This document contains comments about the document "Mass in special relativity" in Wikipedia
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• Immediate followed by some comments
In the last paragraph I explain my own opinion.

Introduction

The article starts with the following sentence.
The word "mass" is given two meanings in special relativity: one ("rest mass" or "invariant mass") is an invariant quantity which is the same for all observers in all reference frames; the other ("relativistic mass") is dependent on the velocity of the observer
The rest mass and invariant mass are called m0. The relativistic mass m or mrel. Throughout this article this difference is not always used.
My understanding is that in each reference frame the rest mass of the same object is the same.
The most difficult part is the concept: "The velocity of the observer". The problem is how to measure the speed relativ to the speed of light.

1. Terminology

The term mass in special relativity usually refers to the rest mass of the object, which is the Newtonian mass as measured by an observer moving along with the object.
How does the observer do that? IMO an observer can never measure the mass of the Earth. The only thing that an observer can do is to weight an object, which value is proportional to the mass of the object.
The invariant mass is another name for the rest mass of single particles. The more general invariant mass (calculated with a more complicated formula) loosely corresponds to the "rest mass" of a "system".
Both sentences are not clear.
Under such circumstances the invariant mass is equal to the relativistic mass (discussed below), which is the total energy of the system divided by c2 (the speed of light squared).
How is the total energy measured?

3. The relativistic energy-momentum equation

The relativistic expressions for E and p obey the relativistic energy–momentum relation:
E^2 - (p*c)^2 = (m*c^2)^2
where the m is the rest mass, or the invariant mass for systems, and E is the total energy.
As such this equation should be written as:
E^2 - (p*c)^2 = (m0*c^2)^2
• Mass-energy_equivalence paragraph 3.
The equation is rather straight forward. The issue is how do you calculate the different quantities in reality.

5. Conservation versus invariance of mass in special relativity

Conservation laws require a single observer and a single inertial frame.
Conservation laws require a single frame or coordination system. That means all parameters used should be either measured or calculated using the same method (or equation).
Such a coordination system requires an origin from which all the distances are measured.
The relativistic mass corresponds to the energy, so conservation of energy automatically means that relativistic mass is conserved for any given observer and inertial frame.
When something is conserved it should be within one inertial frame (see above). As such the sentence is not clear.

5.1 Closed (meaning totally isolated) systems

All conservation laws in special relativity (for energy, mass, and momentum) require isolated systems, meaning systems that are totally isolated, with no mass-energy allowed in or out, over time.
I think this definition is always true.
Both the words "totally" and "meaning" can be removed, because closed and isolated are synonyms in this context.
If a system is isolated, then both total energy and total momentum in the system are conserved over time for any observer in any single inertial frame, though their absolute values will vary, according to different observers in different inertial frames.
Such a sentence requires clarification.

6.2 Relativistic mass

In special relativity, an object that has nonzero rest mass cannot travel at the speed of light. As the object approaches the speed of light, the object's energy and momentum increase without bound.
Difficult sentence to grasp.

Reflection 1

The problem is that a discussion about "Mass in special relativity" does not make sense, because Special Relativity only involves objects at rest or objects in lineair motion. There are no accelerations within SR. That is a problem because when you want to study mass, moving objects should be used. The "falling apple from a tree" is an example in order to study mass.

As such any discussion about "Conservation of energy" within SR does not make much sense, because each example studied always includes many objects which are revolving around each other. The simplest example is a binary system.
In such a system you can call in principle the center of gravity at rest, but not either of the two objects involved.

Reflection 2

Special relativity, related to mass, uses two concept: m0 and m. m0 is the rest mass with v = 0 and m (also written as mrel) is the relativistic mass with v>0.
m = gamma * m0 = m0 /sqr(1 - v^2/c^2)
Special relativity also uses 4 more concepts: E0 and E and p0 and p.
E0 = m0 * c^2. E = m *c^2. p0 = m0*v and p = m*v
The

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Created: 1 November 2016

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