Back to the roots: the concepts of force and energy

3.2.1 Displacement work W _x (transfer of E _pot)

The force ξ _i of displacement work W _x is described by two different terms:

Two variants for one and the same state variable F are an expression of uncertainty. Rule 1 of the cause-effect principle, according to which each Y _i is related to only one ξ _i , is violated.

Newton’s F = Ṗ is applied when it fits, mostly in fluid dynamics [16, 17]. The proponents of F = Ṗ want to explain force, i.e. not only define it as an irreducible or purely relational concept without its own ontological status [18], [19], [20]. F = Ṗ represents an intensive state variable ξ _i whose local gradient dṖ/dx can cause a displacement dx in time. Rule 2 is fulfilled.

The opponents of F = Ṗ defend the achievements of modern theoretical physics [15]. Kirchhoff’s F = ma is mostly used and already taught in school. The analogy to F _g ≈ mg is obvious, where it is known that Newton’s law of gravity is sufficient for practical purposes, but represents an approximation. For strong fields, the more accurate description of general relativity is used today.

The transferred energy E _pot manifests itself in the new position, if, for instance, a spring is tensioned or a body is lifted. It holds E _pot(x) or E _pot(h) of a body, i.e. E _pot belongs to the body. The amount of energy transferred depends on extensive state variables. Rule 3 is fulfilled.

3.2.2 Acceleration work W _v (transfer of E _kin)

The force ξ _i of acceleration work W _v is described by three different terms (cf. Equations (7) and (8) and variants 4–6 in Table 2):

Variants 4 and 5

In Equation (7), Fdx is attributed to acceleration work. This violates Rule 1 of the cause-effect principle, according to which each process equation has its own force ξ _i and effect dX _i . dx is the effect of displacement work, whereas the effect of acceleration work should be dv.

Newton’s F = Ṗ and Kirchhoff’s, Mach’s and Hertz’s F = ma are functional relationships between state variables at a given time t, i.e. state equations. They correspond to Equation (1). If F = Ṗ and F = ma are interpreted as showing that F causes Ṗ [15] or a, Newton’s 2nd axiom is misinterpreted as process equation. Each dynamic process equation represents an energy transfer that takes time (Rule 1). Therefore, the identities F = Ṗ or F = ma do not represent a cause-effect relationship:

If instead the literal interpretations “F causes the change in momentum” [15] or “F causes acceleration” are translated into process equations, i.e. FdP or Fdv, contradictions occur. Neither the product of F and P, nor that of F and v has the unit of energy. Furthermore, the effect dv contradicts Rules 2 and 3 of the cause-effect principle because v is an intensive state variable ξ _i . Just as dx is not the effect of acceleration work, F cannot be the force of acceleration work. In Fdx, cause and effect of acceleration work are not specified.

If Fdx is assigned to both W _x and W _v, not even energy conservation during the free fall can be demonstrated by means of process equations. Lifting work W _h is negative because h decreases, whereas W _v is positive because v increases. With F _gdh for both process equations, the following contradiction arises:

Today, we are accustomed to consider state equations via mgh = m/2·v ², which leads to correct results. However, since the fall is a process in time, especially the process equations Y _i must be able to show energy conservation.

Variant 6

Acceleration means that v is changed during the dynamic process. Transforming Fdx with constant mass m in this sense, mvdv follows. Here, P = mv as extensive state variable X _i is interpreted as force ξ _i . This violates the Rules 2, 3, 5 of the cause-effect principle. Since X _i is a quantity measure referring to the whole system (how much?) and not to the conditions at one point, it cannot have a local gradient (Rule 5) and thus cannot act as force ξ _i (Rule 2). Equation (8) does not represent a process equation.

That P cannot be a force ξ _i will be illustrated by the following example: Let two bodies 1 and 2 with P ₁  ≠  P ₂ , m ₁ ≠ m ₂, and v ₁ = v ₂ (flying in the same direction) contact each other. The momenta differ, but no collision and no acceleration work W _v will take place because no local gradients exist. Let two bodies with P ₁  =  P ₂ , m ₁ ≠ m ₂, and v ₁ ≠ v ₂ contact each other. A local gradient dv/dx exists, and a process is initiated. Decisive is the local gradient of an intensive state variable ξ _i such as v, or F.

3.2.3 Friction work (transfer of E _kin)

In fluid mechanics, the intensive state variable Ṗ = dP/dt is called friction force F _f (cf. Equation 9). This designation takes Newton’s second axiom F = Ṗ literally, but undervalues the fact that there must be a local gradient of the force for a process to occur (Newton’s first axiom). In Equation (9), there is no local gradient dṖ/dx. In this way, the name friction force violates Rules 2 and 3. Even if this is only a problem of naming, it shows the variety of interpretations in mechanics and the lack of awareness for the cause-effect principle in process equations. In thermodynamics of irreversible transport processes, it is well known that dv/dx between adjacent layers of a streaming fluid causes a momentum flux Ṗ between the layers, which represents the effect of the process (see Section 4).

