Shuang-Ren Zhao
email: shrzhao@gmail.com

and the wave of Schrödinger equation

Keywords: photon, electron, retarded wave, advanced wave, time-reversal, absorber, emitter, action-at-a-distance, Maxwell, Poynting, Schrödinger, Dirac, mutual energy, PACS:41.20.Jb, 03.50.De, 03.65.Ta

The relation between the particle of the mutual energy principle and the wave of Schrödinger equation

Shuang-Ren

I. 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 the advanced wave is real. Wheeler and Feynman have introduced the absorber theory which involved the advanced wave [1] [2].

The absorber theory is based on the action-at-a-distance [8,20,23]. 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]. 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], Rumsey's reciprocity theorem [START_REF] Rumsey | Reaction concept in electromagnetic theory[END_REF], 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 application of mutual energy formula in expansion of plane waves[END_REF][START_REF] Zhao | The simplication of formulas of electromagnetic elds by using mutual energy formula[END_REF]. de Hoop's reciprocity theorem [START_REF] Adrianus | Time-domain reciprocity theorems for electromagnetic elds in dispersive media[END_REF]. 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 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, these theorems are an energy theorem. 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 [12 18, 21]. 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 selfenergy 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 photons 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 returned 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 time-reversal 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 a to point b. Here a is the source of the energy ow, b is the sink of the energy ow. It can be proven that the shape of the mutual energy ow is thin in the two ends a and b, it is thick in the middle between a and b. Hence, the mutual energy ow looks like a wave in the middle between a and b and the mutual energy ow looks like a particle at the ends of a and b. Hence, photon is not wave or particle but the mutual energy ow.

In this article the concept of the mutual energy principle, self-energy principle, mutual energy theorem, mutual energy ow theorem is extended to the system of the quantum mechanics, where Schrödinger equation is applied instead of Maxwell equations.

It is often said that the Schrödinger equation only has the solution of the retarded wave.

However, this author found that if we allow the distance of a point to the origin has a negative value, the Schrödinger equation can have the advanced solution. After we obtained the advanced wave solution of Schrödinger equation, all theory of mutual energy can be extended from the electromagnetic elds to quantum mechanics. This all will be show in this article.

II. RETARDED AND ADVANCED WAVE SOLUTIONS FOR THE SCHRÖDINGER EQUATION

We assume that the quantum for example electron runs in the empty space from point a to b. This electron must satisfy the Schrödinger equation,

i ∂ ∂t Ψ(r, t) = -2 2µ ∇ 2 + V (r, t) Ψ(r, t) (1)
where i = √ -1. Ψ(r, t) is the wave function. In the free space the amplitude of the wave function will decrease with distance, hence we have

Ψ(r, t) = 1 r exp(-(jωt -kr)) (2)
where we assume that if the wave is retarded wave, then

r = +||x -x || (3)
if the wave is advanced wave,

r = -||x -x || (4)
x is the eld point. x is the source point. Eq.( 2) is correct at least at the place of far eld where r is not too small. Eq.( 2) can be a retarded wave. Hence normally we speak that Figure 1. The region of the retarded wave and the advanced wave. The distance r can be negative.

For an advanced wave the distance r is negative.

the Schrödinger equation only has the solution of the retarded wave. However, if we allow the the distance r has the negative values4. The Eq.( 2) can also be applied to the advanced wave.

For example when t take a negative value: t = -|t|, r also take a negative value for example r = -|r|, this is a place for an advanced wave. When we allow the distance r has negative value, Schrödinger can have the advanced wave solution. See Figure 1.

III. MUTUAL ENERGY PRINCIPLE FOR SCHRÖDINGER EQUATION

A. Operator of the Schrödinger equation

The Schrödinger equation can be written as, LΨ(r, t) = 0

where, L referred as Schrödinger operator and is dened as, L ≡ -

2 2iµ ∇ 2 + 1 i V (r, t) Ψ(r, t) - ∂ ∂t Ψ(r, t) (6)
We assume the Schrödinger equation also has the source or sink, LΨ(r, t) = S [START_REF] Adrianus | Time-domain reciprocity theorems for electromagnetic elds in dispersive media[END_REF] where S is the source or sink. The source of Schrödinger equation can be at very small region for example, the source of an electron is inside an atom. Some reader perhaps will argue how you know there is a source and sink for Schrödinger equation? This author doesn't know whether or not there are source or sink for Schrödinger equation. However it always possible to have articial source or sink based on Huygens principle. That means the source will be just a place the wave goes to outside from an atomic system to the empty space.

The sink just a place the wave goes from empty space to the inside of an atomic system.

B. A mathematics formula for the operator L

Dene the inner product in the volume V ,

(Ψ b , Ψ a ) V = V Ψ * b Ψ a dV (8)
A mathematical formula can be proved as following,

(Ψ b (r, t), LΨ a (r, t)) V + (LΨ b (r, t), Ψ a (r, t)) V = - " Γ J ab • nΓdt - ∂ ∂t V udV dt (9)
where L is dened at Eq.( 6). V is any volume in the space. Γ is the boundary surface of the volume V . And the mutual energy ow intensity is dened as,

J ab ≡ 2µi (Ψ * b ∇Ψ a -∇Ψ * b Ψ a ) (10)
The mutual energy intensity is dened as,

u ≡ Ψ * b Ψ a (11)
See the Appendix VIII for details of the proof. Eq.( 9) is only a mathematical formula instead of a physic formula, because Schrödinger equation has not applied on it which is the physical formula.

C. Deriving the mutual energy principle from Schrödinger equation

The above Eq.( 9) is a mathematical formula, now let us consider the equation of physics, which is Schrödinger equation, assume in the two point a and b has the sources S a and S b we have the Schrödinger equations,

LΨ a (r, t) = S a (12) LΨ b (r, t) = S b (13)
In the above Schrödinger equation we have add two sources, when we speak a source, it can be also a sink. We assume S a is a source, it sends out the energy of the particle and S b is a sink, it receives the energy of the particle.

Substitute the above two equations to Eq.( 9) we can obtain the mutual energy principle corresponding Schrödinger equation,

-

" Γ J ab • nΓ - ∂ ∂t V udV = (Ψ b (r, t), S a ) V + (S b , Ψ a (r, t)) V (14)
This means, that if we have the Schrödinger equation, we can derived the corresponding mutual energy principle Eq.( 14). In the above formula the energy ow to the inside of the volume is -! Γ J ab • nΓ which is equal to the energy increase inside the volume ∂ ∂t ˝V udV and consumed energy of the two source S a and S b :

(Ψ b (r, t), S a ) V + (S b , Ψ a (r, t)) V .

D. Deriving Schrödinger equation from the mutual energy principle

In other hand, if we have the above mutual energy principle Eq.( 14), comparing it with the mathematical formula Eq.( 9) we can obtained a pair of Schrödinger equations Eq. [START_REF] Shuang Ren Zhao | The modied poynting theorem and the concept of mutual energy[END_REF][START_REF] Shuang Ren Zhao | Antenna calculation in lossy media with mutual energy theorem[END_REF], hence, Schrödinger equations can be derived from the mutual energy principle. The mutual energy principle can be derived from Schrödinger equation and the Schrödinger equation can be derived from the mutual energy principle, does this means that the mutual energy principle and Schrödinger equation are equivalent? This will be discussed in the following section.

