I.      Position of Energy Conservation in PicoPhysics

Conservation of Energy is fundamental law in Contemporary Physics. It is the law that governs universal dynamics. In PicoPhysics it is a level-3 derived law. It governs dynamics of matter (elementary particles) formed as a result of stabilized confinement of Knergy in Space as per Unary law. Conservation of momentum itself is also a level-3 derived law similar to law on Energy conservation. Excluding Energy from the foundations of PicoPhysics was a major decision taken very early in development of PicoPhysics thought process.

II.      Contemporary Physics

Conceptual Energy

 Wikipedia describes Energy as an indirectly observed quantity. In 1807, Thomas Young was possibly the first to use the term “energy”. It is understood as the ability a physical system has to do work on other physical system. Since work is defined as a force acting through a distance (a length of space), energy is always equivalent to the ability to exert pulls or pushes against the basic forces of nature, along a path of a certain length. The total energy contained in an object is identified with its mass. Energy (like mass), cannot be created or destroyed. When matter (ordinary material particles) is changed into energy (such as energy of motion, or into radiation), the mass of the system does not change through the transformation process. A system can transfer energy to another system by simply transferring matter to it (since matter is equivalent to energy, in accordance with its mass). However, when energy is transferred by means other than matter-transfer, the transfer produces changes in the second system, as a result of work done on it. This work manifests itself as the effect of force(s) applied through distances within the target system. In 1853, William Rankine coined the term “potential energy”. It was argued for some years whether energy was a substance (the caloric) or merely a physical quantity, such as momentum.

Contemporary Law on conservation of Energy

Since 1918 it has been known that the law of conservation of energy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time. That is, energy is conserved because the laws of physics do not distinguish between different instants of time.

During a 1961 lecture  Richard Feynman, a celebrated physics teacher described energy using following text;

There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law—it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.

III.      Re-Think on Energy (PicoPhysics Topic)

 Intuition & Conservation

Conservation is embedded into human intuition. Intuitively conservation is applied to matter. It is experienced in every observation we made. It makes us search for missing items (Objects composed of Matter) when not found in assigned location. It is also the basis of theft investigation (Who moved the item from a location).  As an Intuition Embedded Concept it includes conservation across two time-separated events, as well as continuity of geometrical path of conserved object.

Intuitive Conservation has both qualitative as well as quantitative aspects.  Quantitatively it is identified with a measurable property of the object that remains invariant (unchanged) across time of observation. This property can then be used as a measure of the object. It may be quantity of matter, mass or energy or any other property signifying measure of the conserved item.

Intuitive Conservation co-exists with creation and consumption. Human are witness to many changes in nature. Some are cyclic, others are not.  Thus the concept of life cycle – creation, sustenance and disappearance is part of human intuition as well. In Human Intuition, applicability of conservation is subject to exclusion of creation and consumption.

As a result, even if location of an object remains fixed along with dimensions, it is not looked upon as conserved property of object. Since, human experience of flattening of sand dunes etc. the dimensional properties are not identified as conserved.

 Conservation & Neutralization in Physics

Intuitive concept of conservation is included as it is in Physics. The creation and consumption aspects are included as neutralization concept in conservation.  Inclusion of neutralization introduces a mathematical abstraction (found in business transactions). An item is transacted as a business deal. The party (lender) that possess the same transfers the same to the transactional partner (receiver). The reverse transaction is agreed upon, but not completed. If the item is consumed, transformed, lost by the receiver, he has an obligation to return the item to lender. In a way the quantity owned by receiver is negative, and positive by lender. The object item itself may or may not exist. This abstraction of quantity from the object results in negative quantity. However, it introduces symmetry to conservation as well.  (Negative Numbers are further discussed with topic on Infinite Mathematics)

Experience of forces between charged particle, and cancellation of these forces on superposition, is coupled with transactional conservation, to arrive at a conservation concept that includes Neutralization.

 Importance of Neutralization

Energy was described in Newtonian times as capacity to do work. The energy was still considered to exist in separate inter-convertible forms – mechanical, heat & light.  Because of the convertibility, it can be measured to vary by an observer unmindful of other forms of existence.  Discovery of Gravitation was a first sign that the Energy of object changes as it is subject to gravitation forces.

To arrive at a mathematical framework to include gravitational effect, Potential Energy is hypothesized. Decrease in potential energy explains increase in kinetic energy of an object as it falls through gravitational potential (A beautiful theoretical-framework). The concept of conservation from ‘Conservation of Matter’ is extended to Energy. It now includes neutralization.

