Unravelling the Concept of Mass

[RipClaw]

What is mass ??

Text books define it as the "amount" of substance...
You can also use some equations and toss Mass out, giving other definitions.

But my question is about the wording "amount of substance"
> What is this "amount of substance" ?

> Because "amount" refers to counting..
How can you count this "substance" ?

> I know that mass of a cube of butter is not the amount of sub-atomic particles that butter has... then what is it ?

> Some humans have spread the thought that the number & unit 1Kg, refers to the idea of the stuff kept here

This means
the amount of matter present in 1KG of butter is same as the amount of matter present in the reference Platinum-Iridium Alloy. ?
How should I digest the concept ?
How can I compare Butter & the Pl-Ir Alloy> I am fed up of circular definitions where
for eg. Mass can be defined in terms of Force, accel, etc. ..and Force in turn will be defined interms of Mass, accel etc.

 

[russ_watters]

> I know that mass of a cube of butter is not the amount of sub-atomic particles that butter has... then what is it ?

Why not?

> Some humans have spread the thought that the number & unit 1Kg, refers to the idea of the stuff kept here

This means
the amount of matter present in 1KG of butter is same as the amount of matter present in the reference Platinum-Iridium Alloy. ?
How should I digest the concept ?
How can I compare Butter & the Pl-Ir Alloy

Have you taken chemistry yet? Consider this: the mass of an atom is the mass of the protons, neutrons, and electrons added together and the mass of a glob of those atoms is the mass of a single atom times the number of atoms. Why should butter be any different? Its just more types of atoms - but still, the fundamental building blocks are the same and have the same mass as the fundamental building blocks in that hunk of platinum in Paris(?).

 

[3trQN]

I kind of think of it this way, mass is to energy as area is to length...

But I am prob wrong...

 

[Astronuc]

I kind of think of it this way, mass is to energy as area is to length...

Length is one dimension spatially, where as area is 2-dimensional spatially.

Mass is defined as the property of a substance (matter) to resist acceleration, and hence represents a proportionality between force and acceleration.

Mass (symbolized m) is a dimensionless quantity representing the amount of matter in a particle or object.

http://whatis.techtarget.com/definition/0,,sid9_gci549408,00.html

It is dimensionless, i.e. it is not a dimension in the spatial or temporal sense.

Energy is the capacity of a physical system to do work.
http://searchsmb.techtarget.com/sDefinition/0,290660,sid44_gci213564,00.html

Energy may be proporational to mass, e.g. kinetic energy KE = 1/2 mv².

And then there is potential energy.

 

[DaveC426913]

Mass is the drag that an object experiences by its resistance to the Higgs field.

 

[RipClaw]

Mass is defined as the property of a substance (matter) to resist acceleration, and hence represents a proportionality between force and acceleration.

Why is that the concept of Force & Accel brought in ?
Are they not concepts that require time & happen over time OR requires time as a component ?? {For eg. a push or pull happens over time and without bringing in time, the concepts of Force & Acceleration might go absurd..doesn't it ?? }

Can't the idea about mass be brought up without any other basic units ?
[offtopic] I am a Satch fan too :) [/offtopic]

the mass of an atom is the mass of the protons, neutrons, and electrons added together and the mass of a glob of those atoms is the mass of a single atom times the number of atoms. Why should butter be any different? Its just more types of atoms - but still, the fundamental building blocks are the same and have the same mass as the fundamental building blocks in that hunk of platinum in Paris(?)

Do you mean to say that the amount of protons/neutrons etc on 1Kg of butter is equal to what is present in 1Kg of that alloy ?
OR
Do you mean to say that the total mass of the protons/neutrons etc on 1Kg of butter is equal to what is present in 1Kg of that alloy ?