IV. THE DIFFERENCE BETWEEN SCHRÖDINGER EQUATION AND THE MUTUAL ENERGY PRINCIPLE

It should notice that, even we can derive from the Schrödinger equation to the corresponding mutual energy principle and we can derive the Schrödinger equation from the corresponding mutual energy principle, but this does not mean that the Schrödinger equation is equivalent to the mutual energy principle. This can be seen by the following reasons.

1. The mutual energy principle needs at least a pair Schrödinger equations exist simultaneously. That means a pair Schrödinger equations must be synchronized. Since if we have known that,

Ψ b (r, t) ≡ 0, S b ≡ 0 (15)
for example, substituting this to the mutual 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], we can obtain

Ψ a (r, t) = anything < ∞ (16)
Is a solution of the mutual energy principle. However, this is not an accepted solution.

This means that if we started from mutual energy principle, we cannot get a solution which satises only one Schrödinger equation. We can obtained only a solution with a pair of Schrödinger equations. One solution of the Schrödinger equations is not an accepted solution for the mutual energy principle.

In other hand, if we apply the Schrödinger equation as axiom, any the solution which satisfy only one Schrödinger equation is an accept solution.

The concept of a pair solutions, it is suitable to the concept of action-at-a-distance.

In the theory action-at-a-distance [8,20,23], an action need at least two points an source (emitter) and an sink (absorber). Only a source without sink can not be accepted. Only a sink without a source can also not be accepted. A particle is an action which needs a source and a sink. The source give the sink a action, a sink will give the source a re-action.

The action and the re-action is look like a particle. The particle is the action and reaction between a source and a sink.

the Maxwell equations. The self-energy ow of Schrödinger equation J aa , J bb "

Γ J aa • nΓdt = 0, " Γ J bb • nΓdt = 0 (17)
where Γ can be a surface of innite big sphere and where J aa ≡ 2µi (Ψ * a ∇Ψ a -∇Ψ * a Ψ a ) will go outside the universe, that is not possible. It is same for

J bb ≡ 2µi (Ψ * b ∇Ψ b -∇Ψ * b Ψ b ).
The mutual energy ow J ab , in other hand, can not go to the outside of our universe:

" Γ J ab • nΓdt = 0 (18)
Where J ab is related a source and a sink. Ψ b , Ψ a are two waves. Here, we assume that one of them is the retarded wave and one of them is the advanced wave. The two waves reach the innite sphere Γ one is at a future time and another one is at a past time. Hence, the two waves cannot nonzero at the sphere simultaneously. Hence, we have 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]. In other side if the two waves are all retarded wave or all advanced wave, it is not possible to obtain Eq.( 18). Hence, starting from mutual energy principle as axiom, it automatically require the existence of the advanced wave and the advanced wave has to be synchronized with the retarded wave.

3. From mutual energy principle it is easy to obtained the mutual energy theorem and mutual energy ow theorem which can be used to prove that the mutual energy ow looks like a particle in the place of two ends and looks like wave in the middle between the two ends. This will solve the wave-particle paradox. This will be discussed in the next section.

V. THE MUTUAL ENERGY AND THE MUTUAL ENERGY FLOW THEOREMS A. The mutual energy theorem

Assume U = ˝V udV dt. We can assume U (t = ∞) = U (t = -∞). U (t = -∞) is the energy before the particle emitted at the source a, U (t = ∞) is the energy after the particle

has reached b. Hence, U (t = ∞) should equal to U (t = -∞),hence we have, ∞ t=∞ ∂ ∂t V udV dt = ∞ t=∞ ∂ ∂t U dt = U (t = ∞) -U (t = -∞) = 0 (19)
Substituting Eq.( 18) to the mutual energy principle Eq.( 14) we have

- ∞ t=∞ " Γ J ab • nΓ = ∞ t=∞ ((Ψ b (r, t), S a ) V + (S b , Ψ a (r, t)) V )dt (20)
Considering Eq.( 18) we have

∞ t=∞ ((Ψ b (r, t), S a ) V + (S b , Ψ a (r, t)) V )dt = 0 ( 21
)
where V is the whole space. Hence, we can obtained the mutual energy theorem:

- ∞ t=∞ (Ψ b (r, t), S a ) Va dt = ∞ t=∞ (S b , Ψ a (r, t)) V b dt (22)
V a and V b is the place where S a or S b are not zero. This can be rewritten as,

-(Ψ b (r, t), S a ) T Va = (S b , Ψ a (r, t)) T V b (23)
where The word mutual can be drop out. The mutual energy theorem is actually the energy conservation law for the particle. The energy of particle can only emitted from a and received by b. It is clear there are no any other energy go from a to b. If the energy of the particle has moved from a to b, there should have energy ow between a and b. This will be discussed in next subsection. We will also discuss the self-energy does not contributed to the energy ow of the particle in next section.

(Ψ b (r, t), S a ) T Va = ´∞ t=∞ (Ψ b (r, t), S a ) Va dt. (S b , Ψ a (r, t)) T V b = ´∞ t=∞ (S b , Ψ a (r, t)) V b dt. The subscript T = [-∞, ∞]

B. The mutual energy ow theorem

We assume V a and V b are inside V . V a is the region include the source S a . is the energy received by the sink S b . We can also obtain the mutual energy ow theorem,

-(Ψ b (r, t), S a ) T Va = (Ψ b , Ψ a ) T Γ ab = (S b , Ψ a (r, t)) T V b (24)
where,

(Ψ b , Ψ a ) T Γ ab = ∞ t=∞ " Γ J ab • ndΓdt = ∞ t=∞ " Γ ab 2µi (Ψ * b ∇Ψ a -∇Ψ * b Ψ a ) • nΓdt (25)
where Γ ab is a closed surface surround a, or a closed surface surround b. It also can be a innite plane between a and b. The normalized vector n is the norm vector of the surface.

The direction is from a to b. Γ ab can be seen as an arbitrary surface separating V a and V b .

We have written Eq.( 25) as an inner product form. It can be proven that it is really an inner product and satisfy the inner product 3 condition:

I. Conjugate symmetry, (Ψ b , Ψ a ) T Γ ab = (Ψ a , Ψ b ) * T Γ ab (26)
II. Linearity,

(Ψ b , kΨ a ) T Γ ab = k(Ψ b , Ψ a ) T Γ ab (27) (Ψ b , Ψ a1 + Ψ a2 ) T Γ ab = (Ψ b , Ψ a1 ) T Γ ab + (Ψ b , Ψ a2 ) T Γ ab (28) III. Positive dened, (Ψ, Ψ) T Γ ab ≥ 0 (29) (Ψ, Ψ) T Γ ab = 0 if f Ψ = 0 (30)
Where if f means if and only if. J ab is the energy ow intensity. Q = ! Γ J ab • ndΓ is the energy ow. Energy = ´∞ t=∞ Qdt is the all energy from the source a to the sink b.

