many Janus faces of energy

[AntonioLao]

many Janus faces of energy

There are basically two types of mass. These are inertial mass and gravitational mass. They are equivalent without any plausible physical reason. Neither Mach nor Einstein was able to provide a satisfactory explanation. Furthermore, in Einstein’s theories of relativity both special and general there are two more distinctions for mass. These are rest mass and relativistic mass.

On the other hand, there are more ways than twice to describe the different manifestations of energy. To begin, in a Newtonian deterministic mechanical reversible system, there are potential energy and kinetic energy. Kinetic is depended on mass and velocity or half the scalar inner dot product of linear momentum and velocity. Potential energy is depended on the gradient of a force or scalar inner dot product of the force and a directed line segment. Both are scalars as what all descriptions of energy should be by definition. Prior to 1900, the kinetic theory of heat described energy as a form of heat basing on stochastic irreversible thermal system of Boltzmann’s statistical theorem described as the scalar product of Boltzmann’s constant and the absolute scale of temperature E=kT hence deriving the ideal gas law PV=nRT, where P is the pressure, V is the volume, n is the number of moles per Avogadro’s number for a system of kinetic gas molecules. R is the universal gas constant and T is the absolute scale of temperature, k is considered as Boltzmann’s constant. After 1900, Planck and Einstein gave two more energy descriptions: E=ħw and E=mc². These are respectively extreme points of energy near zero and approaching infinity where m becomes the total mass of the Universe and ħ is Planck’s constant divided by 2p, w is the angular frequency of energy wave and c is the speed of light in vacuum.

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[Guille]

Kinetic is depended on mass and velocity or half the scalar inner dot product of linear momentum and velocity. Potential energy is depended on the gradient of a force or scalar inner dot product of the force and a directed line segment.

What if the mass on which kinetic energy depends is relativistic mass, in that case velocity had to be the speed of light and KE=E such that there is no potential energy. This means that if the relativistic mass is equal to the mass used in kinetic energy then the body has no potential energy. This means that there is no force and no directed line segment. What does directed line segment mean?

[AntonioLao]

What does directed line segment mean?

The nomenclature in analytical mechanics is that of position vector. A position vector can be decomposed into its components for a specific coordinate system. The number of components is the same as the number of coordinates in the frame of reference. Nevertheless, the position vector is an invariance. That is to say it is independent of any coordinate system whether 2D, 3D, 4D or 11D.

[Guille]

The nomenclature in analytical mechanics is that of position vector. A position vector can be decomposed into its components for a specific coordinate system. The number of components is the same as the number of coordinates in the frame of reference. Nevertheless, the position vector is an invariance. That is to say it is independent of any coordinate system whether 2D, 3D, 4D or 11D.

1. But the coordinates don't determine the composition completely, do they?

2. What would it mean to a body to have no directed line segment?

Thanks for the explanation.

[mkirkpatrick]

many Janus faces of energy

There are basically two types of mass. These are inertial mass and gravitational mass. They are equivalent without any plausible physical reason. Neither Mach nor Einstein was able to provide a satisfactory explanation. Furthermore, in Einstein’s theories of relativity both special and general there are two more distinctions for mass. These are rest mass and relativistic mass.

On the other hand, there are more ways than twice to describe the different manifestations of energy. To begin, in a Newtonian deterministic mechanical reversible system, there are potential energy and kinetic energy. Kinetic is depended on mass and velocity or half the scalar inner dot product of linear momentum and velocity. Potential energy is depended on the gradient of a force or scalar inner dot product of the force and a directed line segment. Both are scalars as what all descriptions of energy should be by definition. Prior to 1900, the kinetic theory of heat described energy as a form of heat basing on stochastic irreversible thermal system of Boltzmann’s statistical theorem described as the scalar product of Boltzmann’s constant and the absolute scale of temperature E=kT hence deriving the ideal gas law PV=nRT, where P is the pressure, V is the volume, n is the number of moles per Avogadro’s number for a system of kinetic gas molecules. R is the universal gas constant and T is the absolute scale of temperature, k is considered as Boltzmann’s constant. After 1900, Planck and Einstein gave two more energy descriptions: E=ħw and E=mc². These are respectively extreme points of energy near zero and approaching infinity where m becomes the total mass of the Universe and ħ is Planck’s constant divided by 2p, w is the angular frequency of energy wave and c is the speed of light in vacuum.

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Antonio,Janus,was the guardian of doors and gates,maybe he is
guarding the gateway to fusion,shall we knock on that door and demand
entrance!
kindest regards michael.

[AntonioLao]

But the coordinates don't determine the composition completely

This is what made Einstein losing a lot of sleep and causing him a nervous breakdown when he was working on the general theory of relativity but his final answer was the principle of general covariance and the principle of equivalence.

What would it mean to a body to have no directed line segment?

The body would become a scalar boson.

Janus,was the guardian of doors and gates,maybe he is
guarding the gateway to fusion,shall we knock on that door and demand
entrance!

Could we force our way in? This has been done many time in the past without success. Instead of knocking, what I have in mind is to serenade Janus to open the door. But if Janus is a two-face, two-timer man, we need a beautiful four-face four-timer woman for the task.

[austintorn@aol.com]

January is two faced, looking forward and backward; the lovely monthly ladies are named April, May, and June, even July (Julie).