Einstein’s Matter Energy Equivalence I

"The mathematical investigation of calculus ideas associated with position, velocity, and acceleration inspired me to look at the F=ma Idea from another perspective. Essentially F (Force) can be thought of as a mass transfer idea that is derived from a calculation of emerging mass or a momentum differential. Instead of thinking about mass as a constant, we can think of the emerging mass associated with a point as the point rest mass multiplied by a mass multiplier. This mass multiplier can be expressed as position differential contributing to a calculation of momentum; or, the mass multiplier can be expressed as a momentum differential contributing to a calculation of Force.

It is more intuitive to think of the mass multiplier as a position differential leading to a momentum calculation. This position differential can be mathematically expressed as “the point changing in position” with respect to "the point changing in time." Also, a moving mass can be thought of as oscillating with a velocity frequency. The rest mass (m) corresponds to an amplitude and the velocity (v) corresponds to a frequency for the momentum calculation mv. The superposition of the rest mass along with a velocity frequency or velocity oscillation contributes to Emerging Mass or The Momentum Idea which observers experience as Energy.

You can essentially think of rest mass as an energy multiplier or look at the oscillation as a mass multiplier. In my opinion, it would be more intelligent to unify force and momentum as Energy Ideas and think about rest mass as an energy multiplier. Moreover, I think that the entire reality can be described as an Energy Idea. And, all of these Energy Ideas can be mathematically analyzed through a Matter Wave Concept.

Finally, the Emerging Mass Idea is simply an attempt to unify force and momentum mathematically. First, the velocity (m/sec) component of momentum can be thought of as an oscillation. And second, momentum can be thought of as Energy with a multiplier that we call the rest mass. Also, it is more intuitive to use velocity m/sec as an oscillation instead of acceleration m/sec2. This is because acceleration dictates that we use a time area in two dimensions (sec2) instead of a time line in one dimension (sec). This is because the position differential has one moving frame of reference (dt) and the changing position differential has an additional moving frame of reference (dt). Mathematically these two time dimensions must be expressed as a moving frame of reference that is a time area. This time area is expressed within the units for acceleration (m/sec2). So, we can still think of acceleration and velocity as mass multipliers.

These mass multipliers contribute to the Emerging Mass Idea which seems to come about through the observer’s perception of movement. According to a strict interpretation of F=ma, movement can be thought of as a measurement by an observer of a point changing velocity with respect to a point changing time. Or, movement can be theoretically measured as the velocity differential of a point in space; or, the acceleration of a point in space.

I think it's convenient to look at movement in terms of acceleration because classical mechanics and logical reasoning will suggest that everything is moving; and, logic also suggests that there is no REAL zero velocity for any particular object. There is also no REAL constant velocity. Everything is constantly accelerating and decelerating. But we can simplify very small changes in acceleration to constant velocities. This assumption simplifies relativity ideas.





We must always understand motion with respect to an observer. This motion is understood as relative motion which is a critical component in Einstein's Theory of Relativity.

An object that is NOT accelerating relative to an observer can be thought of as moving at a CONSTANT theoretical velocity. An object that IS accelerating relative to an observer is moving with a CHANGING theoretical velocity. If a position is not changing, then we can express the position as a constant; but, to keep our calculus ideas, we still use a moving frame of reference. In this case, quantities like mass and position become constant or scalar expressions; but, they are still referenced with respect to a changing time variable. If mass is not changing then mass becomes a rest mass and if position is not changing then position becomes a rest position. However, they are both observed relative to a moving reference frame which exists as passing time.

The problem is that there is never really a "zero position" for a point mass ... because everything is infintessimally moving with an infintessimal frequency or oscillation with respect to passing time. So, rest mass and rest position can be more accurately described as very small changes in mass or position which are negligible. These small changes can be thought of as spring oscillations that fall within a negligible range. Moreover, these oscillations can get smaller and smaller and become small infinities while approaching zero. The observer, along with an associated moving frame of reference and a changing position, create a system which exists as 1) the perception of change which contributes to 2) the measurement of change. This is what we are expressing with calculus.

Using Calculus Ideas, an observer along with a moving frame of reference can express a changing system using mathematical expressions dx and dt. The observer measures a moving point (dx) with reference to a moving frame (dt). We can consider that this moving frame is always the earth moving around the sun which we consider to be passing time (dt). Vehicles and other moving reference frames can affect the observer’s measurement of change or perception of change. The observer “sees” the effects of other moving frames when he is measuring a moving point (dx). The observer doesn’t immediately “see” the effects of the earth moving around the sun unless he is looking at a clock. Also, the general consensus from academia is that the earth’s complete revolution around the sun is a regular occurrence that is not dependent on an observer.

This idea and similar ideas about our planet and our solar system build up an objective reality which exists as a single universe that exists “autonomously” on its own; and, can exist with or without an observer. What is really intriguing here is that objects that enter our vision window are accelerating based on our perception. In other words, was that object there when we were not looking at it? The nature of the vision window always gives the observer the perception of moving objects as they enter the vision window and as they come into focus; and, this perception of moving objects may be a direct contributor to the emerging mass idea in F=ma.

If you look up Einstein’s Equivalence Principle, you'll find that it basically asserts that the inertial mass idea that has to do with moving objects is equivalent to the gravitational mass idea that has to do with falling objects. If you do some digging, you also might find that Einstein said that the acceleration due to gravity is the result of the earth moving towards us. While I agree with Einstein's calculation using F=ma, I don't feel comfortable with the idea of the earth moving towards us during free fall. Looking a little bit closer, ideas related to force and momentum are very ambiguous and might need to be re-addressed. Although it is quite controversial, I would probably feel more comfortable with the idea that nothing is "really moving" ... everything in the universe is essentially oscillating. Hopefully, I will have a chance to get back to this a little bit later, but this relates to some ideas in one of my earlier articles entitled "Do We Need Physical Space?" In particular it raises the questions. In particular, do we need physical space to create a reality?"