Photons, particles and wavepackets

[jostpuur]

I have some trouble making sense out of photons. I have numerated some key questions in the following story, so that giving answers to specific questions could be easier.

Suppose I had created double slit experiment with light successfully. I would then change the set up as follows. I would replace one light source with two, and place a wall between the two slits so that light from one source reaches only the one slit, and from the other source the other slit. Question is then, do I still have interference pattern?

(I'm not sure if that explanation was sufficient, so I'll explain it with two dimensional coordinates in better detail. First light source was in location (0,-5), there is a wall on line (x,0), and two slits in positions (-1,0) and (1,0). I'll then place a new wall into between points (0,0)...(0,-3), and replace old light source with two that are in positions (-2,-5) and (2,-5). Light from (-2,-5) doesn't reach point (1,0), and light from (2,-5) doesn't reach point (-1,0).)

If I think this classicaly, then why not? Electromagnetic fields should be summed even though they came from different sources. So I should have interference. Also if this experiment was carried out using water waves, the interference would remain.

If I instead think of this with quantum mechanical particles, it is a different story. It is absolutely important, that a wave function of a single particle goes through the both slits, in order to interference appear. If a single particle goes through only one slit, then its propability distribution is going to consist of only one peak. And if I have one million particles, that all have a propability distribution of a one peak, there won't be interference appearing in macroscopic intensity.

So is there interference or not? (1) I would be happier if there were not, because when classical and quantum theory contradict, the quantum one should be more correct. But what about reality? Is there interference in physical experiment? I have never heard of experiment of this kind. Has anyone here?

But things get more confusing. I have often got impression, that we are supposed to consider photons as electromagnetic wavepackets. If photons are quantum mechanical particles, then claiming them to be actually wave packets of macroscopic electromagnetic field doesn't make any sense. If I have a wave packet of classical electromagnetic field, does this wave packet have anything to do with photons? (2)

I've read, that laser is coherent light. Coherent seems to mean, that individual wave packets have the same frequency and no such phase difference, that they could cancel each others. But if I have large amount of photons, each of them carrying some energy, I would assume their total energy to be the sum of the energies of photons. Sounds simple? But if the total energy is simply sum of the energies, then no phase differences should have any effect on the total energy. The idea that energy of light could be lesser if photons canceled each others, seems to assume that photons are indeed wave packets of macroscopic electromagnetic field. If that thought is incorrect, then does the coherent light mean anything? Is it only a confusing way to say that energy spectrum of photons is a sharp peak? (3) If so, does the phenomena of interference have anything to do with light being coherent? (4)

 

[jtbell]

I would replace one light source with two, and place a wall between the two slits so that light from one source reaches only the one slit, and from the other source the other slit. Question is then, do I still have interference pattern?

No, except if you have very special light sources. I think I've read about experiments in which two separate light sources have been made to interfere, but they're difficult to do.

If I think this classicaly, then why not? Electromagnetic fields should be summed even though they came from different sources. So I should have interference. Also if this experiment was carried out using water waves, the interference would remain.

When you do this with water waves (for example producing the waves by dipping mechanical oscillators into water), you have a single continuous wave coming from each source. This is very difficult to do with light sources, which usually contain many many atoms, each of which is a separate light source. Even lasers do not produce perfectly monochromatic light. Accrding to the optics text that I'm looking at right now (Pedrotti, Pedrotti and Pedrotti, Introduction to Optics, 3rd ed.), you can model this non-monochromaticity by letting the phase of each wave vary with time, which causes the amount of interference to vary with time as the waves drift in and out of phase. This variation is slow compared to the wave frequency, but is usually very rapid compared to the time scales of most real detectors.

It is often said, therefore, that light beams from independent sources, even if both sources are the same kind of laser, do not interfere with each other. In fact, these fields do interfere, but the interference term averages to zero over the averaging times of most real detectors.

 

[jostpuur]

Okey, thanks, I didn't fully understand, but got a feeling, that I could understand if I read more. But I just happened to hit into this quote else where in these forums

The quote is due to Paul Dirac (The Principles of Quantum Mechanics, 1930):

"Each photon then interferes only with itself. Interference between two different photons never occurs."

But different radio transmitters and lasers do interfere...

(By Pieter Kuiper in Photon Self-Interference thread)

Just to mix the mess even more Frankly, these statements seem to contradict. Doesn't make fully sense to me yet.

