Shuang-Ren Zhao

Deriving the electromagnetic radiation:(1) photon, (2) anti-photon, (3) unsuccessful radiation through the mutual energy principle and self-energy principle

Keywords: Maxwell, Poynting, Schrödinger, Wheeler, Feynman, Mutual energy, Self-energy, Reciprocity theorem, Electromagnetic eld, Photon, Advanced wave, Retarded wave, Causality, Energy conservation law, Photon, anti-photon

The solutions of Maxwell equations includes the restarted and the advanced waves. There are a few famous scientists supported the concept of advanced wave. Wheeler and Feynman have introduced the absorber theory in1945 which told us the absorbers can send the advanced wave. The absorber theory is based on the action-at-a-distance of Schwarzschild, Tetrode and Fokker, which told us the electric current sends a half retarded wave and a half advanced wave. John Cramer has introduced transactional interpretation in quantum mechanics, which said the retarded wave and the advanced wave have a handshake. What is the advanced wave in electromagnetic eld theory? In 1960, Welch introduced the reciprocity theorem in arbitrary time domain which involved the advanced wave. In 1963 V.H. Rumsey mentioned a method to transform the Lorentz reciprocity theorem to a new formula. In early of 1987 Shuangren Zhao (this author) introduced the mutual energy theorem in frequency domain. In the end of 1987 de Hoop introduced the time-domain crosscorrelation reciprocity theorem. All these theories can be seen a same theorem in dierent domain: Fourier domain or in time domain. This theorem can be applied to prove the directivity diagram of a receiving antenna are equal to the directivity diagram when the receiving antenna are used as a transmitting antenna. According to this theory, the receiving antenna sends the advanced wave. As a reciprocity theorem the two elds in it do not need to be real for all. Hence, for the reciprocity theorem of Welch, Rumsey and Hoop do not need to claim that the advanced wave is a physical wave. However, when Shuang-ren Zhao said it is a energy theorem that means the two waves the retarded wave and the advanced wave in the theorem must be all real physical waves. After the mutual energy theorems has been published 30 years, Shuang-ren Zhao re-enter this eld. First, the mutual energy ow theorem is derived. The mutual energy ow produced by the superposition of the retarded wave and the advanced wave. The mutual energy ow can carry the energy from 1 the transmitting antenna to the receiving antenna. Our textbook of electromagnetic eld tell us the energy is carried by the energy ow of the Poynting vector which is the self-energy ow. Hence, there is a question that the energy of electromagnetic eld is transferred by the mutual energy or self-energy or by both? This author found that only the former can oer a self-consistency theory. This author also proved that the energy is transferred by the self-energy or both all conict with the energy conservation law and hence cannot be accept. If the energy is transferred by the mutual energy, the axioms of the electromagnetic eld needs to be modied. Hence, the mutual energy principle is introduced to replace the Maxwell equations as axioms. The mutual energy principle can be derived from the Maxwell equations. The Maxwell equations can also be derived from the mutual energy principle. However, the mutual energy principle does not equivalent to the Maxwell's equations. Starting from the mutual energy principle, the solution needs to be two groups of Maxwell equations existing together. One group of the Maxwell equation is corresponding to the retarded wave, another is corresponding to the advanced wave. The two waves must be synchronized to produce the mutual energy ow. The conict of Maxwell equations with the energy conservation law further suggest that there exist a time-reversal wave and self-energy principle. Self energy principle tells us that self-energy ow or the energy ow corresponding to Poynting vector does not carry or transfer the energy, because there exist 2 time-reversal waves corresponding to the retarded wave and the advanced wave. The energy ow of the time-reversal waves cancels the energy ows of the self-energy ows of the retarded wave and the advanced wave. This also tell us there are 4 waves for electromagnetic elds, the retarded wave, the advanced wave, the 2 time-reversal waves corresponding to the retarded wave and the advanced wave. The self-energy ow of these 4 waves are all canceled. However the mutual energy ow of the retarded wave and the advanced wave does not disappear. The energy of electromagnetic eld is transferred by the mutual energy ow. Photons can be explained by the mutual energy ows. There is also the timereversal mutual energy ow which can wipe out the half-photon or partial photon. Anti-particle can also be explained by the time-reversal mutual energy ow. This theory has been widen to the quantum mechanics. That means all particles for example electron is also consist of 4 waves and 6 energy ows. There is the mutual energy principle and self-energy principle corresponding to the Schrödinger equation. In this article 3 modes of radiation are introduced which are photon, anti-photon, ant unsuccessful radiation. Photon is consist of one mutual energy ow, self-energy ow for the retarded wave and advanced wave, self-energy ow of the timereversal waves. All self-energy ows are canceled. Hence only the mutual energy ow survive. Anti-photon is consist of the time-reversal mutual energy ow; Time-reversal self-energy ow and self-energy ows. All the self-energy ow canceled. Only the time-reversal mutual energy survived. The last mode is the unsuccessful radiation. The retarded wave is sent out but it did not meat any advanced wave to handshake/synchronized. Hence, the energy is returned, the radiation is unsuccessful. Photon is transfer the radiation energy. Anti-photon is responsible to eliminate the half-photon or partial photon. The unsuccessful radiation is the necessary 2 result that the source and sink both send the waves, one is the retarded wave and the other is the advanced wave.

Introduction

Maxwell equations have the retarded solution and the advanced solution. Many engineers and scientists do not accept the advanced wave based on the consideration of causality. However, there are scientists and engineers believe that the advanced wave is real. Wheeler and Feynman have introduced the absorber theory in 1945, which involved the advanced wave [1] [2]. The absorber theory is based on the action-at-a-distance [21,24,8]. J. Cramer further worked on the absorber theory and introduced the transactional interpretation for quantum mechanics [START_REF] Cramer | The transactional interpretation of quantum mechanics[END_REF][START_REF] Cramer | An overview of the transactional interpretation[END_REF] around 1980. Stephenson oered a good tutorial about the advanced wave [START_REF] Stephenson | The relevance of advanced potential solutions of maxwell's equations for special and general relativity[END_REF].

In classical electromagnetic eld theory the advanced wave is applied on the Welch's reciprocity theorem [START_REF] Welch | Reciprocity theorems for electromagnetic elds whose time dependence is arbitrary[END_REF] in 1960, Rumsey's reciprocity theorem [START_REF] Rumsey | Reaction concept in electromagnetic theory[END_REF] in 1963, Zhao's (this author) mutual energy theorem [START_REF] Shuang Ren Zhao | The application of mutual energy theorem in expansion of radiation elds in spherical waves[END_REF][START_REF] Zhao | The simplication of formulas of electromagnetic elds by using mutual energy formula[END_REF][START_REF] Zhao | The application of mutual energy formula in expansion of plane waves[END_REF] introduced in the rst half of 1987. de Hoop's reciprocity theorem [START_REF] Adrianus | Time-domain reciprocity theorems for electromagnetic elds in dispersive media[END_REF] introduced in the second half of 1987. This author found the above 4 theorems can be seen as one theorem in Fourier domain or in time domain. These theorems have the major dierence comparing to the Lorentz reciprocity theorem [START_REF] Carson | Reciprocal theorems in radio communication[END_REF][START_REF] Carson | The reciprocal energy theorem[END_REF]. Lorentz reciprocity theorem is a mathematical theorem, Shuang-ren Zhao has noticed that these theorems are an energy theorems. This author combined the absorber theory and the mutual energy theorem and further introduced the concept that the photon energy is transferred by the mutual energy ow [START_REF] Shuang Ren Zhao | The principle of the mutual energy[END_REF][START_REF] Shuang Ren Zhao | The photon model and equations are derived through time-domain mutual energy current[END_REF][START_REF] Shuang Ren Zhao | The modied poynting theorem and the concept of mutual energy[END_REF][START_REF] Shuang-Ren Zhao | New testimony to support the explanation of light duality with mutual energy current by denying the reciprocity theore[END_REF][START_REF] Shuang Ren Zhao | Explanation of the duality of the light (wave and photon) by using the mutual energycurrent composed of retarded and advanced potentials[END_REF][START_REF] Shuang Ren Zhao | Antenna calculation in lossy media with mutual energy theorem[END_REF][START_REF] Shuang Ren Zhao | How the mutual energy current of a retarded potential and an advanced potential can produce a photon[END_REF][START_REF] Shuang Ren Zhao | The mutual energy current interpretation for quantum mechanics[END_REF]. And this author further introduced the mutual energy principle [START_REF] Shuang Ren Zhao | Photon models are derived by solving a bug in poynting and maxwell theory[END_REF] and the self-energy principle [START_REF] Shuang Ren Zhao | Self-energy principle with a time-reversal eld is applied to photon and electromagnetic theory[END_REF].

The mutual energy principle tell us that the electromagnetic eld or the eld for photon all should satisfy the formula of the mutual energy principle. The solution of the mutual energy principle is an retarded wave and an advanced wave. Both waves satisfy the Maxwell equations. The formula of the mutual energy principle require that the both waves must be synchronized. The mutual energy ow is the energy ow of the particle. The self-energy principle for photon tells us that the self-energy are canceled by the time-reversal waves. There are two time reversal waves, one corresponding to the retarded wave and another one is corresponding to the advanced wave. The energy ow of the two timereversal waves oset the the self-energy ows. Hence, the self-energy ows do not contribute to any energy transfers of the particle. However, the retarded wave and the advanced wave combined together can build the mutual energy ow, which survived and which can transfer the energy from point 1 to point 2. Here point 1 is a source of the energy ow, point 2 is a sink of the energy ow. It can be proven that the shape of the mutual energy ow is thin in the two ends 1 and 2, it is thick in the middle between 1 and 2. Hence, the mutual energy ow looks like a wave in the middle between 1 and 2 and looks like a particle at the two ends 1 and 2. Hence, photon is not wave or particle but the mutual energy ow.

