Introduction The law of the conservation of energy is the main law in physics. Its existence originates upon the phenomenological view of reality: the local addition and subtracting of energy in relation to the alterations 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 concept of reality. Quantum field theory [1] has replaced the phenomenological view and all the phenomena are thought to emerge from the distinct primary quantum fields. Fields that are existent everywhere in the universe. Albeit not all the distinct 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 we use the phenomenological view to calculate macroscopic phenomena. It is not possible to calculate all the alterations between the distinct quantum fields within a macroscopic volume of space. Even the calculations of all the alterations during a very short time within a volume that encloses a hydrogen atom 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 the observable phenomena within the quantum fields. Because these phenomena represent only partly all the existing quanta in the universe because everywhere in space there is a transfer of quanta. Phenomena like particles 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 1m3 of the volume inside our sun and 1 m3 somewhere in a void between the galaxies. So the question is: "What about the mechanism behind the conservation of energy, caused by the structure of the quantum fields?" The Planck-Einstein relation The only phenomenon that's observable everywhere in the universe is the electromagnetic wave. Thus if we want to discover a "gleam" of the basic structure of the quantum fields within the frame of reference of modern physics we have to examine electromagnetic waves, travelling in space. Page 1 Quanta transfer in space is conserved Henk Grimm (S.E.) gemachtigde@gmail.com Physical phenomena emerge from the quantum fields everywhere in space. However, not only the phenomena emerge from the quantum fields, the law of the conservation of energy must have its origin from the same spatial structure. This paper describes the relations between the main law of physics and the mathematical structure of the "aggregated" quantum fields. The properties of electromagnetic waves – as a stream of single quanta – are described by the Planck-Einstein relation: E = h v = h c λ [h = Planck's constant; v = frequency; l = 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. Unfortunately, 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 all 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 not customary 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 "empiric" argument to reject an invariant basic wave length. Of course, the mutual interactions between local macroscopic phenomena show all the characteristics of curved space-time as described by Einstein's theory of general relativity. That's why in the past the physics text books have taught us that Einstein's space-time is the underlying fabric of the universe, perfect in line with the observations. This in contrast to the axioms of Isaac Newton about absolute space and absolute time. But that's just a believe. There is any proof to support this opinion. Because without phenomena there is still the structure of the creating 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: l = n l [n = integer (variable); l = standard length] So l is a constant and named "standard length" in this paper (the underline is used to show the difference). Now we can rewrite the equation of the PlanckEinstein relation: E = h v = h c n λ The revised equation 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 unmodified equation). The spatial structure of quantum fields Suppose we increase the energy of the electromagnetic wave. The result is a decrease of the number of standard lengths between the beginning and the end of 1 electromagnetic waveform. The limit is n = 1 l, but because of the nature of electromagnetic waves 1 n must be half the size of the electromagnetic wave length. However, what is represented by the size of one standard length? When we think it over we have to conclude that the standard length is a property of the structure of the creating 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 l must be the representation of the size of a spatial unity that forms the basic (aggregated) structure of the quantum fields, like the bubbles in a foam. See Page 2 the schematic figure below with the help of easy to draw cubes. This schematic image cannot be a surprise, because quantum fields must have a spatial structure. The only difficulty is the relation between "the foam" of the universe and Einstein's curved space-time. However, the cause 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 of the phenomena in space and time. Because electromagnetic waves are everywhere in our universe we have to accept that the bubbles tessellate space, like the image above. So every volume in space consist of one or a multiple of the spatial unity that forms the basic structure of the quantum fields. Mathematically spoken, this unity is the element of a mathemat ical set. However, because this mathematical set envelopes everything in the universe, it must be the all-inclusive set that represents the universe. Now it is only a small step to conclude that all the spatial unities together form the main structure of the quantum fields in our universe. In other words: the unities form a mathematical set with topological properties. However, one or more properties of the elements have to be variant, otherwise our universe exists without any alteration. So every element is a topological object that represents a homeomorphism. The element of the mathematical set gets the character "e". So every volume (V) in the universe represents: V = n e [n = integer (variable); e = element] Importing the standard length in the Planck-Einstein relation has consequences. The alterations within the vector part of the basic quantum fields – between the adjacent bubbles of the foam – are restricted to the exchange of Planck's constant (the scalar part of the structure of the elements is not involved in this rough concept of reality). Quantum time The transfer of Planck's constant between adjacent elements of the all-inclusive set – actually the transfer of topological deformation within the mathematical set – has a certain duration: length divided by velocity. Length (l) and velocity (c) are constants, thus time must be a constant too. So T (duration) becomes a multiple of t (underlined to indicate the status as a constant): T = n t [T = time (period); n = integer (variable); t = constant of time] In fact, the transfer of quanta within the basic 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 couldn't exist a quantum of energy like Planck's constant and there couldn't exist a constant speed of light. Conclusion: the velocity of the transfer of a single quantum is independent from the velocity – and the direction – of a transferred concentraPage 3 tion of quanta from which the single quantum originate. The "force" that is responsible for the exchange of quanta between the elements that form the basic structure of the quantum fields is a property of every spatial unity (element). However, this property of alteration must be a constant too. Because we cannot deform topological objects that tessellate space without an identical property of all the elements that is responsible for the alterations between the elements. Moreover, we have to accept that there is no topological deformation without a fluent transfer of an invariant property of every single element. Thus "quanta" are emerging from the synchronized mutual alterations of the elements of the all-inclusive set. If the structure of the quantum fields is composed by elements that only can transfer one quantum (h) with the same velocity (c) during the same time (t) we have to conclude that all the quanta transfer in the universe is conserved. That means that identical volumes – irrespective of their position in the universe – have the same amount of single quanta transfer during iden-1] tical periods of time. Thus the transfer of quanta in space is a constant and is correlated too (the transformations are non-local because the elements tessellate space. Finally, it shows that the conservation of energy cannot be a law of nature. It emerges from the properties of the elements of the all-inclusive set: the basic structure of the quantum fields. Relative time "How can relative time emerge from the constant of time?" When we accelerate a space rocket – or a particle – we change the ratio of the internal alterations, because of the conservation of quanta transfer in the universe. Thus when a phenomenon moves nearly with the speed of light most of the quanta transfer by the involved elements is "consumed" to enable this high velocity. Only a small part of the involved quanta transfer is available for the internal alterations within the boundary of the particle. This is the cause behind the twin paradox. Page 4 References This paper don't have references because the described concept is the result of theoretical research to describe reality with the help of the foundations of mathematics (a bottom-up approach). The website https://www.ephys.blogspot. nl is addressed to clarify the origin of the concept. However, to make the contents of this paper understandable for everyone, most concepts have a link to the description – and the underlying sources – in Wikipedia.