 

[cliowa]

@RipClaw:
You might want to have a look at this:
http://web.mit.edu/physics/facultyandstaff/faculty_documents/wilczek_p@m03_FINAL.pdf"

It's an article written by Frank Wilczek about the "Origin of Mass", which could be quite interesting, in case you want to dig a little deeper.
Best regards...Cliowa

 

[ZapperZ]

The problem with questions such as this has always been defining the bondary of knowledge to which the answer can be given satisfactorily. At some point, if you want the "full-blown" answer, you have to be capable of understanding such an answer, i.e. your boundary of knowledge must be the same as those people who are actually doing research in such a field.

When you start with only wanting to ride a tricycle, then your ability doesn't require that much sophistication since it is realtively easy to learn how to ride such a thing. But if you then say "OK, I now want to be able to drive a car", then you just simply cannot get behind the wheel and drive around blindly. You have to learn how to drive, acquire sufficient skills to drive, learn all the traffic rules, and pass some tests to be allowed to drive.

When you ask "what is mass", you can be given a pedestrian answer that are often sufficient for most purposes. But if you go beyond that and start to extend the boundary to include energy conversion, field theory, gravitational versus inertial mass, etc.. etc., then it gets very involved and requires a solid understanding to be able to comprehend the type of answer being given. For example, would it suffice to say that something with a mass will interact with the Higgs field, while those that don't have any mass will not? This would be the identical answer one would be given when asked for the definition of a "hardron" (something that will interact with the gluon field).

In the end, and this is often true in physics, one needs to figure out if a question actually has any importance to it. Remember, in science, something that is interesting isn't necessary also be important (when one is in this field for a long time, one tends to know how to pick and choose which is which). One needs to figure out where such a definition would be meaningful and important. Was it that important to figure out if the electron neutrino has a mass, or was it more important to discover the neutrino oscillation that implicated that it has a mass? It was the former, not the latter. We simply have waaaay too many stuff on our plates to worry about something that has very little impact.

Zz.

 

[Gokul43201]

Do you mean to say that the amount of protons/neutrons etc on 1Kg of butter is equal to what is present in 1Kg of that alloy ?
OR
Do you mean to say that the total mass of the protons/neutrons etc on 1Kg of butter is equal to what is present in 1Kg of that alloy ?

The first implies the second, and hence, both are true.

The idea of calling mass "the amount of stuff" is a form of passing the buck. What then is "stuff", and what is an "amount" ? But in a sense (ie : if cleaned up some), it does serve as a pretty good approximation. And this is the purpose that it needs to serve for anyone that is not actively involved in research in the field.

Where it doesn't work so well is in answering a question like : Does a "box" with 2 neutrinos have more mass than a "box" with one neutrino ? Then you're back to the more basic question about a specific property of a fundamental particle.

On the other hand, it's perfectly sound to say that mass is nothing but the proportionality constant in some specific relation, so long as all the appearances of the term mass can be derived from that same relation. If you are okay with accepting what a spring constant is, why not mass ?

 

[pmb_phy]

Mass is that property of matter which gives it momentum. I.e. it is the m in p = mv. Mass resists changes to momentum. Mass gives a body inertia.

Pete

 

[Flatland]

mass is the resistence to acceleration or a measurement of inertia

 

[pmb_phy]

mass is the resistence to acceleration or a measurement of inertia

This statement, while it works somewhat in non-relativistic mechanics, is better stated as "mass is the resistance to changes in momentum." Otherwise you'll get people writing the wrong definition of force, i.e. F = ma, rather than the correct definition of F = dp/dt. Hence my phrasing above.

Pete

 

[Astronuc]

Just some of my thoughts

I think that given the definition of momentum as the product of mass and velocity, that a correct definition of mass is that property which resists change in velocity, i.e. acceleration. I suppose its a matter then of semantics, or rather how one gets one's mind around the concept of mass.

Then one has to look at rest mass vs relativistic mass. In which case, mass resists not only change in velocity, but change in itself, since m is dependent on v. In that sense, mass is that property which resists change to momentum.

Face it classical mechanics is seemingly more tangible than relativity and quantum mechanics, and I think that is where the problem lies for some people. Relativity and QM, and related areas require an ability to abstract beyond direct experience (observation).

