Aristotle has a famous saying, "nature hates vacuum". Therefore, he speculates that there is no vacuum in nature. His model explains this lack by filling space with an immeasurable substance, the ether. Now, students and scientists who study physics know that physics hates singularities. When we find a singularity, it usually means that the models we use to describe physical systems or phenomena fail - something happens at the singularity, but we don't know what it is. So, how can we avoid singularity? The answer to this question opens up new possibilities in physics In fact, behind every singularity in physics, there is a secret door leading to a new natural world
Love and hate singularity
Physics is the art of modeling. We use mathematical equations to describe complex natural systems, such as the sun and the planets around the sun. This is a relatively simple model. In short, these equations describe how the function of a variable or group of variables changes over time. Taking planetary orbits as an example, these equations describe how they move in space along their respective orbits.
As a term, people use "singularity" in many situations, including mathematics. The word also appears in speculation about artificial intelligence, such as the day when machines will be smarter than humans. The "singularity" in these contexts is another completely different thing, which is worth writing a separate article. But now, let's continue to understand the singularities in physics and mathematics.
Physicists love and hate singularity. On the one hand, the singularity marks the collapse of a theory or the mathematical model describing it. But on the other hand, they may also be the gateway to new discoveries.
Perhaps the most famous singularity in physics is related to gravity. In Newtonian physics, the gravitational acceleration caused by an object with mass m and radius r = GM / R ^ 2, where G is the gravitational constant (i.e. the universal gravitation constant, which is a measurable value used to set the intensity of gravitation). Now, let's consider the case where the radius r of the object decreases and the mass remains unchanged. When R decreases, the gravitational acceleration g increases. In the limit case (we like to say "limit" in physics and Mathematics), when R approaches 0, the acceleration g approaches infinity. So a singularity appeared.
When is a ball not a ball
This is the singularity described by mathematics. This point has no mathematical definition and its nature tends to infinity. But in physics, will this really happen? Things became interesting from here.
The quick answer is: No. In space, first of all, occupy mass. If the mass is continuously compressed into a smaller volume, where will the mass go? You need new physics to answer this question.
Classical Newtonian physics cannot deal with physical problems at very short distances. You need to add quantum mechanics to the model. Therefore, when you compress the mass to a smaller volume, the quantum effect will help to describe what is happening.
First of all, you need to know that matter itself is not an indestructible object. It is composed of molecules, and molecules are composed of atoms. When a ball becomes smaller and eventually less than one billionth of a meter, it is no longer a ball. It is a collection of atomic clouds superimposed on each other according to the laws of quantum mechanics. At this time, the concept that the object is a "ball" no longer has any meaning.
What if the atomic cloud could be compressed into smaller and smaller volumes? At this time, we need to use the various effects mentioned in Einstein's theory of relativity, such as a mass will distort the space around it. At this time, not only the concept of "ball" has long disappeared, but also the space around it has been distorted. In fact, when the radius of the imaginary ball reaches a critical value, that is, r = GM / C ^ 2 (C is the speed of light), the ball becomes a black hole.
Now, here comes the trouble. The black hole will form an event horizon around it, and its radius is the critical value we just calculated, that is, the Schwarzschild radius. No matter what happens in this range, we can't see it outside. If you don't choose to tell your own event, you can never tell it. As the ancient Greek philosopher Heraclitus once joked, "nature likes to hide itself". Black holes are the ultimate hiding place.
Does such a place exist? existence
In the above exploration, we started with an ordinary ball made of ordinary materials, and then quickly expanded physics to include quantum physics and Einstein's general theory of relativity. By simply taking the limit of a variable (the radius of the ball in the Shangshu example) as 0, the singularity appears. Scientists believe that singularity is the door to new physics.
However, the exploration of singularity has a sense of dissatisfaction with the unfinished mission. We don't know what's going on inside the black hole. Through the calculation of the equation - at least Einstein's equation - we will obtain a singularity at the center of the black hole. There, gravity itself tends to infinity. This is a place in the universe that exists and does not exist at the same time. Remember quantum physics? Quantum physics tells us that a point in space means an infinitely precise position. This infinite accuracy is impossible. Heisenberg's uncertainty principle tells us that the singularity is actually a thing that keeps "shaking"; Every time we try to locate it, it's moving. This means that we can never reach the center of a black hole, even in theory.
New understanding of singularity
Therefore, if we take these theories seriously, the mathematical singularity in the model not only opens the door to new physics, but also cannot exist in nature. Nature seems to have found some way around the singularity, but we know nothing about it. Unfortunately, none of our existing models seem to be able to do this, at least for now. No matter what happens inside a black hole, no matter how fascinated our imagination is, we need a new physics that has not yet emerged.
What makes the singularity more difficult to explore is that we can't get data from the inside of the black hole. Without data, how can we decide which new model is reasonable? No wonder Einstein didn't like black holes, even though it was the product of his own theory. As a realist, Einstein found that some aspects of the natural world were beyond human understanding, which was really annoying. Theoretically, gravitational singularity (also known as space-time singularity) is a point with infinitely small volume, infinite density, infinite gravity and infinite curvature of space-time. At this point, the currently known laws of physics cannot be applied. Maybe there will be some theory combining quantum gravity in the future (such as the superstring theory currently studied), which does not need singularity to explain black holes, but the verification of this theory will take many years.
Here, we have a new understanding. Although we should constantly try to solve the singularity problem, perhaps we should also hold the mentality that it doesn't matter if we can't find the answers to all the questions. After all, the "unknown" is the driving force that drives us to continue our search. British playwright Tom Stoppard once wrote: "it is the desire to know that makes us important." Even if we can't answer the singularity question in the end, the process of exploration will still be of great significance. (Ren Tian)