Wave-Particle Duality: Questions & Answers

[Mr Virtual]

Hi to all

I have a few confusions regarding wave-particle duality. I hope I will get good answers. You need not answer all the questions ( just those that you feel like answering).

1. Light acts as particles called photons. Photons have a definite energy based on their frequency/wavelength. But frequency/wavelength are terms used when we assume light to be acting as a wave. How do we imagine a photon to possesses any wavelength or frequency? How do we explain Double-Slit Experiment i.e. how does a single photon pass through both the slits? How do we explain constructive and destructive interference if we consider light to be a particle?

2.(a). An electron is said to possesses wave nature also. Then what is the definition of a particle or fermion? What is mass? I mean mass is considered to be a property of matter or particle. If ,then, a particle is actually a wave, then how is mass distributed in this wave? We know that energy can be converted to mass. A wave is a kind of energy. Is a particle then just a highly localized chunk of energy/wave ?

2.(b). If an electron is left in complete isolation, how will it behave- like a wave or a particle? A dear friend of mine in this forum told me that an electron will start spreading like a wave if left in isolation. However, if we emit photons to see this wave, it will undergo wavefunction collapse and we will see a particle. Can anyone explain to me how this collapse actually happens? And whether isolation is a necessary condition for the electron to "exhibit" wave nature (isolation in the sense that there are no photons roaming around)?

2.(c). Then ,again, when an electron is made to undergo two-slit experiment, when/how does it decide to convert from its particle character to wave character?

2.(d). Does an electron in an orbital in an atom exhibit wave nature or particle nature, if : i) it is placed in a room full of light/heat (or in other words, the room is full of photons), ii) it is placed in a room devoid of any heat/light?

2.(e). During formation of chemical bonds, interference between the two electrons of the participant atoms is taken into consideration. Is this just a probability wave, or are we really taking electrons to be acting as waves? And if the case is the latter one, then what is the reason that the particle nature of electron is completely neglected here?


Eagerly waiting for your answers...

regards
Mr V

 

[Mr Virtual]

Maybe my questions are too simple. But if anyone could show a little patience and give a good answer, I'd be grateful.

Again, you don't need to answer all the questions. Only those that you feel like.

Mr V

 

[Farzan]

I'm confused about these questions too.

 

[Moridin]

Is Light A Wave or A Particle?

http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html#c4

You cannot explain diffraction, interference or polarization with the particle model. You need to think of photon as a quanta of energy, that is, with definite energy levels.

The Double-Slit Experiment can be explained with photons (quanta of energy; not a classical particle). You can find a basic explanation of it using Heisenberg's uncertainty principle by watching the http://ocw.mit.edu/OcwWeb/Physics/8-01Physics-IFall1999/VideoLectures/detail/Video-Segment-Index-for-L-34.htm with MIT Professor Walter Lewin (RealPlayer is required).

According to HUP, an electron does not have a fixed value for for either of the two quantities until you try to measure it. It is hard to understand at first, but remember that quantum mechanics is about probability.

http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html

An electron can be described with quantum mechanics as well. A better explanation is available here:

https://www.physicsforums.com/showpost.php?p=862093&postcount=2

That is as far as I can get now.

 

[Mr Virtual]

You cannot explain diffraction, interference or polarization with the particle model. You need to think of photon as a quanta of energy, that is, with definite energy levels.

I have never heard of a "photon" having definite "energy levels". What do you mean by "energy levels"?

 

[cristo]

Feynman actually explained diffraction with the particle model: absorption of photon and then its re-emittance.

I've never heard of this. As far as I'm aware, the particle model cannot explain diffraction. Care to provide a reference?

But he shed no light on interference and polarization. Why is it not possible to explain these phenomena on the basis of particle model? Doesn't it sound like when we can't explain a phenomenon by one theory, we apply another one? Photoelectric effect contradicts wave model, and Double slit experiment contradicts the particle model. Doesn't it mean that our own theory is flawed at some level? Because both the things (photoelectric effect and double slit phenomenon) happen in nature, and we don't have a single theory explaining both of them.

The whole point of "wave-particle duality" is that an object in nature admits both the characteristics of a particle and of a wave. If you read the FAQ (the first link in the above post) it may become clearer as to why there is no problem with this.

