GdB - 01 November 2011 11:26 PM

A definition of a physical property is just not the same as our ways of quantifying the property.

I posted a definition of quantity.

Stephen

StephenLawrence - 02 November 2011 12:18 AM

I posted a definition of quantity.

Do not increase the confusion, Stephen. You did not post a conceptual definition of mass.

An operational definition of mass is simple: kkwan’s Avogrado Silicon Ball is one example, the old definition as ‘the mass of 1 liter water at 4 centigrade’ is another one.

But one cannot define what mass is without referring to force, inertia or gravity.

BTW, from here, one of kkwan’s sources:

The term “mass’ was introduced into mechanics by Newton in 1687 in his “Principia”. He defined it as the amount of matter. The generally accepted definition of matter does not exist even today.

<big snip>

Though the definition of mass (“Definition I: The quantity of matter is the measure of the same, arising from its density and bulk conjointly”) given by Newton in his “Principia” was so unclear that scholars are discussing its logical consistency even today, the equations of Newtonian mechanics are absolutely self-consistent.

GdB - 02 November 2011 01:44 AM

StephenLawrence - 02 November 2011 12:18 AM

I posted a definition of quantity.

Do not increase the confusion, Stephen. You did not post a conceptual definition of mass.

I read your post 73 and thought it was relevent and useful to that. I haven’t been following the debate closely enough to know about the wider context you are putting it in.

I do think that your objection that it increases the confuson is unreasonable

Stephen

See, this science stuff is way too complicated.

Come to church Sunday and we’ll have mass…....

GdB - 01 November 2011 12:49 PM

“A bachelor is an unmarried man” is an example of a tautology.
A married bachelor is a contradiction. You do not need an experiment for it.

Now try: “a quantity of matter without inertia”. Or: “a quantity of matter without gravity”. Do you need an experiment for it?

Your Silicon Ball is an operational definition. But it is not conceptual.

Your example of a bachelor is clearly circular and tautological because an unmarried man is a bachelor.

A quantity of matter is an amount of matter or x atoms of matter. Inertia and gravity are properties of the mass which all matter have. However, they play no part wrt the intrinsic value of any quantity of matter.

The silicon ball is just the realization of the concept of mass as “quantity of matter”, not a definition per se.

OTOH, Newton’s quantitative definition of mass as “quantity of matter” is not circular.

From the wiki on matter

Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume.

Now, if mass is defined as “quantity of matter” and matter is defined as anything that has mass and occupies volume, is the definition of mass circular? Not so.

If x is defined as a “quantity of y” and y is defined as anything which has x and occupies v, what it means is whereas y is anything (which has x and occupies v), x is only a “quantity of y” a simple physical quantity with magnitude (scalar) which is distinct from y itself (which has x and occupies v) and is a physical entity. This is Newton’s quantitative definition of mass.

StephenLawrence - 02 November 2011 01:58 AM

I do think that your objection that it increases the confuson is unreasonable

It is unreasonable and misconceived, Stephen.

Your post of the definition of physical quantity is relevant to the issue of what is quantity of matter in Newton’s definition of mass as “quantity of matter”. 

From the same wiki on physical quantity you posted:

Philosophical issue:

The notion of physical quantities is so basic and intuitive in the realm of science, that it does not need to be explicitly spelled out or even mentioned. It is universally understood that scientists will (more often than not) deal with quantitative data, as opposed to qualitative data. Explicit mention and discussion of physical quantities is not part of any standard science program, and is more suited for a philosophy of science or philosophy program.

However, in physics:

The notion of physical quantities is seldom used in physics, nor is it part of the standard physics vernacular. The idea is often misleading, as its name implies “a quantity that can be physically measured”, yet is often incorrectly used to mean a physical invariant.

But, quantity of matter (mass) is that which can be physically measured and is a physical invariant.

From the wiki on mass

The amount of matter in certain types of samples can be exactly determined through electrodeposition or other precise processes. The mass of an exact sample is determined in part by the number and type of atoms or molecules it contains,......

kkwan - 02 November 2011 10:49 AM

Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume.

Let me rephrase this for you:

Mass   = quantity of matter
Matter = anything that has mass

Isn’t that circular?

(Occupying volume plays no essential role in the basics of Newtonian mechanics, as you can see that it very often is just about point masses.)

GdB - 03 November 2011 12:37 AM

Mass   = quantity of matter
Matter = anything that has mass

Isn’t that circular?

No, though it only seems circular if you represent them as equations (which is misleading). Mass is not equal to…......and matter is not equal to…....   

In reality, mass and matter are distinct entities.

Matter (which has mass) is not mass and mass (which has no matter) is not matter.

Mass was defined by Newton as quantity of matter and not as matter per se.

A quantity of matter (mass) is the simple physical quantity with magnitude (a scalar) and it is not an object like matter (a physical object with mass and occupies volume).

For instance, a ball of silicon is matter (a physical object with mass and occupies volume) whereas the mass of the ball of silicon is only the quantity of silicon (a scalar and not a physical object which the ball of silicon is).

As such, there is no circularity.

Write4U - 02 November 2011 09:12 AM

See, this science stuff is way too complicated.

Come to church Sunday and we’ll have mass…....

What is mass? It has no matter.

What is matter? It has mass.

What is gravity? Matter have mass with gravitational fields that are manifested as space-time.

Is it simpler to have mass?

Por favor…..no mass…........