Proof: In the Eq.( 20) V can be arbitrarily chosen. We separate V as two parts, V a and V b . Γ ab is the boundary between V a and V b . We choose V as V a there is only one source S a .

In this case, Eq.( 20) become,

- ∞ t=∞ " Γa J ab • nab dΓ = ∞ t=∞ ((Ψ b (r, t), S a ) Va )dt (31)
In the same way, if V is chosen as V b we have,

- ∞ t=∞ " Γ b J ab • nba dΓ = ∞ t=∞ ((S b , Ψ a (r, t)) V b )dt (32)
Adjust the direction nba in the above formula from b -→ a to a -→ b. Γ ba changed to

Γ ab , considering ! Γ b •n ba dΓ =- ! Γ b
•n ab dΓ, substituting Eq.(31,32) to the mutual energy theorem Eq.( 22) we obtained the mutual energy ow theorem,

-(Ψ b (r, t), S a ) T Va = ∞ t=∞ " Γa J ab • nab dΓ = ∞ t=∞ " Γ b J ab • nba dΓ = (S b , Ψ a (r, t)) T V b (33)
This can be easily extended,

-(Ψ b (r, t), S a ) T Va = ∞ t=∞ " Γa J ab • ndΓ = ∞ t=∞ " Γ ab J ab • ndΓ = ∞ t=∞ " Γ b J ab • ndΓ = (S b , Ψ a (r, t)) T V b (34)
where Γ ab is any surface between Γ a and Γ b . Now we have n = nab the normal vector of the surface. The direction is from a to b. Considering,

(Ψ b (r, t), Ψ a (r, t)) T Γ ab = ∞ t=∞ " Γ ab J ab • ndΓ (35)
We have Eq.( 24).

The mutual energy ow theorem is stronger than the mutual energy theorem, in next section we will explain that the self-energy ow do not contribute to the energy transfer of the particle. Hence, the mutual energy ow is the only energy ow. Hence, the word mutual can be dropped out. It is not only the mutual energy ow theorem but the energy ow theorem.

VI. SELF ENERGY PRINCIPLE

If we assume the mutual energy principle is the axiom of the quantum mechanics, we still obtained two Schrödinger equations. Hence, Schrödinger equations should also satised. If

Schrödinger equation is satised, we still obtained Eq.( 17). There is still the energy going to the outside of our universe. This energy is not received by anything. The problem of the Schrödinger equations still not solved.

One possibility is the wave has collapsed. That means the retarded wave has collapsed to the sink b. The advanced wave has collapsed to the source a. However, there has lot of sinks for example b in the space, it is dicult the retarded wave just collapsed the particular sink b (which is the target of the mutual energy ow). If the retarded wave collapsed, there should be another kind of particle, which is contributed by the self-energy ow. It is same to the advanced wave which needs to collapsed to a source a . It is dicult for the advanced wave just collapse to the place a (the mutual energy ow started from). Hence, there should be another particle corresponding to the advanced wave which collapsed to a . We only seen one kind of particle.

Wave collapse should be a process of physics. But this process has not been described by any formula. Hence, the theory of wave function collapse is dicult to be accepted. Since we have the mutual energy ow theorem which can transfer the energy of the particle, the wave is not necessary to be collapsed.

This author do not think the there is an energy go to outside of our universe. Since there is the mutual energy ow can transferred the energy from the source to sink, it is not necessary for the self energy ow to transfer the energy.

If this author believe the concept the wave collapse cannot be accept. Here the wave collapse is collapse to it's goal. For example the retarded wave sent from the source a is collapsed to the sink b.

L re ≡ - 2 2iµ ∇ 2 + 1 i V (r, t) Ψ re (r, t) - ∂ ∂(-t) Ψ re (r, t) (36)
L re Ψ re (r, t) = 0

(37)
The solution of the time-reverse Schrödinger equation is written as Ψ re (r, t). It is clear that,

Ψ re (r, t) = Ψ * (r, t) (38)
where Ψ(r, t) is the normal wave satised the Schrödinger equation. Hence, the time-reverse wave is the complex conjugate of the of the normal wave. Here the normal wave includes the retarded wave and the advanced wave.

The energy ow of the normal wave can be canceled by the time-reversal wave, i.e.,

∞

t=∞ " It is possible that the time-reversal wave also has the corresponding mutual energy principle, and hence, the mutual energy ow theorem and mutual energy ow theorem. There is the problem that the time-reversal mutual energy ow can also cancel the normal mutual energy ow that means, ∞ t=∞ "

Γ J aa • ndΓdt + ∞ t=∞ " Γ J aare • ndΓdt = 0 (39) ∞ t=∞ " Γ J bb • ndΓdt + ∞ t=∞ " Γ J bbre • ndΓdt = 0 (
Γ J ab • ndΓdt + ∞ t=∞ " Γ J abre • ndΓdt = 0 (41)
where J ab is the mutual energy ow form a to b. J abre is the time-reversal mutual energy ow from b returns to a. If the mutual energy ow is canceled by the energy ow of the corresponding time-reversal wave. There is no energy ow can transfer the energy for a particle. The particle cannot move form a to b. This author assume that if the sink receive an energy of a whole particle, it will not allow the energy return from b to a. If the sink received only a half or partial energy of a particle it will allow the energy to return from b to a. This is the reason why we cannot obtained a partial particle. The self-energy principle tell us there is no energy ow go outside to our universe. Self-energy principle is applied to make the theory selfconsistent. The mutual energy principle is applied to the calculation of the quantum mechanics.

It should be noticed if the mutual energy ow of time-reversal wave existent, it can also be an anti-particle for example the positron (a positive electron) for electron.

After we have the self-energy principle, both the Schrödinger equation and the mutual energy principle can be applied as the axioms of quantum mechanics. If we apply Schrödinger equation as the axiom we need two Schrödinger equations one is for the retarded wave one is for the advanced wave. We need to explain to the reader the advanced wave exists same as the retarded wave. If we apply the mutual energy principle as the axiom of quantum mechanics, we only need one mutual energy principle. The advanced wave and retarded wave can all be derived from the mutual energy principle. Hence, use the mutual energy principle as axiom it is better than the Schrödinger equation.

Since the self-energy principle is only this author's hypothesize, it still needs to be proven.

For example the self-energy ow goes to the innite big sphere perhaps go back from another world or another universe. It go back by a wormhole but not the time-reverse wave. That is also possible.

But mutual energy principle can be proved from Schrödinger equation, it should be correct. We need only compare the mutual energy principle and the Schrödinger equation The problem of Schrödinger equations is the self-energy ow go out our universe, the problem of the self-energy principle is introduction of a new kind of eld that needs to be tested.

The self-energy principle introduced two time-reverse eld, even without proof, it make the theory selfconsistent. Hence it still very valuable.

