrum serves as the Objective Frame of Reference). While many seem to struggle with the idea of a so-called "point" of infinite density, it is important to understand that this is not the kind of discrete finite point you might be used to dealing with. These "points" are useful for reference, but do not culminate or conclude in the sense of our general understanding of cause and effect in discrete finite terms. Rather, the appearance of a singularity represents an infinite progression of physics. Infinity is endless, so what is infinitely dense or infinitely vast is simply a matter of perspective. These apparent phenomena should be understood not as individualized singularities occurring throughout space and time, but as the opposite poles of a singular phenomenon. Properly understood, the Singularity should be recognized as a Universal phenomenon which collectively forms the Objective Frame of Reference for Relativity. It should be noted that Einstein believed there was no frame of reference for Relativity, but in this belief he was wrong again, and I would wager that with a comprehensive evaluation of modern experimentation and observation in physics, he would concede as much. Our failure to contend with the physics of the Singularity in mathematical terms is a result of our failure to understand that no Universal constant can be described with objective accuracy in discrete finite terms. In Einstein's gravitational constant for example, we have two constants that can only ever be approximated: Pi, and the speed of light. Pi as we know is an infinite nonrepeating decimal, and the speed of light is a metric relating the spacial experience of light to the temporal experience of light. In each case, when utilizing these constants, we stipulate to significant digits. In so doing, we embed error in all resulting conclusions. The speed of light should be described as 299,792,458 x/∞ meters per 1 x/∞ second, where every decimal place from .0 to .∞ is relevant in cosmic terms. In order to comprehensively quantify gravity in a cosmic context, you must be able to describe all relevant universal constants in terms of infinite digits. As this is relativistically impossible, the conclusion must be that objective accuracy can be endlessly pursued but never truly accomplished.