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This type of mechanism was briefly alluded to by Maxwell in his Physical Lines of Force.

Here e is roughly the total kinetic energy E_{k} as per classical mechanics, which is E_{k} = E_{t} + E_{r} where E_{t} is the translational kinetic energy and E_{r} is the rotational kinetic which also includes rotational inertia [aka moment of inertia].

Looking at the full equation E = mc^{2} we can see that c^{2} is a constant [the speed of light] and m is the mass of an object. So the equation roughly translates to E = m. That is, energy is equal to mass. If you increase the energy of an object you also correspondingly increase its weight and therefore its mass and therefore its gravity without adding any new atoms into the mass, m.

For example, this equation [E = mc^{2} says: a sphere of mass m, spinning at a certain rpm [revolutions per minute] acquires rotational inertia [E_{r}] based on the spinning rate and therefore in Relativity this new rotational inertia [or rotational energy] of the spinning mass is directly interpreted as an increase in its weight. That is, if the mass weighed X units before the spinning, it now weighs more than X units while spinning, even though no new atoms have been added to this sphere of mass, m. This is the essence of E = mc^{2}.

But this is obviously not true in classical mechanics since energy and mass are clearly defined terms and there is absolutely no room for mixing up or for the interchangeability of these two definitions. In classical mechanics kinetic energy is kinetic energy. Mass is mass [that is a collection of particles or number of atoms].

PmbPhy, your detailed reply prompted me to let you know that I am an amateur science enthusiast. And I do not think that my work is error free, [which is one of the reasons I am on Internet forums]. But when I am shown wrong, I do modify my work suitably. So many thanks indeed for the detailed reply.

And you are right that Faraday developed the concepts of Field lines, and not Maxwell. But the helical mechanism that I have used in my work to explain a Field Line, and its action, was first alluded to by Maxwell.

I always thought of Relativity and QM as non-classical.

For me Relativistic physics changed so many aspects of Newtonian definitions that it seemed non-Newtonian or Non-classical to me. But I will reword my work. It was not my intention to change established nomenclature.

Earlier we agreed that the mass of an object, in Relativity, [via e=m], can increase without new atoms being added to an object. To me this is a big departure from Newtonian physics.

Also, if the mass of an object increases, the object's gravity also increases, correspondingly.

Is there unambiguous proof for this relativity phenomenon?

I am looking for proof in the form of, a test mass, whose strength of gravity [or weight] increases without new atoms [or matter] being added into the object. The derivation of Einstein's field equations might help you. They're on my website at:http://home.comcast.net/~peter.m.brown/gr/einsteins_field_equations.htm

Pmbphy, I am aware of the 1905 paper and its title, "Does inertia of an object depend on its energy", where Einstein first derived his E = mc^{2}. I do mention this in my work. See Section 1.b.

Without relativity, the mass [or number of atoms] of an object remains unchanged no matter how fast it goes.

Abstract - In 1952, Herbert Ives claimed that Einstein's first development of E=mc^{2} was circular, and that he had not been the first to develop that equation. That allegation has been repeated in several more recent works. Earlier, Planck asserted that one of the postulates that Einstein had used in that development was not exact. Those claims and subsequent papers concerning them are examined herein. The surprisingly long history of the mass-energy relation is summarized. In the context of this topic, it is argued that circularity is seldom a legitimate critique of scientific proposals. A simple refutation of Planck's claim is also included.

Thanks for the link; but I was looking for proof in the form of a celestial experiment/observation.

Abstract - If a heavy object with rest mass M moves past you with a velocity comparable to the speed of light, you will be attracted gravitationally towards its path as though it had an increased mass. If the relativistic increase in active gravitational mass is measured by the transverse (and longitudinal) velocities which such a moving mass induces in test particles initially at rest near its path, then we find, with this definition, that M_{rel} = γ(1+β^{2})M. Therefore, in the ultrarelativistic limit, the active gravitational mass of a moving body, measured in this way, is not γM but is approximately 2γM.

I am not willing to buy the argument that the mass [or number of atoms or weight] of an object can increase without the addition of new matter [or atoms], unless an experiment proves this beyond a reasonable doubt.

Until then, E=mc^{2} to me, is simply another one of Einstein's fantastic assertions.

But I would love to see Planck's proof of how an atom [for example] can weigh heavier without the addition of new nucleons.

Please email me the paper you referenced.

I asked for [experimental] proof because if there were such proof, I would have needed to modify my work, because in my work the definition of mass, is essentially the number of atoms. Mass [weight/gravity] of an object can change only when new matter is added to this object. My understanding of mass, has experimental proof.

It just occurred to me how to measure the weight of a moving particle, such as an ion. What you do is create a uniform electric field in a direction opposite to that of the uniform gravitational field in the lab. The electric field will be pointing in the upwards direction since the gravitational field is in the downwards direction.Note: The size of earth based laboratories are so small that the gravitational field inside the lab can be considered to be quite uniform and all the field lines pointing upwards and are all parallel in the lab.Place a positive amount of charge q on the particle (i.e. if it's an atom then remove a few electrons). Then let the particle move in a direction parallel to the ground and thus perpendicular to the direction of the field. The electric field will exert a force on the particle in the direction opposite to the gravitational field. Adjust the magnitude of the electric field until the moving particle does not move up or down but only in the direction parallel to the ground. Then you'll find thatqE = gamma*m*g which means a moving particle weighs more than one at rest.

That is a very interesting idea.

Thanks, Jeff. I appreciate the feedback. We're discussing this on my private forum. I look forward to when you start posting there. We need the support to get the forum going fluently.

PmbPhy, when a particle travels in a circular path, it experiences centrifugal forces, [or g-forces] that causes the particle to become heavier than it really is. But this should not be interpreted as an increase in mass, because the number of nucleons in the particle still remain the same.

Here's a Wikipedia explanation about the Operational and Gravitational definition of Weight. It appears that you might be using the Operational definition of Weight instead of the Gravitational one.

I am not sure I understand by what you mean here.

In my work, I don't disagree that the vibrations or cycles in an atomic clock can slow down when the strength of gravity is increased in the vicinity of the clock. But my work does not consider this as proof of "Time" slowing down; ...

What's the forum, called?