 

[cesiumfrog]

If you have two coherent sources of light, and a photon strikes a screen, you really can't tell which source the photon came from. Regardless of whether the sources are just separate slits or completely separate emitters, the two "paths that the one photon may have taken" interfere and Dirac's statement is justified (otherwise we would expect the pattern to change when we reduce the intensity so that there aren't two photons present simultaneously). However, if the separate light sources don't stay coherent/synchronised, then their phase difference will slowly drift (continually shifting the interference pattern), and the pattern will become completely washed out (so if you want to see interference from cheap lasers, make sure both possible photon paths are from the same laser).

Don't think I've really described any quantum process here yet..

 

[jostpuur]

What then if the phase difference would not drift? Should the interference then appear? If I understood Dirac correctly, the answer is no. Since photons from different sources don't interfere, the phase difference of two sources should not matter at all.

 

[jostpuur]

Sorry cesiumfrog, I may have missed the point in the beginning of the reply. Are you saying, that a single photon could be created so that it has non-zero amplitudes for initially being in both emitters? Sounds striking I'm not sure if that's correct, or what you meant.

(Adding with edit:)

No, cesiumfrog, in fact I think I disagree with this

If you have two coherent sources of light, and a photon strikes a screen, you really can't tell which source the photon came from. Regardless of whether the sources are just separate slits or completely separate emitters, the two "paths that the one photon may have taken" interfere

When photon is emitted from some particular emittor and passes through two slits, the reason why you can't tell which slit it passed through, is that there is a non-zero amplitude for the photon to pass through both slits. Instead, when there is two emittors, A and B, a photon either comes from A or from B. In this case you can't tell where the photon came from for practical reasons, not because of nature of quantum mechanics. The "not knowing where photon came from" is of different nature in these cases.

 

[swain1]

Have you read anything on QED. A good qualititave explanation can be found in Feynman's book of he same name.
I think that would answer all of your questions.

 

[Tomsk]

If I place a high relative permittivity/refractive index material in front of the slits in a normal double slit experiment, do I get an interference pattern? If so, how is that reconcilable with

Each photon then interferes only with itself. Interference between two different photons never occurs.

if the material slows the photons down (i.e. interacts with them)? Does the material not act as a measuring device, collapsing the wavefunction and destroying the interference pattern? If not, why not? I have seen a double slit experiment carried out in air, so I don't see why you wouldn't get an interference pattern if epsilon_rel was larger... My guess is it is something to do with the non commutativity of x and p, but I really don't see exactly how it would work.

 

[jostpuur]

My first thread!

The old problems are the best. I still don't understand this, but I think I can explain the paradox more clearly now.

The Dirac's message is still quite clear.

Each photon then interferes only with itself. Interference between two different photons never occurs.

http://en.wikipedia.org/wiki/Photon_polarization

I think I've read about experiments in which two separate light sources have been made to interfere, but they're difficult to do.

I remain skeptical about such experiments, until I really see the evidence. Even if the small difference in the frequency of two different lasers would destroy the interference pattern, that should not be the true reason for the lack of interference. The true reason is what Dirac says. Different photons don't interfere.

On the other hand, we know that electric field is something we can sum. The electric field around two charges is the sum of the electric fields of them both separately. If we oscillate some charge, then the electric and magnetic fields around it will start oscillating too, and this is electromagnetic radiation. Since the radiation is merely electric and magnetic fields, which can be summed, we conclude that the electromagnetic radiation is summable, and radiation from different sources will interfere. For example, radio waves from different sources interfere.

As we know, the visible light and radio waves are fundamentally the same thing. The just have different frequency.

Then consider this: The light waves from different sources don't interfere. The light waves are the same thing as radio waves, except with a different frequency. The radio waves from different sources interfere.

Well that's the paradox!

I can see that the most popular solution to this is to ignore the Dirac's message, and believe that light waves from different sources would interfere. I cannot accept such solution attempt, because I cannot see how it would not be in contradiction with the quantum theory, and particle nature of radiation.

Other direction where the solution could be tried, is to deny the interference of the radio waves. But that is unacceptable too, because we could start slowing down the frequency arbitrarily, and eventually we would be claiming that almost static electric fields were not summable at all.