Let’s recapitulate:

1. According to Newton mass is a ‘quantity of matter’.
2. Wikipedia: ‘A common way of defining matter is as anything that has mass and occupies volume’
3. A quantity of matter without accompanying gravity is a contradiction.
4. A quantity of matter without inertia against a force is a contradiction.
5. Gravitation without matter is a contradiction.
6. Inertia without matter is a contradiction.
7. Then according to one of your own sources:
  <Newton> defined <mass> as the amount of matter. The generally accepted definition of matter does not exist even today.
8. Same source:
  Though the definition of mass (“Definition I: The quantity of matter is the measure of the same, arising from its density and bulk conjointly”) given by Newton in his “Principia” was so unclear that scholars are discussing its logical consistency even today, the equations of Newtonian mechanics are absolutely self-consistent.
9. Determining the gravity constant G is also known under the phrase ‘weighing the earth’. It is the only way to determine the ‘quantity of matter’ of the earth.

I leave it to other readers (when there still are…) if the concept of mass is clear, and if it is not circular defining it as ‘density times volume’ (quantity of matter), or as defining it with help of gravity and/or inertia.

GdB - 04 November 2011 12:03 AM

1. According to Newton mass is a ‘quantity of matter’.

Yes, with the emphasis on quantity. Newton’s definition is a quantitative definition.

Meaning of quantitative (Merriam-Webster):

1. : of, relating to, or expressible in terms of quantity
2. : of, relating to, or involving the measurement of quantity or amount

2. Wikipedia: ‘A common way of defining matter is as anything that has mass and occupies volume’

Yes.

3. A quantity of matter without accompanying gravity is a contradiction.

Gravity is a property of mass. Matter has mass and exhibit gravity.

4. A quantity of matter without inertia against a force is a contradiction.

Mass of a body is a measure of its inertia.

5. Gravitation without matter is a contradiction.
6. Inertia without matter is a contradiction.

These are just the reverse consequences of 3 and 4.

7. Then according to one of your own sources:
  <Newton> defined <mass> as the amount of matter. The generally accepted definition of matter does not exist even today.

From the wiki on matter

Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume. However, different fields use the term in different and sometimes incompatible ways; there is no single agreed scientific meaning of the word “matter”.

However, in Newtonian physics, matter can be considered as “anything that has mass and occupies volume”. Newton did not define matter.

8. Same source:
  Though the definition of mass (“Definition I: The quantity of matter is the measure of the same, arising from its density and bulk conjointly”) given by Newton in his “Principia” was so unclear that scholars are discussing its logical consistency even today, the equations of Newtonian mechanics are absolutely self-consistent.

OTOH, from another source HERE

So, contrary to nearly everything that has ever been written on Newton’s definitio 1, this definition is not one of “mass”, nor is it circular, as some have opined; rather it is a formula for the quantitative determination of an even experimentally measurable quantity of a body’s material contents.

9. Determining the gravity constant G is also known under the phrase ‘weighing the earth’. It is the only way to determine the ‘quantity of matter’ of the earth.

From this article HERE

Quantum Measurement of Gravitational Constant

The new method involves using an atom interferometer to split a beam of cesium atoms into two, which are then sent along different paths to produce interference fringes (yes, even though they’re atoms - don’t forget about wave-particle duality). By placing a massive object - a 540 kilogram lead weight in this case - near the beams, the path, and therefore the final interference pattern, is affected.

The paper on the new method is HERE

kkwan - 04 November 2011 09:05 AM

These are just the reverse consequences of 3 and 4.

Yes?
I have a piece of matter: but it shows no signs of gravity, and no inertia either. Is it a piece of matter?
There is obviously gravity: can it be that it has another source then mass? (Dark matter!)

kkwan - 04 November 2011 09:05 AM

there is no single agreed scientific meaning of the word “matter”.

kkwan - 04 November 2011 09:05 AM

in Newtonian physics, matter can be considered as “anything that has mass and occupies volume”. Newton did not define matter.

So do we have a definition of mass, independent on gravity and force?

kkwan - 04 November 2011 09:05 AM

Quantum Measurement of Gravitational Constant

This is, from a mechanical point of view, just more of the same. By knowing the mass of caesium atoms and of the lead, measuring the influence on the movement of the caesium atoms (force!), one can calculate G.

GdB - 05 November 2011 12:40 AM

Yes?
I have a piece of matter: but it shows no signs of gravity, and no inertia either. Is it a piece of matter?
There is obviously gravity: can it be that it has another source then mass? (Dark matter!)

Consider this:

From the SEP essay on Newton’s philosophy

2.2 The nature of matter

Since mass cannot be diminished by a body’s spatiotemporal position (unlike gravity), and since it remains a property even of a lonely corpuscle, Newton distinguishes it from gravity, taking it to be an essential quality of all material bodies. Thus if the theory in the Principia uncovers a new essential quality of material bodies, according to Newton, mass is actually the quality, rather than gravity. This indicates that although gravity is not essential to matter, what we might call the basis for gravitational interactions, namely mass, is in fact essential to material bodies.

Thus, if there is only one piece of matter in the universe, it will have mass and inertia but no gravity because it is solitary.

The mass in matter is essential and primal whereas gravity is not.

So, gravity can be considered an emergent property of mass iff there is more than one piece of matter in the universe to interact with each other.

So do we have a definition of mass, independent on gravity and force?

Yes, Newton’s definition of mass as “quantity of matter”.

Newton’s insight into the nature of mass and gravity implies that with one solitary body, mass can be defined as “quantity of matter” independent of gravity or force.