5.2.1 Equations (24)–(27)

Equations (24)–(27) are state equations as defined in Equation (1). They describe the interrelation of E _kin, E ₀ and E at a given time t. The total energy E = E ₀ + E _kin is larger than the rest energy E ₀. Using the respective mass expressions, m has to be larger than m ₀ in real terms if each kind of energy is ponderable as Einstein suggests:

Thus m = γm ₀ in Equation (27) is mathematically correct, logically and fully analog to the expressions of total energy E = γE ₀, length L = L ₀/γ, etc. However, it remains unknown which mass of a moved object is described. Unlike the Lorentz theory [41] that attempts to describe the dynamic effects of the ether on a moved object at different v by means of γ, SR describes observations from inertial frames moving in empty space. In kinematics, no kind of mechanical work is allowed. Based on a purely relational thinking of Mach and the mixing of displacement and acceleration work in Fdx, a definitive departure from dynamic processes takes place. The special feature is here the assertion of real changes in energy, i.e. processes – without a single process equation Y _i  = ΔE with Δt ≠ 0. How does the energy change without processes?

The unsolvable interpretation problem of m(v) is well-known [26]; whole books have been written about it. In a pragmatic way, m(v) is called a “limited recipe” [42]. The irresolvable conflict is: Equation (27) is indispensable to describe the real mass increase of elementary particles with v measured in accelerators. However, the mass of a body cannot depend on the coordinate system from which the body is observed. Therefore, today mostly m ₀ is called real mass, sometimes also m. But everybody, who decides for one of the variants within the framework of SR, must remain wrong. It often goes unnoticed that E = γE ₀, L = L ₀/γ, etc. within SR involve the same interpretation problem.

5.2.2 Equations (28) and (29)

Equations (28) and (29) are state equations as defined in Equation (1). Einstein keeps the force concept of mechanics in SR. This is twice impossible because:

1. F = ma or F = Ṗ represent the force ξ _i of displacement work where E _pot is transferred, not of acceleration work as there exists no process Fdv (cf. Table 2). In SR, E _pot is zero.

2. Observations are logically incompatible with dynamic forces ξ _i .

Hence Equations (28) and (29) have no place in SR. In his first paper on SR in 1905, Einstein vaguely introduces the force concept of mechanics with Equation (28) by avoiding the denotation m ₀ or m. A force is described that is “observed from a system moving at the same velocity as the electron at that moment” [36, p. 919]. Often, what matters is not what is asserted, but what is omitted or avoided. Within SR, it is impossible to commit to m ₀ or m. An acting force cannot be described in good conscience from the point of view of a differently moved inertial system. If just observations are concerned, there exist neither dynamic process nor force ξ _i . The result is a dead relational world without time and without any real change in energy. A world that is even less real than that of the ideal pendulum in mechanics, which also does not know time, but still knows energy conversion and E _pot.

Consequently, the concept of force in SR is even more internally inconsistent than that in mechanics. The vague concept of force manifests itself also in the variable dependencies E _kin(v) and E(P) in textbooks. According to Rule 5, energy has to be a function of an extensive state variable X _i . The desire exists, but E(P) is not realizable within SR.

5.2.3 Equation (30)

Is there really no process equation in SR? According to Einstein’s interpretation

Since mass and energy are equal according to the results of special relativity. [43, p. 241]The mass of a body […] changes with its energy changes. [40, p. 49],

dE = c ²dm is used today to confirm E = c ² m based on processes such as nuclear reactions.

Looking at E = c ²·m, one recognizes a proportionality of two extensive state variables X _i of an object at a given moment t, no equivalence or equality. E = c ²·m is analogous to other proportionalities such as m = M·n with the molar mass M. Both equations are state equations according to Equation (1). It also applies dm = M·dn.

However, interpreting dE = c ²·dm or dm = M·dn as process equations means a strong violation of the cause-effect principle. c ² and M are constants and can never act as a force ξ _i . Rules 2 and 4 are violated because a local gradient dξ _i /dx is impossible. In addition, Rule 1 is violated because attempts are made to reduce a complex natural process described by Equation (3), in which many X _i change simultaneously (each dX _i associated with dE), to one process equation. dE = c ²dm and dm = Mdn are misinterpreted as process equations.

The correct process equation for reactions and particle transport is µdn (cf. Table 3), where µ is variable. A resting body with the same particle number n (and thus the same mass m) may very well have more energy if it is compressed for example. dE = c ²dm disregards that the position itself is an energetic value.

Although E _pot is assumed to be zero, Einstein concluded in SR that mechanical E _pot was ponderable. One of the reasons for this might be the state thinking of mechanics and the historical interpretation of Newton’s second axiom (cf. Table 2). In 1907, Einstein writes:

the fact that an amount of energy E has a mass of E/c ² is valid […] not only for the inertial but also for the gravitational mass. [38, p. 462]

Knowing only Fdx and accustomed to use m/2·v ² = mgh, he assumed that both E _kin and E _pot are ponderable if the inertial mass m _i and the gravitational mass m _g are equal. This is a fatal fallacy because E _pot(r) only depends on the distance r between bodies, not on m, as lifting work shows. Energy conservation and m _i  = m _g can only be explained by means of process equations with ponderable E _kin and non-ponderable E _pot [30].

Due to the high suggestive power of the state equations of mechanics and E = mc ², all “elementary derivations” of E = mc ² (cf. [44, pp. 62–89]) underestimate the necessity of using process equations. Thinking purely mathematically, the logical paradoxes of SR remain ignored: Special relativity asserts processes in the absence of processes.

