What is mass? Force?

[Human001]

I looked through this article: http://en.wikipedia.org/wiki/Mass. It didn't answer the title question. Usually it states

A body's mass determines...

What I want to know is what mass actually means. Does it mean anything? Other than a simple m that's plugged into equations?
Mass is usally meausred in kg, but that leads to the question what is a kg? Something that is equal to the mass of something that weighs 1kg.

From the wikipedia article:

Active gravitational mass is a measure of the strength of an object’s gravitational flux (gravitational flux is equal to the surface integral of gravitational field over an enclosing surface). Gravitational field can be measured by allowing a small ‘test object’ to freely fall and measuring its free-fall acceleration. For example, an object in free-fall near the Moon will experience less gravitational field, and hence accelerate slower than the same object would if it were in free-fall near the earth. The gravitational field near the Moon is weaker because the Moon has less active gravitational mass.

So mass is a testable property of objects, but the test involves equations that were first constructed by assuming objects had a property called mass, which I still don't know what it means.

COme to think of it, what is a force?
From wikipedia:

In physics, a force is any influence that causes a free body to undergo an acceleration. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or which can cause a flexible object to deform.

It appears the definition just mimes Newton's famous equation. And then the intuitive defintion needs an understanding of mass, which I don't know the meaning of.

It seems that physics is inherently tautological. Not to imply it isn't absolutely useful and necessary.

I ask these questions, not as someone trying to rewrite the laws of physics, but I am genuinely confused. The highest physics I dd was A-levels (ony UK people here will know what I mean).

 

[Terry Giblin]

Length, time, mass, charge, spin,.... l,t,m,q,s...., 1,2,3,4...., are all words, letters or numbers.

Ask a philosopher, "What is a number, a letter or a word?

What is a 'philosopher'?

Before asking a mathematician or physicist, we just measure real 'things' and use them in our calculations.

A very circular question and answer.

Light in, Light out.

 

[Human001]

Ask a philosopher, "What is a number, a letter or a word?

Well the formalist ideas in mathematics do say that numbers and operators are just symbols. Mathematics is just a big game, shuffling letters around on a page. This is only one school.
I mean, it is clear to others that numbers are representative of real objects.
$$a^{2}+b^{2}=c^{2}$$ does have real world applications (just ask an ancient Egyptian building a pyramid). So to join the ranks of the formalist (deniers?) who claim all is meaningless tautology is to turn a blind eye to the real world.

But that is another topic. I'm talking about real world properties of mass and force.

 

[AlphaNumeric]

It seems that physics is inherently tautological. Not to imply it isn't absolutely useful and necessary. .

No, its not tautological, what you're referring to is the fact that certain things are axiomatic, in that you have to start somewhere with definitions and then you build things in terms of those definitions.

Metres, seconds and kilograms are units which people have agreed the meaning of so that when I say to someone "I ran 100 metres in 14 seconds" they know what you are referring to. Mass is a measure of the amount of substance something has which can also be related to some standard. For instance $$6.02 \times 10^{23}$$ Carbon 12 atoms have a mass of 12 grams (its slightly different from 12 but I can't remember what, its been 8 years since I did any chemistry) so then you can refer to other objects' masses in terms of that. From that you can define a force as the 'thing' which cases a given mass to alter its velocity in a given way.

The SI standards of mass etc are done in terms of blocks of metal, the motion of light, the variation of emission spectra etc so when someone says "I dropped a m kilogram brick from d metres and it hit the ground with speed v metres per second" then you can refer it all back to something tangable. This is sufficient to do physics because the precise choice of units is not really important. Someone building a bridge would know the tensile or compressive strength of steel and from that they can work out how many cars a given structure might support. What is important is whether one quantity is more than the other, not what the units actually refer to, because everyone agreed on the meaning of force, mass, distance etc so you can work out relationships between those things in any given system.

Before you can understand what the 'physical' properties of mass and force are.

You must first understand the electron.

No, you don't. The electron wasn't discovered till around 1900, yet massive work had been done on forces and mechanics before that. Newton didn't know about the electron but he managed to come up with F=ma and gravity models.

Mass and force can only be explained in terms of energy, light and electrons (matter).

Demonstrably false, as my example of Newton just demonstrated.

The question you should be asking first, is "What is an electron?"