The formula of the mutual energy principle is similar for the electromagnetic eld and quantum mechanics, even the Maxwell equations and the Schrödinger equation are not similar to each other. They all can be written as,

-(S f , ξ f i ) = (ξ Γ f , ξ Γ i ) = (ξ i f , S i )
where (S f , ξ f i ) and (ξ i f , S i ) is a inner product with 3D volume integral and 1D time integral. (ξ Γ f , ξ Γ i ) is a inner product with 2D surface integral and 1D time integral. i is at the initial place which is the source of the particle. f is the nal place which is the sink place of the particle. Γ is any 2D surface between i and f . S f is the sink intensity, S i is the source intensity. ξ f i is the eld at the place f emitted from i, ξ Γ f is the eld at Γ emitted from f . It is similar to ξ Γ f and ξ i f .

Hence, the mutual energy ow should be more general than Schrödinger equation or Maxwell equation. It is also possible we have the mutual energy principle corresponding to hadron, graviton and so on.

VII. HAMILTON AND MOMENTUM OPERATORS

In quantum mechanics when we often speak the energy and momentum of the particle.

We dene the average of the Hamilton operator and say that it is the energy of the particle.

We dene average of momentum operator and say that it is the momentum of the particle.

This author do not satisfy that kind of denition without a proof and think the other reader will also very confused for that. In the following a better proof will be given.

A. Average of the Hamilton operator is the energy of the particle Considering the particle is at the orbit, the wave is static and stable, hence, ∂ ∂t can be omit. Hence, we have

L ≡ - 2 2iµ ∇ 2 + 1 i V (r, t) - ∂ ∂t = 1 i H ( 42
)
where H is the Hamilton,

H = - 2 2µ ∇ 2 + V (r, t) (43)
Hence, we have,

(Ψ b (r, t), LΨ a (r, t)) T Va = (Ψ b (r, t), 1 i HΨ a (r, t)) T Va (44)
According the mutual energy ow theorem Eq.( 24), we have

|(Ψ b (r, t), HΨ a (r, t)) T Va | = |(Ψ b (r, t), LΨ a (r, t)) T Va | = |(Ψ b , Ψ a ) T Γ ab | (45)
In case the electron is on the orbit, we know that the advanced wave and the retarded wave is same, this is similar to the electromagnetic eld wave inside a wave guide, i.e.,

Ψ b (r, t) = Ψ a (r, t) = Ψ(r, t) (46)
V a can be written as V , we have,

|(Ψ(r, t), HΨ(r, t)) T V | = |(Ψ(r, t), LΨ(r, t)) T V | = |(Ψ, Ψ) T Γ | (47)
In the case the wave is stable, the subscript T can be drop out, because it means a integral with time. Hence, we have,

|(Ψ(r, t), HΨ(r, t)) V | = |(Ψ(r, t), LΨ(r, t)) V | = |(Ψ, Ψ) Γ | (48)
where

|(Ψ, Ψ) Γ | = | ! Γ J
• ndΓ| is the absolute value of the total energy of the energy ow of the particle, which is related to the average of the Hamilton |(Ψ(r, t), HΨ(r, t)) V |. This is the reason in quantum mechanics we can use the average of Hamilton as the energy of the particle! This tell us the average of the Hamilton operator is not just an average energy of the particle but it is the tall energy of the energy ow of the particle.

Eq.(47, 48) oers more meaningful result to explain the Hamilton operator.

When we speak about the J ab is energy ow intensity, it can be also mass ow intensity.

Since mass and energy is equivalent according the relative theory. Actually it is normalized mass ow intensity. In the text book of quantum mechanics, it is referred as the probability ow intensity. Since this author do not accept the probability interpretation of Copenhagen school, when we speak the probability ow intensity, it can be understand as the normalized mass ow intensity.

VIII. CONCLUSION

This author notice the fact that the mutual energy principle can be derived from the Schrödinger equation and Schrödinger equation can also be derived from mutual energy principle, however, this two formula as axioms are not equivalent. The mutual energy principle can only derive a pair of Schrödinger equations one corresponding to the retarded wave and one corresponding the advanced wave. The two wave have to be synchronized. This solution is the action and reaction pair solution. In other side the Schrödinger equation can obtained the retarded wave as the solution.

After this author introduced the the self-energy principle, the solution of the Schrödinger equation looks like a probability wave, because there are time-reverse wave which cancel the energy ow of the self-energy ow of the Schrödinger equation. Self-energy ow principle guarantees that the mutual energy ow are actually the energy ow. The word mutual can be dropped. This author has introduced the mutual energy principle and self -energy principle for photon and electromagnetic elds. In this theory, the photon is nothing else but the mutual energy ow. This author would like to bring the same theory to quantum mechanics, but there was a diculty because the Schrödinger equation has no advanced wave solution. In this article the negative distance is introduced which make the advanced wave solution for Schrödinger equation become possible.

After this the mutual energy principle, self-energy principle, mutual energy theory, mutual ow theorem is introduced to quantum mechanics. The mutual energy ow is consist of the retarded wave and the advanced wave which satisfy the Schrödinger equation. The energy ow of the particle is proved as the mutual energy ow.

In the end the author also proved that the energy of the particle is the average of the Hamilton operator. The particle's momentum is the real part of the average of the momentum operator.

The mutual energy ow theorem will be applied to introduce the Huygens principle which will further introduce a updated path integral which will be discussed in a separated article. (Ψ b (r, t), LΨ a (r, t)) V + (LΨ b (r, t), Ψ a (r, t))

V = ∞ t=∞ V (Ψ * b (- 2µi ∇ 2 + 1 i V (r, t) - ∂ ∂t )Ψ a +((- 2µi ∇ 2 + 1 i V (r, t) - ∂ ∂t )Ψ b ) * Ψ a )dV dt = ∞ t=∞ V (Ψ * b (- 2µi ∇ 2 Ψ a ) + (- 2µi ∇ 2 ) * Ψ * b Ψ a +Ψ * b 1 i V (r, t)Ψ a + Ψ * b ( 1 i ) * V (r, t)Ψ a Ψ * b (-)( ∂ ∂t Ψ a ) + (-)( ∂ ∂t Ψ * b )Ψ a )dV dt = ∞ t=∞ V ((- 2µi )(Ψ * b (∇ 2 Ψ a ) -(∇ 2 Ψ * b )Ψ a ) + 1 i (Ψ * b V (r, t)Ψ a -Ψ * b V (r, t)Ψ a ) +(-)(Ψ * b ∂ ∂t Ψ a + ∂ ∂t Ψ * b Ψ a ))dV dt (60)
The rst term inside are,

(- 2µi )(Ψ * b ∇ 2 Ψ a -∇ 2 Ψ * b Ψ a ) = (- 2µi )(Ψ * b ∇ 2 Ψ a + ∇Ψ * b • ∇Ψ a -∇Ψ * b • ∇Ψ a + ∇ 2 Ψ * b Ψ a ) = -∇ • ( 2µi (Ψ * b ∇Ψ a -∇Ψ * b Ψ a )) -J ab (61)
The second term,

1 i (Ψ * b V (r, t)Ψ a -Ψ * b V (r, t)Ψ a ) = 0 (62)
The third term,

(-)(Ψ * b ∂ ∂t Ψ a + ∂ ∂t Ψ * b Ψ a ) = - ∂ ∂t ( Ψ * b Ψ a ) = -u (63)
Proof nished.

  express the inner product also includes a integral with time ´∞ t=∞ •dt. -(Ψ b (r, t), S a ) T Va is the produced energy of the source S a . (S b , Ψ a (r, t)) T V b is the received energy of the sink S b . This energy is the energy of the particle. It is the energy from the source (emitter) S a moving to the sink (absorber) S b .

