To compare Newton’s concept of mass to a unicorn is ludicrous. A unicorn is pure fiction, but mass is real, has physical meaning, properties and effect. Newton will turn in his grave because you compare his fundamental concept of mass to trivial fiction, GdB.

No, it is not. I do not say that mass is fictitious in the way unicorns are. I say that Newton’s ‘quantity of matter’ is not an independent physically operative definition of mass. ‘Mass’ has a meaning, like ‘unicorn’ has a meaning (How could I otherwise make sense of the sentence ‘A unicorn is pure fiction’? If ‘unicorn’ has no meaning I would not know what you are saying.) The difference is that ‘mass’ is connected to things in the real world, because I have operative procedures with which I can measure it. I can put objects on a weighing machine, or I can measure their inertia with a spring. The problem with that is that they are not independent definitions: with the weighting machine I presuppose gravity, with inertia I am presupposing ‘F = ma’. When I define mass as ‘density times volume’, I must ask what ‘density’ is. Well, it is the amount of matter divided by volume… it is perfectly circular.

kkwan - 28 October 2011 12:52 PM

At that point it is appropriate to summarize the properties of mass in Newtonian mechanics:

‘Properties’? Is that against the idea that the definitions are circular?

kkwan - 28 October 2011 12:52 PM

Hence, Newton’s concept of mass is neither fictitious nor trivial and it is “physically operative”.

Exactly. I never said one of these things. But I said that the definitions of mass, force (and I can add gravity to it) are circular, they cannot be defined independently of each other.

It is not easy to distinguish between mathematics and physics. Mathematical theories should be consistent, but nothing that figures in it must really exist. But if we agree that a mathematical theory is about something, we must agree on how at least some of the mathematical symbols refer to reality.

I remember reading a funny dialogue written by Sir Arthur Eddington about this problem in the context of geometry (you sure can Google up more about mass…) See here (search for the prologue), and maybe compare this to the problem of definition of mass. Do some thinking for your self, it can be fun!

How is that possible? We started from chaos (disorder) and due to gravitational forces we see an orderly development and evolution of the universe. How can chaos be related to gravity?

The Big Bang is a state of a extremely low entropy.

Since a finite universe is an isolated system, the Second Law of Thermodynamics states that its total entropy is constantly increasing.

And:

If the universe can be considered to have generally increasing entropy, then—as Sir Roger Penrose has pointed out—gravity plays an important role in the increase because gravity causes dispersed matter to accumulate into stars, which collapse eventually into black holes. The entropy of a black hole is proportional to the surface area of the black hole’s event horizon. Jacob Bekenstein and Stephen Hawking have shown that black holes have the maximum possible entropy of any object of equal size.

No, it is not. I do not say that mass is fictitious in the way unicorns are. I say that Newton’s ‘quantity of matter’ is not an independent physically operative definition of mass.

But you wrote:

But it has no physical meaning, like the unicorn.

Are you saying “quantity of matter” is a logical fiction?

The objects they appear to denote do not have their own being and are not constituents of reality.

They are also called pseudo-objects.

The difference is that ‘mass’ is connected to things in the real world, because I have operative procedures with which I can measure it. I can put objects on a weighing machine, or I can measure their inertia with a spring. The problem with that is that they are not independent definitions: with the weighting machine I presuppose gravity, with inertia I am presupposing ‘F = ma’. When I define mass as ‘density times volume’, I must ask what ‘density’ is. Well, it is the amount of matter divided by volume… it is perfectly circular.

Measurement of objects with apparatus are only operational procedures to obtain “quantity of mass”, not definitions. Also, Newton did not define mass as density times volume.

‘Properties’? Is that against the idea that the definitions are circular?

The properties of mass show that mass is real and has effect. Thus, mass is not a logical fiction.

Exactly. I never said one of these things. But I said that the definitions of mass, force (and I can add gravity to it) are circular, they cannot be defined independently of each other.

You wrote “we cannot use it if we do not make it physically operative” and “no physical meaning” wrt mass as “quantity of matter”.

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

kkwan, please give me the way how you determine the ‘quantity of mass’ of an object, without using any force.

To be more specific, how can you say that the mass of an object e.g. is 1 kg without:

1. Using gravity (a force)
2. Determining its inertia (using some other force)
3. Compare it to another fixed mass (this is just shifting the problem, compare it with Arthur Eddington’s dialogue about length)

I am not making some revolutionary point, it is just that many people do not realise it: that the concepts of scientific theories are circular. But as long as some of the concepts are observables, this is no problem.