Terry, don't try and shoe horn in your delusional nonsense about the electron and the double slit experiment, make your own thread if you want to ramble about your nonsense.

 

[Human001]

Metres, seconds and kilograms are units which people have agreed the meaning of so that when I say to someone "I ran 100 metres in 14 seconds" they know what you are referring to. Mass is a measure of the amount of substance something has which can also be related to some standard. For instance Carbon 12 atoms have a mass of 12 grams (its slightly different from 12 but I can't remember what, its been 8 years since I did any chemistry) so then you can refer to other objects' masses in terms of that. From that you can define a force as the 'thing' which cases a given mass to alter its velocity in a given way.

The SI standards of mass etc are done in terms of blocks of metal, the motion of light, the variation of emission spectra etc so when someone says "I dropped a m kilogram brick from d metres and it hit the ground with speed v metres per second" then you can refer it all back to something tangable. This is sufficient to do physics because the precise choice of units is not really important. Someone building a bridge would know the tensile or compressive strength of steel and from that they can work out how many cars a given structure might support. What is important is whether one quantity is more than the other, not what the units actually refer to, because everyone agreed on the meaning of force, mass, distance etc so you can work out relationships between those things in any given system.

Thanks for the reply. I see what your saying, and I understand the fundamental units (L, M, T...). I understand you can define mass in terms of carbon atoms and one meter can be said to be the distance light travels in... something or other.
One point I would raise is that length is entirely intuitive. The length of my coffee table can be inutively grasped by any human. I say mass is not intuitive. You can say holding a book in your hand gives you an intuition of mass, but that is weight you are feeling, not mass. Also, defining 1kg in terms of carbon atoms leaves me slightly troubled. What is the mass of x amount of silicon atoms? Of course there is an answer, but carbon atoms don't "fit into" silicon atoms. It's like saying if a bag of apples weighs 1kg, so how much does a bag of oranges weigh? I'm not arguing with the physics of it. It's all safe and sound, I'm arguing with the metaphysics of it.

My question is rather more metaphysical and actually difficult to explain.
Let me start again, from this point: I have read several news articles, popsci books on CERN and the Higgs Boson. Aparently, if it exists, it gives particles mass. Instantly my mind was caught by the question, why does there need to be a particle to give anything mass? In fact, what is mass.
I understand this is pop science not physics, but if as you sa,y Mass is a fundamental axiomatic property of matter, why does it need a particle to exist? Is there a Higgs Boson that gives things length? I doubt it.

 

[John Connellan]

I say mass is not intuitive. You can say holding a book in your hand gives you an intuition of mass, but that is weight you are feeling, not mass.

No, mass is highly intuitive - even out of a gravitational field. Imagine you are in the depths of space floating with your friend in spacesuits. Your friend asks you to push on a small rock weighing 2 kg, then he asks you to push on a very small asteroid weighing 10,000 kg. Now which one do you think is going to be harder to get moving?

Thats mass intuition

 

[Green Destiny]

If you can work out a proper definition of energy - which we can, we can also make a proper definition of matter. In a book recently I read called E=Mc^2, energy is just diffused matter. So matter is very much a concentrated energy.

 

[James R]

Human001:

What I want to know is what mass actually means. Does it mean anything?

Yes. Mass is a measure of a body's inertia, or resistance to acceleration. It can be determined experimentally by applying a known force to a body and measuring the body's acceleration.

Mass is usally meausred in kg, but that leads to the question what is a kg? Something that is equal to the mass of something that weighs 1kg.

The standard kilogram is a block of platinum-iridium alloy kept in Paris, France. All other kilograms are compared to that.

So mass is a testable property of objects, but the test involves equations that were first constructed by assuming objects had a property called mass, which I still don't know what it means.

Everything starts somewhere. The definition of mass comes fundamentally from Newton's second law of motion.

Come to think of it, what is a force?

A force is a push or a pull, fundamentally an interaction between two bodies. Wikipedia is right.

It appears the definition just mimes Newton's famous equation.

Not surprising, since Newton was the first person to define terms such as "mass" and "force" rigorously.

It seems that physics is inherently tautological.

No. For example, "force" is derived from basic concepts of mass, length and time.

One point I would raise is that length is entirely intuitive. The length of my coffee table can be inutively grasped by any human. I say mass is not intuitive. You can say holding a book in your hand gives you an intuition of mass, but that is weight you are feeling, not mass.

