What is the downside of using the phrase “rest mass” in place of “mass” in relativity? [closed], being a Copy Paste of A Question I Posted on Stack Exchange.
In a comment on Why is there a controversy on whether mass increases with speed? the user https://physics.stackexchange.com/users/287817/eric-smith says that “There is controversy only over the meaning of the word “mass”. There is no controversy over the actual physics. The “rest mass” of a body is defined so that it cannot (by definition) be velocity dependent. The “inertial mass” of a body, i.e. its energy content, certainly does change with velocity. So the only controversy is whether the unadorned word “mass” should refer to “rest mass” (invariant, never changes) or “inertial mass” (changes). Modern textbooks prefer the former definition, and use “energy” for the latter.”
I would tend to agree with that, based on what I’ve been able to find out, if “modern textbooks” means the latest relativity textbooks. I would summarize Smith’s position as saying that the latest relativity textbooks use the word “mass” to mean “rest mass” (which is invariant and never changes), and use the word “energy” to mean “inertial mass” (which changes depending on it’s speed).
So why not use “rest mass” to mean “rest mass” and avoid using the word “mass” (unadorned) in relativity?
Many people on Physics seem to take the view expressed rather elegantly by John Rennie in a comment, which was “If you use the term rest mass and symbol m0 you are implying other forms of mass and other uses of the symbol m exist. Purge all such considerations from your mind. There is only one quantity called mass and we use the symbol m to denote it.”
I’m guess that Rennie’s position is the majority one among professional relativists. I agree that using “rest mass” implies that you think there is at least one other form of mass, but this implication can easily be negated by explaining as early as possible that “rest mass” is a (useful, I’d argue) misnomer that stands for what some call “inertial mass” and others call “invariant mass” and others call in a relativity context (causing confusion to all except fellow professional relativists, I’d argue) “mass”.”
The thing is, the vast majority of people, and even arguably the majority of physics graduates are already utterly confused about “mass” in relativity, including what it means. “Rest mass” OTOH is clearly understood, both the term and the concept, except perhaps when “zero rest mass” is being talked about, e.g. in the case of the photon. Nearly everyone already is sure that “mass” means “relativistic mass” and that “mass increases with velocity”. They also think that “the rest mass of a photon is zero”, and that “photons have no mass”, and this is because that’s what physics used to teach, up until about 1970 (so I’ve heard), and still seems to teach in many cases (though that is arguably physics getting misrepresented). It is incredibly hard to find out that there is any doubt or problem with the statement “mass increases with speed”. If people saw that neither unadorned “mass” nor unadorned “m”, (nor “relativistic mass”) were mentioned in relativity they would get a clue that they were confused especially if whenever they asked about “mass” they were told that that word is not used in relativity (and maybe why not).
The use of “rest mass” to mean “rest mass” and “invariant mass” could be a measure, at least until such time as people come to understand that “relativistic mass” is not a term or concept used in relativity, and never again will be.
If someone asks, “What is the mass of a photon?”, the professional relativist can answer, “Relativity is hard. We don’t use the word “mass” unadorned in relativity”, or “What kind of “mass” are you asking about?”. If they say, “I’m asking about the rest mass of a photon.”, the reply can be, “There’s no frame in which a photon is at rest, so “rest mass” is a little bit of a misnomer when applied to a photon, but in relativity, the rest mass of a photon is zero, but a photon does have energy and momentum and a gravitational field and when trapped in a bottle with other photons adds to the total mass of the bottle including its contents. Relativists used to say that energy has mass and therefore a photon has mass but that way of talking causes severe problems, so we don’t say that now. Did I mention that relativity is hard?”
If someone asks, “What is the rest mass of photon?” the answer is “Zero”.
If someone asks, “What is the relativistic mass of a photon?”, the reply can be, “Relativistic mass” is a term avoided in relativity these days, due the severe problems that the concept causes. What you call relativistic mass corresponds most closely to what, in relativity, we call “energy”, which is the total “energy” of the thing including its rest mass and kinetic energy and any other energy it might have.” I hope I got that last bit right.
Using the term “rest mass”, and the symbol m
subscript zero to represent it in equations, and avoiding the terms “relativistic mass” and “invariant mass” would prevent an awful lot of misunderstanding and controversy, as well as being crystal clear in meaning, and arguably more consistent with the way the word “mass” is used in most of physics. The professional relativists would be able to think and calculate in in the way they have become accustomed to during the last fifty years (?), while the public and a good few fellow physicists would be less confused and/or unhappy.
What I want to know is what, if any, would be the downside (apart from the extra ink and breath needed) of replacing “invariant mass” with “rest mass”, and rather than (unadorned) “mass” saying instead “rest mass” and using the symbol m
subscript zero instead of the symbol m
in calculations, while having a convention of avoiding the terms “invariant mass” and “relativistic mass” as far as possible?
Or is the only downside the hassle of an extra syllable in speech, an extra four letters in writing, and an extra subscript in equations?
Besides a convention of avoiding the terms “relativistic mass” and “invariant mass”, the concept of “relativistic mass” could perhaps by convention not be introduced to students except when explaining why it is not used in physics, if it is considered to be bad to use it in physics (I admit I’m out of my depth on the latter question).