My Awesome Stack Exchange Question about how the word “mass” is used in Relativity. A copy paste of the final version. “Deleted by a community bot?”

What is the downside of using the phrase “rest mass” in place of “mass” in relativity? [closed]

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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? One might also ditch “invariant mass” on the grounds that it means the same as “rest mass” but has more syllables, albeit arguably less of misnomer (but maybe using a slightly misnomeric term is not a big deal). An advantage to this would be that use of “mass” (or “relativistic mass” or “invariant mass”) would indicate, or at least give a clue to, that one did not know about the latest textbooks of relativity theory, or one was not talking about relativity and was e.g. talking about Newtonian mechanics. Indeed, there’s quite a lot of times when having to say, “neglecting relativistic effects” could be dispensed with by signalling that by using the plain word “mass”, and/or the letter m

to represent it. Thus F=ma would indicate nonrelativistic physics, while F=m0a would indicate relativistic physics or more likely F=m0γa would. m0 would mean rest mass and be pronounced “rest mass” while γ

stands for the Lorentz factor (https://en.wikipedia.org/wiki/Lorentz_factor). Another advantage would be that by “mass” you show that you are up to speed on the latest developments in relativity, and conversely those ignorant of these would immediately signal that fact by using “mass” while talking about relativity. While not conclusive, it might in the near future be a big clue, and one day might even be conclusive, if relativists decided overwhelmingly that the downside of avoiding plain “mass” is not prohibitively large. Please note the more people that are noticed to be confused about mass in relativity, by themselves or others, the more people can be made aware of their shortcomings, and hence or otherwise be helped to greater level of knowledge. I myself until coming to SE a year or two ago, had ignorantly concluded that a lot of physicists simply had conflated rest mass with mass and that was the reason that they thought photons had no mass. I was ignorant of the “method to their madness” so to speak. This would never have happened had physicists told me that the word “mass” is not used in relativity, and neither is “relativistic mass”.

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 “mass” nor “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 rest 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 m0

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 m0

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).

A comment by Dale said that the subscript zero would be inconvenient because one often wants to add subscripts in physics, which is a great point IMHO. That made me think that instead of “rest mass” and m subscript zero, one could have concise new terms and symbols, “rass” being a portmanteau of “rest” and “mass” and some letter (preferably with a one syllable name, unlike “omega”, but like “mu”) maybe from Greek or Hebrew or some other alphabet as symbol for it.

Because as soon as you admit the concept of relativistic mass students (quite reasonably) start asking why everything moving fast enough relative to us doesn’t turn into a black hole.

John Rennie

Jul 4 at 8:49

  • @JohnRennie It says in the question, “while having a convention of avoiding the terms “invariant mass” and “relativistic mass” as far as possible”.
  • Matthew Christopher Bartsh
  • Jul 4 at 10:00
  • 6

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.
  • John Rennie
  • Jul 4 at 11:43
  • 3
  • What John said. If someone asks “What’s the mass of a photon?” we can simply answer “Zero”. End of story. But if they ask “What’s the rest mass of a photon?” then we kind of have to say “A photon has no rest mass because there’s no frame in which a photon is at rest”. And then a long discussion often ensues, based on misconceptions connected to rest mass. OTOH, I guess it can be appropriate to use the term “rest mass” when communicating with someone who appears to be following the “relativistic mass” convention, but I don’t know whether it helps, or if it just prolongs the confusion. ;)
  • PM 2Ring
  • Jul 4 at 15:25
  • @PM2Ring I edited my answer to address your points.
  • Matthew Christopher Bartsh
  • Jul 5 at 6:34
  • @JohnRennie I added some text to address the points you made.
  • Matthew Christopher Bartsh
  • Jul 5 at 7:03
  • @PM2Ring The intro to this article en.wikipedia.org/wiki/Energy%E2%80%93momentum_relation says invariant mass is also known as rest mass and states that E² = (pc)² + (m subscript zero c²)² which of course contains the symbol m subscript zero. Do you really take issue with this? How would you express it better?
  • Matthew Christopher Bartsh
  • Jul 5 at 13:29
  • @JohnRennie I put to you the same question I put to PM 2Ring just now about the intro to the Wikipedia article.
  • Matthew Christopher Bartsh
  • Jul 5 at 13:31
  • Personally, I just found a big disadvantage with your suggestion. I had to go through your question and change all of the “m subscript zero” text into properly formatted LaTeX. But requiring subscripts is a generally bad idea particularly when subscripts are being used for something else in a text, as they frequently are in physics. FYI, I avoid “rest mass” entirely and use only “invariant mass”. Otherwise it is confusing to talk about the mass of a rotating disk or a gas.
  • Dale
  • Jul 5 at 13:44
  • 1