It's not even weight you are feeling. You're feeling a contact force between your hand and the book. We have no direct feeling of weight. Mass is intuitive, however. The idea that you have to push a more massive object harder in order to make it accelerate faster is quite intuitive.

Also, defining 1kg in terms of carbon atoms leaves me slightly troubled.

That's not how "1 kg" is defined. The mass of a carbon atom is a secondary result, not a definition.


Terry Giblin:

Length, time, mass, charge, spin,.... l,t,m,q,s...., 1,2,3,4...., are all words, letters or numbers.

Ask a philosopher, "What is a number, a letter or a word?"... [snip]

This is the physics and math forum. Please take your nonsense to Philosophy.

Before you can understand what the 'physical' properties of mass and force are.

You must first understand the electron.

No. See Alphanumeric's reply to you. Electrons were totally unknown in Newton's era.

Mass and force can only be explained in terms of energy, light and electrons (matter).

Wrong again.

 

[M00se1989]

Length, time, mass, charge, spin,.... l,t,m,q,s...., 1,2,3,4...., are all words, letters or numbers.

Ask a philosopher, "What is a number, a letter or a word?

What is a 'philosopher'?

Before asking a mathematician or physicist, we just measure real 'things' and use them in our calculations.

A very circular question and answer.

Light in, Light out.

A philosopher is a person who finds ground to stand upon in his life. We stand upon our iron in ways of war, architecture, arrhythmia, travel, as well as our universe. That is why it is the philosophers stone. It gives all people something to stand upon and gaze into their own soul. But I ask, "If God were as dead as Iron, what would it take to bring him back to life?"

What light shines through any existence, shines also beneath it. Is there any harm in applying a circular infinite into another infinite?

replace any infinite such as zero or ∞ as "π!"

and replace both infinities as a physical object.

 

[BenTheMan]

A philosopher is a person who finds ground to stand upon in his life. We stand upon our iron in ways of war, architecture, arrhythmia, travel, as well as our universe. That is why it is the philosophers stone. It gives all people something to stand upon and gaze into their own soul. But I ask, "If God were as dead as Iron, what would it take to bring him back to life?"

What light shines through any existence, shines also beneath it. Is there any harm in applying a circular infinite into another infinite?

replace any infinite such as zero or ∞ as "π!"

and replace both infinities as a physical object.

Let's not pursue this discussion anymore, please.

Human's question has a scientific answer, and a non-scientific one.

We would all do well to know the difference between the two.

 

[temur]

it all starts with position, velocity, and acceleration and C^ = a^2 + b^2


conservation of energy and momentum are the 2 things you should be looking at.

You mean E=mc^2=ma^2+mb^2?

 

[AlphaNumeric]

or should I stop?

Yes, as it doesn't appear you even think coherently.

 

[Emil]

The mass is the amount of substance.
It gives information about the amount of atoms.

It is equal to the number of atoms multiplied by the number of proton and neutron content of that atom.

m = nrX(Z + N)
nr- the number of atoms
Z-Atomic number,equal to the number of protons
N-number of neutrons

 

[Human001]

[quote = JamesR]Yes. Mass is a measure of a body's inertia, or resistance to acceleration. It can be determined experimentally by applying a known force to a body and measuring the body's acceleration.[/quote]

I see. But then this "known force" is known how? Now I know you can calculate a force. I'm just pondering what it means to do so.

In general my point is how are the "measurable" quantities not arbitrary? I used the quote marks on purpose, because it seems that measuring anything presupposes we know another thing. It's circular and tautological. It's like a dictionary. Reaidng a dictionary, technically, you are getting no knew information, since the definition of anyword is bound up in the definitions of a dozen other words, and those definitions are...

Now this is just an off the cuff thought experiment. Let's say I am an alien and I have never heard of Newton, Einstein, Galileo. I play a game of pool and watch the motions of the balls rolling along the table and I decide I have come up with some laws for their motion.
First I create some "measurable" quantities, X, Y, Z that are not any of mass, time, length etc. (because I'm inventing some new arbitrary units of measurement - which I think may be possible, hypothetically,as the deifnition of mass is resistance to force, and force is something that pushes or pulls, which can only be measured when it acts on an object of mass (thinking classically) and we end up wondering what mass is again.)

