What exactly is mass? Loosely defined its the amount of matter in a body, but thats qualitative. There’s no direct way to measure it. My question is, if I measure mass by :

1> Measuring the ratio of force to acceleration for that body (F/a) and obtain the value m1. (This is what common balances do in principle).

2> Measuring the energy liberated by a body in the E=mc2 way, call this measurement m2.

3> Measuring the energy needed to heat it up in the m = mCp/(Delta)T way. Call this m3.

Then (assume all instruments have comparable accuracy and precision) is m1=m2=m3 exactly, necessarily true ??

Does gravitational mass equals intertial mass or other kinds of mass ?

You know, I’m noticing that I’m really betraying my physicist/nerd side to the board at large tonight… Oh well.

The 1st experiment would give you inertial mass; I’m not sure which the second would give you, because mass is just mass, as it turns out. The third might be a bit bogus as the formula isn’t strictly correct (you need an integral in there somewhere). You could also measure gravitational mass, as you noted.

You’d find, though, that gravitational and intertial mass are the same; this is something known as the principle of equivalence, and it’s been experimentally verified to high accuracy. There’s various methods to measure this, but things really got going 100 years ago or so with a Hungarian guy named Eotvos who found that the two masses were the same to within one part in 10[sup]8[/sup] or so by some clever experiments involving torsional balances. Later experiments have improved this bound quite a bit more.

As for what mass IS, Ring has given a better definition than I ever could.

Is this still true when matter and antimatter annihilate each other? I always thought that in that case all the mass is turned into energy. Did you really mean, in normal earth-bound nuclear reactions, only a small part of the mass is converted into energy?

Side question - somewhat related - is there a “quantum” of mass? I’d guess it’s somehow related to a quantum of energy via m = E / c[sup]2[/sup] and probably with Planck’s constant thrown in for good measure. But doesn’t the energy content of a quantum depend on the frequency of the photon? Hmmm… Why have I heard so much about energy being quantized, but not mass, since the two are interchangeable?

"mass is the energy of an object or system that can’t be transformed away. " – Ring

I don’t quite agree with that description. I don’t agree with the assertion that mass is energy. I would prefer to say that mass is a property of a collection of energy that is “contained”.

Good examples of “contained” energy would be nuclear binding energy, heat, anything within a black hole, or the universe itself.

So I do agree that changes in mass are only local if local is meant to contrast universal. The mass of the universe as a whole never changes.

If you take the system of a electron/positron pair, if those 2 particles collide and annihilate, the mass of the system drops to zero, as the energy in that system is no longer contained.

Even considering “our accuracy to measure it” its not exactly equal. here .

Although this difference does’nt have any effect on newtonian mechanics, it may have quantum mechanics implication.

QUOTE]*Originally posted by g8rguy *
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The third might be a bit bogus as the formula isn’t strictly correct **
[/QUOTE]

Sorry the formula should be m3 = Q/(Integral (Cp (Delta T)). Or for an ideal gas m3 = MPV/RT where M is the molecular weight. I call this thermal mass.

I don’t see anything in that page that suggests a lack of equivalency. It says “They obtained a limit of less than 9 X 10[sup]-13[/sup]”. My interpretation was that there was no difference down to that level of measurability. Did I miss something?

I don’t think the third measurement is truly a measurement of mass, since Cp is an empirical quantity. In other words, any discrepancy means you should adjust Cp, not m3.

I’ve been curious about a hyperaccelerated object increasing in mass. Could a 10kg object accelerated to 0.9999…c have a calculated mass equal to a small moon, and if so, would it exert similar gravitational effects on other objects as it streaked past?

Bryan, this is where we get to the rather ugly concept of “relativistic mass”. Relativistic mass is really an outmoded term, not used by physicists anymore. If we maintain mass to mean “rest mass”, which is what physicists now do, mass does not change due to high velocity. Momentum and energy both approach infinity as the relative velocity approaches c.

So the answer is no, a fast moving object does not increase its gravitation. If it did, we would have some fundamental problems-- like the possibility an object having sufficient mass to become a black hole in some reference frames but not in others.

Well, actually as you say mass and energy are properties of a system, and not things in their own right, but the mass and energy of any closed system cannot change. The reason they can’t change is because momentum must be conserved.

m[sup]2[/sup] = E[sup]2[/sup] - p[sup]2[/sup]

So if the momentum can’t change then neither can the mass.

No, the mass for the system stays the same for the same reason as above. It’s true that the particles annihilate, but the property of the system that we call mass stays the same.

Some folks may have thought I was a little overexcited about units in that thread, but what you said here is a perfect example of the flaw that occurs when units are ignored.

c = 1? Sort of.

c = 1 light-sec/sec

That’s the true value. Dropping that unit invalidates you equation.

So lets look back at the total energy equation again:

m[sup]2[/sup] = E[sup]2[/sup] - p[sup]2[/sup] ?

not exactly.

m[sup]2[/sup] x light-sec[sup]4[/sup]/sec[sup]4[/sup] = E[sup]2[/sup] - p[sup]2[/sup] x light-sec[sup]2[/sup]/sec[sup]2[/sup]

Starting to see the flaw here? Should we run through an example case using realistic mass and momentums for a colliding electron/positron pair?

I did not intend the question to get to this level. But since we are here, please clarify the following about rest mass :

1> Rest is a “relative state”. So what exactly is rest mass since nothing is at truly at “rest” in the universe.

2> Heisenberg’s uncertainity principle would say that if you considered a particle at rest (momentum (velocity) zero with no uncertainity) then the position the particle is at, will have infinite uncertainity. So, if you don’t even know where the particle is, how will you measure its mass ???

Sorry, I’m not a psysicist and my understanding is limited to High school physics and “Brief history of time”.

P.S. – another critical thing to watch in those equations is that the value “pc” is really a breakdown of kinetic energy, which is a scalar. But when there is more than one particle, you must resolve kinetic energies for the particles first, because your source p’s are vectors.

“Rest is a “relative state”. So what exactly is rest mass since nothing is at truly at “rest” in the universe.” – andy_fl

Excellent question.

“Rest mass” is the mass that you would perceive an object to have if you observed it to be at rest. Still that’s really a bad term, because it presents itself with an implication that the mass might be different if you observed it otherwise (i.e. the relativistic mass).

This is why that Relativity FAQ (see “Does mass change with velocity?” link above) does the much smarter thing and avoids the term “rest mass” as well. They use the term “invariant mass”, which is the same as “rest mass”.

“Heisenberg’s uncertainity principle would say that if you considered a particle at rest (momentum (velocity) zero with no uncertainity) then the position the particle is at, will have infinite uncertainity. So, if you don’t even know where the particle is, how will you measure its mass ???” – andy_fl

Well, that just means you can’t know the exact mass. But if you can tell the the object is moving less than a foot/year relative to you, you can get a pretty good estimate of its mass.

I said the above kinda tougue-in-cheek, so lemme just nit-pick myself before someone else does.

Of course you can’t measure anything exactly and in any case, you generally determine the mass of an object by observing its intertial behavior or its gravitational influence, either of which can be observed without being totally at rest with respect to the object.

So best bet is to forget all about the implications of the term “rest mass” and thing “invariant mass” instead.