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In the Newtonian sense, "mass" is representative of a body's general resistance to motion. Einstein derived $E = mc^2$ but it was in the context of the amount of mass lost after a body emits some amount of light with energy $E$. In that context, $m$ is more like a $\Delta m$. Another interpretation of $E = mc^2$ is, for a body of mass $m$, $E$ is the total amount of electromagnetic energy you could get out of it if all of its mass were converted to light radiation.

Both interpretations of $E = mc^2$ seem to refer to specific thought experiments/hypotheticals, and it seems that $E$ always refers to the energy carried by light in any of these interpretations, so we are constrained to conceive of it in that way.

My question though is: is it possible, since we do have a relation between $E$ and $m$, to simply eliminate the concept of inertia entirely? For example, why not just substitute $\frac{E}{c^2}$ as $m$ into ${\bf F} = m{\bf a}$ and work instead with energies, forces, and motions? In this setting, we have to conceive of energy as "the capacity for a body to perform work on its surroundings," rather than a constant of motion that arises from a time-translation symmetry. "Mass" becomes a potency for a body's ability to both create light and perform work.

Wouldn't this eliminate a concept ("mass," whatever it is) and streamline the theories? But maybe the classical interpretations are just more attractive over thinking in terms of potency all the time. Not to mention the practical aspect of having extremely large numbers to work with once the speed of light is baked into all the equations.

Qmechanic
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HelpMe
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3 Answers3

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In this answer, by "mass," I mean "rest mass" (sometimes called the "invariant mass").

Mass isn't equivalent to energy -- if you take the word "mass" and simply replace it with "energy" everywhere you find it written in a physics books, you will end up with some incorrect or at best very misleading statements. Mass is a form of energy. In particular, mass is the lowest energy that a particle can have -- it is the energy of a particle at rest (so long as the mass is larger than zero). We can distinguish particles by whether their mass is zero or non-zero. Furthermore, the mass of a particle sets the energy scale at which that particle becomes relevant; one reason (not the only reason) it took so long to discover the Higgs in the history of particle physics, is that its mass is quite large (compared to, say, the electron and proton), so it took a while to build generators that could produce collisions with energies large enough to produce a Higgs.

Therefore, I do not think it would be useful to retire the concept of mass. Mass is a type of energy that tells us several useful things about a particle's intrinsic properties. The total energy of a particle also includes information about its state of motion and its interaction with other particles, which are not intrinsic to the particle.

Andrew
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You're basically asking if you can absorb the concept of energy to also include mass. Sure, they're just words.

The distinctions between "mass" and other forms of energy would still exist. It wouldn't make mass more similar to other forms of energy.

In QFT, we already make heavy use of the mass-energy tensor, and use "natural units" that make mass and energy the same units. That helps streamline the theory, calling mass "energy" wouldn't help streamline it any more.

In the classical regime, using $\frac{E}{c^2}$ wouldn't provide any advantage over using rest mass. It's still got unique units $\frac{J \cdot s^2}{m^2}$

Señor O
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The speed of light is a constant, so we can work in a system of units where $c = 1$. In that case: $$E^2 = m^2 + p^2 => m = \sqrt{E^2 - p^2}$$ Different observers would disagree on the energy of the object, but would agree on its mass. Mass is an invariant scalar of an object, while energy depends on the particular frame.

Claudio Saspinski
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