Please note: If Einstein writes “The mass of a body is a measure of its energy content.” [37, p. 641], he interprets E _pot as an intrinsic property because a real body always possesses E _pot, e.g. tensional energy.

6.2.1 Equation (32)

Just like F = ma, F = m·GM _E/r ², and Δφ = 4πG·μ, the equation G _µν  = κ·T _µv with the constant κ is a state equation as defined by Equation (1). It is well-known that gravity is the expression for a specific abstracted force, not for a process. If Einstein interprets his field equations as process equations and if T _µv is interpreted as causing the spacetime curvature:

The field equations of gravitation […] provide the equations of the process completely. [52, p. 810]The field equation shows how the stress-energy of matter generates an average curvature (Einstein = G) in its neighborhood. [4, p. 42][…] particles and other sources of mass-energy cause curvature in the geometry. [4, p. 47],

process and state equations are confused. Rules 1–5 of the cause-effect principle are violated. Equation (32) describes no energy transfer dE[J] = δY _i with dt ≠ 0. κT _µv represents nothing else than a substitution of Newton’s gravitational potential in Equation (33), which is claimed to be equal to the curvature G _µν of spacetime. The identity G _µν  = κT _µv , however, openly conflicts with Einstein’s idea of the spatially separated entities “gravitational field and matter” [52, p. 802]. Interaction between separated entities needs time. Thus, Equation (32) represents a physical impossibility with serious internal contradictions (cf. Table 4).

In the following, selected conceptual problems connected with G _µν  = κT _µv and the separation of “matter” and “gravitational field” are discussed:

T _µv refers to real systems such as “liquid bodies” [52, p. 771]. The tensor components include kinetic energy E _kin and radiation hv . This approach is more realistic than the point idealization of mechanics and contradicts SR because now is admitted that both E _kin and hv contribute in real terms to the gravitational mass of a system. Whereas m(v) in SR is only observed, m(v) in T _µv is real like Lorentz suggested [41].

However, the greater realism of T _µv is thwarted by the unrealistic term G _µν :

1. G _µν is intended to replace the classic gravitational field. In the desire to keep SR with E _pot = 0 as a boundary case, Einstein subsequently introduces E _pot in GR by assuming a gravitational field G _µν next to matter. Roger Penrose speaks of “disembodied gravitational energy” [54, p. 464] that is interpreted as interaction energy. This interpretation of field theories has already become commonplace today. And yet, is represents a fundamental reinterpretation. In mechanics and TD, E _pot is positional energy that belongs to the body. Energy conservation can be only demonstrated by means of embodied E _pot [30].

2. If E _pot is “disembodied” interaction energy, it is assigned to G _µν that replaces the gravitational field. With E = mc ² of SR, E _pot has to be ponderable. However, G _µν ’s motto is “I weigh all that’s here.” It cannot be both co-cause and effect, i.e. it has to be, but cannot be ponderable. This is an irresolvable contradiction. Thus, physicists tried to include E _pot in T _µv , which implies the unacknowledged concession that E _pot belongs to the body (matter). However, all attempts have failed [4], [5], [6]. Until today T _µv does not describe the energy-momentum of the gravitational field itself [5, p. 198].

   Should not the leading theory of gravity be able to describe E _pot?

   Please note minor inconsistencies: i) If the gravitational field is described by G _µν , but matter by T _µv , one separates E _pot “outside the body” from E _pot of its components, ii) If the gravitational field G _µν and the electromagnetic field in T _µv are spatially separated, their unification becomes impossible from the outset.

3. To increase the confusion, G _µν is identified with the curvature of the non-Euclidean spacetime. The flat Minkowski spacetime of SR is abandoned:

Euclidean geometry is not valid in the gravitational field even in first approximation. [52, p. 820]

With the identity G _µν  = κT _µv , the Einstein tensor G _µν is both a dynamic and a kinematic term. Therefore, the essence of spacetime has remained undecidable until today. Sometimes spacetime is interpreted as honey, other times as pure metrics. There are families of interpretive positions [55, 56], all of which must remain incorrect because already Minkowski’s assumptions on space and time are physically incorrect. The contradictio in adiecto “geometrodynamics” is an irresolvable conflict. By reducing all dynamic processes to kinematic translation, the dead world of SR is further potentiated in GR. Strictly speaking; real physical quantities are excluded if G _µν is used.

1. G _µν reduces nature to observer impressions and geometrical considerations. In this way, processes in time are denied and the 2nd law of TD is abandoned. Although GR claims to be a cosmological theory, it cannot describe evolution in one direction. There is no physical expression for the arrow of time. The becoming is openly denied:

Therefore, it seems more natural to think of the physically being as a four-dimensional being instead of, as before, as the becoming of a three-dimensional being. [39, p. 121]

The solution to the problems is: While T _µv is real, G _µν is not required. The gravitational field belongs to a body just like m, E _pot, and other abstracted state variables connected in state equations. It cannot be separated. κT _µv is an expression for the gravitational potential that lacks no mass because E _pot(r, h, V, …) is not ponderable if one admits the independent energetic relevance of spatial state variables. T _µv describes the direct dynamic force effect on matter (including radiation) quite well, as already Steven Weinberg assessed:

It simply doesn’t matter whether we ascribe these predictions to the physical effect of gravitational fields on the motion of planets and photons or to a curvature of space and time. [57, p. 147]

6.2.2 Equation (34)

Equation (34) corresponds to Paul Gerber’s formula for the perihelion shift of 1898. Gerber emphasizes the importance of lifting work, recognizes that E _pot is a function of distance (not of mass), and calculates the propagation of interaction with the finite velocity c [58].

