# Gaining Mass

#### Nim

People say that the faster something moves the more mass it gains. I remember someone else saying that it doesn't gain actual mass, and explained it a different way. I can't remember what they said though. Anyone know what I am talking about or know if there is any truth to it? Is saying that the faster something is going the more mass it gains just a simple way of putting it? The thread was on the HSW forums which have closed down unfortunately.

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First of all, in relativity you always have to say "moving really fast" realative to what? Because the person moving at a steady speed does not feel himself moving (this is all worked out in a vacuum where there isn't any wind rushing past you as you go).

So let's say there is a home base somewhere that regards itself as at rest, and it's observing a spaceship that is moving fast, near the speed of light.

Both the people on the home base and the people on the ship can do physics experiments and get numbers the same as if both of them were at rest. It's only when they try to measure things in each other's "frame of reference" that the relativity expansion comes in.

When the base tries to measure the ship's mass and energy, or the ship tries to measure mass and energy on the base, a multiplier comes in, because of the theory of relativity. And this is where the disagreement you mentioned comes about.

The relativity math allows one of the two things, mass and energy, to remain constant, and the other to increase by the speed multiplier. The physics doesn't care which you pick, it's something like picking a coordinate system.

In older books physicists reasoned, "Energy should be conserved, so we will pick energy to be constant and mass to increase with relative speed".

But in more recent times there has been a lot of use of relativity to analyze particles moving very fast relative to experimental equipment in accelerators and cosmic rays. In this kind of work it's convenient to have the mass of the particle stay constant and vary the energy. So that's the way they teach it now. This means the energy has to be given by a formula with the speed in it (actually the momentum) and you will see this formula around E^2 = p^2c^2 + m^2c^4 where c is the speed of light, p is the size of the momentum, and m is the mass.

#### Ambitwistor

The issue is that there are just two different definitions of "mass" floating around. When relativity was invented, it was popular to speak of mass increasing with velocity; nowadays, it's popular to speak of it not increasing with velocity. (The velocity-increasing kind of mass is now more often called "relativistic mass" or "mass-energy".) Here is a FAQ:

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

#### pmb

Originally posted by Nim
People say that the faster something moves the more mass it gains.
Whether that is true depends on what the person means by the term "mass." They may mean either "relativistic mass" (aka "inertial mass") or "proper mass" (aka "rest mass").

Rel-mass is the m in p = mv, i.e. m is defined such that mv is conserved. For details on what that means please see

http://www.geocities.com/physics_world/sr/inertial_mass.htm

As such m is a function of speed, i.e. m = m(v). The quantity m(0) is called the "rest mass." The v is the relative velocity of oberver and particle. To each different inertial frame of referance one can assign an observer. Each observer measures a different mass.

People who use that definition include the Associate Director of Fermilab

http://www.fnal.gov/pub/inquiring/questions/accel_obj.html

For a list of examples of modern usage see
http://www.geocities.com/physics_world/relativistic_mass.htm

I remember someone else saying that it doesn't gain actual mass, ..
Whomever said that was not being completely honest about it. If you asked about the mass increase then if the person who answered you knew what they were talking about should have explained that he was refering to a different definition of mass. Sometimes people mean "rest mass" when they use the term "mass." It usually depends on what field of physics a given person works in. Particle physicists tend to mean "rest mass" since that is what they study. But that term is not always meaningful. Particle physicists only study particles. If one wants to speak of the mass of a cooling rod which is moving then there is no meaningful way, in general, to say that the mass of the moving body does not depend on speed. Cosmologists, on the other hand, tend not to use that definition.

Anyone know what I am talking about or know if there is any truth to it? Is saying that the faster something is going the more mass it gains just a simple way of putting it?
Yes. There certainly is truth in what you say. There was an attempt to ban relativistic mass from the physics literature. The attempt was not completely successful. In fact it angered some relativists. See

http://www.geocities.com/physics_world/rindler_article.htm

"In defense of relativistic mass,"T.R. Sandin, Am. J. Phys. 59 (11), November 1991

If you'd like to read it but don't have access to a library then I'd be happy to scan it and mail it to you.

Pete

#### pmb

Re: Re: Gaining Mass

That is an old version. The newer, correct, version is

The old one incorrectly claimed
In modern physics texts, the term mass when unqualified means invariant mass, ..
That is incorrect. It has been corrected. It now reads
In modern physics texts, the term mass when unqualified means invariant mass in most cases, ..
I disagree since it does not hold in most cases either.

