Confused about mass

[geft]

1) The classic definition of mass accepted in most textbooks is 'the amount of matter in an object'. Is this scientifically correct? Since matter consists of atoms and molecules, which number is measured in moles, how can this be correct when the the same number of molecules of lead and carbon have different mass?

2) Can you achieve different mass by configuring molecular structure?

3) F=ma. Does that mean an object in uniform motion (a=0) have 0 force?

4) e=mc2. Does that mean light have mass since m=0 equals e=0, and light is basically pure energy? Does it imply that high-energy light such as gamma ray is heavier than radio wave?

[jtbell]

Physicists don't consider "quantity of matter" to mean simply the number of molecules (or moles).

[Andy Resnick]

There is not yet a theoretical framework that describes the origin of mass, or that relates the idea of 'mass' (a positive number) to a specific object. One of the major mysteries that is incorporated into General Relativity is that *any object* experiences the *exact same* acceleration due to gravity.

This apparently obvious statement is is not true of any other physical quantity- electric fields do not affect all objects the same. Different materials are made of different things, with differing densities, state (solid, liquid, magnetic, transparent...)., etc. And yet, all objects accelerate the exact same amount in a gravitational field.

[Gerenuk]

1) The classic definition of mass accepted in most textbooks is 'the amount of matter in an object'. Is this scientifically correct? Since matter consists of atoms and molecules, which number is measured in moles, how can this be correct when the the same number of molecules of lead and carbon have different mass?

"Amount of matter" still sounds pretty vague. Experimentally one can determine a certain rest-mass for all elementary particles. So in way all you have to do is do count the particles in their object and sum up their individual masses. This will give you an estimate of the total rest mass of the object. But...


2) Can you achieve different mass by configuring molecular structure?

That's the tricky bit. Interacting masses can experience a slightly different total gravitational attraction than you would predict from summing up their rest-masses. But for that it's better to ask general relativity experts.


3) F=ma. Does that mean an object in uniform motion (a=0) have 0 force?

Yes, the total net force equals zero.


4) e=mc2. Does that mean light have mass since m=0 equals e=0, and light is basically pure energy? Does it imply that high-energy light such as gamma ray is heavier than radio wave?
Depends on what you define as energy. In a way everything is energy. But true that photons are energy only and has no rest-mass.
Light does indeed get attracted my gravity despite having no rest-mass. I hope an expert can clarify this :smile:

[Bob S]

You can get a pretty good estimate of "the amount of matter" or mass in an object by counting the number of protons and neutrons in an object. Lead has roughly 206/12 times as much mass as carbon per mole. But there are several different isotopes of lead, with different number of neutrons. Some are radioactive, and some stable. But mass can be converted into energy. Deuterium D and tritium T can be converted into heluim He plus a neutron n, and the He + n has less mass than the D + T, the excess having been converted into energy.
Bob S

[geft]

Yes, the total net force equals zero.
What happens when said force interact with a resting object? Obviously there is some force involved, or am I actually confusing it with momentum?

Depends on what you define as energy. In a way everything is energy. But true that photons are energy only and has no rest-mass.
Light does indeed get attracted by gravity despite having no rest-mass.

According to Einstein, everything with mass has energy and vice versa. Perhaps it's something to do with the duality theory? I also read somewhere that light has momentum, which is why it can be pulled by gravity, hence the m in p=mv cannot be 0.

[Naty1]

What happens when said force interact with a resting object? Obviously there is some force involved, or am I actually confusing it with momentum?

I'm not sure what you are getting at here. Do you mean if there is a frictional force greater than an applied force, then nothing happens. If you mean a force like that on your feet when you stand on a floor, then that force is opposing gravitational acceleration (attraction) and there are classical and relativistic explanations representing slightly different viewpoints of the same physical phenomena.


According to Einstein, everything with mass has energy and vice versa. Perhaps it's something to do with the duality theory? I also read somewhere that light has momentum, which is why it can be pulled by gravity, hence the m in p=mv cannot be 0.

All energy has momentum; photons (light) therefore have momentum but not rest mass. Gravity affects things with mass, energy or pressure;that is any of the three cause gravitational attraction. For example when a neutron star collapses and pressure increases, that pressure generates enough gravitation attraction so as to aid the collapse rather than oppose it. Very unexpected classically.

Can you achieve different mass by configuring molecular structure

Several ways to think about this..one is binding energy which varies among elements. I believe Wikipedia, for example, discusses binding energy.
Another is that if two moving objects crash together and remain stationary,say, their combined mass is greater than that of the constituents when those were at rest...that is, their kinetic energy prior to collision is now part of the stationary mass..its a different object!!!!! (Richard Feynmann discusses this in his classic lectures SIX NOT SO EASY PIECES.., Chapter 4. )
In fact I think he answers all your questions there in his own unique way...its a paperback, and used copies are only a few dollars...as at Amazon or other sources...it's only about 140 pages...his only undergraduate teaching effort.