7.2.1 Equation (35)

In terms of its formal structure, Equation (35) is a realistic differential equation, comparable, for example, to a first-order time law k c  = d c /dt for describing the time evolution of matter (such as the radioactive decay) in chemical kinetics. Solutions of such type of differential equation are exponential functions y = A exp(–kx) with the specific form of the factors A and k depending of the problem. In general, such equations are approximations.

Equation (35) was interpreted quite differently. According to the Copenhagen interpretation, wave properties and particle properties are two complementary sides of reality (principle of complementarity), which are mutually exclusive. Particles or waves only become real when they are observed (measured). This means that there exists no objective reality, which exists independently of the measuring process. This contradicts Erwin Schrödinger’s understanding of its own equation, who interpreted particles, starting from De-Broglie’s matter waves, as real waves (cf. Table 5):

It is necessary to ascribe to ψ a physical, namely an electromagnetic, meaning […] A definite ψ distribution in configuration space is interpreted as a continuous distribution of electricity (and of electric current density) in actual space. [75, p. x]

Equation (35) is time-symmetrical, i.e. it suggests that all quantum processes are reversible. It is known that kinetics cannot describe the direction of processes because it is not an exact theory, but derived from TD under idealizing assumptions. Schrödinger described Equation (35) as not complete, which not only concerns the spin of particles:

Thus there still seems to be something lacking in the wave law for the ψ function, – corresponding to the “reaction of radiation” of the classical electron theory, which may result in a dying away of the higher vibrations in favour of the lower ones […]. This necessary complement is still missing. [75, p. xi]

7.2.2 Equations (36) and (37)

The fundamentally new feature in Equation (36) is the extension of the concept of kinetic energy E _kin by connecting the so-called “rest energy” E ₀ of particles and the electromagnetic energy h ν with E _kin. Understanding his equation as “a step from classical point-mechanics towards a continuum-theory” [75, p. 45], Schrödinger describes a “free particle” as vibration:

In the first instance, this equation is stated for purely periodic vibrations sinusoidal with respect to time […] It contains a “proper value parameter” E, which corresponds to the mechanical energy in macroscopic problems, and which for a single time-sinusoidal vibration is equal to the frequency multiplied by Planck’s quantum of action h. [75, p. ix]

However, since H was not interpreted free from the accepted force and energy concepts of mechanics, SR and classical field theories, conceptual problems arise:

1. Formally, T(P) corresponds to Rule 3 of the cause-effect principle. However, T(P) is only written down, while T(v) is used. While in 1926, Schrödinger still considered a variable mass m(v) [64, p. 361], he corrected himself in 1928 in the English version of the same paper and neglected “the relativistic variation of mass”. [75, p. 1]

   By taking SR as given, one adopts its concepts such as the unsolved problem of m ₀ and m(v), the blurring of kinematics and dynamics, the special role attributed to photons, and the idea of point-like particles – a concept that contradicts Schrödinger’s idea of (spatially extended) vibrations. Equation (37) is, for example, a priori unable to describe:

   1. The real variable mass m(v) of particles as detected in particle accelerators because m(v) in SR is observer-dependent, and

   2. The conversion of parts of E ₀ into E _kin and vice versa as measured for the oscillating mass of neutrinos.

1. V(q) formally satisfies Rule 3 of the cause-effect principle. Nevertheless, the conceptual problem of V(q) in the Hamiltonian H is even more serious than that of T(P):

   In mechanics and Hamiltonian mechanics, E _pot is the positional energy of a body. The operator for E _pot in H , however, covers Coulomb energy V _C = qΦ if a charged particle in an electrostatic field is described. The field is described as an entity next to matter and Coulomb energy is called E _pot, an interpretation of quantum field theories (QFT) that has become commonplace today. And yet, the reading is conceptually questionable:

   1. It represents an essential shift in meaning compared to mechanics.

   2. If electromagnetic energy of charges, which is released due to attractive binding, is interpreted as E _pot(r), this contradicts the statement of Schrödinger that electromagnetic vibrations are described via E _kin(P). Whereas E ₀, h ν and E _kin refer to motion, E _pot(r) refers to positional energy, i.e. just the opposite. Whereas released binding energy h ν is ponderable and reduces the mass of a bound charge, E _pot is not ponderable.

   3. Coulomb’s law (just like Newtons gravitation law or Einstein’s field equations) are state equations as defined in Equation (1). They describe how the state variables of one system are interrelated at t. Since interaction between separated entities needs time, this conflicts the idea of separated entities electromagnetic field – matter.

      That not only E _pot = mϕ(r), but also V _C = qΦ(P) depends on r between two objects, points the way to a unified understanding of interaction (see Section 8).

7.2.3 Equation (38)

Equation (38) provides the lower limit for the measurement accuracy of quantum properties. Heisenberg’s reading that a quantum object is indeterminate in real terms, i.e. does not has a definite position, energy, etc. because we cannot measure them, represents a positivistic shift in meaning, which foregrounds observations, denies the reality of quantum processes, and allows to violate energy conservation as long as Equation (38) is fulfilled.