In this article we simplied the whole theory and try to allow the reader more easily to understand the concept of the theory for the mutual energy and self-energy.

2 Why we need the mutual energy principle 2.1 Derive the mutual energy principle from the Maxwell equations

The Maxwell equations are,

-∂ ∂t ( E) + ∇ × H = J -∇ × E -∂ ∂t (µH) = 0 (1)
where E is the electric eld, H is the magnetic eld, J is electric current intensity, is permittivity and µ is permeability.

In this article when we speak about the Maxwell equation, we mean this two equation, the other two Maxwell equation is not too important to the radiation waves and are omit here. Maxwell equations can be written as,

Lξ = 1 τ (2)
where ξ = [E, H], τ = [J , K], K = 0 is the magnetic current intensity. The operator L is dened as

L = -∂ ∂t 1 ∇× -1 µ ∇× -∂ ∂t (3)
We can dene inner product,

(ξ 2 , ξ 1 ) V = V ( E • E + µ H• H)dV (4)
It can be obtained easily,

Lξ 1 = -∂ ∂t 1 ∇× -1 µ ∇× -∂ ∂t E 1 H 1 = -∂ ∂t E 1 + 1 ∇ × H 1 -1 µ ∇ × E 1 -∂ ∂t H 1 (5)
and, hence,

(ξ 2 , Lξ 1 ) V = V (-E 2 • ∂ ∂t E 1 + 1 E 2 •∇×H 1 )+µ(- 1 µ H 2 •∇×E 1 -H 2 ∂ ∂t H 1 )dV = V (-E 2 • ∂ ∂t E 1 -∇ • (E 2 ×H 1 ) -∇ • (E 1 × H 2 ) -µH 2 ∂ ∂t H 1 )dV (6)
We can also obtain,

Lξ 2 = -∂ ∂t 1 ∇× -1 µ ∇× -∂ ∂t E 2 H 2 = -∂ ∂t E 2 + 1 ∇ × H 2 -1 µ ∇ × E 2 -∂ ∂t H 2 (7)
(Lξ 2 , ξ 1 ) V = V ( (-E 1 • ∂ ∂t E 2 + 1 E 1 •∇×H 2 )+µ(- 1 µ H 1 •∇×E 2 -H 1 • ∂ ∂t H 2 ))dV = V (-E 1 • ∂ ∂t E 2 -∇ • (E 1 × H 2 ) -∇ • (E 2 × H 1 ) -µH 1 • ∂ ∂t H 2 )dV (8)
Hence, we can obtained the mathematical formula,

∞ -∞ ((ξ 2 , Lξ 1 ) V + (Lξ 2 , ξ 1 ) V )dt = - ∞ -∞ V ( E 1 ∂ ∂t E 2 + E 2 ∂ ∂t E 1 + µH 1 ∂ ∂t H 2 + µH 2 ∂ ∂t H 1 )dV - " Γ (E 1 × H 2 + E 2 × H 1 ) • ndΓ (9)
where V is a volume, Γ is the boundary surface of the volume V . n is the unit normal vector of the surface Γ.

ξ 1 = [E 1 , H 1 ]. ξ 2 = [E 2 , H 2 ].
In this article, we assume ξ = [E, H] and ξ T = E H are same vector. Hence, we do not need to write the Matrix transfer symbol T .

The above formula is not a physical formula, it is only a mathematical formula according to our denition of the Maxwell operator Eq.( 3).

Substitute the Maxwell equations Eq.(2) to the above formula Eq.( 9) we obtained,

∞ -∞ ((ξ 2 , 1 τ 1 ) V + ( 1 τ 2 , ξ 1 ) V )dt = - ∞ -∞ V ( E 1 ∂ ∂t E 2 + E 2 ∂ ∂t E 1 + µH 1 ∂ ∂t H 2 + µH 2 ∂ ∂t H 1 )dV dt - ∞ -∞ " Γ (E 1 × H 2 + E 2 × H 1 ) • ndΓdt (10) or - ∞ -∞ " Γ (E 1 × H 2 + E 2 × H 1 ) • ndΓdt = ∞ -∞ V ( E 1 ∂ ∂t E 2 + E 2 ∂ ∂t E 1 + µH 1 ∂ ∂t H 2 + µH 2 ∂ ∂t H 1 )dV dt + ∞ -∞ V (E 1 • J 2 + E 2 • J 1 )dV dt (11)
The above formula is referred as the mutual energy principle. It is a physical formula because Maxwell equations are applied. Hence, we have proved the formula of the mutual energy principle from the Maxwell equations.

The mutual energy principle can be rewritten as,

- 2 i=1 2 i=1,i =j ∞ -∞ " Γ (E i × H j ) • ndΓdt = 2 i=1 2 i=1,i =j ∞ -∞ V ( E i ∂ ∂t E j + µH i ∂ ∂t H j )dV dt + 2 i=1 2 i=1,i =j ∞ -∞ V (E i • J j )dV dt (12)
If there are N charges instead of 2 charges, the mutual energy principle can be widen to

- N i=1 N i=1,i =j ∞ -∞ " Γ (E i × H j ) • ndΓdt = N i=1 N i=1,i =j ∞ -∞ V ( E i ∂ ∂t E j + µH i ∂ ∂t H j )dV dt + N i=1 N i=1,i =j ∞ -∞ V (E i • J j )dV dt (13)

Derive the Maxwell equations from the mutual energy principle

If we know the mutual energy principle, we would like to found the solution of mutual energy principle, we compare the mutual energy principle Eq.( 11) the mathematical formula Eq.( 9), we can obtained 2 groups of Maxwell equations,

Lξ 1 = 1 τ 1 (14) Lξ 2 = 1 τ 2 (15)
Two groups of the Maxwell equations must exist together. Where L is dened in Eq.( 3).

It should be noticed that, Lξ 1 = 1 τ 1 alone is not a solution of the mutual energy principle. Since if ξ 2 =0, τ 2 = 0, substitute this to the mutual energy principle we obtain ||ξ 1 || < ∞ which is not an accepted solution for ξ 1 .

Similarly Lξ 2 = 1 τ 2 alone is also not a solution of the mutual energy principle. The two groups of the Maxwell equations must be satised the Maxwell equations simultaneously.

If the mutual energy principle used as axioms of the electromagnetic eld theory, it requires that the two groups of the Maxwell equations exist simultaneously. If the Maxwell equations used as an axioms of the electromagnetic eld theory, only one group of Maxwell equations is OK. This is the major dierence about which should be used as axioms of the electromagnetic eld theory, Maxwell equations or the mutual energy principle.

The energy conservation law

Assume there are N charges. the i-th charge's electric current is J i . The power of J i to the j-th charge is ˝V (E i •J j )dV . Since if i-th charge oer some energy to j-th charge, j-th charge's energy is increased, the energy of i-th charge will decrease, the total energy will not increase or decrease and hence we have,

N i=1 N j=1,j =i ∞ t=-∞ V (E i • J j )dV dt = 0 (16)
This is the energy conservation law of the electromagnetic charges system. This system have only N charges otherwise is nothing. This formula should be seen as self-explanatory. Now we have two dierent axioms for the electromagnetic eld theory. Which is correct? The energy conservation law will be applied as touchstone. Only the one agrees with the energy conservation law should be survived.

Derive the energy conservation law from the mutual energy principle

Compare the mutual energy principle Eq.( 13) and the energy conservation law we know that if we can prove the two following terms as 0, we can derive the energy conservation law from the mutual energy principle, i.e.,

N i=1 N i=1,i =j ∞ -∞ V ( E i ∂ ∂t E j + µH i ∂ ∂t H j )dV dt = 0 (17) N i=1 N i=1,i =j ∞ -∞ " Γ (E i × H j ) • ndΓdt = 0 (18)
We will prove these only in the situation where

N = 2, i.e., ∞ -∞ V ( E 1 ∂ ∂t E 2 + E 2 ∂ ∂t E 1 + µH 1 ∂ ∂t H 2 + µH 2 ∂ ∂t H 1 )dV dt = 0 (19) ∞ -∞ " Γ (E 1 × H 2 + E 2 × H 1 ) • ndΓdt = 0 (20)
Assume the volume V is innite big sphere. Γ is the boundary of the surface. τ 1 = [J 1 , 0] and τ 2 = [J 2 , 0] are two electric current of the two charges. τ 1 and τ 2 are inside the volumeV . If this two charges all send the retarded wave or all send advanced wave it is clear the surface integral cannot be 0 at the surface Γ.

However if one sends the retarded wave and another sends the advanced wave, the two waves reach the surface Γ one is at a future time and another is at a past time. Hence, the two waves cannot no zero at the same time on the sphere surface Γ. Hence, the surface integral on Γ is 0, i.e, "

Γ

(E 1 × H 2 + E 2 × H 1 ) • ndΓ = 0 (21) hence, we have ∞ -∞ " Γ (E 1 × H 2 + E 2 × H 1 ) • ndΓdt = 0 (22)
In other hand,

∞ -∞ V ( E 1 ∂ ∂t E 2 + E 2 ∂ ∂t E 1 + µH 1 ∂ ∂t H 2 + µH 2 ∂ ∂t H 1 )dV dt = ∞ -∞ dU = U (∞) -U (-∞) = 0 (23)
where

U = V ( E 1 E 2 + µH 1 H 2 )dV (24)
is the space energy of the electromagnetic eld, this energy should be equal at the time t = -∞ and t = ∞. We assume there is an energy from move from the source 1 to the sink 2. The energy in the space is changed when the energy move from 1 to 2. However, in the time t = -∞ the moving process has not started and at t = ∞ the energy moving process has nished. The energy in the space for this two particular time are same. Hence, we have U (∞) = U (-∞).