With regard to

Are they not concepts that require time & happen over time OR requires time as a component ??

Well, mass exists in space-time, and as far as we know, there are three fundamental spatial dimensions and one temporal dimension, and they coexist. For $\Delta{t}$ = 0, mass and existence would be meaningless.

 

[Gokul43201]

This statement, while it works somewhat in non-relativistic mechanics, is better stated as "mass is the resistance to changes in momentum."

In that sense, mass is that property which resists change to momentum.

Am I missing something here ?

If I double the mass, it does not take twice the force to produce the same change in momentum (it still takes the same force).

 

[Astronuc]

The net force should be defined as the rate of change of momentum.

http://hyperphysics.phy-astr.gsu.edu/Hbase/limn2.html See all three plates.

I just realized that this forum is Classical Physics.

Newton's second law.

 

[Gokul43201]

The net force should be defined as the rate of change of momentum.

I didn't disagree with that. I disagreed with the definition of mass as that which resists change in momentum.

 

[pmb_phy]

Just some of my thoughts

I think that given the definition of momentum as the product of mass and velocity, that a correct definition of mass is that property which resists change in velocity, i.e. acceleration. I suppose its a matter then of semantics, or rather how one gets one's mind around the concept of mass.

I try to avoid saying that mass is what resists changes in momentum. If I said that here then I retract it. The most precise definition of mass that works best is that of Weyl and that's m = p/v. The definition of mass as that which resists changes in velocity can be attributed to Mach as I recall.

Pete

 

[Gelsamel Epsilon]

But my question is about the wording "amount of substance"
> What is this "amount of substance" ?

Not sure if there is any way you can get the discription more dumbed down then that. Mass is how much "stuff" there is there. There that is my best effort if you don't understand it then I don't know what to say.

> Because "amount" refers to counting..
How can you count this "substance" ?

Obviously, you count it, and the amount of it is reprisented as Mass.

> I know that mass of a cube of butter is not the amount of sub-atomic particles that butter has.

That is basically what it is, it is actually a bit more complicated then that, but at a basic level that is exactly what mass is.

 

[pervect]

In many situations, the equation

m = p/v

will not be what the author is talking about, so assuming that this is a universal defintion of mass will be quite, quite, wrong.

For instance, the mass of a photon is zero, however p/v for a photon is not zero.

When we say the photon has no mass, we are talking about the SR notion of invariant mass:

m = sqrt(E^2 - p^2c^2)/c^2

(Note that this question about the "mass" of a photon comes up about once a week, so see any of the numerous threads for more information.)

There are many other defintions of mass that are used in GR, three of the most common are ADM, Bondi, and Komar mass. This is not a complete list by any means, which should server as a warning that the subject starts to become complicated.

The bottom line is that "mass" is an ambiguous concept. While for most pedestrian non-relativistic purposes one can use m = p/v, this defintion is hardly universal.

 

[pmb_phy]

The question "What is mass?" is not an easy one to answer. Modern textbooks never really get into this question very deeply so students go on to think that they've mastered the concept with a simple answer that they've satisfied themselves with. But the question is hardly simple. As Max Jammer comments in Concepts of Mass in Contemporary Physics and Philosophy, page ix

The present monograph does not presume to resolve the problem of mass. Its purpose rather is to show that the notion of mass, although fundamental to physics, is still shrouded in mystery

If anyone truly wants to get into this question deeply then this book is a must read.

Pete

 

[Farsight]

Apologies if it's not relevant, but I've picked up a concept that basically says matter can be likened to slip knots of space. Like you can get on a fishing line - pull it tighter and it gets harder to move it down the line. Maybe a better analogy would be to say that matter has the same sort of substance as a crease. Search Google on "matter" and "pure marble" and "geometry" to find some interesting reading.

http://www.google.co.uk/search?hl=en&q="matter"+"pure+marble"+geometry&meta=

"Einstein’s grand strategy was to "turn wood into marble" – that is, to give a completely geometric origin to matter. In retrospect, we can probably spot Einstein’s error. We recall that the laws of Nature simplify and unify in higher dimensions. Einstein correctly applied this principle twice : in Special and in General Relativity. However on his third try, he abandoned this fundamental principle. He blindly tried a number of purely mathematical approaches. He apparently thought that “matter” could be viewed as kinks, vibrations, or distortions of space-time. However, without any more solid leads or experimental data, this idea led to a blind alley. It would be left to an obscure mathematician to take the next step which would us to the 5th-dimension..."