Hence I'm forced to conclude that radio waves and visible light are fundamentally different. That means, that the frequency is not the only difference, but there is more to it. This is in contradiction with what all books tell, but I don't think that is immediately absurd claim. After all, the birth mechanism of visible light and radio waves is fundamentally different too. The visible light originates from quantum mechanical systems, and the radio waves originate from oscillating charges.

Maxwell was wrong? (to mentors: please, no locking without warnings first)

 

[Demystifier]

One should not mix electromagnetic field with the 1-photon wave function. They satisfy the same Maxwell equation, yet they are different. In particular, the former is real while the latter is not. Nevertheless, they both can be expressed as c-numbers originating (in DIFFERENT ways!) from QED.
It seems to me that all confusion comes from mixing these two different concepts.

So, can 2 photons interfere with each other? Yes they can. However, their common wave function lives in the 2X4=8 dimensional configuration space, not in the ordinary 4 dimensional spacetime. Therefore, they do not interfere in the ordinary spacetime. Still, the electromagnetic field associated with this 2-photon state lives in the 4 dimensional spacetime. Essentially, it is the average value of the EM field operator in the 2-photon state. This c-number valued EM field interferes in the ordinary 4 dimensional spacetime.

 

[OOO]

If I instead think of this with quantum mechanical particles, it is a different story. It is absolutely important, that a wave function of a single particle goes through the both slits, in order to interference appear. If a single particle goes through only one slit, then its propability distribution is going to consist of only one peak.

I think quantum mechanics is not that different from classical field theory. Classical electrodynamics can be easily expressed in the language of hermitean operators. It's mainly because QFT describes infinitely many more degrees of freedom that QFT seems so complicated. Where in classical field theory you consider only one field configuration in spacetime, in QFT you consider all field configurations (even classically forbidden ones) and their respective probability amplitudes. This is how the functional integral approach describes QFT.

Having said this, let's go back to single particle quantum mechanics: don't think of a particle as a little black spot somewhere in space. If you send an electron beam (with 1 "particle" on average) onto a double-slit, there isn't any particle in this beam. It behaves completely utterly like a wave and nothing else ... until it hits the screen - then it behaves like a little black spot.

Do you know about Occam's razor ? It says that we ought to find the most economic description of nature. Of course you might imagine that there is also a little black spot riding on the wave or something. But with your current experiment you are totally unable to detect that little black spot - until it hits the screen. So what is more economic ? A little black spot surfing on a wave (probably with a grin on its face...), which you cannot detect in your experiment however, or just a wave the effects of which you detect in your experiment ?

So if you say something like "If a single particle goes through only one slit" you fool yourself by implying that a single particle cannot go through both slits. No ! It's the wave that goes through both slits if you don't cover one of them. And that's absolutely the same thing as for the photon. In either case you get an interference pattern if the input was monochromatic.

But things get more confusing. I have often got impression, that we are supposed to consider photons as electromagnetic wavepackets. If photons are quantum mechanical particles, then claiming them to be actually wave packets of macroscopic electromagnetic field doesn't make any sense. If I have a wave packet of classical electromagnetic field, does this wave packet have anything to do with photons? (2)

No, a photon in the true sense of the word is a monochromatic plane wave of definite polarisation, and as such it covers all space, from here to infinity. In theory one creates a photon by applying the ladder operator of one single wave vector. A wave packet consists of many wave vectors, so photons are not wave packets. Again the impression cannot be avoided that you fool yourself by thinking of photons as little black spots.

 

[jostpuur]

OOO, I'm afraid you did not understand my point. Did you understand the part where I explained the experiment being modified by an extra wall? I don't have problems with a wave function passing through two slits simultaneously, but in this (mind) experiment I was forcing the particles to go through only one slit.

little black spot surfing on a wave (probably with a grin on its face...)

I remember seeing an electron being described like this somewhere. There was a picture of the electron, and it had a text "artist's impression".

 

[Anonym]

But what about reality? Is there interference in physical experiment? I have never heard of experiment of this kind. Has anyone here?

Hanbury Brown-Twiss (HBT) intensity interferometer. R. Hanbury Brown and R.Q. Twiss, Nature,177, 27 (1956).

