THE 3 LEVELS OF PHYSICS ARE FUNDAMENTAL, QUANTUMM, AND CLASSIC.
VERN BENDER
In the equation, E = m c2, E stands for energy, m stands for an object’s mass, and c2 represents the speed of light (186,000 miles per second) multiplied by itself. Think of mass as simply the quantity of matter present. Energy is a tougher concept, but it is okay to think of it as a property of heat or light.
Originally, E=mc2 appeared (not precisely in this form, but never mind technical details) in Einstein’s 1905 paper. This was a groundbreaking moment in the history of physics, where he demonstrated that the inertial mass of an object is proportional to its energy content. That energy content has to be measured, of course, in the object’s rest frame of reference. Neither inertial mass nor a rest frame of reference, so E=mc2 plays no role.
Later on, it became evident that E=mc2 is just a particular case of a more general equation that is valid in all reference frames, not just the rest frame of reference of the object in question:
E2=(mc2)2+(pc)2, E2=(mc2)2+(pc)2,
where p, of course, is the object’s momentum. In the object’s rest frame of reference, p=0, we are left with E=mc2.
For photons, the situation is different. They have no rest frame and no inertial mass, so for them, we have instead E=pc.E=pc. That is to say, a photon’s kinetic energy is proportional to its momentum. This, of course, is a well-known formula that characterizes electromagnetic radiation, so there.
So you see, maybe those generations of physicists were not so dumb after all and knew what they were doing. Allow me to offer an additional tidbit that you may find fascinating in the form of a thought experiment. This experiment, while theoretical, is a powerful tool to understand the concept. As I said, photons have no energy content, rest frame of reference, or inertial mass. However, now imagine something else: a box lined on the inside with perfect mirrors. This ingenious setup allows us to explore the implications of E=mc2 tangibly. Allow some light in and seal the box. Those photons inside the box bounce back and forth forever, always reflected by those perfect mirrors. Photons have no rest mass. But what about the energy content of the system, i.e., the box with photons inside?
Well, think about it. Suppose you try to push the box, accelerating it. Photons impinging on the inside of the wall you are pushing receive a small amount of extra momentum since the wall is accelerating toward them due to your push. Photons on the opposite side weaken the inside wall because they accelerate away from them. The net result? The near wall is more challenging to push; the far wall receives less assistance from the photons inside… Overall, it became harder to push the box! So, the inertia of the box increased. Increased by how much, you wonder? Well, by precisely the energy of the photons inside the box, as measured in the box’s reference frame.
So there you have it: even though photons are massless, their kinetic energies can contribute to the energy content, i.e., the inertial mass of the box that contains them. It’s a surprising revelation that challenges our intuitive understanding of mass and energy.
Moreover, while this thought experiment may be hard to realize (for starters, perfect mirrors do not exist), the energy content of trapped photons can represent a not insignificant contribution to the mass of a star (incredibly giant stars). In the early universe, there was an epoch, the radiation-dominated era,” when the universe’s mass was dominated by its photon content, not matter. This historical period underscores the profound influence of photons on the evolution of the cosmos
Originally, E=mc2 appeared (not precisely in this form, but never mind technical details) in Einstein’s 1905 paper. This was a groundbreaking moment in the history of physics, where he demonstrated that the inertial mass of an object is proportional to its energy content. That energy content has to be measured, of course, in the object’s rest frame of reference. Photons have neither inertial mass nor a rest frame of reference, so E=mc2 plays no role.
Later on, it became evident that E=mc2 is just a particular case of a more general equation that is valid in all reference frames, not just the rest frame of reference of the object in question:
E2=(mc2)2+(pc)2, E2=(mc2)2+(pc)2,
where p, of course, is the object’s momentum. In the object’s rest frame of reference, p=0, we are left with E=mc2.
For photons, the situation is different. They have no rest frame and no inertial mass, so for them, we have instead E=pc.E=pc. That is to say, a photon’s kinetic energy is proportional to its momentum. This, of course, is a well-known formula that characterizes electromagnetic radiation, so there.
So you see, maybe those generations of physicists were not so dumb after all and knew what they were doing. Allow me to offer an additional tidbit that you may find fascinating in the form of a thought experiment. This experiment, while theoretical, is a powerful tool to understand the concept. As I said, photons have no energy content, rest frame of reference, or inertial mass. However, now imagine something else: a box lined on the inside with perfect mirrors. Allow some light in and seal the box. Those photons inside the box bounce back and forth forever, always reflected by those perfect mirrors. Photons have no rest mass. But what about the energy content of the system, i.e., the box with photons inside?
Well, think about it. Suppose you try to push the box, accelerating it. Photons impinging on the inside of the wall, you will receive a small amount of extra momentum since the wall is accelerating toward them due to your push. Photons on the opposite side weaken the inside wall because they accelerate away from them. The net result? The near wall is more challenging to push; the far wall receives less assistance from the photons inside… Overall, it became harder to push the box! So the inertia of the box increased. Increased by how much, you wonder? Well, by precisely the energy of the photons inside the box, as measured in the box’s reference frame.
So there you have it: even though photons are massless, their kinetic energies can contribute to the energy content, i.e., the inertial mass of the box that contains them.
Moreover, while this thought experiment may be hard to realize (for starters, perfect mirrors do not exist), the energy content of trapped photons can represent a not insignificant contribution to the mass of a star (incredibly giant stars). /’; In the early universe, there was an epoch (the “radiation-dominated era”) when the universe’s mass was dominated by its photon content, not matter.