We have proved when N = 2 the two terms Eq. [START_REF] Shuang Ren Zhao | How the mutual energy current of a retarded potential and an advanced potential can produce a photon[END_REF][START_REF] Rumsey | Reaction concept in electromagnetic theory[END_REF] are indeed as 0. This can be easily widen to the situation where charge number N > 2. Hence, we have derived the energy conservation law from the mutual energy principle.

The conict of the Poynting theorem with energy conservation law

Assume the Maxwell equations Eq.( 1) is satised. From Maxwell equations the Poynting theorem can be derived which is,

-

" Γ (E × H) • ndΓ = V ( E ∂ ∂t E + µH ∂ ∂t H)dV + V (E • J )dV (25)
The superposition principle for electromagnetic eld can be written as,

E = N i=1 E i , H = N i=1 H i , J = N i=1 J i (26)
Substitute the superposition principle to the Poynting theorem we obtain,

- N i=1 N i=1 ∞ -∞ " Γ (E i × H j ) • ndΓdt = N i=1 N i=1 ∞ -∞ V ( E i ∂ ∂t E j + µH i ∂ ∂t H j )dV dt + N i=1 N i=1 ∞ -∞ V (E i • J j )dV dt (27)
This can be divided as two formula,

- N i=1 ∞ -∞ " Γ (E i × H i ) • ndΓdt = N i=1 ∞ -∞ V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt + N i=1 ∞ -∞ V (E i • J i )dV dt (28)
and

- N i=1 N i=1,i =j ∞ -∞ " Γ (E i × H j ) • ndΓdt = N i=1 N i=1,i =j ∞ -∞ V ( E i ∂ ∂t E j + µH i ∂ ∂t H j )dV dt + N i=1 N i=1,i =j ∞ -∞ V (E i • J j )dV dt (29)
The Eq.( 28) is the self-energy formula or Poynting theorem for all N charges.

The Eq.( 29) is the mutual energy principle Eq.( 13). If each terms in Eq.( 28) are 0, we obtained the mutual energy principle, from the derivation of last few subsections we can prove the energy conservation law Eq.( 16). Every thing is ne. However, we cannot prove each terms of Eq.(28) is 0. Since one term of the Eq.( 28) is Poynting theorem for i-th charge. If i-th term of the formula Eq.( 28) is 0 then the electromagnetic eld of i-th charge is 0. We know that i is arbitrary and, hence, this means that all the electromagnetic elds are 0. This cannot be accepted. We know the electromagnetic eld is not 0. If there are the terms in Eq.( 28) not 0, we cannot prove the energy conservation law from the Maxwell equations with the superposition principle. This means the Maxwell equations and the superposition principle are conict with the energy conservation law.

Actually from Maxwell equations we have proven that the formula Eq.( 16)

is an energy theorem, we can call it as the mutual energy theorem. In order to prove it is an energy conservation law we have to prove in the space there is no any other kind of energy transfer. That is the reason we need all terms of Eq.(28) as 0.

Since the Maxwell equations can be derived from the mutual energy principle, this also means that the mutual energy principle has also the problem.

However, the problem of the mutual energy principle is less than the Maxwell equations, because the problem of the mutual energy principle is only through the the Maxwell equations indirectly. The problem of the Maxwell equation is direct.

If we can solve the conict between the Maxwell equations together with the superposition principle and the energy conservation law, we have solved all the problems. The mutual energy principle will also not conict with the energy conservation law. and if it collapse back it goes back to the sink (absorber).

Introduce the self-energy principle

The wave function collapse back can be described by a time-reversal process which is obtained by the transform t → -t = τ to the formula of the electromagnetic eld, for example, Maxwell equations. Considering,

E(t) → E(-t) = E(τ ) (30) ∂ ∂t E(t) → ∂ ∂t E(-t) = - ∂ ∂(-t) E(-t) = - ∂ ∂(τ ) E(τ ) (31) ∂ ∂t H(t) → ∂ ∂t H(-t) = - ∂ ∂(-t) H(-t) = - ∂ ∂(τ ) H(τ ) (32)
J = ρv = ρ(t) ∂x(t) ∂t → ρ(-t) ∂x(-t) ∂t = ρ(-t) ∂x(-t) -∂(-t) = -ρ(τ ) ∂x(τ ) ∂(τ ) = -ρv = -J (33)
Hence substitute Eq.(31, 32, 33) to the Maxwell equations Eq.( 1) we can obtain the time-reversal Maxwell equations which are,

∂ ∂t ( e) + ∇ × h = -j -∇ × e + ∂ ∂t (µh) = 0 - " Γ (e × h) • ndΓ = -V ( e ∂ ∂t e + µh ∂ ∂t h)dV -V (e • j)dV (35)
The above formula is obtained by substitute Eq.(31-33)) to the Poynting theorem Eq.( 25). This is the time-reversal Poynting theorem, it is corresponding the time-reversal self-energy ow.

Actually we do not need all terms in the Eq.( 28) are 0. What we need is the self-energy terms do not carry and transfer energy. This author noticed, if there are a time-reversal electromagnetic eld which satisfy the time-reversal Maxwell equations, the time-reversal energy ow can cancel the normal energy ow, hence, we can have,

- ∞ -∞ " Γ (E i × H i ) • ndΓdt + ∞ -∞ " Γ (e i × h i ) • ndΓdt = 0 (36) ∞ -∞ V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt + ∞ -∞ V ( e i ∂ ∂t e i + µh i ∂ ∂t h i )dV dt = 0 (37) ∞ -∞ V (E i • J i )dV dt + ∞ -∞ V (e i • j i )dV dt = 0 (38)
There exist the time-reversal wave which satisfy the time-reversal Maxwell equations and can cancel the normal self-energy terms. These are referred as the self-energy principle. After the introduction of the self-energy principle is introduced, Eq.( 28) do not carry any energy in the space. Hence, the Maxwell equations together with the self-energy principle Eq. [START_REF] Shuang Ren Zhao | Explanation of the duality of the light (wave and photon) by using the mutual energycurrent composed of retarded and advanced potentials[END_REF][START_REF] Shuang Ren Zhao | The mutual energy current interpretation for quantum mechanics[END_REF][START_REF] Shuang Ren Zhao | The photon model and equations are derived through time-domain mutual energy current[END_REF] can also derive the energy conservation law. The conict between the (Maxwell equations, the superposition principle) and the energy conservation law is solved.

The above formula means the source for the time-reversal wave just negative value of the normal current (assume the source is in very short time for example δ(t)). The above formula can also be seen as the self-energy principle. The selfenergy principle Eq. [START_REF] Shuang Ren Zhao | Explanation of the duality of the light (wave and photon) by using the mutual energycurrent composed of retarded and advanced potentials[END_REF][START_REF] Shuang Ren Zhao | The mutual energy current interpretation for quantum mechanics[END_REF][START_REF] Shuang Ren Zhao | The photon model and equations are derived through time-domain mutual energy current[END_REF]) can be derived from the time-reversal Maxwell equation, if we know that,

J = -j (39) When E i increase, e i decrease, ∂ ∂t e i =-∂ ∂t E i , H i increase, h i decrease, ∂ ∂t h i =- ∂ ∂t H i . The j is a implicit current.
3 The mutual energy theorem and the mutual energy ow theorem

The mutual energy theorem

We have derived the energy conservation law from the mutual energy principle and self-energy principle. When the N = 2, we have,

2 i=1 2 j=1,j =i ∞ t=-∞ V (E i • J j )dV dt = 0 (40) Or ∞ t=-∞ V (E 1 (t) • J 2 (t) + E 2 (t) • J 1 (t))dV dt = 0 (41) Or ∞ t=-∞ V2 (E 1 (t) • J 2 (t) = - ∞ t=-∞ V1 E 2 (t) • J 1 (t))dV dt (42)
This is W.J. Welch's reciprocity theorem [START_REF] Welch | Reciprocity theorems for electromagnetic elds whose time dependence is arbitrary[END_REF]. This can be widen to,

∞ t=-∞ V2 (E 1 (t + τ ) • J 2 (t)dV dt = - ∞ t=-∞ V1 E 2 (t) • J 1 (t + τ ))dV dt (43)
This is the Hoop's reciprocity theorem [START_REF] Adrianus | Time-domain reciprocity theorems for electromagnetic elds in dispersive media[END_REF]. After make the Fourier transform from Hoop's reciprocity theorem, it become,

V2 (E 1 (ω) • J * 2 (ω)dV = - V1 E * 2 (ω) • J 1 (ω))dV (44)
This is Rumsey's reciprocity theorem and this is also the mutual energy reciprocity theorem of the Shuang-ren Zhao [START_REF] Shuang Ren Zhao | The application of mutual energy theorem in expansion of radiation elds in spherical waves[END_REF]. Hence, in case there are only two charges in the empty space, these theorems actually are the energy conservation law.

We assume that the charge 1 is a source which sends the retarded wave. We assume the source 2 is a sink which sends the advanced wave, these theorems tell us that the energy sucked by the advanced wave E 2 (ω) on the source current J 1 (ω) is equal to the retarded wave E 1 (ω) applied the energy on the sink current J 2 (ω).

This theorem apply to the antenna, that means the energy received by the receiving antenna is equal to the energy sends out by the transmitting antenna, if we assume that there are only these two antennas in a otherwise empty space.