  V b is the region include the sink V b . -(Ψ b (r, t), S a ) T Va is the energy send by the source S a . (S b , Ψ a (r, t)) T V b

  40)Here J aare is the self energy ow intensity of the time-reverse wave corresponding the retarded wave. J bbre is the self-energy ow of the time-reverse wave corresponding the advanced wave. Eq.(39,40) are referred as self-energy principle. The self-energy principle tells us, there exists the time-reverse wave which can cancel the self-energy ow. The self-energy ow of the retarded wave is canceled by the energy ow of the corresponding time-reversal wave of the retarded wave. The self-energy ow of the advanced wave is canceled by the energy ow of the corresponding time-reversal wave of the advanced wave. Here when we speak the cancel we mean the energy ow is canceled, the retarded wave and the corresponding time-reversal wave are not cancel each other. The advanced wave and the corresponding time-reverse wave are all existent.

  which is more close to the nature. If we do not derive Schrödinger equations from the The mutual energy principle, the mutual energy principle will has no problem. All the problem of the mutual energy principle comes only through the Schrödinger equations (Here we speak about the problem of Schrödinger equation, which is the self energy ow of Schrödinger equation goes to outside of our universe.). Hence, even without the self-energy principle we should also apply the mutual energy principle as the axioms. Most reader perhaps would like to accept the problem of the Schrödinger equations than to accept the self-energy principle.

  If wave doesn't collapse where it goes? This author thought it returns. That means that the retarded wave returns to the source. The advanced wave returns to the sink. The return process can be described by a time-reversal process which should satises, the time-reverse Schrödinger equation. The time-reverse Schrödinger equation can be obtained by substitute -t to t in the Schrödinger equation, which is,

This author believe that the mutual energy principle can be applied as a correct axiom for quantum mechanics. The Schrödinger equation has the same problem same as

B. Average of the momentum operator is the momentum of the particle

In our new quantum mechanics (using the mutual energy principle and self-energy principle as axioms), I hope that the momentum can be dened as,

Where ρ µ is mass intensity. J µ = ρ µ (x)v is mass ow intensity, it is the momentum for the unit volume.

where ρ is the normalized mass intensity or the probability intensity. We have,

where J = ρv is normalized mass ow intensity (or the probability ow intensity). It should be notice that this author do not support the concept of probability and the probability ow intensity. Hence, here when we speak the probability intensity it just a normalized mass intensity, the probability ow intensity is just a normalized mass ow intensity.

C. Quasi-plane wave

The wave the electron inside its orbiter can be referred as quasi-lane wave. In this situation we have,

where p = i ∇.

Hence the momentum of the particle is,

In the case for example the wave is in a wave guide or an electron is on its orbit inside an atom, the wave can be seen as quasi-plane wave. In the case of quasi-plane wave, the retarded wave and the advanced wave are the same, each has the half value of the total eld.

Hence, we can take away the subscript of the wave function. In this case we have

Here Ψ A is the retarded wave send from point A which is an emitter. Ψ B is the advanced wave send from B which is an absorber. Ψ is either

where is take the real part for a complex number. This example tell us even we started from the probability ow intensity J p ≡ µ V J dV = ( V (Ψ * pΨ)dV )

Hence, ´V (Ψ * pΨ)dV can be seen as complex momentum.

In quantum mechanics, the average of momentum of the particle is dened as,

It is noticed that < p > is not only the average of the momentum of the particle, it is the a complex value of the momentum of the particle. Take the real part it is the momentum of the particle, i.e., p = (< p >) = ( V (Ψ * pΨ)dV )

(59)


Philippe Robin
email: philippe.robin@trialog.com

Sylvain Robert
email: sylvain.robert@cea.fr

Michel Sall

Sébastien Berthier

Market Enabler for Retarget-able COTS Components in Embedded Domain

Keywords: Components, Off-The-Shelves, Real Time Embedded, Reuse, CCM, OSEK

come

Introduction

The paper structure is as follows: section 2 describes MERCED project contents. Then, section 3 focuses on Real-Time and embedded concerns.

The MERCED approach

Components Reuse Environment for realtime and embedded systems

The first goal of the MERCED project is to offer a components reuse environment which will provide a support for components storage & classification on the one hand, and components selection and retrieval on the other hand. In the proposed scheme, two actors are distinguished. The first is the components developer who feeds the components repository with his products. He has to provide a description with each component. This description has to be compliant with the MERCED RTE components taxonomy. Then, the second is the components user, who needs to retrieve specific components. The MERCED environment offers tools to support the user in his search (e.g. search engine), as well as in the following steps: component validation, simulation, and testing.

Components classification and retrieval MERCED will provide a component meta-model that gives a common and unified component specification. This meta-model will help automating many activities related with searching, retrieving, qualifying, testing and integration, since prior to usage it is already known which specification information can be manipulated. The meta-model will be used to characterize components within the reuse environment. Doing so, the information required for selecting and using components will be available to search tools. The meta-model will include extendable taxonomy means for testing concepts (mockup environment, test suite definition, test driver components, stub components, qualification level, etc). Then, a suitable approach for component documentation and searching with extendibility capability will also be provided. The initial taxonomy for non functional and functional properties will be defined in such a way that it can easily evolve overtime: proper taxonomy extendibility mechanisms are thus to be defined and provided.

Component validation and qualification tools

To make the embedded real time software development teams confident in reusing components, these components must reach the qualification level they need. This qualification level is project-dependent and can be one of the components characteristics. For example, an avionic integrator will need that a component be certified at the "DO-178B level A" level to be integrated into some critical subsystem. This qualification level can be part of the component description. Moreover, in the component selection process, the potential reuser has to ensure himself that the selected component description matches his needs, and will then also need to be confident in the fact that the component is conform to its description. To achieve component qualification, a test platform at the hardware and OS abstraction level will be provided by MERCED. The test platform will allow defining and possibly running the component test suites in a virtual environment simulation.

System simulation tools

The selection of an existing component to be integrated in the designed system lays on a "search, select and try" process. The "search" and "select" steps are achieved by the presence of a description of each existing component in the repository and the associated searching and filtering tools based on this description. The "try" step, consists of quickly verifying that component interacts as expected inside the system. Powerful means for the inspection of the component interactions inside the system will be provided in a simulation environment providing traces, break conditions, system state inspection, and other debugging features that will not be available on the final target or induce heavy supplementary overhead.