 

[ZapperZ]

Feynman actually explained diffraction with the particle model: absorption of photon and then its re-emittance. But he shed no light on interference and polarization. Why is it not possible to explain these phenomena on the basis of particle model? Doesn't it sound like when we can't explain a phenomenon by one theory, we apply another one? Photoelectric effect contradicts wave model, and Double slit experiment contradicts the particle model. Doesn't it mean that our own theory is flawed at some level? Because both the things (photoelectric effect and double slit phenomenon) happen in nature, and we don't have a single theory explaining both of them.
If the existing theory is the correct one, then am I not right in saying: What is a particle? - A wave. And what is a wave? - collection of particles (photons). What are particles and waves?

This is not true. QM can describe ALL of these observations with one single, consistent formalism.

I have mentioned the Marcella's paper[1] that clearly derived, using QM, a single-slit, double slit, and multiple slit patterns. Please download that Eur. J. Phys. paper if you have access to it. We don't teach students that because it is a lot more involved and tedious, so we continue to use the wave model when we encounter such situation.

Furthermore, you also seem to miss Feynman's path integral formalism of QM. The most important aspect of QM is the principle of superposition. When quantum objects have the ability to assume more than one state, then all of these states are in a superposition of states. When quantum objects encounter a multiple slit, then you have a superposition of paths! When you stick to this idea, then you'll realize that it doesn't matter if it is a photon, an electron, a proton, a neutron, a buckyball, etc... if they are coherent quantum particles and they have more than one path to go through, then you'll have a superposition of paths for these particles that resulted in the interference pattern. So this ONE principle explains ALL of these observations for all these particles.

Zz.

[1] T.V. Marcella Eur. J. Phys. v.23 p.615 (2002).

 

[technobot]

I'm not an expert, so take this with a grain of salt, but my understanding is that photons/electrons/etc are neither particles nor waves, but rather some other form of entity, which we do not fully understand, but which has the characteristics of both. The wave model and the particle model are then each an approximation, each approximating some properties well and other properties poorly.

If I am to borrow the elephant analogy from somewhere else, consider this: One blind man feels the leg of the elephant and says 'it's a thick round column'. Another blind man feels the ear of the elephant and says 'it's a big flat sheet'. In fact it is neither - and both.

We can then in each situation use the model which fits the situation better, to get an approximate result - often it is still accurate enough. Or, we can use a much more complicated model that takes all aspects into account, and get a more accurate result - but the mathematical complexity of such calculations often makes this approach overkill, and the extra accuracy isn't always worth the complexity. This is how science works in many cases.

Hope that helps.

 

[Rainbow]

2.(a). An electron is said to possesses wave nature also. Then what is the definition of a particle or fermion? What is mass? I mean mass is considered to be a property of matter or particle. If ,then, a particle is actually a wave, then how is mass distributed in this wave? We know that energy can be converted to mass. A wave is a kind of energy. Is a particle then just a highly localized chunk of energy/wave ?

A matter wave is not the matter itself. It is just a probability wave which gives the probability of the particle being in a small region centered around the point of observation. Now the question arises, how does the electron travel between the origin and the point of detection? What makes its path so unpredictible that we cannot predict where the electron will be detected(we can only calculate probabilities)?

 

[jtbell]

1. Light acts as particles called photons. Photons have a definite energy based on their frequency/wavelength. But frequency/wavelength are terms used when we assume light to be acting as a wave. How do we imagine a photon to possesses any wavelength or frequency? How do we explain Double-Slit Experiment i.e. how does a single photon pass through both the slits? How do we explain constructive and destructive interference if we consider light to be a particle?

Welcome to quantum physics, where the fundamental entities (photons, electrons, etc.) are neither classical waves nor classical particles, but rather, quantum objects that have characteristics of both. We do not have to "switch" between waves and particles when analyzing them. The mathematics of quantum mechanics and quantum field theory contains both kinds of characteristics, and predicts the results of experiments very successfully. When Feynman and other physicists write about particles, these are the kind of particles that they refer to, not the purely classical kind.

As far as I know, no one has come up with a "classical-like picture" of the way these things "really are." You can find such pictures, used as analogies to help describe quantum experiments, but they always break down somewhere so you have to take them with a grain of salt.