For sure normally there are other antennas and also the environment which can also receive the energy sent from the transmitting antenna. However, we can assume an ideal situation, there are only a transmitting antenna and a receiving antenna in an otherwise empty space, these theorem become the energy conservation law for the antenna system with one transmitting antenna and one receiving antenna.

The mutual energy ow theorem

In the derivation of the energy conservation law from the mutual energy principle, we assume the surface Γ is a innite big sphere surface. If we assume this surface is not at innite big sphere, in general we cannot obtained the surface integral is 0, hence, generally we have,

- N i=1 N i=1,i =j ∞ -∞ " Γ (E i × H j ) • ndΓdt = N i=1 N i=1,i =j ∞ -∞ V (E i • J j )dV dt (45) Or if N = 2, we have, - ∞ -∞ " Γ (E 1 × H 2 + E 2 × H 1 ) • ndΓdt = ∞ -∞ V (E 1 • J 2 + E 2 • J 1 )dV dt (46)
Here the volume V is arbitrary. Inside the volume there are two currents J 1 and J 2 . We assume J 1 is the source which sends the retarded wave E 1 , H 1 and J 2 is the sink which sends the advanced wave E 2 , H 2 . See Figure 1 for details.

If we take the

V as V 1 , J 1 is inside V 1 , and Γ become Γ 1 which is the boundary of V 1 , we can obtained, - ∞ -∞ " Γ1 (E 1 × H 2 + E 2 × H 1 ) • n12 dΓdt = ∞ -∞ V1 (E 2 • J 1 )dV dt (47)
In the above formula, we have considered J 2 is at outside of V 1 . That n12 is the norm unit vector of the surface Γ 1 , which is direct to the outside of V 1 , that is from volume 1 direct to volume 2. Hence, the subscript of 12 is applied for the norm vector n. Details please see Figure Similarly we have,

- ∞ -∞ " Γ2 (E 1 × H 2 + E 2 × H 1 ) • n21 dΓdt = ∞ -∞ V2 (E 1 • J 2 )dV dt (48)
In equation Eq.( 47) and (48) the direction of the norm vector are dierent.

We can adjust n21 to n12 which is at the direction to the inside of the volume V 2 . The details can be seen in Figure 3. Change the direction of the norm vector of the surface n21 to n12 the above formula become,

∞ -∞ " Γ2 (E 1 × H 2 + E 2 × H 1 ) • n12 dΓdt = ∞ -∞ V2 (E 1 • J 2 )dV dt (49)
Substituting the above two formula Eq.(47, 49) to the mutual energy theorem Eq.(42), we obtained,

- ∞ -∞ V2 (E 2 • J 1 )dV dt
V 1 , J 1 sends the retarded wave [E 1 , H 1 ]. J 2 sends the advanced wave [E 2 , H 2 ]. The norm vector of the surface is n12 = ∞ -∞ " Γ1 (E 1 × H 2 + E 2 × H 1 ) • n12 dΓdt = ∞ -∞ " Γ2 (E 1 × H 2 + E 2 × H 1 ) • n12 dΓdt = ∞ -∞ V2 (E 1 • J 2 )dV dt (50)
In the above formula there are two surface Γ 1 and Γ 2 . This is the mutual energy ow theorem. See Figure 5 for details.

Actually the surface can be any surface Γ between V 1 and V 2 . Hence, we have,

- ∞ -∞ V2 (E 2 • J 1 )dV dt = ∞ -∞ " Γ (E 1 × H 2 + E 2 × H 1 ) • n12 dΓdt = ∞ -∞ V2 (E 1 • J 2 )dV dt (51)
Figure 5: In the volume V 1 , there are only the source J 1 , in the volume V 2 there is the sink J 2 , J 1 sends the retarded wave

[E 1 , H 1 ]. J 2 sends the advanced wave [E 2 , H 2 ]. Γ 1 is the boundary of volume V 1 . Γ 2 is the boundary of volume V 2 . Γ is surface between V 1 and V 2 .
The norm vector of the surface are all in the direction from 1 to 2, hence is written as n12

The above is the mutual energy ow theorem. Γ can be taken at any place between volume V 1 and V 2 . Γ can be a close surface for example a sphere or a innite plane. The Mutual energy ow theorem gave more details of the explanation of the mutual energy theorem. Mutual energy theorem tell us there are energy from source move to sink. The sink received energy is equal to the energy radiated out by the source. The mutual energy ow theorem further tells us the energy that goes in the space is accounting to the mutual energy ow, which is dene as,

Q = " Γ (E 1 × H 2 + E 2 × H 1 ) • n12 dΓ
The total energy go through the surface

Γ from time t = -∞ to t = ∞ is Energy = ∞ -∞ " Γ (E 1 × H 2 + E 2 × H 1 ) • n12 dΓdt
The mutual energy ow intensity is corresponding to the mixed Poynting vector:

S 12 = E 1 × H 2 + E 2 × H 1 (52)
which is dierent comparing to the Poynting vector,

S 1 = E 1 × H 1 (53)
There is also the Poynting vector corresponding the advanced wave,

S 2 = E 2 × H 2 (54)
In the theory of Poynting theorem, only the source can radiate the energy, the radiation is nothing to do with the sink. In the theory of mutual energy of this author, the energy ow is depended only on the mutual energy ow which is corresponding to the mixed Poynting vector S 12 instead of the Poynting vector which is S 1 .

In this author's mutual energy theory, S 1 is corresponding to the self-energy ow. This part of energy ow does transfer and carry energy because there are time-reversal waves. The energy ow of self-energy terms is canceled by the energy ow of the corresponding time-reversal wave. This is also true for S 2 which is the energy ow of the advanced wave. The energy is transferred only by the mutual energy ow. Hence, the mutual energy ow is the energy ow.

The word mutual can be wipe o. The mutual energy principle is the energy principle. However, we still call it as mutual energy principle for history reason.

Possible modes of the electromagnetic eld radiations

In this section the possible modes of the radiation is discussed. We often head photons. However consider the physics law should be symmetric, it should be also the anti-photon. In the author's assumption the source randomly sends the retarded wave, the sink also randomly sends the advanced wave. It is possible the retarded wave cannot matches any advanced wave from many absorbers. The advanced wave send from an absorber is also possible cannot found a retarded wave to match. In this case the radiation process cannot be done.

Mode 1) invalid radiation

In this situation, the retarded wave is sent out by the emitter, but it doesn't nd an advanced wave to synchronize. Hence, the retarded wave is returned by the corresponding time-reversal wave.

The advanced wave is sent out by the absorber but it doesn't nd a retarded wave to synchronize. Hence, the advanced wave is returned by the corresponding time-reversal wave. In the above both situations, there is no any mutual energy ow is produced. The retarded wave and the advanced wave both satisfy the Maxwell equations, which further can derive the Poynting theorems, -

" Γ (E i × H i ) • ndΓdt V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt + V (E i • J i )dV dt (55)
and the time-reversal Maxwell equations can derive the time-reversal Poynting theorem,

" Γ (e i × h i ) • ndΓdt V ( e i ∂ ∂t e i + µh i ∂ ∂t h i )dV dt + V (e i • j i )dV dt (56)
In this situation the self-energy principle is, In the above situation all self-energy terms are canceled. Hence, the wave did not carry the energy. Or we can say the energy is collapse back. We assume the current J i randomly changed and hence, the wave is randomly sent out.

- ∞ -∞ " Γ (E × H i ) • ndΓdt + ∞ -∞ " Γ (e i × h i ) • ndΓdt = 0 (57) ∞ -∞ V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt + ∞ -∞ V ( e i ∂ ∂t e i + µh i ∂ ∂t h i )dV dt = 0 (58) ∞ -∞ V (E i • J i )dV dt + V (e i • j i )dV dt = 0 (59)
In this situation there is no mutual energy ow produced and, hence, there is no energy which have been sent out. Even, the self-energy items sends out the energy, the energy is collapse back through the time-reversal wave. Since, the collapsed-back wave is the time-reversal wave, all self-energy ow are canceled.

Hence, it looks like that no any energy has been sent out ever.

In this situation J i =-j i . We assume J i is happened at a very short time for example as δ(t), this time interval close to 0. Hence, we can have,

J i +j i = 0 (60)
This means the current is also recovered to the situation before the radiation.

We call this unsuccessful radiation. The current J i has tried to make a radiation, the wave is sent to the space, however, since it doesn't nd an advanced wave to match, the wave sends to the end of our universe and then it automatically returned or collapses back through the time-reversal wave to the source. In the place of source a negative current is produced. The negative current element cancel the original current element which tries to produce the radiation. Finally this radiation is not successfully sent out. The current element come back to the original state.

The sink (absorber) all can also sends the self-energy wave out. This wave is advanced wave. This waves are also canceled by the corresponding time-reversal waves.

We assume the emitter randomly sends the energy out, if this wave cannot nd a advanced wave to match it, it will be returned by the time-reversal waves.

In this situation we have 3 formulas, 2 Poynting theorems Eq.(55,56) and one self-energy principle Eq.(42-44). The 3 formulas can fully describe this phenomena. In this situation the mutual energy principle is not involved.