As noted by others mass (like energy,space,time, for example) are all at a fundamental level unclear...and yet likely related as they all popped out of the big bang (or little bang)...gravitational mass and accelerated mass equivalence was noted by Einstein in general relativity and Feynmann notes that a coincidence, not a requirement of our world...I do wonder about that....I think we have lots more the learn...
and if that were not enough, dark mass and dark energy constitute 96% or so of our universe..and we know little about either....

[geft]

I'm not sure what you are getting at here. Do you mean if there is a frictional force greater than an applied force, then nothing happens.
I'm not familiar with the concept of frictional/applied force, care to elaborate? I meant something like the impact of someone being hit by a truck.

For example when a neutron star collapses and pressure increases, that pressure generates enough gravitation attraction so as to aid the collapse rather than oppose it.

I'm not really clear about the last part, maybe a little to mind-boggling for me at the moment. I was thinking of the way scientists rearrange the atomic structure of carbon atoms to form the strong and light carbon nanotube.

[pervect]

1) The classic definition of mass accepted in most textbooks is 'the amount of matter in an object'. Is this scientifically correct? Since matter consists of atoms and molecules, which number is measured in moles, how can this be correct when the the same number of molecules of lead and carbon have different mass?


I believe that this definition was originally offered by Newton, though I don't have my reference material handy to confirm. It's reasonably close to being correct for the Newtonian concept of mass, though it's a little vague. It shouldn't be regarded as "the" definition of mass, however, just as an attempt to point the person in the right direction. Mass, however, is not the same thing as the number of molecules - as you point out, this is related to the concept of moles.


2) Can you achieve different mass by configuring molecular structure?


The effect is predicted by relativity. It's too small to measure as far as I know with chemical reactions. Nuclear reactions have readily observable changes in masses. Measurements have mostly been done at the small scale, though large scale 'experiments' such as nuclear weapons detonations have been carried out :-). However, there are certain measurement difficulties in measuring the mass of the reaction products for such large scale demonstrations. On the small scale, though, you can lookup the mass change for various common nuclear reactions which have been measured with high precision.


3) F=ma. Does that mean an object in uniform motion (a=0) have 0 force?


In the Newtonian concept, yes. The language changes a bit in GR, where we say that force-free motion of "test bodies" is geodesic motion.


4) e=mc2. Does that mean light have mass since m=0 equals e=0, and light is basically pure energy? Does it imply that high-energy light such as gamma ray is heavier than radio wave?

See the sci.physics.faq on this topic.

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html

Basically, the commonly accepted answer is no, light does not have mass. Most of the argument here is over semantics. Because there are a couple of commonly used definitions of mass in SR, there tends to be a lot of pointless semantic argument over this point.

Max Jammer has a couple of books about the history and modern concept of mass, some classical, some contemporary.

Note that things get even more interesting in GR, where there are several different sorts of "mass" defined, which differ from the SR definition.

See for instance http://adsabs.harvard.edu/abs/2006PhTea..44...40H


There Is No Really Good Definition of Mass
Hecht, Eugene
The Physics Teacher, Volume 44, Issue 1, pp. 40-45 (2006).

There seems to be a fairly prevalent belief in the physics community that the basic concepts of our discipline (mass, force, energy, and so forth) are well understood and easily defined.1 After all, there are dozens of textbooks on every level that supposedly define all the terms they introduce. Apparently, we teachers can pass this wisdom on to our students without any cautionary notes and without any concern for subtleties. Remarkably, this is most certainly not the case, and anyone who has studied the foundational literature in physics over the last several centuries knows that none of the fundamental ideas is satisfactorily defined.


I'd personally take a slight issue with the wording here - the problem isn't really that there are not any good definitions of mass, the problem is that there are too many "good" definitions of mass. This is particularly true in GR, where we have ADM mass, Komar mass, Bondi mass, and several sorts of quasi-local mass.

[geft]

Great answers there. Personally, I'm fine with the modern definition of mass as 'a measure of inertia' and I agree that teachers have been imparting scientific knowledge in a 'matter-of-fact' way, which is then taken for granted by students like me.

I'm glad I've been reading 'Einstein for Dummies', which led me to ask these questions. Great book for beginners, it allows me to think of physics in a more fundamental way.

[Naty1]

geft
I agree that teachers have been imparting scientific knowledge in a 'matter-of-fact' way, which is then taken for granted by students like me.


Teachers must focus on some something...and learning about how F = Ma applies for example is deemed more important than learning about the three constituents in great detail. I think they teach in this way because you really need other knowledge to fully understand, say mass, and providing a "survey" of many physical interactions rather than spending weeks and weeks on,say, just mass gives students some more practical knowledge. Also it provides time for students to gain other skills, such as math and chemistry, maybe materials science in college, and so begin to be able to link different skills together....unfortunately nobody has figured out how to teach everything all at once...

Even Einstein had this problem....he cnceptually understood his equivalence principle and had keen insights into gravity, but he lacked the math skills (like Riemann geometry) to formulate a formal approach...he got help from his teacher and friend Marcel Grossman....