Fundamentally, there is (so far) no generally accepted picture, or interpretation of the way things "really are" at the quantum level. There are various competing interpretations of QM, but they are all based on the same mathematics and give the same results for the results of actual experiments. They differ in things that cannot be tested by experiment, even in principle, and they all have non-classical features.

 

[Rainbow]

1. Light acts as particles called photons. Photons have a definite energy based on their frequency/wavelength. But frequency/wavelength are terms used when we assume light to be acting as a wave. How do we imagine a photon to possesses any wavelength or frequency? How do we explain Double-Slit Experiment i.e. how does a single photon pass through both the slits? How do we explain constructive and destructive interference if we consider light to be a particle?

It's not the frequency/wavelength of the photon. When talk about the energy of the photon, then it is dependent on the frequency of the corresponding wave.
For the next part of the question, I don't think a single photo can pass through both the slits. It is the probability wave that passes through both the slits, and the photon has equal probability of passing through anyone of the slits.
Now for the interference- It is the waves that undergo interference and form bright and dark fringes on the screen. Now, as the intensity of the fringe gives the relative probability of a photon absorption, the photons tend to be absobed at the maxima, and tend not to be absorbed at the minima, and the probability of absorption is intermediate for intermediate intensities.

But I should tell you that I'm still confused regarding this wave-particle duality.

 

[Feynman diagram]

I think the biggest problem people have understanding the wave-particle duality is imagining that something is definitely a wave or definitely a particle. To explain diffraction for example we think of photons as waves. They are not waves - neither are they particles. That is the whole point. They are both at the same time but exhibit certain properties which imply particle-like behaviour sometimes, and wave-like behaviour other times. If you take the mathematics of quantum theory as a description of the actual processes involved then you end up with statements that appear to defy logic - mathematically, in the double slit experiment, the electron goes through neither hole, and both holes, and only one hole, and only the other hole, all at the same time. Maybe that's exactly what actually happens, but our brains can't deal with this kind of paradox. Or maybe not - if maths is just a way of getting an answer that matches experimental outcomes then it could happen entirely differently.

 

[Sojourner01]

There is no such thing as a wave or a particle. They are mathematical constructs. Even a body of water doesn't implicitly 'know' it's undergoing wave motion. There shouldn't be any paradoxical confusion because there were never two objects called wave and particle for the quantum to be split between. They are not coherent physical concepts in themselves. A quantum isn't a wave and a particle, or partly wave, partly particle, it's a quantum. You wouldn't need either of the former to fully describe and understand the latter.

 

[Mr Virtual]

Thanks for your replies.

Furthermore, you also seem to miss Feynman's path integral formalism of QM. The most important aspect of QM is the principle of superposition. When quantum objects have the ability to assume more than one state, then all of these states are in a superposition of states. When quantum objects encounter a multiple slit, then you have a superposition of paths!

Yeah, sorry I forgot about this principle. So what you mean to say is that QED superpositions both wave model and particle model. The experiment in which the amplitude is favourable to wave nature, it has the highest probability of displaying wave-nature of electron/light, whereas if the amplitude is favourable to particle nature, it has the highest probability of displaying particle nature of electron. Right?
So it really depends on the type of experiment whether we will observe wave nature or particle nature.

When quantum objects encounter a multiple slit, then you have a superposition of paths!

What does that mean? I mean: suppose there are two slits. The electron has some amplitude to pass through the first slit, and it has some amplitude to pass through the second one. But how can there be an amplitude that it passes through both the slits? Basically, how can a particle be present in two places at once (if we completely ignore the wave model of electron here)? It would be nice of you to explain it a bit more.

A matter wave is not the matter itself. It is just a probability wave which gives the probability of the particle being in a small region centered around the point of observation.

This is what I thought previously. But it is a proven fact that "a matter wave is actually the matter itself".

As far as I know, no one has come up with a "classical-like picture" of the way these things "really are." You can find such pictures, used as analogies to help describe quantum experiments, but they always break down somewhere so you have to take them with a grain of salt.