By keeping the empty space of SR, the real existing quantum fluctuations were interpreted as emerging from nothing and vanishing into nothing. This interpretation allowed to maintain the conventional separation matter – force field in line with the point mechanics and E = mc ² of SR. And yet, if in QFT three of four abstracted force fields are quantized by means of carrier particles (gauge bosons), this implies a complete departure from continuous energy and deeply contradicts Schrödinger’s wave approach.

8.2.1 Return to the ether in a new old form

The wave nature of matter, even atoms, has long been experimentally confirmed [84]. Until today, the intuitive idea has persisted that particles are not point-like and not separate from what surrounds them:

Many physicists think that particles are not things at all but excitations in a quantum field, the modern successor of classical fields such as the magnetic field. But fields, too, are paradoxical. [72, p. 42]

The field as an entity separated from matter, in which an abstracted state variable of an object is reified and materialized, is indeed questionable. It represents an artificial and paradoxical concept, because interaction between separated entities takes time, which is not described in state equations such as G _µν  = κT _µv or Δϕ = 4πGρ. The idea of a separate field is based on the misinterpretation of state equations as process equations, as already done in the case of Newton’s second axiom F = ma.

Not paradoxical, however, is the ether, which Einstein defined away in 1905 in favor of a theory of point-like particles in empty space. What is meant here is not the unacceptable idea of a medium next to matter like in the Maxwell or the Lorentz theory. Meant is the ether as a kind of primordial matter in which elementary particles represents different forms of excitation. Already Immanuel Kant understood matter as ether condensed in different degrees. In 1902, Henri Poincaré summarized related viewpoints of physicists:

One often goes even further and regards ether as the only original matter or even as the only real matter. […] According to Lord Kelvin, for example, what we call matter is only the location of points in which the ether is agitated by vortex-like movements; […]. For other more recent authors, Wiechert or Larmor, it is the place where the ether undergoes a kind of torsion of a very particular nature. [85, p. 169]

While this conception is new compared to contemporary physics, where the ether has fallen into disrepute, it actually represents a self-evident fact. If particles are created by excitations, they are not spatially separated from the ether, but represent ether energy in a special form. Their excitation energy distinguishes them from the unexcited ether medium that can be understood as an absolute reference system. This directly leads to Walther Nernst’s idea of the ether as a “supply of connected, continuous energy” [49] with natural constants:

PLANCK’s constant h, similar to the speed of light, now becomes a parameter characteristic of the light ether. [49, p. 116]

Here it can be extended that also c ² is a material constant of the ether, namely the mass-specific excitation energy. To distinguish this ether notion from the Lorentz ether, the terms quantum ether [86] or quanton ether are proposed, following a suggestion of Jean-Marc Lévy-Leblond, who called all fermions and bosons quantons [87, p. 22].

8.2.2 New particle concept

If Augustin Jean Fresnel (1788–1827) attributed light to ether vibrations, now all quantons are attributed to ether excitations. Photons no longer play a special role. By abandoning the ideas of point-like particles and empty space, each quanton occupies a spatial area:

a quanton is an object that cannot be located in a point, […]; a priori, a quanton occupies the entire space available to it – in understandably very specific, particular forms. [87, p. 22]

From Equation (41) follows that the total energy E _Q of a quanton Q is given by its ponderable excitation energy E _ex,Q and its non-ponderable energy E _pot,Q:

where E _{0, Q} = m ₀ c ² is the intrinsic excitation energy. Thus, quantons are discrete and countable, but also represent spatially continuous energy. E _pot,Q is their positional energy in the medium, no binding energy. If Schrödinger describes a “free particle” as vibration:

It contains a “proper value parameter” E, […] which for a single time-sinusoidal vibration is equal to the frequency multiplied by Planck’s quantum of action h. [75, p. ix],

this means that the Hamiltonian H only exhibits E _{ex, Q}, while non-ponderable E _pot is missing. There are further points deviating from the Copenhagen interpretation (CI):

1. All quantons are real, no matter how stable or unstable they are. As Schrödinger suggested, ψ represents an expression for a real wave in the real space.

2. Quantons are compact wave packets (“particles”) connected with long-range spatial de Broglie waves that become weaker with increasing distance. Quantons are not either “particle” or wave (like in CI), but both, and both are real matter waves.

3. A quanton propagates with v in space. Its trajectory can be followed directly by considering also its quantum potential as suggested by David Bohm and others [71, 88].

4. The uncertainty relations describe the lower limit for the measurement accuracy of quantum properties. They do not justify any statement about the non-reality of quantum phenomena or the violation of energy conservation.

5. The properties of quantons such as “rest mass”, spin, charge, or color charge, are caused by their (mostly) hidden internal dynamics that can be described by non-linear wave equations [77]. Whereas m ₀ is proportional to the quantity of E _0,Q, other properties are attributed to the spatial quality of E _0,Q. This is connected with concrete vividness.

6. As emergent entities, quantons are neither “elementary” nor “particles” nor independent nor timeless. Irreversibility is to be found also on the quantum level [28]:

Thus there still seems to be something lacking in the wave law for the ψ function, – […] a dying away of the higher vibrations in favor of the lower ones. [75, p. xi]

As already Schrödinger admitted, his equation is an approximation. QM is incomplete.