#### Ambitwistor

Re: Re: Re: Gaining Mass

Originally posted by pmb
I disagree since it does not hold in most cases either.
In most, well, modern modern physics texts, I have found that it does, but we're probably looking at different texts.

In any case, textbooks always lag behind current usage, and if you attend conferences and seminars, you will find that both the high-energy physics community, the relativity community (and in my limited experience with talks in that field, yes the cosmology community too, which is increasingly being influenced by particle theory) have largely adopted the term "mass" to mean "invariant mass". The holdouts are usually the older scientists, or scientists who are using the more well-known older usage to explain something to laymen.

I know you're an eternal champion of "mass" to mean "relativistic mass", but I think you have to accept that it has become minority usage among those practicing scientists who use relativity the most. You correctly note that it is relativistic mass-energy (density) and not invariant mass which contributes to the gravitational field, but even gravitational physicists hardly use "mass" to mean "relativistic mass" anymore.

Yes, there are still people who use the older terminology, some of them prominent. There are many others who don't. And though you may have good reasons you have to prefer the older term, there are also good reasons to prefer the newer one.

Either way, the fact of the matter is that the terminology has simply changed -- for better or worse -- among the younger generation of physicists, for the most part. (Of course, they're not the ones who write the books --- but you will see the new use prominently in the journals.) This leads to confusion, because most laymen are not aware of this change. So, as you say, it's always good to point out that the term is used in more than one way.

#### pmb

Re: Re: Re: Re: Gaining Mass

Originally posted by Ambitwistor
In most, well, modern modern physics texts, I have found that it does, but we're probably looking at different texts.
In all texts that I've read, each and every author clearly states whether he means "rest mass" or "relativistic mass" when he simply writes "mass" and then continues from there.

I'm referring to the following texts:
"A first course in general relativity," Schutz (uses term "inertial mass" instead of "relativistic mass")
"Gravitation," Misner, Thorne and Wheeler, page 141
"Cosmological Principles," John A. Peacock, Cambridge University Press, (1999)
"Relativity: Special, General and Cosmological," Rindler, Oxford Univ., Press, (2001)
"Basic Relativity," Richard A. Mould, Springer Verlag, (1994)
"Introducing Einstein's Relativity," Ray D'Inverno, Oxford Univ. Press, (1992)
"Concepts of Mass in Contemporary Physics and Philosophy," Mass Jammer, Princeton University Press (200)
"Applications of Classical Physics," Thorne and Blanchard (not yet published)

None of those texts are too ingorable. All of which are well known relativity texts and used quite often.

Then there are articles in the American Journal of Physics.

I've asked from proof of claims that you've made and have gotten only repeats of those claims. Nothing to back them up.

#### pmb

Nim

If you'd like a copy of that American Journal of Physics Article "In Defense of Relativistic Mass" then please e-mail me at peter.brown46@verizon.net and I'll be happy to e-mail you a copy.

Pete

#### Ambitwistor

Re: Re: Re: Re: Re: Gaining Mass

Originally posted by pmb
In all texts that I've read, each and every author clearly states whether he means "rest mass" or "relativistic mass" when he simply writes "mass" and then continues from there.
So ... ?

#### pmb

Re: Re: Re: Re: Gaining Mass

Originally posted by Ambitwistor
I know you're an eternal champion of "mass" to mean "relativistic mass", but I think you have to accept that it has become minority usage among those practicing scientists who use relativity the most.
Please provide proof of this claim. I.e. find the percentage and the source of the percentage calculation

..but even gravitational physicists hardly use "mass" to mean "relativistic mass" anymore.
Please provide proof of this claim. I.e. find the percentage and the source of the percentage calculation.

I've seen one person (Rinlder) say 60%/40% for rest-mass/rel-mass while others swear that its 100%/0%

..if you attend conferences and seminars, you will find that both the high-energy physics community, the relativity community [..] have largely adopted the term "mass" to mean "invariant mass".
So what? I can't imagine any reason why they'd discuss anything else. Its their job to investigate the intrinsic properties of particles. They've adapted terminology to fit their needs. Its a term which they use as a short hand way of saying rest mass. High-energy physicists study the intrinsic properties of particles. They don't study relativity per se. They use relativity. As such they've adopted a short hand language and each knows what the other means. E.g. A particle physicist will say that the lifetime of a free neutron is ~15 minutes. In actuality its the proper life time that is 15 minutes. The actual lifetime is velocity dependant. Same with mass. If a particle physicist says that mass of a proton is 938 MeV then he means that the proper mass is 938 MeV. The inertial mass is velocity dependant.