The photon situation

In the photon situation, the mutual energy ow is produced, which is decided by the mutual energy principle,

- N i=1 N i=1,i =j ∞ -∞ " Γ (E i × H j ) • ndΓdt N i=1 N i=1,i =j ∞ -∞ V ( E i ∂ ∂t E j + µH i ∂ ∂t H j )dV dt + N i=1 N i=1,i =j ∞ -∞ V (E i • J j )dV dt (61)
In this situation, the emitter (an electron) has spring done from the higher level to lower level. The the electron in the absorber from lower level spring to the higher level, the current J i and J j are not 0. The self-energy ow satises the Poynting theorem,

- N i=1 ∞ -∞ " Γ (E i × H i ) • ndΓdt N i=1 ∞ -∞ V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt + N i=1 ∞ -∞ V (E i • J i )dV dt (62)
This author assume that there is the time-reversal wave which satisfy the time-reversal Poynting theorem,

- N i=1 ∞ -∞ " Γ (e i × h i ) • ndΓdt = - N i=1 ∞ -∞ V ( e i ∂ ∂t e i + µh i ∂ ∂t h i )dV dt - N i=1 ∞ -∞ V (e i • j i )dV dt (63)
And the time-reversal self-energy ow can cancel the normal self-energy ow through the self-energy principle, i.e.,

+ ∞ -∞ " Γ (E i × H i ) • ndΓdt - ∞ -∞ " Γ (e i × h i ) • ndΓdt = 0 (64) - ∞ -∞ V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt - ∞ -∞ V ( e i ∂ ∂t e i + µh i ∂ ∂t h i )dV dt = 0 (65) - ∞ -∞ V (E i • J i )dV dt -V (e i • j i )dV dt = 0 (66) ´∞ -∞ ! Γ (E i × H i )
• ndΓdt is the self-energy ow go outside the volume V . -´∞ -∞ ! Γ (e i ×h i )• ndΓdt is the energy ow go inside the volume -´∞ -∞ ! Γ (e i × h i ) • ndΓdt. This two energy ow has the same value and dierent direction and hence canceled.

-´∞ -∞ ˝V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt is the energy decrease of volume V . When this decrease, -´∞ -∞ ˝V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt will increase the value.
-´∞ -∞ ˝V (E i • J i )dV dt is the energy oered by the source J i . -˝V (e i • j i )dV dt is energy is the energy received by the direction of j i . This two terms cancel each other.

Hence, all self-energy items together have no eect on the current J i . Hence, we can safely say that the self-energy ow has no any physical eect.

All physical eect comes from the mutual energy terms Eq.( 61), this formula tell us that the electron in the emitter has spring from higher level to a lower level. For the absorber the electron has spring from a lower level to a higher level.

The electron spring from level to another level can be explain as the current J i .

The mutual energy ow bring the energy from emitter to the absorber. This energy is the energy of the photon. Hence, we can say that the photon is the mutual energy ow.

Anti-photon

Anti-photon can be described by the time-reversal mutual energy principle which satises,

N i=1 N i=1,i =j ∞ -∞ " Γ (e i × h j ) • ndΓdt = N i=1 N i=1,i =j ∞ -∞ V ( e i ∂ ∂t e j + µh i ∂ ∂t h j )dV dt + N i=1 N i=1,i =j ∞ -∞ V (e i • j j )dV dt (67)
For an anti-photon the time-reversal self-energy ow satises,

N i=1 ∞ -∞ " Γ (e i × h i ) • ndΓdt N i=1 ∞ -∞ V ( e i ∂ ∂t e i + µh i ∂ ∂t h i )dV dt N i=1 ∞ -∞ V (e i • j i )dV dt (68)
and the self-energy ow satises,

- N i=1 ∞ -∞ " Γ (E i × H i ) • ndΓdt N i=1 ∞ -∞ V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt + N i=1 ∞ -∞ V (E i • J i )dV dt (69)
The time-reversal self-energy ow is canceled by the self-energy ow through the self-energy principle,

- ∞ -∞ " Γ (E i × H i ) • ndΓdt + ∞ -∞ " Γ (e i × h i ) • ndΓdt = 0 (70) ∞ -∞ V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt + ∞ -∞ V ( e i ∂ ∂t e i + µh i ∂ ∂t h i )dV dt = 0 (71) ∞ -∞ V (E i • J i )dV dt + ∞ -∞ V (e i • j i )dV dt = 0 (72)
For an anti-photon the energy is transferred by time-reversal mutual energy ow Eq.( 67). We do not assume that the retarded wave E i , H i and the advanced wave E j , H j will produce any mutual energy ow. If it produces the mutual energy ow, this energy ow will cancel the time-reversal mutual energy ow. In this situation the anti-photon will not produced. We assume it is possible the anti-photon does not produced, but it is also possible an anti-photon is produced.

The anti-photon often cancel the partial photon or half photon. If two absorbers receive the energy of one photon (energy is sent from one emitter), each absorber can only get the energy of a half photon. The electron in the absorber can only spring to a half way from lower level to the higher level. In this situation the anti-photon will produced, the half photon is canceled by an anti-half photon. The electron spring up a half way to the higher level will spring back to the low level again. This way the anti-photon can eliminate all half photons or partial photons.

Summary

There 3 dierent radiation modes, 1) unsuccessful radiation. This radiation make the wave become a probability wave. The wave is happened but there is no any energy sending out. The wave looks like ghost wave or probability waves.

2) Photon situation, the radiation is successful. The retarded wave sent out has met an advanced wave. Hence, produced the mutual energy ow. The photon's energy is carried by the mutual energy ow. The mutual energy ow bring the energy from the emitter to the absorber. The self-energy terms are all canceled by the time-reversal waves. The time-reversal waves do not produce any time-reversal mutual energy ow. The mutual energy ow is produced by the synchronized of the retarded wave and the advanced wave. Since the retarded waves and the advanced wave are randomly sends out by the emitters and absorbers, The synchronization of the two waves is also a random events.

Hence, the photon sends from the source can only be randomly received by many absorbers in the screen. Since the mutual energy ow is produced by the retarded wave and the advanced wave, if there are double slits, the mutual energy ow can have interference stripes.

3) Anti-photon. Anti-photon is just the mirror situation of the photon.

Anti-photon can cancel the normal photon. However, normally the anti-photon happens when the energy is equal to a half-photon or a partial photon. Since the exist of the the anti-photon, all half-photons and partial photons are eliminated.

4) Since there is the anti-photon, the energy can oscillate between the light source and the light receive screen. Among these oscillates, perhaps there will some absorber received much much more energy, if received energy larger than a photon, the absorber can receive, this energy is a photon. The overplus of the energy is sent back through an anti-photons. In the photon-receiving screen, the place where can received a photon is propositional to the size of the area and the square of the amplitude of the retarded wave. This explains the reason of the probability in the quantum mechanics.

It should be noticed, the charge movement of the absorber is not because of the the electromagnetic eld of the emitter. This movement randomly happens and is independent to the emitter. If the movement of the charge in absorber is because of the emitter, for example the emitter's electromagnetic eld drive the charge to move, if the absorber become innite far a way from the emitter, the eld become innite small, and there is no any possibility to obtained enough energy as large as a photon. However we know the absorber can always receive a whole photon even it is innite far away from the emitter.

According to the traditional electromagnetic eld theory, the charge movement is because of the eld of the source. The energy ow is carried by the energy ow corresponding to the Poynting vector, which is the self-energy ow of the charge. When the absorber is far away from the emitter, the absorber can receive one whole photon means its eective scattering section area become innite. A emitter can have a innite scattering section area means the energy ow calculation based on the Poynting vector is wrong. Self-energy ow do not carry the energy, the energy ow is the mutual energy ow.

If we apply the theory of the mutual energy principle, the current of the absorber is independent to the current of the emitter. Both are randomly run, however there is a energy ow from emitter go to the absorber.

This can be widen to the tradition electromagnetic eld theory, for example a current inside a receiving antenna or a secondary coil of a transformer, is not caused by the electromagnetic eld of the transmitting antenna or primary coil of the transformer. The charge inside the receiving antenna or a secondary coil of a transformer runs randomly and spontaneously. The movement of the the charge inside the receiving antenna or a secondary coil can obtained energy from through the mutual energy ow built between the transmitting antenna and the receiving antenna or between the primary coil and the secondary coil. When this charge received the energy the movement is encouraged and conrmed, this will further increase the movement. Otherwise there is always a randomly happened movement which is at the opposite direction and will cancel the movement.

Dierent axiom systems

In this section we discuss which formula should be chosen as axioms. What is the advantage and disadvantage of these choices.

The mutual energy principle can be applied as axiom

What should be chosen as axioms for the radiation system. For example in the case of photon see subsection 4.2, the axioms can be chosen is the mutual energy principle, The Maxwell equations can be derived from the mutual energy principle, hence, the Maxwell equations do not need to be applied as axioms.

The time-reversal Maxwell equations and the self-energy principle should also be applied as axioms. The time-reversal Maxwell equations has two equations which can be replaced by the corresponding Poynting theorem, which is only one formula. This axiom system has 3 formulas, i.e., one mutual energy principle, one self-energy principle and one time-reversal Poynting theorem. The selfenergy principle which tell us that the self-energy ow is canceled by the timereversal self-energy ow.

In this situation the superposition principle is not necessary. The superposition principle can be derived from the mutual energy principle. Assume in the system there are N charges.

Axiom 1) the mutual energy principle:

-

N i=1 N i=1,i =j ∞ -∞ " Γ (E i × H j ) • ndΓdt N i=1 N i=1,i =j ∞ -∞ V ( E i ∂ ∂t E j + µH i ∂ ∂t H j )dV dt + N i=1 N i=1,i =j ∞ -∞ V (E i • J j )dV dt (73)
Axiom 2) time-reversal Poynting theorem:

∞ -∞ " Γ (e i × h i ) • ndΓdt = ∞ -∞ V ( e i ∂ ∂t e i + µh i ∂ ∂t h i )dV dt + ∞ -∞ V (e i • j i )dV dt (74)
One Poynting theorem is equivalent to the two Maxwell equation formulas. This is also true to the time-reversal Poynting theorem.