Momentum isn’t p=()v

. It is p=m(γv). By reading your question it is really difficult to address it as it appears to have some misconceptions. However, at this point I would just recommend you to follow @JohnRennie ‘s advice: purge all considerations on “relativistic mass”. It is a difficult, unnecessary, complicating factor that you don’t need. Just call m the mass and get used to write p=mγv, instead of p=mrv

  • .
  • J. Manuel
  • Jul 5 at 14:05
  • @Dale Awesome editing. I must learn how to use LaTeX. What sort of subscripts might find the subscript zero in the way? Would it be a big deal to have a presubscript or presuperscript if those are words instead? Or how about instead of m subscript zero a special new symbol so that there is space for a subscript?
  • Matthew Christopher Bartsh
  • Jul 5 at 14:05
  • I cannot fathom the revisionism that rejects one of the most profound scientific discoveries of all time: mass-energy equivalence. Of course, it’s still there, hidden in the math, but math isn’t physics.
  • John Doty
  • Jul 5 at 14:05
  • @JohnRennie You’re talking about a “physics” curriculum that turns out students who can’t use a battery, a wire, and a light bulb to make light. They’re lost in abstraction.
  • John Doty
  • Jul 5 at 14:09
  • @Dale Regarding the mass of a rotating disk or a gas, “rest mass” is, as you correctly point out, a bit confusing. But this is I think only because “rest mass” is slightly misnomeric and most people who are thinking or talking about the mass of a rotating body in the context of relativity should be well aware that “rest mass” is a slight misnomer and well aware of the exact meaning with which it is used in relativity, which if understand it, is the same as “invariant mass” (but that’s such a mouthful, and is confusing and offputting to people (majority) who think that mass varies with speed).
  • Matthew Christopher Bartsh
  • Jul 5 at 14:19
  • @PM2Ring If you say the mass of a photon is zero, people will likely conclude that a photon has no mass in any shape or form, and so will have no gravitational field, and maybe even no momentum. When you use “rest mass”, do you point out that this is the only kind of mass in modern relativity? If so, how does it prolong the pain and confusion? The meaning of “rest mass” is crystal clear to everyone, despite being harmlessly misnomeric in some contexts. It’s “mass” that is likely to be interpreted according ones pre/mis -conceptions. BTW do you ever use the term “relativistic mass”?
  • Matthew Christopher Bartsh
  • Jul 6 at 8:47
  • @PM2Ring Do you specify rest energy in kilograms or joules? Would you ever specify kinetic energy in kilograms? What about the term “inertial mass”? It it useful? Is it a synonym of “relativistic mass”? Regarding the Wikipedia article, you are correct of course that it’s not an academic standard. I only mentioned it because it seemed to make so much sense to me, and because Wikipedia does tend to represent what the majority of people interested in a topic think, or if not, the dominant group among them. Using the word “mass” seems not to have worked to get the word out about true relativity.
  • Matthew Christopher Bartsh
  • Jul 6 at 9:00
  • Let us continue this discussion in chat.
  • Matthew Christopher Bartsh
  • Jul 6 at 9:46
  • @JohnRennie In modern relativity, is it the case that, on the one hand, it is wrong to say that each quantity of energy regardless of type has a mass, while. on the other hand, it is correct to say that it has a weight if there is gravity?
  • Matthew Christopher Bartsh
  • Jul 14 at 17:38

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