I then come up with a set of equations
For example:
Y = f(X,Z)
dY/dX = k*g(Z) for constant k.
etc etc...

Would my equations necessarily resemble the euqations of physics we know?

 

[zfalll]

the simplest way to define mass and force:
-mass: The weight of an object when gravitational acceleration is not into account.
-force: a symptom which causes something to change shape, to move, to change speed, or to change direction.

 

[Human001]

The mass is the amount of substance.
It gives information about the amount of atoms.

That would mean atoms don't have mass, which they do. Also, oyu haven't exlpained "substance".

It is equal to the number of atoms multiplied by the number of proton and neutron content of that atom.

m = nrX(Z + N)
nr- the number of atoms
Z-Atomic number,equal to the number of protons
N-number of neutrons

I'm not sure that will give me mass (in metric units). You probably need to multiply Z by the mass of a proton and N by the mass of a neutron. But, still this is an equation for mass for an object, that is built of atoms, and presupposes we know the weight of an atom, or its constituents.

Your equation and your definiton give no answer to a proton's mass.

 

[Emil]

That would mean atoms don't have mass...

Please explain.

Also, oyu haven't exlpained "substance".

Substance:

Substance may refer to:
Chemical substance, a material with a definite chemical composition
Matter, the substance of which all physical objects are made
Substance theory, theory positing that a substance is distinct from its properties.
Substantial (rapper) a US musician
Substance (Joy Division album)
Substance 1987, a New Order album
"Substance", a song by Haste the Day from That They May Know You
Metal Gear Solid 2: Substance, an update of the video game Metal Gear Solid 2: Sons of Liberty

From Wikipedia, Substance

I'm not sure that will give me mass (in metric units). You probably need to multiply Z by the mass of a proton and N by the mass of a neutron.

Conversion factor between atomic mass units and grams.

The standard scientific unit for dealing with atoms in macroscopic quantities is the mole (mol), which is defined arbitrarily as the amount of a substance with as many atoms or other units as there are in 12 grams of the carbon isotope C-12. The number of atoms in a mole is called Avogadro's number, the value of which is approximately 6.022 × 1023 mol-1. One mole of a substance always contains almost exactly the relative atomic mass or molar mass of that substance (which is the concept of molar mass), expressed in grams; however, this is almost never true for the atomic mass. For example, the standard atomic weight of iron is 55.847 g/mol, and therefore one mole of iron as commonly found on earth has a mass of 55.847 grams. The atomic mass of an 56Fe isotope is 55.935 u and one mole of 56Fe will in theory weigh 55.935g, but such amounts of pure 56Fe have never been found on Earth.
The formulaic conversion between atomic mass units and SI mass in grams for a single atom is:

where Mu is the Molar mass constant and NA is the Avogadro constant.

From Wikipedia Measurement of atomic masses

But, still this is an equation for mass for an object, that is built of atoms, and presupposes we know the weight of an atom, or its constituents.

Your equation and your definiton give no answer to a proton's mass.

Atomic number

In chemistry and physics, the atomic number (also known as the proton number) is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element. In an atom of neutral charge, the atomic number is also equal to the number of electrons.
The atomic number, Z, should not be confused with the mass number, A, which is the total number of protons and neutrons in the nucleus of an atom. The number of neutrons, N, is known as the neutron number of the atom; thus, A = Z + N. Since protons and neutrons have approximately the same mass (and the mass of the electrons is negligible for many purposes), the atomic mass of an atom is roughly equal to A.
Atoms having the same atomic number Z but different neutron number N, and hence different atomic mass, are known as isotopes. Most naturally occurring elements exist as a mixture of isotopes, and the average atomic mass of this mixture determines the element's atomic weight.

From Wikipedia Atomic number

 

[D H]

A bunch of replies. The opening post first:

What I want to know is what mass actually means.

First off, you need to start with the basic science. Don't try jumping off into the depths of relativity, quantum mechanics, or celestial mechanics before you understand the basics. Rhetorical question: If you don't understand mass in terms of good old Newtonian mechanics, how can you possibly understand mass in a more advanced setting?

So, a working definition of mass, a definition that has worked quite well for thousands of years:

Mass is the measure of the quantity of some object as measured by an ideal balance scale.​

That, coupled with a couple of other facts regarding mass sufficed for a long, long time. These facts are

1. Mass is additive. If you place two objects on one side of a balance scale and measure their combined mass, this combined mass will be the sum of the individual masses of the two objects.
2. Mass is conserved. If you split an object with a known mass into parts and measure the masses of those individual parts you will find that the sum is equal to the whole.