Re-thinking Energy

When Einstein’s mass-energy equation E=mc² is applied to Newton’s law of gravitation, we reach very interesting results as below;

The potential energy varies inversely with separation between objects. Further it is negative (as per Newton’s law of Gravitation). So when the objects falls though gravitational field, it gains speed and looses potential energy. The increase in speed can be reduced to nil, by taking kinetic energy away from the object. The remaining energy of the object is rest-mass energy (Einstein’s mass-energy equation E=mc² ). Thus rest-mass energy of the object decreases as it falls through gravitational potential.

Gravitational field acts as a catalyst promoting conversion of internal mass-energy to Kinetic energy of the object.

Gravitons: In contemporary physics we look for particle Graviton that will represent quanta of gravitation field as photon is quanta of electromagnetic field. When we apply Einstein’s mass-energy equation E=mc², we find the concept of graviton is not sustainable. Since gravitational field contain no energy. It is promoter of transformation of rest-mass energy into kinetic energy.

Gravitational field contain no energy.

In electromagnetic field the total energy of object changes when it acts on the object. In Gravitational Field there is no such change. Electromagnetic field contains energy but gravitational field does not.

Black-Hole event horizon : The value (Negative) can theoretically reach infinite with distance approaching zero. The mass-energy on the other hand is finite. So, as an object falls through gravitational potential a stage can be reached when rest-mass has been fully converted to kinetic energy. In this state, the speed of the object will be speed of light as per Einstein’s mass-energy equation E=mc². Further fall though gravitational field will result in negative rest-mass with further increased kinetic energy if conservation of energy is sustained.

Rest-mass of black hole is negative.

Tachyon : The hypothesis of conservation of energy now includes the concept of negative mass and matter. The negative mass particle shall be traveling with speed greater than speed of light.

Thus Tachyon may represent a hyper-active state of normal particles induced by gravitation.

If rest mass is negative, why is kinetic energy positive? This needs to be investigated and answered.  Is the mass in expression for kinetic energy not rest mass?

Negative Matter & Mass : Let us consider a case, when a particle is allowed free fall till half of it’s rest-mass is converted into kinetic energy. By a separate interaction, this kinetic energy is taken away. Now particle has half the energy, but is present at a location near the surface of event horizon. It will cross event-horizon as rate of conversion (with distance) of mass-energy into kinetic energy is reduced by half. It will still have positive rest-mass at event horizon. Thus inside event horizon, we have particles with +ive as well as –ive rest mass.

Negative mass and negative matter is hypothesized along with conceptualization of energy as conserved.

Heisenberg uncertainty principle:  The principle defines fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known.

Conservation implies un-ambiguous (accurate) result on measurements of a conserved object parameter with respect to change in other parameters. So it is just possible first to measure energy of the object, without reference to its position or time. Now during actual observation, just locate the object, without reference to energy. Now as the object is precisely located, at the time of observation event, the precision can theoretically be better than given by Uncertainty principle. Conservation per say, relates the measurement at two time separated events. (The determination of energy and time is forced independent. Advantage of conservation of energy is taken to define energy when an accurate time measurement is executed.). In a way, with uncertainty principle this determination of energy is speculative. The two can co-exist only when the uncertainty is built into conservation.

Energy conservation has to keep room for uncertainty principle. Conservation of Energy is not absolute.

IV.      Knergy Vs Energy

We get interesting results when available knowledge about nature is applied to conservation of energy.

• Gravitational field acts as a catalyst promoting conversion of internal mass-energy to Kinetic energy of the object.
• Gravitational field contain no energy.
• Rest-mass of black hole is negative.
• Negative mass and negative matter is hypothesized along with conceptualization of energy as conserved.
• Conservation of Energy is not absolute.
• Energy conservation has to keep room for uncertainty principle.

The PicoPhysics interpretation of conservation of energy is derived property of matter formed out of Knergy. PicoPhysics align Energy, Inertia Mass & Gravitational Mass with corollary of Unary Law – Knergy consumes Space.

Energy is a measure of rate of space consumption by Knergy contained in the object. The rate of consumption is proportional to square of Knergy density.

The discussion continues under title ‘Konservation’.  Konservation is based on logic of Infinte Maths. Title ‘Konservation’ will be added after ‘Infinite Maths’.