What Are Your Thoughts on Dual Meanings in Physics Terminology?

[pmb_phy]

I wass wondering what people here think about the use of terminology when it can have multiple meanings. E.g. "mass" can mean either relativistic mass or rest mass, "momentum" can mean linear mechanical momentum or it can mean canonical momentum. Some people prefer to hold that the Lagrangian defines kinetic energy whereas others believe that the lagrangian itself is defined in terms of kinetic energy.

Do these dual meanings bother you? I'd love to hear your thoughts on this point.

Pete

 

[Critical_Pedagogy]

"Pete"; There aren't enough words to describe everything. There's only a few million words and trillions of 'things'. As a result, every word stands for more than one 'thing'.

The human race needs to create a new language with 10^100 letters. That would allow each word to represent it's own 'thing'. The United Nations should consider it.

 

[bernhard.rothenstein]

I wass wondering what people here think about the use of terminology when it can have multiple meanings. E.g. "mass" can mean either relativistic mass or rest mass, "momentum" can mean linear mechanical momentum or it can mean canonical momentum. Some people prefer to hold that the Lagrangian defines kinetic energy whereas others believe that the lagrangian itself is defined in terms of kinetic energy.

Do these dual meanings bother you? I'd love to hear your thoughts on this point.

Pete

it bothers me not at all as long as i know what about i am speaking. some times problems of semantics arrise. if m means mass then mcc means energy and the invariance of c makes that i speak about the same thing as Molier's character who did not know that he speaks in prose.

 

[robphy]

To me, a "term" is a convenient abbreviation for a "precise definition" which tries capture or model some [generally] "abstract idea".

So, as others have suggested, it shouldn't be a problem as long as we agree sufficiently on the [working] definition in the context of our problem. As one expands the context of the problem, sometimes these previously defined "terms" clash and the definitions may have to be revised and refined. In redefining a "term", it may be useful to consider "what would get me to next level, in a more general setting?", which could certainly vary from researcher to researcher.

 

[pmb_phy]

To me, a "term" is a convenient abbreviation for a "precise definition" which tries capture or model some [generally] "abstract idea".

So, as others have suggested, it shouldn't be a problem as long as we agree sufficiently on the [working] definition in the context of our problem. As one expands the context of the problem, sometimes these previously defined "terms" clash and the definitions may have to be revised and refined. In redefining a "term", it may be useful to consider "what would get me to next level, in a more general setting?", which could certainly vary from researcher to researcher.

I recall in grad school one day that the text said something to the effect "by 'momentum' we mean canonical momentum" and it was deep into the first volume as I recall. That's what I was thinking about when I wrote this question. I guess it'd be too redundant to keep calling it the canonical momentum and simply call it momentum. I guess this is what happened withe the term "rest mass" too, yet another reason I asked all this.

Pete

 

[robphy]

I recall in grad school one day that the text said something to the effect "by 'momentum' we mean canonical momentum" and it was deep into the first volume as I recall. That's what I was thinking about when I wrote this question. I guess it'd be too redundant to keep calling it the canonical momentum and simply call it momentum. I guess this is what happened withe the term "rest mass" too, yet another reason I asked all this.

Pete

It's all fine as long as the definition is made clear...and everything is used consistently.

In my opinion, however, any important statement that might be quoted (possibly out of context) should be stated with precision, i.e. with the adjectives that may be redundant or inconvenient in the original text, so that it is as self-contained and unambiguous as possible.

 

[mannyfold]

Well, "mass" usually means "rest mass" unless otherwise stated. It gets a little hairy in a relativity course, but in real life mass is rest mass.

 

[pmb_phy]

Well, "mass" usually means "rest mass" unless otherwise stated. It gets a little hairy in a relativity course, but in real life mass is rest mass.

Thanks for your input mannfold. I'm trying to staying away from this example in this thread since we discuss it so much elsewhere. Thanks.

Pete

ps - I will say this though: In Gravitation, Misner, Thorne and Wheeler (MTW), a staple for most GRist nowadays, on page 404 the authors state "Mass is the source of gravity." What do you think they meant by "mass" here?

 

[robphy]

I will say this though: In Gravitation, Misner, Thorne and Wheeler (MTW), a staple for most GRist nowadays, on page 404 the authors state "Mass is the source of gravity." What do you think they meant by "mass" here?

[This reply addresses the related question in your PM: "...whereby mass they mean mass-energy? I.e. why not just say that Mass-Energy is the source of gravity" and be done with it?" (Sorry if this spoils the fun... but my response here might be useful for this thread.)]


Of course, I'm no expert in MTW [in its content, philosophy, and prose]... but my guess is that it probably didn't sound good or catchy enough. As you see in the next few sentences, they clarify the initial statement... with mass-energy.

As you probably know, lots of such memorable "slogans" appear in Wheeler's writings. For example, MTW p.5 has the famous "Space acts on matter, telling it how to move. In turn, matter reacts back on space, telling it how to curve" that sloganizes the previous sentences. Here, as well, one might ask... why not "...reacts back on spacetime"? (Other examples are "mass without mass" and "charge without charge"...)

In my opinion, the "slogans" capture the heart of the abstract idea but are not to be taken literally as one would do with a mathematical theorem [especially when the words in the slogan are not all carefully defined]. One has to look further at what specifics the slogan is trying to convey...otherwise, the slogan can be open to [mis]interpretation.

robphy

 

[HallsofIvy]

The human race needs to create a new language with 10^100 letters. That would allow each word to represent it's own 'thing'. The United Nations should consider it.

That would be unspeakable!

 

[pmb_phy]

"Pete"; There aren't enough words to describe everything.

For that reason there are qualifiers such as "proper" in "proper mass," and "relativistic" in "relativistic mass," "canonical" as in "canonical momentum" etc.

Ever notice that every dictionary usually has more than one meaning to any given word?

Pete

 

[Stingray]

Qualifiers are impractical to use all the time. That's why we have context. I don't really recall ever being confused as to which definition of some concept was being applied. At least not in any textbook, paper, or discussion with another physicist/physics student. There are confusions when discussing things with "amateurs" or beginning students who don't really know the "culture" behind each word.

I don't understand your example from MTW. It was clearly an imprecise statement meant to give a feel for the concept. These are everywhere in physics, and most people realize that that's all they are. If you'll notice, that paragraph ends with "Therefore the stress-energy tensor T is the frame-independent 'geometric object' that must act as the source of gravity." I don't think anyone says that the stress-energy tensor is the same as the mass. MTW started out with an intuitive idea and then made it more precise.