## Comments about "Mass" in Wikipedia

This document contains comments about the subject "Mass" in Wikipedia
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.
In Newtonian physics, mass can be generalized as the amount of matter in an object.
This is the most common view: mass and matter are equivalent. However the difference is more subtle: all objects have mass (weight) independent of where it is made from, its inernal structure. With matter or material we identify that objects can be more different.

### 2 Definitions of mass

Every experiment to date has shown these seven values to be proportional, and in some cases equal, and this proportionality gives rise to the abstract concept of mass.
Why use the term: abstract concept?
IMO mass is a strictly mathematical concept. See
1. The amount of matter in certain types of samples can be precisely determined by electrodeposition or other atom-counting approaches. etc
2. Inertial mass is a measure of an object's resistance to acceleration when a force is applied. etc
3. Active gravitational mass is a measure of the strength of an object's gravitational flux etc
4. Passive gravitational mass is a measure of the strength of an object's interaction with a gravitational field. etc
5. Energy also has mass according to the principle of mass–energy equivalence. etc
6. Curvature of spacetime is a relativistic manifestation of the existence of mass etc
7. Quantum mass manifests itself as a difference between an object's quantum frequency and its wave number.
The above list shows that there are seven concepts of mass.

### 2.2 Inertial vs. gravitational mass

Although inertial mass, passive gravitational mass and active gravitational mass are conceptually distinct, no experiment has ever unambiguously demonstrated any difference between them.
The reason that no experiment can detect the difference between passive and active gravitational mass is because the two are in essence the same.
Part of the problem is that both use the concept of a gravitational field which can only be calculated by means of a point mass. Both involve accelerations which can only be calculated when more objects are involved.
Inertial mass involves lineair motion. A such there exist no experiment to calculate the inertial mass of for example the earth. The only thing you can do is give the mass of the Earth a predefined constant value and use that as a measure to calculate the gravitational mass of the other objects in the universe (using gravitational fields). As a result all are identical.
The details of these calculations are important. Dependent if you use Newton's Law or GR the gravitational mass calculated will be different.
Newton's Law third law implies that active and passive gravitational mass must always be identical etc offers no compelling reason why the gravitational mass has to equal the inertial mass. That it does is merely an empirical fact.
As I wrote already there exist no experiment to calculate the inertial mass.
The reader should consider that calculating the gravitational mass with either Newton or Gr will give different results.
The most important consequence of this equivalence principle applies to freely falling objects.
IMO the most important issue is the relation between the mass of one falling small object towards the earth, versus the mass of the earth.
Suppose we have an object with inertial and gravitational masses m and M, respectively.
You must at least specify how m and M are measured.
If the only force acting on the object comes from a gravitational field g, combining Newton's second law and the gravitational law yields the acceleration
F = m * a = M * g yielding: a = M/m * g
That is undeniable true, but what does it mean.

### 2.3 Origin of mass

The problem is complicated by the fact that the notion of mass is strongly related to the gravitational interaction but a theory of the latter has not been yet reconciled with the currently popular model of particle physics, known as the Standard Model.
The mass of an object is the sum of the mass of each of its constituents, but what does that mean. In some sense you can only compare the mass of two objects.
Two objects at the same distance from the ground undergo the same acceleration and have the same gravity or g. The force they feel is different and depent about their mass.

### 4.2 Universal gravitational mass

In contrast to earlier theories (e.g. celestial spheres) which stated that the heavens were made of entirely different material, Newton's theory of mass was groundbreaking partly because it introduced universal gravitational mass: every object has gravitational mass, and therefore, every object generates a gravitational field.
I would write this different: Every object generates a gravitational field and the strength of this graviational field is coupled to the mass of the object.

### 4.3 Inertial mass

Inertial mass is the mass of an object measured by its resistance to acceleration.
How is that mass measured? This is a very weak definition.
In classical mechanics, according to Newton's second law, we say that a body has a mass m if, at any instant of time, it obeys the equation of motion
F = m*a
This sentence does not mention how the mass m is measured
This equation illustrates how mass relates to the inertia of a body. Consider two objects with different masses. If we apply an identical force to each, the object with a bigger mass will experience a smaller acceleration, and the object with a smaller mass will experience a bigger acceleration. We might say that the larger mass exerts a greater "resistance" to changing its state of motion in response to the force.
Yes that is true, but it is too simple.

### 6.1 Special relativity

In special relativity, there are two kinds of mass: rest mass (invariant mass),and relativistic mass (which increases with velocity).
See next.
Rest mass is the Newtonian mass as measured by an observer moving along with the object.
This implies that the observer and the object involved have the same speed. How does an observer performs such a measurement? IMO it is impossible.
Anyway what has an observer to do with this.
Relativistic mass is the total quantity of energy in a body or system divided by c^2. The two are related by the following equation:
m_relative = gamma*(m_rest)
The equation of relativistic mass is: E = m_relative*c^2 or E = m*c^2
The more practical equation is written as: m = gamma * m0, with m0 being the rest mass.
To test this equation how does an observer do this?
Thus, mass and energy do not change into one another in relativity; rather, both are names for the same thing, and neither mass nor energy appear without the other.
IMO it is better to write that each object has both mass and energy.

### 8. See also

Following is a list with "Comments in Wikipedia" about related subjects

### Reflection 1 - Matter versus Mass

In some sense the word "matter" is a much better word to describe all what is surrounding us. The word matter or material takes into account, condidering our earth, from which everything is made of and has a certain structure. These are the molecules, atoms, protons, neutrons, electrons, photons and even the gravitons.
The concept that links all of this is energy i.e. the law that the total energy in a closed evironment is constant. In order to define energy the rather abstract mathematical concept mass is introduced.

### Reflection 2 - Rest mass versus Relativistic mass

In the context of Special Relativity we speak about Rest mass versus Relativistic mass or m0 versus m. The equivalence principle applies to free falling objects. What is the importance of this for the movement of the planets around the Sun. IMO the concepts m0 and m can not be used to describe these movements.

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Created: 1 November 2016
Updated: 2 February 2017
Updated: 22 October 2017

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