Fundamentally, there is (so far) no generally accepted picture, or interpretation of the way things "really are" at the quantum level. There are various competing interpretations of QM, but they are all based on the same mathematics and give the same results for the results of actual experiments. They differ in things that cannot be tested by experiment, even in principle, and they all have non-classical features.

That is what I was saying- that though we have all the maths for quantum mechanics, we do not have a concrete theory about why things are the way they are. Even QED just says that a particle is a wave, and a wave is a bunch of particles, but why? How? No answer for that.

It's not the frequency/wavelength of the photon. When talk about the energy of the photon, then it is dependent on the frequency of the corresponding wave.

Agreed. But can you explain how that wave is formed with the help of these photons? I mean frequency/wavelength represent the oscillations of the wave, but where are these oscillations taking place in the photon stream? A wave is a continuous oscillating thing, but photons are separate from each other- there are gaps between them.

For the next part of the question, I don't think a single photo can pass through both the slits. It is the probability wave that passes through both the slits, and the photon has equal probability of passing through anyone of the slits.

But it is shown in the Double Slit experiment that when a single photon is fired, it passes through both slits and interferes with itself. It is easily explained using wave theorem, but not so with the particle model.

Now for the interference- It is the waves that undergo interference and form bright and dark fringes on the screen. Now, as the intensity of the fringe gives the relative probability of a photon absorption, the photons tend to be absobed at the maxima, and tend not to be absorbed at the minima, and the probability of absorption is intermediate for intermediate intensities.

Could you please explain this phenomenon more elaborately. I mean what happens to photons during destructive and constructive interference? What do you mean by "absorption" of photons.


regards
Mr V

 

[Mr Virtual]

I read this in Wikipedia

There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature

Wow! What an illuminating statement. Does every physicist think like that- keep on finding mathematical answers without having a clue as to what it practically implies, or how it happens in reality?

 

[Feynman diagram]

What does that mean? I mean: suppose there are two slits. The electron has some amplitude to pass through the first slit, and it has some amplitude to pass through the second one. But how can there be an amplitude that it passes through both the slits? Basically, how can a particle be present in two places at once (if we completely ignore the wave model of electron here)? It would be nice of you to explain it a bit more.

A particle can actually, physically be in 2 places at once. This has recently been shown in an experiment (I'll post a link to the paper when I can find it).
However, bear in mind that it's not the electron but the wavefunction for the electron (or rather, part of the wavefunction) which passes through both slits at the same time, just as it is part of the wavefunction which goes through one slit or another and also neither. You get bogged down in paradoxes when you start thinking of a physical object doing this. This is just what the maths tells us happens. No-one has ever seen a wavefunction or can assert that one actually exists but it is the best description we have for now.
Even if you think of the electron as a wave this doesn't make sense - a physical wave cannot go through both slits and only one and neither at the same time. The wavefunction does, at least mathematically.

 

[Mr Virtual]

A particle can actually, physically be in 2 places at once. This has recently been shown in an experiment (I'll post a link to the paper when I can find it).

Really? I am anxiously waiting for the link.

However, bear in mind that it's not the electron but the wavefunction for the electron (or rather, part of the wavefunction) which passes through both slits at the same time, just as it is part of the wavefunction which goes through one slit or another and also neither.

Oh please don't disappoint me. Is it the particle or the wavefunction? Even if it is a wavefunction, how does there exist an amplitude that the electron (a particle) can pass through both the slits at once?

 

[ZapperZ]

I read this in Wikipedia

There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature

Wow! What an illuminating statement. Does every physicist think like that- keep on finding mathematical answers without having a clue as to what it practically implies, or how it happens in reality?

I can come in and re-edit that Wikipedia entry to be something else. Now what?

Please do NOT pay that much emphasis on stuff you read on Wikipedia. I have a hard time already trying to correct the misconception that people get from legitimate sources. I do not need the added burden of correcting information from dubious sources.

Really? I am anxiously waiting for the link.Oh please don't disappoint me. Is it the particle or the wavefunction? Even if it is a wavefunction, how does there exist an amplitude that the electron (a particle) can pass through both the slits at once?

There's a whole slew of experiments that directly tests and measure the phenomenon of superposition. That is what I have been trying to impress upon you, and it is something you seem to have missed. The bonding-antibonding states of H2 molecule is something very familiar in chemistry, and that can only be explained by the superposition of the electron's position between the two H nuclei. Furthermore, there's a whole slew of experiments, namely the Stony Brook and Delft experiments that deal with this. Do a search on here.