A particle physicist doesn't work with anything except particles or things which they can treat as particles. A particle physicist will never measure the mass of a moving capacitor. In fact nobody has ever accelerated a capacitor to near light speeds. Yet its perfectly reasonable to speak of the inertial mass of such a capacity. And the full description is found in the stress-energy-momentum tensor. Rindler does just that here

http://www.geocities.com/physics_world/rindler-87.gif

And no. People don't choose rest mass over proper mass because they are old and don't want to change their ways. Look at Rinlder vs Okun. They're about the same age and have radically different opinions. Same with A.P. French. In his text he states that people sometimes use "mass" to refer to inertial mass. This debate is nothing new. It goes back for many many decades. This debate has been around before I was even born.

#### Ambitwistor

Re: Re: Re: Re: Re: Gaining Mass

Originally posted by pmb
Please provide proof of this claim. I.e. find the percentage and the source of the percentage calculation
You first; you're the one who actually thinks this is important. Please be comprehensive, and include all seminars and conferences in the world, as well as all papers and books published in the last 10 years, and provide evidence that you haven't selected a biased sample. We'll see what the statistics favor.

So what? I can't imagine any reason why they'd discuss anything else.
So, you admit that they use invariant mass to be "mass"?

Its their job to investigate the intrinsic properties of particles.
You will note, by the way, that I included relativists and cosmologists in my experience, not just particle physicists.

They've adapted terminology to fit their needs. Its a term which they use as a short hand way of saying rest mass.
Yes, that's the point. The term "mass" in common usage among practicing physicists who use relativity has been changed to mean invariant mass, because that's the most useful definition.

And no. People don't choose rest mass over proper mass because they are old and don't want to change their ways.
Largely, they do. Waving around one or two examples doesn't mean anything.

This debate is nothing new. It goes back for many many decades. This debate has been around before I was even born.
Certainly. What is new is that the balance has switched from most people using mass to mean relativistic mass, to most using mass to mean invariant mass.

In any case, feel free to keep tilting at windmills. I've had my say on the matter: the common usage of the term mass has come to mean "invariant mass" among most active physicists who use relativity -- particle and otherwise. I say this on the basis of the papers I read, and the talks and conferences I attend --- which, not books, are what reflect the current state of physics. You are of course welcome to start taking your own statistics on papers and talks and try to prove me wrong, but I don't particularly care. You will notice that whenever you bring this up with practicing physicists, they usually disagree with you. There may be a reason for this, other than a vast international conspiracy to supress the true definition of mass.

P.S. Whatever happened to abandoning the forums?

#### pmb

Re: Re: Re: Re: Re: Re: Gaining Mass

Originally posted by Ambitwistor
You first; you're the one who actually thinks this is important.
I never claimed that it was important. You seemed to be claiming that all high-energy physicists etc. use mass to mean "invariant mass" and then you went on to make a whole big deal about it.

P.S. Whatever happened to abandoning the forums?
Why do you ask? If you must know one of the moderators talked me out of it. Does that ease your curiosity?

#### Integral

Staff Emeritus
Gold Member
There is no point to this disagreement. We need to understand that there are 2 points of view concening mass. So it needs to be stated what you mean when using the word. It is impossible to prove what the dominate usage is in this format. There is no point in arguing it. PMB you need to get past it. It simply is not necessary to sway anyone to your viewpoint. You are free to use that term mass as you wish, as long as it is understood which meaning you are given it.

End of dissucssion. If this thread cannot get past this disagreement it will be locked.

#### chroot

Staff Emeritus
Gold Member
Originally posted by Integral
End of dissucssion. If this thread cannot get past this disagreement it will be locked.
I almost said the same thing -- then I went back and looked at the thread starter's question, and the discussion actually seems relevant!

- Warren

#### pmb

Originally posted by Integral
There is no point to this disagreement.
Why? This is the very topic of this thread. One particular person had once made the same claim to me as someone made to Nim. I didn't believe him. And he became very irritated with me for not believing him. And since others thought he knew what he was talking about they got upset with me for not believing that person. Well it turned out to be wrong. I see no point in letting Nim think that he was given the wrong information. And that person used the exact same arguements being given here.
We need to understand that there are 2 points of view concening mass.
Yup. And that is the topic here.
It simply is not necessary to sway anyone to your viewpoint.
Oy! Where did you get the idea that I was trying to sway someone to my viewpoint. I've stuck only to facts. Not opinions. I have not tried to convince anyone that my opinion is better either.

Pete

#### pmb

Originally posted by chroot
I almost said the same thing -- then I went back and looked at the thread starter's question, and the discussion actually seems relevant!

- Warren
Yes! Exactly! Thank you!

Pete

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