(I'm not sure if that explanation was sufficient, so I'll explain it with two dimensional coordinates in better detail. First light source was in location (0,-5), there is a wall on line (x,0), and two slits in positions (-1,0) and (1,0). I'll then place a new wall into between points (0,0)...(0,-3), and replace old light source with two that are in positions (-2,-5) and (2,-5). Light from (-2,-5) doesn't reach point (1,0), and light from (2,-5) doesn't reach point (-1,0).)

When photon is emitted from some particular emittor and passes through two slits, the reason why you can't tell which slit it passed through, is that there is a non-zero amplitude for the photon to pass through both slits. Instead, when there is two emittors, A and B, a photon either comes from A or from B. In this case you can't tell where the photon came from for practical reasons, not because of nature of quantum mechanics. The "not knowing where photon came from" is of different nature in these cases.
Since the radiation is merely electric and magnetic fields, which can be summed, we conclude that the electromagnetic radiation is summable, and radiation from different sources will interfere. For example, radio waves from different sources interfere.

Are you ask questions or provide explanations? I find your explanations beautiful.

I can see that the most popular solution to this is to ignore the Dirac's message, and believe that light waves from different sources would interfere. I cannot accept such solution attempt, because I cannot see how it would not be in contradiction with the quantum theory, and particle nature of radiation...
Maxwell was wrong?

I guess that the most popular solution to this is presented by A.Einstein, Phys.Zeit. 10,185,(1909). The first term is “the Dirac's message” and the second is due to intensity fluctuations (Maxwell).

Regards, Dany.

 

[f95toli]

What then if the phase difference would not drift? Should the interference then appear? If I understood Dirac correctly, the answer is no. Since photons from different sources don't interfere, the phase difference of two sources should not matter at all.

There are a few experiments where photons coming from different sources have been shown to interfere.
See e.g,. Kaltenback et al PRL 96, pp 240502 (2006) which also gives are good background to the topics.

The conditions are essentially that the two sources are well synchronized and that the photons are indistinguishable when they arrive at the detector.

 

[OOO]

OOO, I'm afraid you did not understand my point. Did you understand the part where I explained the experiment being modified by an extra wall?

I think I did.

But I can't see your problem. As others have said, its a matter of phase correlation. If you don't believe it, replace your light sources by two microwave emitters and scale the experiment respectively. If you're able to control the phase correlations between them by means of an electronic circuit then you will see an interference pattern, otherwise not.

If you try the same with thermal light sources or even lasers you won't succeed for practical, not theoretical reasons.

Maybe it helps you if you read again what cesiumfrog has said about it.

 

[lightarrow]

I think quantum mechanics is not that different from classical field theory. Classical electrodynamics can be easily expressed in the language of hermitean operators. It's mainly because QFT describes infinitely many more degrees of freedom that QFT seems so complicated. Where in classical field theory you consider only one field configuration in spacetime, in QFT you consider all field configurations (even classically forbidden ones) and their respective probability amplitudes. This is how the functional integral approach describes QFT.

Having said this, let's go back to single particle quantum mechanics: don't think of a particle as a little black spot somewhere in space. If you send an electron beam (with 1 "particle" on average) onto a double-slit, there isn't any particle in this beam. It behaves completely utterly like a wave and nothing else ... until it hits the screen - then it behaves like a little black spot.

Do you know about Occam's razor ? It says that we ought to find the most economic description of nature. Of course you might imagine that there is also a little black spot riding on the wave or something. But with your current experiment you are totally unable to detect that little black spot - until it hits the screen. So what is more economic ? A little black spot surfing on a wave (probably with a grin on its face...), which you cannot detect in your experiment however, or just a wave the effects of which you detect in your experiment ?

So if you say something like "If a single particle goes through only one slit" you fool yourself by implying that a single particle cannot go through both slits. No ! It's the wave that goes through both slits if you don't cover one of them. And that's absolutely the same thing as for the photon. In either case you get an interference pattern if the input was monochromatic.

No, a photon in the true sense of the word is a monochromatic plane wave of definite polarisation, and as such it covers all space, from here to infinity. In theory one creates a photon by applying the ladder operator of one single wave vector. A wave packet consists of many wave vectors, so photons are not wave packets. Again the impression cannot be avoided that you fool yourself by thinking of photons as little black spots.

I coloured in blue what I repeat from a lot of time; I was also hardly criticized for having said it.
Hope you will have more lucky.

 

[OOO]

I coloured in blue what I repeat from a lot of time; I was also hardly criticized for having said it.
Hope you will have more lucky.