Zz.

 

[Mr Virtual]

I can come in and re-edit that Wikipedia entry to be something else. Now what?

Oh please do that, so that it does not mislead anyone else.

 

[Mr Virtual]

there's a whole slew of experiments, namely the Stony Brook and Delft experiments that deal with this. Do a search on here.

Yeah, I am just going to do that. After that I will tell you whether I understood or not.

 

[Gza]

A particle can actually, physically be in 2 places at once.

Perhaps my ignorance is showing here, but how exactly do we go about measuring both positions of the particle (since the first measurement causes collapse to a specific eigenstate of the position operator, and doesn't allow us to say much about the second position)

 

[ZapperZ]

Perhaps my ignorance is showing here, but how exactly do we go about measuring both positions of the particle (since the first measurement causes collapse to a specific eigenstate of the position operator, and doesn't allow us to say much about the second position)

You don't. But remember that if you measure a non-commuting observable, the original observable will STILL be in a superposition and has not been "collapsed". That is what is done in the Stony Brook/Delft experiments, where they measured the "coherence energy gap". This energy gap arises when there is a superposition of currents around the SQUID in both directions simultaneously. The same thing applies to the bonding-antibonding state in H2 molecule, where it arises out of the superposition of the electron's position at both H atoms.

Zz.

 

[Proof.Beh]

I read this in Wikipedia

There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature

Wow! What an illuminating statement. Does every physicist think like that- keep on finding mathematical answers without having a clue as to what it practically implies, or how it happens in reality?

Thanks because of your best answer. QM is weakest science for describing physical cases. Since with probability, we cann't expaire physics concepts.
I believe that God does NOT play Dice with the universe, Too.

Thanks.
------------------------
Formulate Realities.

 

[Moridin]

I read this in Wikipedia

There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature

Wow! What an illuminating statement. Does every physicist think like that- keep on finding mathematical answers without having a clue as to what it practically implies, or how it happens in reality?

Thanks because of your best answer. QM is weakest science for describing physical cases. Since with probability, we cann't expaire physics concepts.
I believe that God does NOT play Dice with the universe, Too.

There are so many incorrect statements in that post I do not know where to begin.

It is correct to say that all science is approximations. However, with time, experiments and tested predictions, certain scientific knowledge becomes a better and better approximation and a more probable approximation. The idea that the Earth orbits our sun with all data is an approximation, just a very accurate approximation.

Probability is used everywhere in science. A quote from The Feynman Lectures on Phyiscs (Volume I 12-1) will perhaps make it more clear.

What is a chair? Well, a chair is a certain thing over there...certain?, how certain? The atoms are evaporating from it from time to time - not many atoms, but a few - dirt falls on it and get dissolved in the paint; so to define a chair precisely, to say exactly which atoms are chair, and which atoms are air, or which atoms are paint that belongs to the chair is impossible. So the mass of a chair can be defined only approximately. [..] so we can deal with it only as a series of approximations and idealizations.

Be continued research approximations are getting better and better all the time. There is a certain probability, that at any given time, so and so many atoms will evaporate from the chair. Does this mean that research on it is useless, that all scientific data gathered are useless? No, because the approximations will get better and better to reality as more data is coming in, predictions and explanations will get better and better.

Quantum Mechanics makes some of the most accurate predictions in physics. Feynman once said it is like measuring the width of North America and having a margin of error of the width of a hair.

Just because physical descriptions of quantum mechanics is counterintuitive means absolutely nothing at all. A lot of experimental data supports quantum mechanics and mathematical derivations are solid, otherwise known as physics.

We can weight a chair at any given time, finding out its approximate mass, even though there is a certain probability of atoms evaporating and condensation. However, that in itself does not make the approximate weight useless.

Furthermore, quantum mechanics in itself is very solid science. It is testable, observations can be repeated, it is falsifiable, it produces useful knowledge and can make powerful and accurate predictions.

 

[Proof.Beh]

There are so many incorrect statements in that post I do not know where to begin.