Axiom 3) the self-energy principle:

-

∞ -∞ " Γ (E i × H i ) • ndΓdt + ∞ -∞ " Γ (e i × h i ) • ndΓdt = 0 (75) ∞ -∞ V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt + ∞ -∞ V ( e i ∂ ∂t e i + µh i ∂ ∂t h i )dV dt = 0 (76) ∞ -∞ V (E i • J i )dV dt + V (e i • j i )dV dt = 0 (77)
This 3 formulas can be summed together and hence put in one formula. Hence, we only count them as one formula.

In this situation Maxwell equations can be derived from the mutual energy principle. This has been done in subsection 2.2.

The superposition principle can also be derived from the mutual energy principle. However, it is should be noticed, the superposition principle derived from the mutual energy principle is a reduced superposition principle, which says that all the retarded waves can be superposed or all advanced waves can be superposed. Or the superposition is that with a test charge. This problem is more complicated we have a separated paper to deal the problem [START_REF] Shuang Ren Zhao | 5 dierent superposition principles with/without test charge, retarded waves/advanced waves applied to electromagnetic elds or the photons[END_REF].

It should be make clear about the current J i . J i is current when an electron from higher energy level spring down to an energy lower level or an electron from a lower level spring up to a higher level. This current doing work to both mutual energy ow and self-energy ow. For simple we assume N = 2. Considering J 1 is the source. The work is done for the mutual energy is

∞ -∞ V (E 2 • J 1 )dV dt (78)
The work is done for the self energy is,

∞ -∞ V (E 1 • J 1 )dV dt (79)
J 1 can be seen as a current source, E 2 and E 1 can be seen as two loads to the source J 1 . The two loads are connected in series, See Figure 6.

Since the two loads are connected in series, it can be divided as two independent circuits Figure .

For j 1 it connected also a load e i see Figure 8. The two works done by the current J 1 and the return current j 1 has canceled part, the results of cancellation is that only the work corresponding to the mutual energy is left, see Figure 9. That is the following part of work corresponding to the mutual energy is left.

∞ -∞ V (E 2 • J 1 )dV dt (80)
This means the self-energy principle allow the time-reversal Maxwell equations cancels the contribution of the Maxwell equations. After this, only the work corresponding to the mutual energy survived.

Maxwell equations for the superposed eld and superposition principle as axiom

Axiom 1) the the Maxwell equations for the superposed eld, which is, E, H.

The Maxwell equation can be replaced by the Poynting theorems:

-

∞ -∞ " Γ (E × H) • ndΓdt = ∞ -∞ V ( E ∂ ∂t E + µH ∂ ∂t H)dV dt + ∞ -∞ V (E • J )dV dt (81)
Axiom 2) the superposition principle which are:

     E = N i=1 E i H = N i=1 H i J = N i=1 J i (82) Axiom 3) time-reversal Poynting theorem: ∞ -∞ " Γ (e i × h i ) • ndΓdt = ∞ -∞ V ( e i ∂ ∂t e i + µh i ∂ ∂t h i )dV dt + ∞ -∞ V (e i • j i )dV dt (83)
Axiom 4) the self-energy principle:

-

∞ -∞ " Γ (E i × H i ) • ndΓdt + ∞ -∞ " Γ (e i × h i ) • ndΓdt = 0 (84) ∞ -∞ V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt + ∞ -∞ V ( e i ∂ ∂t e i + µh i ∂ ∂t h i )dV dt = 0 (85) ∞ -∞ V (E i • J i )dV dt + V (e i • j i )dV dt = 0 (86)
In this situation, substitute axiom 2) to axiom 1) we can obtain,

- N i=1 N i=1 ∞ -∞ " Γ (E i × H j ) • ndΓdt = N i=1 N i=1 ∞ -∞ V ( E i ∂ ∂t E j + µH i ∂ ∂t H j )dV dt + N i=1 N i=1 ∞ -∞ V (E i • J j )dV dt (87)
consider the self-energy principle 4) the self-energy terms has no contribution to the energy transfer, it can taken away from the above formula that means all the terms

- N i=1 ∞ -∞ " Γ (E i × H i ) • ndΓdt N i=1 ∞ -∞ V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt + N i=1 ∞ -∞ V (E i • J i )dV dt (88)
can be taken away from Eq.( 87). Hence we obtain,

- N i=1 N i=1,i =j ∞ -∞ " Γ (E i × H j ) • ndΓdt N i=1 N i=1,i =j ∞ -∞ V ( E i ∂ ∂t E j + µH i ∂ ∂t H j )dV dt + N i=1 N i=1,i =j ∞ -∞ V (E i • J j )dV dt (89)
This is the mutual energy principle. Hence, we have proved from the second axiom system to the rst axiom system.

Maxwell equations for the single charge is applied as axioms

Maxwell equations for single charge can be written as,

Lξ = 1 τ (90)
where

L = -∂ ∂t 1 ∇× -1 µ ∇× -∂ ∂t (91)
From this we can derive the mutual energy principle, by using the Mathe-

matical formula, ∞ -∞ ((ξ 2 , Lξ 1 ) V + (Lξ 2 , ξ 1 ) V )dt = - ∞ -∞ V ( E 1 ∂ ∂t E 2 + E 2 ∂ ∂t E 1 + µH 1 ∂ ∂t H 2 + µH 2 ∂ ∂t H 1 )dV - " Γ (E 1 × H 2 + E 2 × H 1 ) • ndΓ (92)
Hence, we obtained the mutual energy principle,

∞ -∞ ((ξ 2 , 1 τ 1 ) V + ( 1 τ 2 , ξ 1 ) V )dt = - ∞ -∞ V ( E 1 ∂ ∂t E 2 + E 2 ∂ ∂t E 1 + µH 1 ∂ ∂t H 2 + µH 2 ∂ ∂t H 1 )dV - " Γ (E 1 × H 2 + E 2 × H 1 ) • ndΓ (93)
Then we need also add the self-energy principle and time-reversal Maxwell equations.

5.4 Compare the two axiom systems advantage of the rst axiom system is the formulas are less. The mutual energy principle is applied as axiom which can easily to derive the mutual energy theorem and mutual energy ow theorem. The Maxwell equation can be derived from the Mutual energy principle. Here, the important thing is there are two group Maxwell equations that are synchronized. These theorem can be applied to electromagnetic eld calculation.

The advantage axiom of the second system is it more close to the current text book of the electromagnetic eld theory. We only need to add the self-energy principle and the time-reversal Poynting theorem on the top of the original electromagnetic eld theory of the current text book.

The advantage axiom of the third system is that it also works. The only things is if the Maxwell equations of single charge applied as axiom, when we derive the formula of mutual energy principle, it is dicult to realize that the mutual energy principle is the real physical formula, hence, we need to solve the mutual energy principle to obtain a pair of single charge. Hence, if the Maxwell equation for single charge used as axiom we should mention that the Maxwell equations should paired. One is for the retarded wave and the other is for advanced wave. However, this make things too complicated. The complicate things for example, it the retarded wave and the advanced wave should put in the simple formula and is derived later.

Hence, this author would like to apply the mutual energy principle as the axioms for electromagnetic eld theory. The mutual energy principle should be derived out from the original electromagnetic eld theory plus to consider the energy conservation law.

6 Compare the theory of the mutual energy principle with the traditional electromagnetic theory

In this section we summary what the dierence is between the author's theory of the mutual energy principle and the traditional electromagnetic theory.

The author's theory can also started from Maxwell equations for single charge,

-∂ ∂t ( E i + ∇ × H i = J i -∇ × E i -∂ ∂t (µH i ) = 0 (94)
This author assume that the energy conservation law is correct:

N i=1 N j=1,j =i ∞ t=-∞ V (E i • J j )dV dt = 0 (95)
However, this author does not assume the superposed Maxwell equations together with superposition principle is correct,

-∂ ∂t ( E) + ∇ × H = J -∇ × E -∂ ∂t (µH) = 0 (96)      E = N i=1 E i H = N i=1 H i J = N i=1 J i (97)
From Maxwell equations Eq.(94) we can derived the mutual energy principle,

- N i=1 N i=1,i =j ∞ -∞ " Γ (E i × H j ) • ndΓdt N i=1 N i=1,i =j ∞ -∞ V ( E i ∂ ∂t E j + µH i ∂ ∂t H j )dV dt + N i=1 N i=1,i =j ∞ -∞ V (E i • J j )dV dt (98)
From the mutual energy principle, we can derive the mutual energy theorem which is just the energy conservation law Eq.(95). This further tell us the mutual energy principle is correct. From mutual energy principle we can further derive that the Maxwell equations which must pair together, i.e. there are two groups Maxwell equations, one is for the retarded wave and another is for the advanced wave.