The MERCED Execution Platform for Real-Time and Embedded systems

The second purpose of MERCED is to develop an execution framework for RTE systems. The base technology chosen for this framework is the CORBA component Model in its lightweight version [START_REF]Object Management Group, Real-Time CORBA specification version 2[END_REF]. This latter enforces an original execution model, based on a strict separation of concerns between business and non-functional aspects. All business logic is gathered in applicative components, while all non-functional processing is embedded into containers. Containers provide an execution context to components: they mediate all interactions to/from the external environment and doing so, shield components from any execution platform-dependent issues. The MERCED framework itself is mainly made of the following parts (Figure 1): the execution infrastructure, comprising technical services the containers to fill the gap between the components and the execution infrastructure the administration service allowing assembly, configuration and deployment of the components and their containers a tool allowing to build the containers according to the application requirements some predefined components, providing generic services The main purpose of this part of the project will be to realize a reference implementation of this framework on top of Real Time CORBA [START_REF]Object Management Group, Real-Time CORBA specification version 2[END_REF], according to the definitions and requirements issued from users, which are gathered and analyzed also in the context of the project. The aim is to design a retarget-able framework, i.e. a framework easily portable to another execution infrastructure. In order to demonstrate this ability, a porting will be performed during the project.

Interaction models

In its original shape, the CORBA component model offers limited interaction support. In the context of real time and embedded systems, it is necessary to make available an extensive range of highly customizable interaction mechanisms, with e.g., QoS enforcement. This task thus aims at adapting accordingly the CCM. A significant amount of work has already been performed on this task, and some results are available. The core idea resides in adding "connectors" to the CCM. These new elements are software entities dedicated to interaction management [START_REF] Balek | Software connectors and their roles in component development[END_REF], which are used to interconnect components. All necessary modifications of the CCM have already been performed to include this new software entity, and a large part of prototyping has been performed. More details on this topic can be found in [START_REF] Robert | How ADLs can help in adapting the CORBA Component Model to Real-Time Embedded Software Design[END_REF].

Container runtime reference implementation

The purpose of this task is to specify and implement the container runtime so that the CCM containers can integrate nicely all the technical properties that are to be provided to the components. It should be noted that some parts of the containers implementation may depend on the underlying execution platform. The starting point is the Lightweight CCM OMG specification, and the reference implementation is Real Time CORBA based. Guidelines for porting on another infrastructure will also be provided.

Container Building Support

In the CCM approach, containers are generated. First, a description of components, is written in a dedicated language, namely the Interface Definition Language (IDL). Then this description is used as input to a generation tool which produces the container code. Since the MERCED project will largely impact the contents of containers (in order to specialize them for real time support), it is necessary to provide the corresponding generation tools. Note that the generation tool is also part of the retargetable environment. A first version will be provided to generate Real Time CORBA compliant container, but porting rules will also be issued, and a porting will be performed.

Predefined components implementation

The framework will be completed by predefined components; these latter are components that contain processing which is at the same time specific (to a given application domain, e.g. telecom) and generic (the processing is of interest for all applications of the given domain). These predefined components will be implemented for two application domains: software radio and electrical distribution. It should be noted that as these components are, by construction, plain components, they will benefit, as any application component, from the hosting support provided by the execution platform and that therefore their integration will be obvious.

Configuration and Deployment Suite

The CCM is accompanied by another OMG specification, which provides guidance in application assembly and deployment [START_REF]Specification for deployment and configuration of component-based applications -draft adopted specification[END_REF]. The "Assembly" is a step in which the application architecture is described, in terms of components instances, and interconnections. This description is based on a dedicated (XML) format, also defined in the specification. Once the assembly is done, a deployment tool is fed with the architecture description, and it performs accordingly components instantiations and interconnections. All these facilities will be adapted in the scope of the MERCED project in order to fulfil RTE-specific requirements, and then will be implemented. A particular attention will be paid to the embed-ability of the deployment tool.

Port of the Execution Support on top of OSEK

As said before, our aim is to design an easily portable framework. In order for us to assess the retarget-ability of the MERCED approach, a porting of an OSEK framework has been realised to a micro controller well-known in the embedded world together with the porting of the CCM framework on top of this OSEK framework. This is discussed in the following section.

CCM framework in the OSEK environment

OSEK is an execution infrastructure widely used in the automotive industry. Being an ISO standard it attracts a growing number of other industrial fields. Therefore it is a good candidate for ERTS projects

The OSEK environment

OSEK is specialised for highly constrained hardware platforms. It is mainly composed of two parts : an operating system (OSEK-OS [START_REF] Osek | [END_REF]) coupled with a communication environment (OSEK-COM [7]).

Operating system support offered by OSEK OSEK-OS is a multi-tasking operating system. It is highly static: all parts that can be stored in ROM are stored there to minimise the amount of required RAM. The declaration of tasks, events, counters, alarms, resources are defined in a static configuration, and so are tasks and resources priorities.

Communication infrastructure under OSEK

The OSEK-COM specification defines a simple message-based communication means. Messages are defined statically, meaning that their sender, receivers and maximum size are defined statically. The message content is defined by means of a socalled message object. There are two types of Message Objects, a static with a fixed structure and a constant length and a dynamic whose length is variable.

OSEK implementation OSEK-OS has been ported on an ARM7 microcontroller with 256 Kb ROM and 64 Kb RAM.OSEK-OS occupies 6% of the ROM and 0.3% of the RAM. Some trials have shown that typically the library (lib C/C++) needed by the components occupies about 17% of the ROM and 12% of the RAM. Integration on OSEK-COM is under way.

Component localisation and communications

Component localisation

The different components of an application can be localised on the same CPU (see figure 2) or distributed on several CPUs (see figure 3).

Inter components communication and execution

The figure 4 shows the interaction between components from the business developer point of view. But in reality, this interaction is achieved through the use of containers which mask the mechanisms used to perform it (see Figure 5). This masking allows components to be unaware of whether the call is local or remote. It also lets them be independent of the actual mechanisms used for the interaction.

C1 C2

C1 C2

Component Component Containers with implentation specific mechanism Suppose that C1 wants to call a function implemented in C2 (see figure 4). This call is intercepted by the container associated to C1. This container interacts with the container associated to C2 through a mechanism described below. And finally, this container calls the targeted function of C2.

Three mechanisms have been found necessary and sufficient for inter components communication and execution in the context of OSEK. : synchronous call asynchronous call periodic activation. For local interactions, these mechanisms, depicted in figure 6 below are.

synchronous call : The container of C1 directly calls the container of C2 asynchronous call : the container of C1 sends an event to the container of C2 periodic activation : this mechanism is achieved through the use of alarms and counters together in interaction with a timer component which is part of the framework. Note : In order to simplify the drawing, containers of figure 5 have not been shown on figure 6.

For remote calls, synchronism and asynchronism will be achieved through the exchange of messages via OSEK-COM as depicted on figure 7.

C1 C3 C1 C3

Stands for Asynchronous OSEK message Legend : b a

OSEK and CCM generation chain

The application architect searches for existing COTS using MERCED search tool and looks for application specific components when no suitable COTS exists (each component is delivered with its IDL description). Then he specifies the architecture deployment which details the components layout on CPUs.