How is that possible? We started from chaos (disorder) and due to gravitational forces we see an orderly development and evolution of the universe. How can chaos be related to gravity?

The Big Bang is a state of a extremely low entropy.

Since a finite universe is an isolated system, the Second Law of Thermodynamics states that its total entropy is constantly increasing.

And:

If the universe can be considered to have generally increasing entropy, then—as Sir Roger Penrose has pointed out—gravity plays an important role in the increase because gravity causes dispersed matter to accumulate into stars, which collapse eventually into black holes. The entropy of a black hole is proportional to the surface area of the black hole’s event horizon. Jacob Bekenstein and Stephen Hawking have shown that black holes have the maximum possible entropy of any object of equal size.

This is very confusing.
As I understand it, in its most simple form entropy is a gradual loss of energy, in the form of heat. But what does that have to do with gravity (a universal constant) itself?
If it were not for gravity, the universe would never have acquired order to begin with. Lest we forget, the BB created energy, gravity created matter.

Wiki shows an example of entropy with ice melting in a glass of ice-tea, thus converting an ice cube into liquid randomnness, but simultaneously cooling the ice-tea. There will be loss of heat in the process of cooling the tea.
But that has nothing to do with gravity.

Now I’m told that gravity is responsible for entropy through the forming of denser matter (mass, shape, form) from random molecules, creating heat (not cold as the ice cube) which then eventually disappears into a black hole, presumably ending up in a chaotic state of extremely dense (massive) randomness which does not produce heat?
But does it lose gravity?

Thus we have randomness at both ends, an ice cube becoming less solid (chaotic) but cooling its environment and a galaxy becoming more solid (order) and heating its environment until it becomes so dense that it does no longer generate heat? Something is missing from this equation.

Maybe the entropy in a black hole is what produces dark matter and dark energy. Apparently we are short 21% matter and 75% energy for the universe to behave (orderly) as it does. Given 14 billion years of entropy, that sounds about the right amount of both.

But then we are talking about conversion, not entropy (i.e. not thermodynamic). IMO, the universal potential of the cosmos remains constant, it just changes its expression…

p.s. Just saw a program on “The Universe”, which explained that (according to gravitational law), the outer spirals of a galaxy should move in a slower (larger) orbit around their galaxial black hole than the inner bodies which are subject to greater gravitational pull. Strangely, these outer spirals do not move slower, defying the planetary model of gravity. That is the main reason for the proposition of Dark Matter and Dark Energy.
But does that have anything to do with Entropy?

To be more specific, how can you say that the mass of an object e.g. is 1 kg without:

1. Using gravity (a force)
2. Determining its inertia (using some other force)
3. Compare it to another fixed mass (this is just shifting the problem, compare it with Arthur Eddington’s dialogue about length)

I am not making some revolutionary point, it is just that many people do not realise it: that the concepts of scientific theories are circular. But as long as some of the concepts are observables, this is no problem.

That is true for macro objects, but it is not compelling evidence of conceptual circularity.

Mass is not weight. The weight of an object varies depending on gravity, whereas the mass remains constant. In other words, even with minimal gravity, mass is the same. Mass is invariant whereas weight is not.

The mass of an object is a fundamental property of the object; a numerical measure of its inertia; a fundamental measure of the amount of matter in the object. Definitions of mass often seem circular because it is such a fundamental quantity that it is hard to define in terms of something else.

Also,

The weight of an object is defined as the force of gravity on the object and may be calculated as the mass times the acceleration of gravity, w = mg. Since the weight is a force, its SI unit is the newton.

By measuring an object’s weight (which involves gravity etc.), one can determine its mass. However, that does not imply the definition of mass as “quantity of matter” is circular because the act of measurement is actually measuring its weight and not its mass per se.

However, for micro objects like the proton, from this article HERE

At Long Last, Physicists Calculate the Proton’s Mass

Ever since the proton was discovered 89 years ago, physicists have been able to measure the mass of the particle—which, along with another called the neutron, makes up the atomic nucleus. But even with the best computers, theorists had not been able to start with a description of the proton’s constituent parts and calculate its mass from scratch.

kkwan, you did not answer my main question: give me the way how you determine the ‘quantity of mass’ of an object, without using any force.

