I rarely discuss definitional matters, for the simple reason that I do not necessarily understand them more clearly than anyone else, nor is my knowledge necessarily more accurate. However, having just discussed mass-related issues with a fellow enthusiast, I would like to share some thoughts with you.
The initial question was whether energy can be converted into matter. I felt that according to E=mc^2, it is clearly possible. As for an example, I first thought of how the vacuum in quantum field theory constantly produces and annihilates electron-positron pairs; this can serve as evidence. However, this feels a bit too distant from daily life, so I searched the internet. The content I found was largely similar:
When the energy of radiant photons is high enough, as they pass by an atomic nucleus, under the action of the nuclear Coulomb field, the radiant photons may be converted into a positron and an electron. This process is called the electron pair effect.
(Electron-positron pair effect)
I then went on to tell my friend that in relativity, mass and energy are essentially equivalent and are not explicitly distinguished; therefore, where there is energy, there is mass, and vice versa. He then asked: If there are energy changes in chemical reactions, does that mean the Law of Conservation of Mass is no longer satisfied?
In fact, from the perspective of relativity, the Law of Conservation of Mass was never a truly correct law to begin with. It is only because, in low-energy macroscopic situations, the degree of deviation from the conservation of mass is so small that general measuring instruments find it difficult to detect; thus, the law is generally considered correct. In relativity, the Law of Conservation of Mass-Energy is the correct one. But the next question followed: Chemical reactions are merely the recombination of atoms and molecules; no matter is lost or added, so how can there be a change in mass?
First, let us set aside whether the mass of atoms changes after a chemical reaction and ask: If mass increases, does it necessarily reflect an increase in specific physical matter? Let us start with the definition of mass.
What is the definition of mass? I vaguely remember my middle school physics book saying: The amount of matter contained in an object. I memorized it back then, but now it seems like an absurd definition. First, it does not define what “matter” is, and second, it does not define what this “amount” is. In other words, it defines no measurement at all! In physics, to define a quantity, one must simultaneously derive a measurement method from the definition. More accurately, physical quantities should be defined based on measurement. For example, to define distance, one must explain how to measure it—such as establishing a coordinate system in space, where the difference between the coordinates of two points defines the distance. Without measurement, there is no definition.
Returning to mass, intuitively speaking, mass can be defined as the magnitude of inertia. However, my friend mentioned that his textbook stated inertia can only be said to be “possessed,” not to have a “magnitude.” I was immediately speechless—what an absurd physics book! It defines a characteristic that all objects possess but claims this characteristic cannot describe specific features! If that were the case, the concept of inertia itself would be useless. It would be like saying “everyone has something, but this thing is invisible and untouchable (unperceivable)”—what is the difference between that and not having it at all? Therefore, I insist that mass is the magnitude of inertia.
Inertia is the inherent characteristic of an object to maintain its state of motion. Obviously, according to Newton’s Second Law F=ma (though it is not perfectly accurate), the greater the mass, the harder it is to change the object’s state of motion. So, saying mass is the magnitude of inertia is not wrong; in fact, it is the case. This is the definition of inertial mass.
There is another type of mass in physics called gravitational mass. As the name suggests, it is defined according to the Law of Universal Gravitation. It states that mass is the source of gravity. That is to say, anything capable of producing a gravitational field is a manifestation of mass. This definition is even broader; it does not say that mass must be embodied in specific matter. In fact, energy can also produce gravitational effects (this falls within the domain of General Relativity), so energy also possesses the characteristics of mass. As for gravitational mass and inertial mass, Einstein (and all other supporters of General Relativity) believed that the concepts of mass defined by both are identical—that is, they are the same thing. (In other words, they might use different units, but they are inherently identical; it is certainly not a case where one is time and the other is length.)
Having said all this, we still haven’t defined mass strictly through measurement, but we have gained some intuitive understanding: it produces inertia and it produces gravity, so we define it conversely. For instance, measuring inertial mass can be done by applying a force to an object and measuring the resulting acceleration. By applying a force of the same magnitude, an object with smaller inertial mass will gain a greater acceleration than an object with larger inertial mass. An object with larger mass is said to have greater inertia. Measuring gravitational mass is similar, though demonstrating the gravitational effect of energy requires observations on an astronomical scale.
Having said all this, I am not sure if I have made myself clear. Actually, this is a bit like showing off one’s slight skill before a master; I just wanted to express my views on this issue based on my current level of knowledge. Perhaps after some time, I will have new perspectives, and looking back at this article then will surely have a different flavor.
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