Generations tools are used to generate : a makefile OIL description files (one per CPU) [START_REF] Osek | OIL: OSEK Implementation Language version 2[END_REF] Container sources and to select components (objects or libraries for COTS, sources for application specific ones).

Those files are compiled and linked to build the application executables (one per CPU). The complete chain is described on Figure 8.

During this process, the only manual operations performed are: searching, selecting and trying the required COTS, eventually developing the missing components, defining the deployment architecture. All other operations are automatically executed by tools developed during the MERCED project. These tools are part of the CCM and OSEK frameworks.

Compile and link Tools

Industrial use cases

Use cases are a way for the Merced project to test the solutions and concepts proposed by the consortium. Altogether they hightlight the following issues : create a component in compliance with the "Merced Component Model"; publish a component so that it will catch the interest of a potential customer; download a component and integrate it in an execution environment providing services as required by the component description; assemble and deploy components; generate and distribute an application over a set of CPUs connected through a communication layer. One of these use cases is implemented on top of OSEK for the electrical distribution.

Conclusion

In this paper, we sketched the main contents of the MERCED European project. This project proposes to compensate the rise in complexity in the RTE domain by enforcing a COTS-based development approach which would permit to decrease development costs while keeping a sufficient level of reliability. In order for COTS to achieve their breakthrough in the embedded system area, proper tools and methods have been defined by MERCED. The main difficulty the project had to deal with was to select and adapt a subset of the MERCED lightweight CCM to static platforms like OSEK. Three partners from the electrical distribution, software radio, metal processing domains are currently validating this approach.

Figure 2 :Figure 3 :

 23 Figure 2 : All the components (e.g. C1 and C2) of the application are running on a single CPU

Figure 4 :

 4 Figure 4 : Interaction between components from component point of view.

Figure 5 :

 5 Figure 5 : Interaction between components as it is in reality.

Figure 6 :

 6 Figure 6 : Synchronous call (a), asynchronous call (b), periodic activation (c) for local calls.

Figure 7 :

 7 Figure 7 : Remote synchronous call (a), remote asynchronous call (b).

Figure 8 :

 8 Figure 8 : The complete generation chain

Acknowledgement

The authors acknowledge the contribution of their colleagues to this work. The comsortium is made of the following companies and institutes : Axlog , CEA-LIST , Schneider Electric, THALES Communications TIMA-INPG ; Trialog (France) ; ENEA (Sweden) and DS2, European Software Institute, MSI, TELVENT, UPM (Spain)


P Joussain
email: philippe.joussain@embeddedtouch.com

Keywords:

The convergence of embedded systems in aeronautics and in automotive industry via software components and standards.

P.

The convergence of embedded systems in aeronautics and in automotive industry via software components and standards.

Introduction

Automotive industry and Aeronautics are 2 sectors with their own characteristics which have led to different approaches for the development of embedded systems. Aeronautics focuses on the development of highly-reliable systems that must guarantee the respect of security and safety-critical requirements. The development of embedded systems in automotive industry is characterized by very short innovation cycles and important product volume at low cost. This first chapter presents a synthetic comparison of the main characteristics of each approach. We have mainly considered the development of embedded software point of view.

Market characteristics

Aeronautics:

• There are a few manufacturers and suppliers

• 2000 units are manufactured per year

• The average price of an aircraft is 100 million € • Series product is the most complex aspect.

• The most important requirements in aeronautics are safety-critical requirements

• The life cycle of an aircraft is several decades (until 30 years)

Automotive industry:

• There are many manufacturers and suppliers.

• 64 million units are manufactured per year.

• The average price of a car is 25 000 €.

• Mass production is the most complex aspect.

• The most important requirements in automotive industry are the cost constraints on realization. • The life cycle of a car is less than 10 years and the innovation cycle is faster than in Aeronautics.

Development Process characteristics

Aeronautics:

• Most systems in an aircraft are safety critical; the breakdown of the system in subsystems depends on criticality level of the subsystem (and not on the domain); the quality assurance is an important part of an avionic project. • The software must be certified by a public authority • The whole development process is well defined and must be implemented by all subcontractors and suppliers. The software is developed according to a real V-cycle model; at first requirements will be acquired and the corresponding test will be defined; requirements and test cases will be detailed step by step until the software coding phase. Due to the enormous effort needed for changes, only necessary changes will be done. • The traceability of changes is guaranteed.

Automotive industry:

• Innovations are currently more important for a car manufacturer than the quality and the stability of the software in a car. • There are no certification requirements for the software in a car.

• No common standard for the development process which is implemented by all OEMs and Tier 1 suppliers; specification from OEM are not precise enough; test case are difficult to define and to link to requirements. • There are often late changes and no traceability of changes (due to incomplete specification).

Convergence via software components and standards

Introduction

The convergence of embedded system development methods is mainly based on the use of COTS products and the use of common standards for the development of embedded systems (system engineering standards and modeling standards).

In Europe, Aeronautics and automotive industry have chosen to introduce and to generalize the use of software components with the adoption of new modular architecture:

• Open IMA for Aeronautics • AUTOSAR for Automotive industry However, Open IMA is a concept used in the Airbus 380 programme but the first ECU compliant to AUTOSAR will be "on the road" in 2008 or 2009.

If UML is already used by Aeronautics and Automotive industry, SysML and AADL are two emerging standards which might be adopted by both industries.

IMA

IMA is an architecture which allows multiple software functions of different criticality level to be integrated on a single avionic computing device.

IMA concept [START_REF] Butz | Integrated Modular Avionic (IMA):State of the Art and future Development Road Map at Airbus Deutschland[END_REF] has brought a solution to the limit of the classical concept: "one function = one computer" which have reached its limit with the strong increase of embedded computers necessary for always more complex critical functions or missions in aircrafts (and the necessity to remain compatible with the strong constraints of volume, weight, power consumption and cost of avionic).

The A direct consequence is that the Open IMA concept allows third party avionic suppliers to provide has the modules and the communication devices according to the specification owned by Airbus. The aim is to develop a market for the open IMA standard in order to control the costs by competition.

Another consequence is that Airbus has modified the conventional development processes and responsibilities. The IMA system development and integration procedure development is split between:

• the avionic module supplier, • the aircraft system manufacturer, • And Airbus (IMA system integrator).

AUTOSAR

Due to the increasing number of networked components, a level of complexity has been reached which cannot be managed using traditional development processes. The automotive industry addresses this challenge through a paradigm shift from a hardware and component-driven to a requirement and function-driven development process, and a stringent standardization of infrastructure elements. One central standardization initiative is the AUTomotive Open System ARchitecture (AUTOSAR) [START_REF] Cousot | Interview of P. Cousot for ERTS 2006[END_REF]. AUTOSAR aims at facilitating the re-use of software components between different vehicle platforms, OEMs and suppliers. To achieve this, AUTOSAR defines a methodology that supports a distributed, functiondriven development process and standardizes the software architecture for each ECU in such a system. AUTOSAR also specifies compatible software interfaces at application level. The abstraction encourages effectively the usage of "commercial off the shelf" hardware.