A few reactions on you Great Googling:

I nowhere said that mass is weight. I just asked you how you can determine the ‘quantity of mass’ without using any force, or just compare it with another mass (did you already read Eddington’s dialogue?)

Yes, I know the mass of the proton was calculated. But as input the mass of the Xi, K and pi hadrons were used. And these were measured independently. And you forget the essence of the calculation. By getting the measured weight of the proton the calculation shows that QCD is able to reproduce the coherence of the weights of Xi, K, pi hadrons and that of the proton.

kkwan, you did not answer my main question: give me the way how you determine the ‘quantity of mass’ of an object, without using any force.

You still don’t get it.

If force is used to determine the mass of an object, is it circularity?

Take the mass of the earth. From this article HERE

Because we know the radius of the Earth, we can use the Law of Universal Gravitation to calculate the mass of the Earth in terms of the gravitational force on an object (its weight) at the Earth’s surface, using the radius of the Earth as the distance.

Just because the gravitational force on an object (its weight) is used to calculate the mass of the earth does not imply that the definition of mass as “quantity of matter” is circular.

A circular definition is one that uses the term(s) being defined as a part of the definition or assumes a prior understanding of the term being defined.

For example, if a circle is defined as a round object, it is circular.

OTOH, mass was not defined by Newton as something which is massive.

He also did not define mass starting from F=ma.

Hence, there is no circularity in using force to determine mass.

The gravitational constant appears in Newton’s law of universal gravitation, but it was not measured until 71 years after Newton’s death by Henry Cavendish with his Cavendish experiment, performed in 1798 (Philosophical Transactions 1798). Cavendish measured G implicitly, using a torsion balance invented by the geologist Rev. John Michell. He used a horizontal torsion beam with lead balls whose inertia (in relation to the torsion constant) he could tell by timing the beam’s oscillation.

The Gravitational Torsion Balance is oriented so the force of gravity between the small balls and the earth is negated (the pendulum is nearly perfectly aligned vertically and horizontally).

Historical background:

Despite the lack of direct evidence for any such attraction between everyday objects, Isaac Newton was able to deduce his law of universal gravitation.

However, in Newton’s time, every measurable example of this gravitational force included the Earth as one of the masses. It was therefore impossible to measure the constant, G, without first knowing the mass of the Earth (or vice versa). The answer to this problem came from Henry Cavendish in 1798, when he performed experiments with a torsion balance, measuring the gravitational attraction between relatively small objects in the laboratory. The value he determined for G allowed the mass and density of the Earth to be determined.

Thus, it is possible to determine G without first knowing the mass of the earth (or vice versa).

Yep. But one must (again!) measure a force (or even worse, measuring acceleration). So we are back to my point.
In the Cavendish experiment gravitation is measured by taking known masses, and measure the force between them. Via Newton’s gravity law F = G.M1.M2/(r^2). We can determine G. When we know G we can tell the mass of the earth, because we know the acceleration of free falling objects. That is the reason why sometimes the determining of G is also called ‘weighing the earth’.

Your other 2 experiments are of the same kind: they relate measured forces and known masses to calculate G.

You are missing basic understanding of mechanics, kkwan. You need knowledge to be able to set your Googlings in the right context.

Did you read the dialogue of Eddington? Read the whole dialogue to get the full picture.

With the gained insights you might be able to understand why the operational definitions of mass and force are interdependent.

Newton’s definition explicitly is one of “quantitas materiae”. This quantity of matter is the
subject of Newton’s definition, and the definition he gives for it is a quantitative, not a semantic one: “Quantity of matter” is defined through a quantitative, mathematical term: it is the quantity that is represented by the product of “density times volume”. And Newton makes this definition compulsory, saying “I mean this quantity whenever I use the term ‘body’ or ‘mass’ in the following pages.”

Hence, the operation to determine weight (which is a force) and then use it to obtain mass, i.e. quantity of matter, is not relevant to his quantitative definition at all and as such, it is not circular.

Incidentally, there are ongoing projects to define the kilogram (the base unit of mass) as a certain number of atoms, i.e. quantity of matter.

Though not offering a practical realization, this definition would precisely define the magnitude of the kilogram in terms of a certain number of carbon‑12 atoms.

Avogadro project:

Another Avogadro constant-based approach, known as the Avogadro project, would define and delineate the kilogram as a softball-size (93.6 mm diameter) sphere of silicon atoms.