In thinking about my previous blog post “Coordinate Singularities in Physics and the Actual Properties of the Universe”, in which I address the appearance of values of infinity within equations related to the density and size of blackholes and the big bang singularity.
Sometimes some crazy and unexpected things happen in equations, but they are equations. They are parts of larger models. The models help us to understand the universe. They can be said to be more or less accurate and more or less representative of what happens in our actual universe. As was stated previously, anomalies and singularities that occur within equations are not always actual phenomenon in the universe. The are only phenomenon that occur in equations, but not the real universe.
Some phenomenon that occur in equations do not actually occur in our real universe which the equations and models are trying to describe and act as models. It reminds me of the old saying “The map is not the territory.” It is a simple truth, but an important truth. Models and theories of the universe have a similar relationship to reality. Certain models and theories are used to understand and predict phenomenon and objects within our universe, but these models are not the universe itself, even if they are very accurate at predicting phenomenon.
The use of models, theories, and equations is necessary to the work of Science. If a model or theory works 99% of the time and explains 99% of the universe, it is still important to consider those parts of the model or theory that fail to account for certain phenomenon within the universe or which are not accurate representations of the universe.
Models and theories of the universe are not the universe.
In the actual universe the actual density of a blackhole, a collapsed star, may be very large. Stars have very large masses and densities. Yet finite stars or finite matter also have finite densities, and a blackhole is only a finite collapsed star, without any additional matter added to it. Gravity may work different, may be stronger or weaker, but the actual density of a solid can only ever be finite, or else what would it mean that something is infinitely dense? Is that to say its density is immeasurable and that an actual value cannot be assigned to it?
A thing may be very very large, or very very small, but certain rules of the universe are constant, even if equations break down. An equation breaking down only means the equation doesn’t have anything to say about what it is describing. Saying the universe was infinite small, smaller than a piece of fruit, may not be accurate if we are talking about the fact that energy is neither created nor destroyed.
So all the energy & and matter existing in our universe now came from a time long ago called the Plank Era when matter didn’t even exist, only radiation. But all that radiation surely existed in some amount of space. It would go on to be the material from which all the first elementary particles and atoms of the early early universe were formed. Fast forward to our universe today, and can we still say that energy, and the energy in the entire universe, has remained constant and has neither been created nor destroyed, but merely changed?
And now what about the empty space our universe now sits within and which simultaneously sits within our universe? If you fill an empty glass with water, then the time before you filled the glass full of water is surely a time when the empty glass itself still existed. In this case, the water is the energy and matter in the universe, and the empty glass is the empty space in which it now occupies.
While the flow of water is dynamic from the start of filling the glass to when the water is finished being poured, the shape of the glass does not change. You’d be right to point out that our universe is actually expanding, and so this metaphor breaks down. And yes, we need not fear about water overflowing or our imagined empty glass breaking because of the water contained within it.
Black holes are known to still have size and sizable event horizons. Within a blackhole and within its event horizon are the remains of a once living star. Each particle of that star could theoretically be accounted for. While it is often said that space-time ends at a black-hole’s event horizon, the fact is that the universe around the black-hole still exists with its own space and time. Furthermore, the space and time within a black-hole, although not suitable for life, is not any different from any other astronomical object, be it star or planet, that is not hospitable to life.
Just as blackholes are not infinitely small, but have sizable event horizons and the remnants of their former stars within them, then a universe with billions of galaxies each with billions of stars, each with their own sizes, matter, and energy, surely could not have once existed in an infinitely small space. Even if equations point to it once existing in a much smaller state that it’s current state, “much smaller” and “very small” are very different from infinitely small. Trusting an equation or math in general is not enough, as we know equations often fail and break-down in other circumstances and the values the equations give us are not accurate to the phenomenon they were created to model.
Therefore, it is important to remember that models of the universe are not the universe.