The next step is consider the superposition principle with the Maxwell equations Eq.( 96). This Maxwell equations are not same as the Maxwell equations for N charges. Substitute the superposition principle to the Maxwell equations we obtain,

- N i=1 N i=1 ∞ -∞ " Γ (E i × H j ) • ndΓdt = N i=1 N i=1 ∞ -∞ V ( E i ∂ ∂t E j + µH i ∂ ∂t H j )dV dt + N i=1 N i=1 ∞ -∞ V (E i • J j )dV dt (99)
This can be divided as the mutual energy part,

- N i=1 N i=1,i =j ∞ -∞ " Γ (E i × H j ) • ndΓdt = N i=1 N i=1,i =j ∞ -∞ V ( E i ∂ ∂t E j + µH i ∂ ∂t H j )dV dt + N i=1 N i=1,i =j ∞ -∞ V (E i • J j )dV dt (100)
and the self-energy part,

- N i=1 ∞ -∞ " Γ (E i × H i ) • ndΓdt N i=1 ∞ -∞ V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt + N i=1 ∞ -∞ V (E i • J i )dV dt (101)
Eq.( 100) is the mutual energy principle which we have accept it as correct, but we got another extra-formula Eq.(101). In order to solve the problem of the extra-formula we have to introduce the self-energy principle and the timereversal Maxwell equations,

-∂ ∂t ( e i ) -∇ × h i = j i ∇ × e i -∂ ∂t (µh i ) = 0 (102)
and the self-energy principle,

- ∞ -∞ " Γ (E i × H i ) • ndΓdt + ∞ -∞ " Γ (e i × h i ) • ndΓdt = 0 (103) ∞ -∞ V ( E i ∂ ∂t E i + µH i ∂ ∂t H i )dV dt + ∞ -∞ V ( e i ∂ ∂t e i + µh i ∂ ∂t h i )dV dt = 0 (104) ∞ -∞ V (E i • J i )dV dt + V (e i • j i )dV dt = 0 (105)
After we have assumed the above self-energy principle and time-reversal Maxwell equations, the superposition principle superposed Maxwell equations can also be applied. The conict of the electromagnetic eld theory is solved.

In the derivation of this section we can see that we still started from Maxwell equations for single charge.

For myself, we rst meet the mutual energy theorem for two antenna,

V2 (E 1 (ω) • J * 2 (ω)dV = - V1 E * 2 (ω) • J 1 (ω))dV (106)
I did not realize it is an energy conservation law. However when I wrote the widened version for N charges,

N i=1 N j=1,j =i ∞ t=-∞ V (E i • J j )dV dt = 0 (107)
This author realize it is a energy conservation law. Eq.( 106) can be easily understand as a energy theorem, but it is dicult to be realize as an energy conservation law for only two charges.

Hence, this author would just started from Maxwell equations, that is traditional electromagnetic eld theory. On this base plus the energy conservation law. Pointer out the conict. From this conict, we obtained the formula of the mutual energy principle. Then we need point out the mutual energy principle now is the new axiom of the electromagnetic eld theory.

Then started from the mutual energy principle, we can derive the pair of Maxwell equations, one is for the retarded wave, one is for the advanced wave.

When the we obtained two Maxwell equations we can derive the Poynting theorems, the Poynting theorem will tell us there will have the self-energy ow, the self-energy ow oers additional energy on the top of the energy conservation law. In order to satisfy the energy conservation law, we must introduce the selfenergy principle and the time-reversal Maxwell equations. After introduced the time-reversal Maxwell equations and self-energy principle, the self-energy ow do not have any contribution to the energy transfer. This further guarantees the energy conservation law is satised.

Conclusion

This article compared the two axioms system, one is Maxwell equations, another one is the mutual energy principle and self-energy principle introduced by this author. The two system are equivalent in the meaning they can be derived by each other. The mutual energy principle can be derived from the Maxwell equations, the Maxwell equations can also be derived from the mutual energy principle. However the two systems are not exactly same. That is because if the mutual energy principle is applied as axiom, it need two groups Maxwell equations together as a solution. One group of the Maxwell equations is corresponding the retarded wave, another is corresponding the advanced wave. A retarded wave alone or an advanced wave alone is not the solution of the mutual energy principle, but it is a solution of the Maxwell equations.

This author also found that the Poynting theorem and hence, Maxwell equa- In this article we have also introduced 3 modes of radiation: (1) photons,

(2) anti-photons, (3) unsuccessful radiation. Photon is the mutual energy ow.

Anti-photon is the time-reversal mutual energy ow. Unsuccessful radiation is the situation the retarded wave is sent out but it did not found any advanced wave to synchronized and hence collapse back. The energy of a photon is transferred by the mutual energy ow. The self-energy principle guarantees the energy still travel in space will be cleared. The retarded wave and the advanced wave together build the the mutual energy ow, but the mutual energy ow is additional energy ow, the original energy ow of the retarded wave and the advanced wave still in space. It need to be cleared.

Figure 1 :

 1 Figure 1: In the volume V , there are source J 1 , sink J 2 , J 1 sends the retarded wave [E 1 , H 1 ]. J 2 sends the advanced wave [E 2 , H 2 ].

Figure 2 :

 2 Figure 2: In the volume V 1 , there are only the source J 1 , the sink J 2 is at the outside of the volume V 1 , J 1 sends the retarded wave [E 1 , H 1 ]. J 2 sends the advanced wave [E 2 , H 2 ].

Figure 3 :

 3 Figure 3: In the volume V 2 , there are only the source J 2 , the source J 1 is at the outside of the volume V 2 , J 1 sends the retarded wave [E 1 , H 1 ]. J 2 sends the advanced wave [E 2 , H 2 ]. The norm vector of the surface is n12 .

Figure 4 :

 4 Figure 4: In the volume V 1 , there are only the source J 1 , the sink J 2 is at the outside of the volume V 1 , J 1 sends the retarded wave [E 1 , H 1 ]. J 2 sends the advanced wave [E 2 , H 2 ]. The norm vector of the surface is n12

3. 3

 3 The relation of Maxwell equations vs the mutual energy principle and the self-energy principle solution of M axwell equation ⊃ solution of mutual energy principle The solution of Maxwell equations include the retarded wave solution and advanced wave solution. The solution of Mutual energy principle has the solution only when the retarded wave and the advanced wave are synchronized. solution of (M axwell equation+self energy principle+timereversed M axwell equation) = solution of (mutual energy principle+self energy principle+timereversed M axwell equation) The solution of Maxwell equations are bigger concept set than the solution of the mutual energy principle. The solution of Maxwell equations has some kind of solution we can call it as weak solution in physics, that is the retarded wave and the advanced wave alone without synchronization. There is the strong solution in physics, which are the solutions satisfy the mutual energy principle that is the solution the retarded wave and the advanced wave can be synchronized hence there is the mutual energy ow produced. self-energy principle together with the self-energy principle is the new restrict condition. With this new restrict condition the weak solution in physics has been role out from the Maxwell equations, the rest are the strong solution which satisfy the mutual energy principle.This also means that the really new principle are the self-energy principle and the time-reversal Maxwell equations. The mutual energy principle and Maxwell equations can be exchangeable. However, since the mutual energy principle is only one formula, the Maxwell equation is two formulas, the mutual energy principle is simpler than Maxwell equations. Maxwell equations cannot work without superposition principle. The mutual energy principle do not need the support of the superposition because the superposition can be derived from the mutual energy principle. Another advantage of the mutual energy principle is the mutual energy ow theorem and the mutual theorem (the conservation law) can be derived from the mutual energy principle easily. All these are usually dicult to be obtained from the Maxwell equations or at least confused people, the reason is most scientist work at Maxwell equations do not accept the advanced wave, since the advanced wave doesn't obey the traditional causality consideration. If we apply the mutual energy principle as the axioms, the advanced wave have to be accept.

  It is notice we have use Poynting theorem replaced the Maxwell equations and use the time-reversal Poynting theorem replace the time-reversal Maxwell equations. This replacement will reduce the number of formula. Because the Poynting theorem is the necessary and sucient condition of the Maxwell equations.

Figure 6 :

 6 Figure 6: Two loads are connected as series.

Figure 7 :

 7 Figure 7: Two loads can be see as two separated circuits.

Figure 8 :

 8 Figure 8: The work is done by the self-energy.

Figure 9 :

 9 Figure 9: The work is done by the mutual energy is left.

  tions together with the superposition principle conict with the energy conservation law. However, the mutual energy principle does not directly conict with the energy conservation law. The mutual energy principle only conict with the energy conservation law through the Maxwell equations. Hence, the author realized that the Maxwell equations need to be modied. Hence, the author introduced the self-energy principle. The self-energy principle tell us that there are another kind of the electromagnetic elds, which satises the time-reversal Maxwell equations. The energy ow of the time-reversal wave can cancel the energy ow of the normal electromagnetic elds. The energy ow of the timereversal wave corresponding to the retarded wave can cancel the energy ow of the retarded wave. The energy ow of the time-reversal wave corresponding to the advanced wave can cancel the energy ow of the advanced wave. All self-energy ows are all canceled. Hence, the self-energy ow do not carry the energy. However, the mutual energy ows survived. There are two kinds of mutual energy ows: the mutual energy ow and the time-reversal mutual energy ow. The energy of photon is transferred by the mutual energy ow. Hence, we can say that photon is the mutual energy ow. The transferred energy from the transmitting antenna to the receiving antenna is also the mutual energy ow.The mutual energy theorem and the mutual energy ow theorem guarantees the energy is transferred by the mutual energy ow. The self-energy principle guarantees the self-energy ow do not transfer or carry any energy. The self-energy ow is the energy ow corresponding the Poynting vector. The time-reversal mutual energy ow can eliminate the half or partial photons which we have discussed before on another article the mutual energy ow interpretation of quantum mechanics.

