is inside that closed surface—for example, if there are five units of negative charge and eight units of positive charge, the net electric charge inside would be 8 – 5 = 3 units of positive charge. The simplest way to find out would be to track down all the bits of charge inside, measure them, and add up their values. But that might not always be possible—for example, if the charges are in the interior of some extremely hot substance, or perhaps they are inside a very grouchy grizzly bear that swallowed a bit of electricity with its morning salmon. Then Gauss’s law gives us an alternate way to accurately find how much charge is in a particular volume or region, solely from information on its enclosing surface or boundary!
(ideally, the sections should be as tiny as possible), and (i) measure the outward force felt in each section, (ii) multiply that force by the area of that particular section, and (iii) finally add up those products we get from all the sections. That will give us exactly how much net electric charge is inside the surface—without ever having to look inside the surface!
. All matter in the universe exerts gravitational force on all other matter. Just as we did for electric charge, if we want to determine how much mass or matter is contained within a closed surface, we can figure it all out from the inward gravitational force felt at various points on the surface.
Thus, physical laws confirm that surface features do matter quite a lot and are not to be dismissed cavalierly. But to realize how in our lives we are completely dependent on surface features, we need to appreciate how truly inaccessible much of what is beneath the surface is. One of the most staggering thoughts we could ever have is to comprehend and hold in our minds, even if briefly, how utterly alone each one of us really is. It is not a thought that comes easily and is even harder to hold on to, because it is really like peering into an abyss. It is such an elusive thought that although it is easy enough to describe it in words, it is impossible to convey its dizzying feel unless you realize and feel it yourself—it is sort of like trying to get someone else to experience the grandeur of the Grand Canyon by describing it in words. But let me give the words a shot anyway: just try to realize in your mind that everything you have ever experienced, everything that exists, all of reality as you know it are all just in your head and in your head alone. No matter how close you are to anyone, you will always be trapped in your head and in your body, and you will never get to experience even the minutest thing from the consciousness of another person. You can never, ever know how it feels to experience life as another individual. Everything exists because you exist—as far as you really know. From your solitary perspective, everything will cease to exist when your consciousness ceases to exist. Our only validation to the contrary is that we see people around us die and disappear, and the universe continues to exist, and we extrapolate and assume the same has to be the case when we die . . . but we can never really be completely sure! As far as you are concerned, you are the most important person in the universe, and everything exists because you exist.
. We sum these all up to define the identity of the person inside those surface elements, very much like Gauss’s law in . But, even in the physical world, Gauss’s law, although always true in principle, can be accurately used only when the surfaces are simple—like a sphere—where we can find the area of the surface easily, but if the surfaces are complicated, then doing the actual sum over the surface elements can be quite difficult, and only approximate answers can be found in regard to the amount of the net electric charge inside. People are even more complex than anything nature presents, and we will truly need to access an almost infinite number of facets to form a complete picture of any person. We cannot even come close to that possibility in our brief lifespans and the even briefer interludes of interaction with any particular person, no matter how close and intimate we might be. So our knowledge of anyone remains essentially incomplete.
The notion of all relevant information about a system being on its surface has found much deeper and more profound implications in recent decades. One of the most important developments in contemporary theoretical physics, simply known as the holographic principle, suggests (in its broadest and most speculative claims) that the entire universe can be thought of as being encoded on a two-dimensional “surface” that forms its cosmological boundary. The more rigorous versions of this essentially make a similar claim but not for the entire universe, rather for specific regions of space and all the matter and energy it contains—the description of such a region and basically all the information it contains is encoded on its boundary or surface. That volume of space might be the one that includes our solar system and all of humanity, as well. Unlike Gauss’s law, the holographic principle is not an experimentally proven fact, but rather an attractive and logically consistent hypothesis.
—we can state with certainty that there are five units of electric charge inside the spherical surface shown. With Gauss’s law, we would not be able to differentiate whether all of it is on one object at the center or distributed equally among five objects, and in the latter case, the five bits of charge could be located anywhere inside the surface without changing the conclusions of Gauss’s law. There is a very similar situation with gravity: We can imagine an enormous imaginary surface enclosing the earth and the moon. By applying the gravitational equivalent of Gauss’s law, we could tell what the total mass of the earth-moon system is by measuring the inward force at all points on the surface. But if the moon were to fall into the earth, we would still get the same answer, and if the moon and the earth got compressed to the size of a peanut forming a black hole, we still would not be able to tell the difference from the surface measurements, because the amount of mass or matter within the surface remains the same.
Electric charge is just bits of electricity, the smallest bit being carried by the subatomic particles, electrons and protons. In a neutral atom, there are equal numbers of negatively charged electrons and positively charged protons; therefore, although everything is made of atoms, including ourselves, most objects do not appear “electrically charged.” But sometimes, electrons can be knocked out of atoms, breaking the balance of charge inside atoms. This is what happens when winter coats rub against our clothes or body, and we build up “static electricity,” meaning that electrons from the atoms in the coat are being knocked off onto our body or vice versa, making the one with a deficit of electrons “positively charged” and the other with an excess of electrons “negatively charged.” Static discharge happens when we then touch another object, like a doorknob or another person, as electrons jump across to even out the imbalance.
The holographic principle is anchored in the physics subfield of string theory, which is based on the hypothesis that the fundamental entities in the universe are not point-like particles, but tiny “strings.” The interest in string theory is largely motivated by the thought that it is one of the most promising routes to reconciling Einstein’s theory of gravity with quantum mechanics, two great pillars of modern physics that have continued to be incompatible so far.