Please note: The realistic interpretation of Schrödinger, de Broglie, Bohm, and others [64, 71, 75, 77, 78, 81, 82] cannot only describe all quantum phenomena, but is far superior to CI, because it does not suffer from logical and epistemological problems (cf. Section 7) and can explain the phenomena.

8.2.3 New interaction concept – unified description of interaction

The above particle concept leads to an understanding of interaction far away from quantum field theories. QFTs and the new interaction concepts are contrasted in Figure 1.

Figure 1:

Quantum field theories (a), and the new interaction concept (b).

The main conceptual idea of QFTs is the classic separation of particles (matter) from the field that mediates interaction. This implies that E ₀ and E _kin (of objects) and E _pot (of the field) are spatially separated (cf. Figure 1a) and corresponds to Einstein’s idea of a “clean distinction” [89] between two distant objects P₁ and P₂. Since Einstein additionally assumed an empty space and E = mc ² for the total energy, the classical field could not remain continuous either. Therefore, the idea arose to quantize the four abstracted force fields by means of four different carrier particles (gauge bosons), which mediate the interaction by momentum exchange. The electromagnetic, strong, and weak forces were quantized by virtual particles or quantum fluctuations of the vacuum that emerge from nothing and vanish into nothing. The quantization of gravity, however, remained impossible. As discussed above, the spatial separation of particle and field is based on a misinterpretation of state equations. The particle–field concept, the additional idea of four different carrier particles, and the focus on state equations deprive modern physics of the ability to describe interaction in a unified way.

The cause-effect principle and non-ponderable E _pot suggest another understanding (cf. Figure 1b). Knowing that E _kin can be generalized as done by Schrödinger and that quantons Q (and quanton clusters) are far extended wave entities as suggested by de Broglie, the spatial separation between E ₀/E _kin and E _pot, which contradicts the structure of state equations, can no longer be maintained. The quantons and the fields are located in the same spatial area. This means that force, field lines, equipotential lines, etc. symbolize the quanton’s own properties. The new interpretation satisfies i) mechanics and thermodynamics, ii) the wave character of matter, and iii) the fact that nature is characterized by processes:

1. Interaction is realized via matter waves. By knowing that Ṗ and v are different driving forces, there are more degrees of freedom for describing interaction. The matter waves of quantons interact twice: Firstly, by means of their long-rang De Broglie waves (of two or more binding partners), where the momentum flow Ṗ becomes real and causes their ordered aggregation. Secondly, by means of collisions due to their propagation with v as a whole in the medium, which causes the disaggregation of quantons. In each case, the interaction represents a transfer of energy, i.e. a process, and reflects the antagonism of rest (E _pot) and movement (E _kin), where one kind of energy is dialectically preserved in the other and can be transformed into each other. Here, the standard models attempt to describe only the differently abstracted forces Ṗ. They neglect i) the processes δY _i  = dE _pot, and ii) interaction by means of collisions, i.e. δW _v = dE _kin = vdmv.

2. As quantons are open systems, every natural quantum process is complex, i.e. several X _i of the quanton change simultaneously. Equation (3) is to be applied.

   Example α: Electromagnetic binding W _e,1

   If two charged quantons or clusters (such as an electron and a proton) begin to attract, they change their matter wave network in an internal binding reaction W _e,1 changing the quality of E _ex in the two-body system. Simultaneously, photons hν are emitted; the momenta P and the positions r of the binding partners change, etc. Thus, W _e,1 is combined with exchange processes such as heat transfer Q, momentum work W _P, lifting work W _r, and others. For the quantitative change in the total energy E of the two-body system holds:

   (43) d E = δ Q + δ W P + δ W r + ⋯ = d ( h ν ) + v  d P + F g d r + ⋯

   Since during the exothermic reaction, electromagnetic binding energy E _ex,C =  h ν (heat Q) is emitted and the momenta P are changed, this is connected with a mass defect describing the energetic effects of Q(P) and W _P(P), but not that of W _r(r):

   (44) Δ m = m bound − ∑ i m i , free < 0  .

   Example β: Gravitational binding W _e,2

   If a non-charged quanton or cluster (such as a body) is lifted, the changed position r is accompanied by a simultaneous change in the matter wave network of the binding partners. This internal binding reaction W _e,2 can be accompanied by the emission of gravitational waves gw (a process Q _g that is analogous to Q), momentum work W _P, a changing space filling, etc. For the change in the total energy E of the two-body system holds:

   (45) d E = δ Q g + δ W P + δ W r + ⋯ = d ( g w ) + v  d P + F g d r + ⋯ ,

   where Q _g(P) and W _P(P) cause a change in mass, while W _r(r) does not. Here it is to be noted that also the quanton photon υ is subject to gravity. When it moves away from earth, it reduces its dynamic mass m _υ =  h ν /c ² by means of momentum work W _P, which is known as gravitational red shift [90]. Since simultaneously the non-ponderable positional energy E _pot of the photon increases by means of W _r, energy conservation is ensured [29, 30].

   The result is: While state equations only allow a separate description of gravitational or electromagnetic forces, process equations allow a unified description of interaction. The binding reaction in the examples α and β is always realized via De Broglie waves.