(34)The corresponding time-reversal Poynting theorem can be derived from the time-reversal Maxwell equations which are,


F Corbier

L Kislin

E Fourgeau

How Train Transportation Design Challenges

Keywords: Transportation, EN50128, Model based Design, Virtual Prototyping, Progressive Integration, Validation, Software Quality, Certification

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

A train is a complex system where many professions and different engineering disciplines are involved: from boiler-making to passenger safety engineers, including Traction-Brake or Quality Services. In this context, electronics take a large place (Figure 1) on one hand in intelligent equipments (doors, traction, brake, light, fire detection…) on the other hand, in the train vertebral column (train control and maintenance system). With the growth of electronic equipments and networks in the train, and the increase of customer quality services and certification constraints, transportation suppliers have been looking for both methods and development tools that are able to:

• Validate the functional specifications and requirements as soon as possible in the project, • Analyse the quality of customer services,

• Validate the safety (equipments and passengers),

• Qualify electronic control units and electro mechanical equipments of suppliers with progressive integration, • Easily manage all changes (requirement modification…) while staying compliant with transportation rules & standards, like EN50128. In the following pages, we are illustrating how novel processes and tools can be successfully used on today's most advanced train projects (intercity, tramway, metro, high speed train).

Historical development cycle

Traditionally in the train transportation industry -and in other industries alike -the design process for embedded electronic boards was built upon a certain number of elementary practices:

• Paper specifications exclusively, prior to the C code elaboration phase which was either generated manually or with programming tools, • Many complicated and mandatory reviews for specification validation, • A "Gate Review" which marked the final decision step before execution, • Back and forth painful iterations between Business Units, Central Office and Sub-Contractors, • Slow project starts due to a lengthy exchange process in the early stage of the project.

Consequently a certain number of productivity issues had to be dealt with:

• A lot of projects missed their delivery deadlines,

• Too much effort was spent on "Paperwork" rather than on development and integration, • Too much time was spent in "meeting" specifications, even in sharing them and making them clear and understandable by all development groups involved, • No "re-use" possible of high level design intellectual investment, • Software Quality was becoming an important concern, • Projects costs were difficult to keep within budget, • Important managerial issues had to be addressed.

Introducing a drastic change

In early 2003, breakthrough decisions were made. Notably, one of the world leading transportation companies moved from a paper based specification approach to an executable specification process, in order to speed up development cycles and meet deadlines.

The process was first launched with Electronic Control Units for Train Control & Monitoring System projects. The ControlBuild technology from TNI-Software was chosen as the common tool platform to achieve new productivity related objectives:

• Use of open ECU hardware platforms,

• Design of a virtual reference prior to any implementation, • Automated allocation of functions on targeted resources with model transformation and code generation, • Scalability to the full train (traction for example),

• Risk mitigation with progressive implementation on HIL platforms (Factory Acceptance Tests),

• Automatic documents generation.

Since then, most of the ControlBuild productivity development technologies have been deployed; their use has been spread along the entire life cycle of the train and equipments, among architects, developers, and integrators.

Concept: Component Based Design

ControlBuild uniqueness is to cover design, validation, hardware integration and verification tests steps in a single integrated process, from components assembly to electronic devices design.

Using components: why? Even though all trains may look different from one another, they have many elements in common, such as functional components, (i.e. the "all doors are closed" function …) and many others. Hence there are sound benefits for a transportation company to manage disciplinary know-how in components libraries.

What is a component?

• A component prime attribute is to be reusable (notably in as many projects as possible). • Therefore a component is not hardware platform dependent; ideally a component is not located in the train, for optimum reuse flexibility reasons. • A component is being defined either as an atomic function (i.e. "select the active cab"), an equipment (i.e. one door sub-system) or the train itself. • A component is described as a multi facetted element, according to several domains viewpoints (Figure 2): end-user, customer, designer, quality engineer or supplier. Creating the functional hierarchy of a sub-system:

The design methodology is based on a top down approach. The first decomposition level identifies all the specific parts of the sub-system (Figure 3). At each level, the expert analyst defines elementary sub functions, and for each one, its interfaces with other functions, the requirements covered, and a rich set of textual descriptions (generalities, usage, functional specification, fault detection, operating modes, availability, safety…). Reuse of know-how: Inversely at each level of the system composition, system engineers have to determine if the functionality exists or not in the company libraries.

They will establish a link on the reusable components so that they don't have to be described again. Users can classify, archive, and reuse their company's know-how in design rule standards and component libraries, so as to improve the productivity and quality of their designs.

Reusability at this level is of significant benefit; it is a mean to win time and money and improve quality.

There are indeed many software tools on the market that allow for "code" reuse: but code reuse only! ControlBuild uniqueness is to enable reuse on all component facets: requirements, behaviour/knowhow models, HMIs, graphical views, textual descriptions, qualification scripts, tests, execution reference...

Design Specifications

Each function can be described using given formalisms -standard languages are favored -that enable component descriptions to be executed. Hence, whatever its granularity, each function comes with an executable model; the model becomes an intrinsic part of the specification, enabling at any stage of the system composition, non ambiguous and interactive discussions between the various actors of the development chain, customers included.

Two execution views are possible, based upon two different use cases:

The first one, called dynamic function execution is using the description language best suited to the function, from either:

• IEC61131-3: this applies to most sequential or combinatory processes, • Low Voltage Schematics: when security levels are implemented on hardware, • Physical models: to describe sensors and actuators, and also physical laws.

The second one is used to show the resulting function to a customer or end-user who is not necessarily a technical expert but owns the high level requirements and specifications of the function.

In this case the execution is providing a highly abstract view of the system, using graphical representations and HMIs (Figure 4). Changing scope from software to hardware centric is not an easy task; in fact ControlBuild is of great help in this process, as described step by step in the methodology detailed hereafter.

Hardware description: First, hardware architecture has to be described in terms of physical resources (virtual targets) and tasks.

Mapping software on hardware architectures: Each function of the virtual train model should be mapped on one task of the hardware architecture (Figure 5).

Eventually the functional models are mapped on the individual hardware resources available and transformed into tasks on the target. Code generation: once each physical target is declared and configured (re: operating system, network address, cycle time of each task…), the software code of each one (Figure 6) will be generated and linked with the dedicated environment (make, libraries …).

Figure 6: Code Generation multi-target/multi-CPU whichever modifications or upgrades are made to the project.

Conclusion

The quantitative value proposition of such an approach in terms of productivity gains and organizational effectiveness is promisingunfortunately it is not public information.

Figure 1 :

 1 Figure 1: two hundred networked ECUs There are today stiff requirements to become more efficient in designing and delivering on-board electronic devices, notably: • To keep control on costs despite increasing challenges set by electronics complexity, • To compensate by a better use of technology the organisational issues imposing less people to do more and faster.

Figure 2 :

 2 Figure 2: A Component with multiple Views

Figure 3 :

 3 Figure 3: Mixed Top-Down & Bottom-Up methodology

Figure 4 :

 4 Figure 4: Graphical end-user view This second view is called the animated graphical prototype. With this view, ControlBuild offers powerful means to verify as early as possible the system's conformance to the requirements. Other viewpoints or component facets can be described, such as specifications and design documents, qualification scripts, formal tests, maintenance profiles, integration guidelines,… 5.3. Hardware-Software Integration At this step of the development cycle, all functionalities and requirements have been taken into account and validated by engineers from both customers & suppliers sides. Now comes the time for the Transportation Company to change scope and start mapping the functional model on the target networked hardware architecture.Changing scope from software to hardware centric is not an easy task; in fact ControlBuild is of great help in this process, as described step by step in the methodology detailed hereafter.

Figure 5 :

 5 Figure 5: Mapping functions on hardware

  Intangible benefits are not to be left behind either: Executable specifications allow: o Easy validation and design reviews with both internal and external non experts groups o Robust implementation with virtual simulation. Integration/simulation/test platforms can be created at a fraction of time compared to before. Full Functional HIL validation is possible, with on time delivery. ECU Electronic Control Unit ERTS Embedded Real Time Software HIL Hardware In the Loop SRS Software Requirement Specification SDS Software Design Specification SAD Software Architecture Description SMDS Software Modules Design Specification SMTP Software Modules Tests Procedure TCMS Train Control and Monitoring System

	8. Glossary

Requirements and specifications: the output of this step is a Requirement & Specification Document for the equipment manufacturer. The elaboration of this document is entirely automated.

Progressive Integration

The integration of all train functions is progressive. By this we mean first integration and validation of individual ECUs and equipments, then integration and validation of ECUs contributing to a train function, finally integration and validation of all train functions. Each integration step is implementing real equipments. It is obviously much simpler to integrate single equipment from a given supplier, than to proceed to the complete integration of all electronic equipments of the train, in one go -not only for costs reasons, but primarily since it is quite impossible to get all of the 200 ECUs of the train simultaneously! The risk mitigation approach enabled by ControlBuild at this stage is unique : starting from the virtual model of the complete train architecture, the tool provides mechanisms to declare physical equipments as they become available for integration. Equipments available for integration are then connected to the integration test bench and disabled in the virtual model.

Figure 8: Multiple levels of connexion

Hence the virtual model progressively integrates the real physical elements, at the same time as it provides a virtual environment model for these same physical elements (Figure 9). This approach brings high value benefits: it allows a productive support of system evolutions over the complete train lifecycle, i.e. 30 to 40 years. This is notably the case with all non regression tests mandated by the progressive obsolescence over time of some ECUs.

Documentation management

The various steps of a given train transportation development project are producing an incredible amount of documents (re: EN50128). Previously this was a huge burden on designers, who had to keep focus on writing these documents. With the novel ControlBuild processes, designers are spending time on design and much less on paperwork : "make it work", "make it work according to customers requirements" is of essence. During the composition, modeling and validation phases, each component at each level receives textual information (functions, operation modes, safety, …) as well as requirement coverage scores. This is enabling a fully automated document generation step, capable of covering the entire project needs, notably:

Software Requirement Specification Software Design Specification Software Architecture Description Software Modules Design Specification Software Modules Tests Procedure…

Centralizing/binding all project information in a global model, ensures that all project related documents always stay consistent and cohesively updated,