I'll try hard.

 

[Anonym]

I think I did.

No, you didn’t. It is better to use the correlation terminology. You talking about the quantum (phase) correlations, but Jostpuur talking about also the classical intensity correlations.

radiation from different sources will interfere. For example, radio waves from different sources interfere.

Is it news for you? And you can’t explain the black body radiation curve without that. In addition, I consider your post #11 absurd.

Regards, Dany.

 

[OOO]

No, you didn’t. It is better to use the correlation terminology. You talking about the quantum (phase) correlations, but Jostpuur talking about also the classical intensity correlations.

Thank you very much for explaining to me what I was talking about.

Is it news for you? And you can’t explain the black body radiation curve without that. In addition, I consider your post #11 absurd.

I certainly didn't claim to be able to explain black body radiation with a double slit experiment. So much for absurdity.

 

[Anonym]

I have some trouble making sense out of photons… I would then change the set up as follows. I would replace one light source with two… If I think this classicaly, then why not? Electromagnetic fields should be summed even though they came from different sources. So I should have interference… If I instead think of this with quantum mechanical particles, it is a different story. It is absolutely important, that a wave function of a single particle goes through the both slits, in order to interference appear.

I certainly didn't claim to be able to explain black body radiation with a double slit experiment. So much for absurdity.

You don’t understand OP questions, it is about photons and their properties, QED vs CED and not once again about double slit. Change diskette. In addition, if you don’t want to know, nobody force you.

Regards, Dany.

 

[OOO]

You don’t understand OP questions, it is about photons and their properties, QED vs CED and not once again about double slit. Change diskette. In addition, if you don’t want to know, nobody force you.

Regards, Dany.

QED ? What is QED ? Creation and annihilation processes ? Absorption and Emission ? I'm so confused now... Before you've pointed that out to me, I'd have sworn that I've read something about a double slit. Luckily changing the "diskette" did the trick.

But seriously, I'm getting the impression that something I have said has touched one of your belief systems.

 

[Anonym]

But seriously, I'm getting the impression that something I have said has touched one of your belief systems.

Not at all. OP asks:” I have never heard of experiment of this kind. Has anyone here?” You didn’t answer. Instead, you tell fairytales what you think about QM and QFT. But OP is right and apparently there is the contradiction between QED and CED. I gave the example where they are living in the peaceful coexistence.

Regards, Dany.

 

[OOO]

I gave the example where they are living in the peaceful coexistence.

You're the saviour of us all. I've already started burning all my books...

 

[Anonym]

You're the saviour of us all. I've already started burning all my books...

Pity. It is written there. Especially, M&W.

Regards, Dany.

 

[jostpuur]

There are a few experiments where photons coming from different sources have been shown to interfere.
See e.g,. Kaltenback et al PRL 96, pp 240502 (2006) which also gives are good background to the topics.

The conditions are essentially that the two sources are well synchronized and that the photons are indistinguishable when they arrive at the detector.

If this is reality, then I can accept it, but how is this not in contradiction with what Dirac is saying? Different photons don't interfere!

Maybe it helps you if you read again what cesiumfrog has said about it.

Do you mean this:

Regardless of whether the sources are just separate slits or completely separate emitters, the two "paths that the one photon may have taken" interfere and Dirac's statement is justified

Now we get into quantum mechanics.

When photon is emitted from some particular emittor and passes through two slits, the reason why you can't tell which slit it passed through, is that there is a non-zero amplitude for the photon to pass through both slits. Instead, when there is two emittors, A and B, a photon either comes from A or from B. In this case you can't tell where the photon came from for practical reasons, not because of nature of quantum mechanics.

 

[jostpuur]

Hanbury Brown-Twiss (HBT) intensity interferometer. R. Hanbury Brown and R.Q. Twiss, Nature,177, 27 (1956).

Kaltenback et al PRL 96, pp 240502 (2006)

About these experiments. Are the two light sources really physically two different light sources, or do they use one source, split the beam, and then call it two sources?