   Lifting work (without changing m of a two-body system) and emission of waves (with changing m) both accompany the binding, which explains the analogous form of Coulomb’s and Newton’s law. The differences between the binding processes are i) the type of the De Broglie waves and their entanglement, superposition, etc., and ii) the type of the waves released (electromagnetic or gravitational). This leads to the task to model the special types of de Broglie waves of quantons and their interaction in the Euclidean space in order to explain the different binding strengths, and attraction and repulsion.

1. E _pot can be treated uniformly and explained. If the distance r between two quantons Q₁ and Q₂ is increased, lifting work is performed, and E _pot of the two-body system increases, quite analogous to the tensioning of a spring (cf. Table 7). Here only changes in E _pot are described, not absolute energies. E _pot can becomes minimal or optimal, but never zero. Each quanton is subject to a ground tension in the condensed ether medium (cf. Equation (42)). Although measurable positional E _pot is caused by the quality and quantity of the partially hidden and partially not hidden excitation energy in the ether medium, it represents the opposite, namely the tensional energy in a continuous wave network.

With Figure 1b, basic concepts of modern physics change:

1. Today, concurrent process equations, i.e. Y _i that run side by side, are mixed together. For example: The binding reaction W _e,1 is accompanied by the release of hν via Q and lifting work W _r. In potential curves (Lennard–Jones potential, etc.), released electromagnetic binding energy E _ex,C =  h ν is interpreted as potential energy. However, h ν is the opposite: excitation energy. If non-ponderable E _pot(r) and ponderable E _ex,C(P) are called both potential energy, conceptual clarity is lost. It becomes necessary to stop calling E _ex,C potential energy. It also becomes obvious that it is not the force that is quantized in the quantization efforts of the standard models, but rather the process Q, i.e. the emission of waves such as photons hν , that occurs simultaneously during binding.

2. Quantons are countable and discrete due to their excitation energy. This also applies to weakons, gluons, photons, and Higgs bosons. It is unquestionable that these “particles” exist. However, the role attributed to them in the Feynman diagrams and the Standard Model of particle physics becomes obsolete. As weakons, gluons, and photons, just like fermions, are created by excitation, they are neither only potential energy nor carrier particles of the force. Weakons, for example, can be interpreted – like in chemical kinetics – as an intermediate product of a physical-chemical reaction. In case of the Higgs bosons, their mass is to be explained by the ether like that of any other quanton. The Higgs boson field of 1964 represents a subsequently introduced, insufficient “ether substitute concept” [26].

3. It is out of question that quantum fluctuations, i.e. very short-lived, instable quantons, exist. They are an expression of the activity of the condensed medium, real in each case, do not violate energy conservation, and contribute to the limited accuracy in measuring the trajectories of stable quantons. Fluctuations can affect the stable quantons, if they appear and disappear in the spatial area occupied by them, and can occur as intermediate products in binding or decay reactions. However, they are not “carrier particles” of the force.

4. If real dynamic processes in time are described, the notion of spacetime loses its meaning. Higher-dimensional spacetimes are not required for a unified description of interaction.

8.2.4 Momentum work and the Lorentz transformations

With the developed quanton ether concept, the idea of inertial frames of reference becomes obsolete. Inertial systems, just like point particles, are conceivable idealizations within a thought experiment, but do not describe reality for at least two reasons:

1. A quanton is not independent of the ether medium, but represents itself ether medium in a new quality. As an emergent object it is permanently influenced by its “nutrient medium” and in turn affects it and its side-excitations. There are only dynamic processes in nature.

2. Since each kind of excitation energy E _ex(P) is connected with waves, there are no uniform rectilinear, i.e. force-free movements in nature.

The reinterpretation of the Lorentz equations by inertial frames in SR is thus unrealistic. Consequently, all questions about Lorentz invariance or variance of state variables from the point of view of observers become obsolete. Lorentz’ own ether theory is based on realistic ideas. However, he assumed an ether “with a certain degree of substantiality” next to matter, i.e. separated from it [91, p. 230]. Therefore, the ether concept proposed here differs from his theory in several respects, but still harmonizes in basic equations, as will be shown below.

While unstable quantons almost instantaneously disappear, stable ones can propagate with v within the medium. Each quanton propagates with its specific (optimal) self-velocity v that correlates with the amount and spatial nature of its internal wave packets and the corresponding interaction with the continuous wave network. Here, a rule of thumb is that quantons with less intrinsic excitation energy E _{0, Q} move faster.

If v is to be changed, a process must take place that does not change v alone. Firstly, the self-velocity v of quantons (just as their internal velocity) is inseparably linked with their mass m (cf. Table 7). For the momentum work W _P that is performed, e.g. on an electron, applies:

Secondly, W _P is an abstraction. Several X _i of the quanton change simultaneously, e.g. by displacement work W _r against the continuous wave network, in the broadest sense also by volume work W _V, and interfacial word W _A; even excitation energy like hν can be emitted. According to Equation (3), for the total energy of the electron applies:

Equations (46) and (47) will be discussed below.

Equation (46)

Since E _kin(P) is mass-proportional excitation energy E _ex(P) (cf. Equation (42)), we can write:

On the one hand, Equation (48) can be transformed into:

which immediately shows that the slope of the function m = f (v) is positive because of v < c. If v ≪ c applies, the increase in m with v is infinitesimal and negligible due to the very large denominator, whereas with increasing v, the slope increases.