It is correct to say that all science is approximations. However, with time, experiments and tested predictions, certain scientific knowledge becomes a better and better approximation and a more probable approximation. The idea that the Earth orbits our sun with all data is an approximation, just a very accurate approximation.

Hey guy, don't mistake

If you Look at my writing again careful, will see that APPROXIMATION isn't equal probability. Approximation of Newton in relativity isn't a probability. If you say that "i'll go to uneversity at 6 Approximately", you go there however you laten. But whenever you are saying "i'll go to uneversity at 6 PROBABLY", it is possible that you don't go NONE.

Thanks.
---------------------------
Formulate realities.

 

[Mr Virtual]

To ZapperZ

There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.

I just found out another thing. Wikipedia says that this statement was made by Niels Bohr himself. So it isn't a throw-away comment made by a fool (as far as wikipedia is concerned). What say? Are you still sure you can re-edit Bohr's statement?

 

[cristo]

To ZapperZ


I just found out another thing. Wikipedia says that this statement was made by Niels Bohr himself. So it isn't a throw-away comment made by a fool (as far as wikipedia is concerned). What say? Are you still sure you can re-edit Bohr's statement?

Therein lies the problem-- don't back up your arguments with things you read on Wikipedia. It turns out that this quote is apparently attributed to Bohr. Here's a letters page to physicstoday that I've found http://www.physicstoday.org/vol-57/iss-10/p15.html . Unfortunately, I don't have the subscriptions to read the articles at the moment, but I'm sure others will.

 

[Mr Virtual]

So it turns out it isn't Bohr's statement.
If people like you keep a check on the material presented on such sites, we won't have to take in the whole lot of crap they give.
Thanks a lot

Mr V

 

[ZapperZ]

To ZapperZI just found out another thing. Wikipedia says that this statement was made by Niels Bohr himself. So it isn't a throw-away comment made by a fool (as far as wikipedia is concerned). What say? Are you still sure you can re-edit Bohr's statement?

Yes I can, because

1. Bohr did not live to see what we now know of physics and QM.

2. Bohr holds a strong belief in solipsism. While I also holds similar views on it (i.e. I'd rather talk about things that we CAN empirically verify, while others are nothing more than a matter of tastes), I would NOT extend that to categorize the whole world we live in as that.

3. Copenhagen interpretation that Bohr formulated and championed, is not the only way to look at what QM is telling us. Bohr didn't live to see many of the others and the various ways of looking at QM.

If you hold Bohr's view so dearly, do you also still hang on to the Bohr's model of the atom?

Zz.

 

[Mr Virtual]

What is solipsism? I am not that good at english.

 

[ZapperZ]

So it turns out it isn't Bohr's statement.
If people like you keep a check on the material presented on such sites, we won't have to take in the whole lot of crap they give.
Thanks a lot

Mr V

I'm sorry, but we have had this "complain" before. Read the many differnt threads on the problems with Wikipedia that have already been discussed on here. You KNOW fully well the intrinsic fault of the system that you use. It is your own fault for not caring the quality of the information that you are receiving. To blame us for not correcting the wrong info that you are reading is utterly ridiculous.

It is YOUR responsibility to pay attention to the nature of the source. It is time that you take the responsibility for your own actions and not blame it on someone else.

Zz.

 

[Mr Virtual]

If you hold Bohr's view so dearly, do you also still hang on to the Bohr's model of the atom?

I knew this was coming! Do I still believe bohr's model? Of course not

 

[Mr Virtual]

It is your own fault for not caring the quality of the information that you are receiving. To blame us for not correcting the wrong info that you are reading is utterly ridiculous

Oh MY! I am not complaining! You misunderstood me. What I meant was that there should be people like you, not that you should be there to handle everything.
I was only complementing cristo's help to make me understand that what I read was wrong. That's all. No offence was intended.

 

[cristo]

I was only complementing cristo's help to make me understand that what I read was wrong.

I'm not sure that I did help you understand. If you read my post again I said that the quote is attributed to Bohr. At the bottom of that article is the reference to the article in which (I presume) it is attributed to him. However, since I do not have the priveledges at home, I cannot view that article, and so cannot comment further.

 

[Mr Virtual]

And, of course, from now on I will keep a check on the validity of what I am reading on the net.
Thanks