The top priority of the AUTOSAR project is to ensure that proven AUTOSAR Architecture and high quality specifications are available by the end of 2006. Basic software specifications were split into 2 releases. Release 1.0 has been completed within the project and prototype implementations have been started to validate Release 1.0. Release 2.0 is planned to be completed at the end of 2005 based on the stable architecture of Release 1.0. Through feedback from implementation and integration later on the quality and maturity of the specifications will be verified and stabilized.

First of all an infrastructure is needed and afterwards functionality can be integrated. Referring AUTOSAR three more years are necessary to develop applications which will fit to the AUTOSAR infrastructure (basic software). In 2008 or 2009 the first AUTOSAR ECUs will be "on the road".

System Engineering standards

The increase of the complexity of real time embedded systems is a major reason to use system engineering standards to design the system architecture. The most popular are SysML, AADL, AFs (Architecture Frameworks), ATAM (Architecture Trade off AnalysisM), EAST-EEA (Embedded Architecture and Software Tools). Among these standards, SysML and AADL are two emerging standards which are appropriate for aeronautics systems as well as automotive systems.

SysML (System engineering Modeling Language):

• SysML is a modeling language based on UML 2.0 intended for system engineering • SysML is a modeling language designed to provide a multi-discipline and multi-domain support for system engineering in order to facilitate systems analysis, specification, design, verification and validation. • It must be able to support implementation of systems engineering based on models, whilst also being able to represent physical systems, derive views according to the application domain or the level of detail provided, and automate certain tasks, such as, test cases, simulation, integration or deployment.

AADL (Architecture Analysis and Description Language):

• AADL is a system architecture description language, used to describe both software and hardware components in a system, and also the interfaces between components. This language allows functional interfaces to be described (like data flows and input/output control flows) as well as non-functional aspects of components (sequences, performance, security). • The main goal is to facilitate interaction between system architects and application developers by using a formal method which guarantees the coherence of specifications and interface descriptions. Such an approach allows to reduce the risk of incomprehension or incoherence between different stages of the development cycle to be reduced, (especially where changes take place in more developed stages of the project).

Modeling standards

Widely used today, UML has become standard in the modeling of all types of systems, not solely in software modeling. However, in the latest version (previous to 2.0), gaps were noted showing that UML is lacking and therefore can not efficiently deal with problematic complex real-time or distributed systems.

Following work carried out within the OMG by industries, tool providers and academics, the following main weaknesses were identified:

• Poor support for complex system modeling using the principle of breakdown in autonomous communicating entities. Usually, modelers define rules to complement UML in order to then be able to deal with their complex architectures. • Inability to build executable models, hence, the need to enhance them with a programming language (for example:C, C++ or Java code), or a specialised notation, in order to produce an executable application. This is a possible cause of disruptions in standards. • Poor support for sequence diagram organisation, leading to incomplete specifications which then require additional documentation for correct comprehension.

• Absence of an exchange format independent from tools providers, and which enables the transfer of models and their diagrams.

In addition, the OMG tried to improve the language's definition by cleaning the metamodel and clarifying its semantics.

These problems were acknowledged and have led to major changes in the new UML version, version 2.0, which is currently in the process of being accepted by the OMG. It is a combination of UML's previous versions' strong points (at a structural level), and SDL / MSC (at a behavioural level), due to the adding or enhancing of certain concepts and diagrams, briefly presented below.

Some obstacles to the convergence

EmbeddedTouch has interviewed different embedded system experts (Patrick Cousot [START_REF] Cousot | Interview of P. Cousot for ERTS 2006[END_REF], Mike DeWalt [START_REF] Dewalt | Interview of M. Dewalt for ERTS[END_REF], Thomas Scharnhorst [START_REF] Scharnhorst | Interview of T. Scharnhorst for ERTS[END_REF]), on the trends of the convergence of embedded systems development methods applied in different industrial sectors (aeronautic, space, automotive, train, etc).

According to these experts, there are several difficulties which might slow down the convergence of embedded system development and verification methods.

Requirements for development methods in terms of cost are different: The tendency is to want strict development methods but at a very low cost, which is contradictory. That automatically means a lack of rigor in development methods (uncomplete definition of the system, insufficient verification, difficulty in going up the chain in the case of a bug). A rigorous method is essential for the development of safetycritical software when economic criteria are often more important for non safety-critical software.

Formal verification methods are mainly used for safety-critical software development: All the software industry has not got as a first objective to have programs which work. For example, it is largely admitted that a microcomputer can crash, which the legislation allows. The legislation does not go beyond what people can do. That situation will carry on as long as consumers do not protest. We can measure the cost of a catastrophe afterwards, but we rarely assess the cost of a catastrophe we can avoid. Also, the cost can become enormous when the system becomes complex. These different aspects limit the diffusion of formal verification methods in the other fields that are not safety critical or mission critical. I think that the new formal verification methods (now available with industrial tools) are going to increase the standards and the responsibilities of designers who have not applied the best of the state of art. This might lead to an evolution of the legislation towards more responsibilities with the hazardous usage of using computing solution which does not work correctly. There will be a real fault when formal verification tool will be able to prove that an error has not been corrected.

Formal verification methods needs today a real expertise: Formal methods are based on complex mathematical theory. But the great majority of engineers involved in the development of real-time embedded software are not familiar with these concepts and the use of formal verification tools.

Perspective

Introduction

In Europe, we have noticed during the past 5 years an increasing cooperation between Aeronautics and Automotive Industry in research projects related to embedded system development.

These projects gather aeronautic and automotive partners who have both experimented and validated new technologies or new methods.

We present hereafter some of these projects which contribute to the convergence of embedded system development methods.

SafeAir II Project -ASDE

The project SafeAir II Project [START_REF] Gaudré | SafeAir II Project -The Advanced Systems Development Environment (ASDE): A methodology and a tool-set designed to develop aeronautics, automotive and space safety-critical software systems[END_REF] • OVALIE: a project proposed to extend the use of statical analysis for the verification of embedded software.

Conclusion

Even if Aeronautics and Automotive industry are characterized by their strong particularities, a real convergence of embedded system development methods has appeared. The most visible results of this convergence are the use of similar development methods and standards, the use of COTS and the cooperation through research projects between both industries.

The increase of the development of real-time (and/or safety-critical) embedded systems should speed up this convergence. But the automotive sector has difficulties to make up for lost time because it is faced with the problem that all of its wishes are met with economic obstacles. Problems of confidentiality and competition run in opposition to the transparency between cars manufacturers and automotive suppliers who often supply to the competition.

The convergence of embedded system development methods might go on thanks to:

• The strengthening of the cooperation between Aeronautics and Automotive Industry through research projects; • But also an increasing interest of industrials to experiment these technologies and methods.

3. 5

 5 Future cooperationThe cooperation between Aeronautics and Automotive Industry should increase in the next years with the different projects and initiatives organized or proposed in Europe:• The next phases of the ASSERT Project (The ASSERT main goal is to improve the systemand-software development process for critical embedded real-time systems, in the Aerospace and Transportation) • The next phases of the TopCased project (now a project of the French competitiveness pole Aerospace Valley).

Glossary