 

[OOO]

Do you mean this:

No, I mean this:

If you have two coherent sources of light, and a photon strikes a screen, you really can't tell which source the photon came from.

and this

However, if the separate light sources don't stay coherent/synchronised, then their phase difference will slowly drift (continually shifting the interference pattern), and the pattern will become completely washed out

Jostpuur, have you ever heard of indentical particles ? If you could tell "where a photon comes from" this would amount to stamping labels on them (e.g. the labels "A" and "B" or say ... a grin on the face). But, according to quantum mechanics this is not possible. The two photons actually contribute to the same wave functional in a perfectly symmetric way and so there is not the slightest shadow of a doubt that they will interfere as long as the coherency conditions are met, which is quite difficult for different sources, as other posters have emphasized.

 

[jostpuur]

I understand the phase drifting part, but not this

If you have two coherent sources of light, and a photon strikes a screen, you really can't tell which source the photon came from

I suppose that you disagree with my response:

...when there is two emittors, A and B, a photon either comes from A or from B. In this case you can't tell where the photon came from for practical reasons, not because of nature of quantum mechanics.

I cannot believe that a single particle could be created in two different light sources so that it starts in the superposition. Once a particle has been created somewhere, I understand that it can take different paths with different amplitudes later on.

I haven't considered consequences of the Bose statistic in this experiment yet. If it is relevant, I'll return with it later.

 

[OOO]

I suppose that you disagree with my response

Yes indeed, I disagree with that.

I haven't considered consequences of the Bose statistic in this experiment yet. If it is relevant, I'll return with it later.

It is relevant. Statistics always sounds so frightning and irrelevant to practical applications since it seems to contradict intuition. But statistics is the reason why it makes no sense thinking of two photons as two little black spots surfing on a wave. With a certain probability amplitude you have a two-photon state in your wave functional and you can't decide which photon's which.

 

[OOO]

I cannot believe that a single particle could be created in two different light sources so that it starts in the superposition.

Saying this is equivalent to

"I cannot believe that it is possible to synchronize two different light sources."

It is certainly difficult at the considered frequencies, and I would even have said that it is impossible practically, but apparently - I haven't looked at the cited paper - it is possible though difficult.

 

[Demystifier]

If this is reality, then I can accept it, but how is this not in contradiction with what Dirac is saying? Different photons don't interfere!

See my post #10.
Shortly, their electromagnetic fields do interfere.

 

[f95toli]

About these experiments. Are the two light sources really physically two different light sources, or do they use one source, split the beam, and then call it two sources?

They use two sources. The paper is freely available on the arXiv
http://www.arxiv.org/abs/quant-ph/0603048

 

[Anonym]

There are a few experiments where photons coming from different sources have been shown to interfere. See e.g,. Kaltenback et al PRL 96, pp 240502 (2006) which also gives are good background to the topics… The paper is freely available on the arXiv.

The referred paper is the engineering/applied physics achievement trivial from the theoretical POV. Only Fig. 3(d) is relevant to the OP question. The paper doesn’t contain theoretical background to the topics.

See my post #10. Shortly, their electromagnetic fields do interfere.

Why you consider EM fields and not potentials?

Regards, Dany.

 

[f95toli]

The referred paper is the engineering/applied physics achievement trivial from the theoretical POV. Only Fig. 3(d) is relevant to the OP question. The paper doesn’t contain theoretical background to the topics.

Regards, Dany.

The main result in the paper is the HOM dip seen in figure 3a.
And I never claimed that the paper gave a comprehensive theoretical background to the topic; only that they give some background to the topic and put their experiment in a context. The relevant theory can be found in their list of references.

Also, their "trivial" achievement is extremely impressive from an experimental point of view. Can you please give a reference to some other experimental work that meets your "high standards"?

 

[Anonym]

The main result in the paper is the HOM dip seen in figure 3a.
And I never claimed that the paper gave a comprehensive theoretical background to the topic; only that they give some background to the topic and put their experiment in a context. The relevant theory can be found in their list of references.

Also, their "trivial" achievement is extremely impressive from an experimental point of view. Can you please give a reference to some other experimental work that meets your "high standards"?

You should not consider my post above in the negative spirit and I qualify the paper as achievement and not the “trivial” achievement. However, the authors might add a few paragraphs in the introduction to make the paper readable for the students also.

You also should agree that for any theoretician the paper do not contain any surprise or new information. It is my problem that I still don’t know what the consistent orthonormal basis that describes adequately that experiment is and I blame for that only myself. However that experiment don’t help me.

Regards, Dany.

P.S. Also the purpose of my post was to make clear to everybody participated in this sessions what we are talking about.