The law of the conservation of energy is the main law of physics. Its existence originates upon the phenomenological view of reality: the addition or subtracting of energy in relation to the alteration of observable phenomena. This point of view presupposes a fundamental difference between the phenomena and the surroundings of the phenomena in the universe.

Modern physics has abandoned this frame of reality. Quantum field theory has replaced the phenomenological view and all the phenomena are thought to emerge from the distinct quantum fields that are existent everywhere in the universe. Albeit not all the phenomena have a consistent theoretical description in quantum field theory. For example gravity.

Quantum reality is far more complicated than reality by the phenomenological view, because the latter is a simplification of quantum reality. Therefore, it is natural that physicists use the phenomenological view to calculate phenomena. It is not possible to calculate all the alterations between the distinct quantum fields within a macroscopic volume of space. Even the calculation of all the alterations within the volume of a hydrogen atom during a very short time is impossible without implementing empiric data.

Notwithstanding the fact that the law of the conservation of energy originates from the phenomenological point of view, the conservation of energy must be consistent in quantum field theory too.

However, the concept of quantum field theory is not restricted to phenomena within the quantum fields. Phenomena represent all the existing quanta in space only partly because everywhere in the universe there is transfer of quanta. Phenomena are just concentrations of quanta that have only partly independent properties during a limited period of time.

We cannot postulate the conservation of energy between volumes of space – in fact volumes of enclosed quantum fields – with the same size and shape. It is clear that there is an energy difference between 1m

^{3}of a volume inside a star like our sun and 1 m

^{3}somewhere in a void between the galaxies. So the question is: “What about the mechanism behind the conservation of energy caused by the distinct quantum fields?”

The only phenomenon that’s observable everywhere in the universe is the electromagnetic wave (e.g. visible light). Therefore, if we want to discover a “gleam” of the underlying structure of the quantum fields “within modern physics” we have to examine electromagnetic waves, travelling in space.

The properties of electromagnetic waves – as a stream of single quanta – are described by the Planck-Einstein relation:

[

*h*= Planck's constant; v = frequency; λ = wave length; c = speed of light]The equation is really remarkable because nearly every quantity is a constant. The only exception is the wave length (frequency is a quantity determined by the constant speed of light, divided by the wave length).

Nevertheless, an equation with all constants and only 1 exception – a property that is a variable – is logically inconceivable. Why should the universe make a difference between the nature of properties that are 100% related to each other? All are constants and one is a variable? They emerge from the interactions between the basic structure of the distinct quantum fields, so why are some properties constants and other variables?

Why isn't the wave length a constant? Probably because it was unaccustomed to imagine that the curvature of space – Einstein's theory of general relativity – can have a constant that determines length. However, the wavelength of electromagnetic waves is enormous in relation to the smallest elementary particles so there is no theoretical argument to reject an invariant basic wave length (there are no hidden properties within the Planck-Einstein relation).

Of course, the mutual interactions between local macroscopic phenomena show all the characteristics of curved spacetime as described by Einstein's theory of relativity. That's why the physics text books have taught us that Einstein's spacetime is the underlying fabric of the universe, far more accurate than the axioms of Isaac Newton. But that's just a believe. There is any proof to support this opinion. Because without phenomena there is still the fabric of the underlying quantum fields. And what's beyond.

The Planck-Einstein relation shows the determination of the energy by the wave length. Therefore, we can express the size of the wave length with the help of a new constant:

__λ__

*is a constant – the underline is used to show the difference – and named “standard length” in this post. Now we can rewrite the equation of the Planck-Einstein relation:*

The revised equation is well composed and shows that energy is inversely proportional to the number of standard lengths by which a single quantum is transferred (the outcome is equal to the "old" equation).

Suppose we increase the energy of the electromagnetic wave. The result is the decrease of the number of standard lengths between the beginning and the end of 1 electromagnetic waveform. The limit is

*n*= 1

__λ__, but because of the nature of electromagnetic waves 1

*n*is half the electromagnetic wave length.

However, what is represented by the size of 1 standard length? When we think it over we have to conclude that the standard length is a property of the structure of the underlying quantum fields. Moreover, the equation makes no difference in relation to the direction of the transfer of quanta in space. In other words, the standard length

__λ__must be the representation of the size of a spatial unity that forms the structure of the quantum fields (like bubbles in a foam).

That is no surprise, because quantum fields must have a spatial structure. The only difficulty for physicists is the relation between “the foam” and Einstein’s spacetime. However, the causation of the difference is the magnitude of the observed phenomena. General relativity describes the mutual relations between macroscopic phenomena and quantum field theory describes the structure that is responsible for the emerging phenomena in space and time.

Because electromagnetic waves are everywhere in our universe we have to accept that the “bubbles” tessellate space. Every volume in space is one or a multiple of the spacial unity that forms the structure of the quantum fields. Mathematically spoken, this unity is the element of a mathematical set.

Now it is only a small step to conclude that all the spatial unities together form the structure of the quantum fields in our universe. In other words: they form a mathematical set with topological properties. One or more properties of the elements must be invariant, so every element is a topological object that represents a homeomorphism.

The element of the mathematical gets the character "

*e*". So every volume is:

[

*V*= volume;

*n*= integer (variable);

*e*= element]

Anyway, importing the standard length in the Planck-Einstein relation has consequences. The alterations within the vector part of the quantum fields – between adjacent “bubbles” of the foam – are restricted to the exchange of Planck’s constant (rest mass is not a subject of the explanation so the scalar part of the quantum fields is not involved).

However, the exchange of Planck’s constant between adjacent elements has a certain duration: length divided by velocity. Length (

__λ__) and velocity (

*c*) are constants, thus time must be a constant too. So T (duration) becomes a multiply of

__(underlined to indicate the status as a constant):__

*t*In fact, the exchange of quanta within the structure of the quantum fields is impossible without a constant velocity. Because the consequence of a variable velocity is a variable exchange of energy, so there cannot exist a quantum of energy (Planck’s constant).

The “force” that is responsible for the exchange of quanta between the elements that form the structure of the quantum fields is a property of every unity (element). However, this property of alteration must be a constant too, otherwise our universe cannot be homogeneous and isotropic (so there is no speed of light, Planck’s constant, etc.,etc.).

The consequence is an extension of the law of the conservation of energy: the quanta transfer between the elements that form the structure of the quantum fields is conserved.

That means that identical volumes – irrespective of their position in the universe – have the same amount of single quanta transfer during identical periods of time. Thus the transfer of quanta in space is a constant and is correlated (the transformations are non-local).

Next chapter: "Planck mass"