I can here the objection already: Relativity says that mass is not additive and quantum mechanics says that mass is not conserved. As I said earlier, don't go diving off into the deep end until you understand the basics first. These were deemed to be true up until the end of the 19th century.

For now, let's go with that definition and those "facts". That definition remains the basis of the current definition of the kilogram, the International Prototype Kilogram stored at the BIPM (International Bureau of Weights and Measures; the acronym is French). In our everyday, slow-moving, macroscopic world that standard kilogram forms the basis for our concept of mass.


James R:

Mass is a measure of a body's inertia, or resistance to acceleration. It can be determined experimentally by applying a known force to a body and measuring the body's acceleration.

I disagree with this definition of mass. The current interpretation of Newton's second law is that it defines the concept of force. Defining mass in terms of force and force in terms of mass would be just what Human001 complained about: A tautology. Mass, acceleration, and inertial reference frames are concepts whose definitions must precede Newton's second law. Newton's second law defines force in terms of what it does to objects. Specifically, in an inertial frame of reference, a force is something that makes objects accelerate in inverse proportion to the objects' masses.


Alpha:

Mass is a measure of the amount of substance something has which can also be related to some standard.

There are in fact two such standards. I have already talked about the one used in our everyday, slow-moving, macroscopic world, the IPK.

For instance 6.02×10[sup]23[/sup] Carbon 12 atoms have a mass of 12 grams (its slightly different from 12 but I can't remember what, its been 8 years since I did any chemistry) so then you can refer to other objects' masses in terms of that.

First off, a minor correction: 1 mole of Carbon 12 atoms masses exactly 12 grams by definition. That is the other standard to which I alluded above. (Are you thinking of the archaic Oxygen 16 standard, which was tossed back in the 1960s?)

So why are there two standards, one for the macroscopic world and another for the atomic? The obvious thing to do is to go with the deeper atomic definition. That has already been done with time and length, where one standard rules at the everyday, quantum, and relativistic worlds. The reason this hasn't been done yet with mass is simple: Lack of precision and lack of replicability.

Switching from a prototype-based mass standard to a deeper definition requires greater precision in measurement than currently exists and requires an ability to replicate those standard definitions. Avogadro's number is 6.02214179(30)×10[sup]23[/sup]. That (30) represents the uncertainty in the value, 1 part in 20 million. By physics standards that is not all that good, and it is not nearly good enough to justify a switch to a carbon-12 based mass standard.

Aside, somewhat: That 1 per per 20 million uncertainty is not nearly as lousy as the 1 part in 10,000 uncertainty in the universal gravitational constant G. That uncertainty in G is indicative that physicist's do not quite understand what mass is (yet).

Getting back to an atomic basis for the definition of mass: Switching to such a basis has been the express goal of the international standards community for quite some time now. This goal has been accomplished for time and length. I suspect that the prototype kilogram will be tossed within the next decade or so, and possibly quite a bit sooner.

 

[Human001]

Thanks for replying DH. True, I don't know relativity or QM, so I'm quite happy to think classically.

Mass is the measure of the quantity of some object as measured by an ideal balance scale.

And what is a balance scale? And what is an ideal balance scale? Something that measures mass? I think you have a circular problem here, as you pointed out to James R.

I want to point out again, I'm not being facetious or pedantic. I know what a scale is, and I know how to measure mass. This is more metaphysics than physics.

That definition remains the basis of the current definition of the kilogram, the International Prototype Kilogram stored at the BIPM (International Bureau of Weights and Measures; the acronym is French). In our everyday, slow-moving, macroscopic world that standard kilogram forms the basis for our concept of mass.

Yes, but if the definition is circular, it doesn't matter whether you have a standard from which to measure against - no new information is gained.

If the definition of Mass requires an understanding of Mass, saying the mass of any particular object is 1kg offers no information.
I could say all matter possesses property X, and define X circularly. Then say, for instance, my teacup will be the base measuremnt. My teacup's X value is 1 schgram. What is the X value of my saucer? You don't know and you can't know, because X is an empty property.

 

[AlexG]

It seems a basic definition of mass would be it's that property of matter which resists changes in motion.