 

[AGBROKO EJOVWOKE]

i think all is correct but let just think of mass simply as the total makeup of a substance, particle and the like if you see it just as the total content you can get the sense clear. and that explains why the mass of the particle can't change. as for the butter it means the mass of 1kg of it is the sum total of all that it has in 1kg.

 

[Astronuc]

But if one says m = p/v to someone, who is trying to understand mass, then would the someone be expected to know or understand momentum? I would expect somewhere, the momentum is given as p = mv.

 

[DaveC426913]

..a correct definition of mass is that property which resists change in velocity, i.e. acceleration.

This is simply a circular definition.

Worse, it is simply a derived definition. Of the three properties (M,v,m), mass is the intrinsic one, the rest should be derived from it.

But I state the obvious.

 

[Farsight]

If you search Google on "mass" "knot" "spacetime" you see other Physics Forum discussions on the subject.

http://www.google.co.uk/search?hl=en&q="mass"+"knot"+spacetime&btnG=Google+Search&meta=

For example

http://forum.physorg.com/index.php?showtopic=1365&st=15

 

[marlon]

Mass is defined as the property of a substance (matter) to resist acceleration, and hence represents a proportionality between force and acceleration.

Indeed, this is the correct definition. We are so used to using the word "mass" that we forget about the fact that mass m is even not that important in classical physics. The key factor is, as Astronuc pointed out, the relation between acceleration and force. The m-term is just a factor to get equality between F and a. So, one can do classical physics without talking about mass.

marlon

 

[Gokul43201]

This is simply a circular definition.

Worse, it is simply a derived definition. Of the three properties (M,v,m), mass is the intrinsic one, the rest should be derived from it.

But I state the obvious.

I don't know what your (M,v,m) represent, but I see nothing circular about defining mass (if you want to define it as something) as the proportionality between force and acceleration. Acceleration can be defined entirely independent of mass and so can force. Eg : The force between two bodies is the extension or compression of a standard spring attached to the two bodies.

 

[Andrew Mason]

Not sure if there is any way you can get the discription more dumbed down then that. Mass is how much "stuff" there is there. There that is my best effort if you don't understand it then I don't know what to say.

Is "stuff" the total number of protons and neutrons? Mass of a substance is only approximately the measure of the total number of nucleons contained in a substances.

That does not explain the differences in mass between two deuterium atoms and a ⁴He atom. Do two moles of D have the same "stuff" as 1 mole of ⁴He?

AM

 

[Farsight]

If m = p/v what about when v = 0?

 

[ZapperZ]

If m = p/v what about when v = 0?

This is exactly why this is physics and not mathematics, i.e. you simply cannot manipulate mathematical equations without knowing that it means.

You need to figure out which is the independent variable and which is the dependent variable, and how the equation is defined. Secondly, if v changes, do you think p remains constant? What is p when v=0? If p remains constant as v changes, that equation makes no sense physically.

Zz.

 

[vroom]

can't one interpret mass, simply as a proportionality constant, in a sense the cause for inertia. ( that's inertial mass )

 

[tehno]

Mass is the drag that an object experiences by its resistance to the Higgs field.

I believe they still know nothing about Higgs field & particles.
Existance included

 

[lalbatros]

Would it not simply be a singularity of the gravitational field?
Like the electric charge is a singularity of the EM field.

With one marked difference, maybe: can we rule out the possibility that the nonlinearities in the gravitational physics could produce these singularities spontaneously? For the EM this is obviously excluded because of the linerarity.