On the other hand, integration of Equation (48)

leads to:

Equation (52) corresponds to Equation (27) for the so-called relativistic mass m(v). Already in 1908, Equation (52) was derived from c ²dm = vd(mv) for a “beam of radiation” without relativity by the physical chemist Gilbert Newton Lewis [48, p. 711]. He proposed “a method of distinguishing between absolute and relative motion” [48, p. 717], but adopted Einstein’s total energy E = mc ² of a system:

We should then regard mass and energy as different names and different measures of the same quantity. [48, p. 708]

Lewis’ work was heavily criticized [92], the main criticism being, surprisingly, that he assumed “that all energy is of the same nature as radiant energy” [92, p. 657]. This criticism was justified, while that of W _P = vd(mv) not if the cause-effect principle is taken into account. However, while W _P = vd(mv) was rejected, the total energy E = mc ² within SR was accepted by the scientific community. Lewis’ paper went largely unnoticed because i) no theoretical justification for vd(mv) was given, and ii) contradictions do indeed occur if momentum work W _P = ΔE _kin is equated with changes in the total energy E of a system.

With Equation (42) that describes only excitation energy E ₀(P) and E _kin(P) as ponderable, Equation (52) can be interpreted realistically:

1. The increase in mass with v is real (as already suggested by Lorentz [41]) and experimentally confirmed for electrons and other particles in particle accelerators.

2. Since the propagation of a quanton is wavelike, i.e. not uniform and rectilinear, the velocity vector components v _x , v _y , and v _z are to be considered.

3. The large mass of protons and neutrons (mass surplus compared to their constituents) is due to the increased velocity v of quantons like gluons under confined conditions.

4. Knowing that mass is linked to velocity and can be deduced from one principle (amount of excitation energy), m ₀ and m are no longer different variables. Since also E ₀ is due to motion, E ₀ and E _kin are just as convertible into each other as E _kin and E _pot. This can be used to explain the oscillating mass m ₀ of the three neutrino types.

5. It becomes self-evident that there is no “rest-mass”, no “Lorentz-invariant mass” and no mass conservation, while energy conservation is always fulfilled (cf. [30]).

Analogous to Equation (52), the expression for E _ex is:

Equation (47)

While P is changed by momentum work W _P = ΔE _kin, the position r of a quanton like an electron is changed simultaneously by displacement work W _r = ΔE _pot (Rule 1 of the cause-effect principle). In a non-force-free space, the spatial propagation of an electron represents work. Since a quanton (as a spacious deformable wave structure) is a complex open system, also volume work W _V (the explanation of the Michelson–Morley experiment) takes place.

If v and m increase, the gravitational potential of the electron increases. It interacts more strongly with the continuous wave network or the medium, i.e. Ṗ becomes stronger – the resistance of the quanton ether to changing the self-velocity v. As early as 1906, Henri Poincaré, who preferred the Lorentz theory to Einstein’s interpretation his whole life, explained length contraction as volume work W _V performed by the ether on the electron:

I tried to determine this force, I found that it can be considered as a constant external pressure, acting on the deformable and compressible electron, and whose work is proportional to the changes in the volume of this electron. [93, p. 130]

Thus, both the mass increase and the length contraction with v are due to a real interaction with the ether medium. The increased Ṗ also affects the internal excitation energy of an accelerated “clock” (quanton cluster), which is why atomic oscillation transitions slow down. The “clock” (matter) is changed, not time [46]. This interpretation, which was also prioritized by philosophers and protophysicists, concedes the primacy of matter over geometry:

The Lorentz contractions or Einstein dilatations resulting from Lorentz metrics, on the other hand, can be interpreted – as in the case of Lorentz – as shortening of bodies or slowing down of movements. One does not need to speak of a revision of space and time. [94, p. 7]

8.2.5 Quanton thermodynamics

The consistent application of the cause-effect principle leads to the insight that quantons, just as quanton clusters (bodies, liquids, etc.), are open systems, whose properties ξ _i and X _i are to be modeled. Isolated and closed systems are idealizations. While on the macroscopic level, several X _i can be kept constant by applying suitable process conditions, this is not yet possible for quantum processes. In each natural quanton process, many X _i change simultaneously. Just as there is no invariable (“Lorentz-invariant”) mass m ₀, there is no invariable (“Lorentz-invariant”) entropy S. Unchangeable state variables are idealizations being valid only in the special case of low velocity v and under the assumption of reversible processes.

As processes are the key to understanding, not states, thermodynamics extends not only mechanics at the macroscopic level, but also quantum mechanics at the microscopic level. This implies a unification of mechanics, thermodynamics, and quantum theory and a return of TD and irreversible processes to fundamental theoretical physics. Even the propagation of the (not timeless) quanton photon in the ether medium is a dynamic process because Schrödinger’s “dying away of the higher vibrations in favour of the lower ones” [75, p. xi] has to be considered.

In this context, the claim of completeness of equations, such as the Schrödinger equation and E = mc ², has to be revised. In case of G _µν  = κT _µv , the spacetime interpretation must be abandoned. For each process, the real interaction via De Broglie waves and collisions is to be modeled by means of combined process equations.