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I don't have access to the Scientific American

Who has any clue as to what the dimentions beyond ^3 may be. Use a simple cube as an example. Apart from length, width and height, what else can there be? Hmmm...

Scientific American is carried by most public libraries.

A spatial dimension beyond the usual 3 is not necessarily imaginable and not necessarily physical in the sense you are thinking.

To answer the question of where something is requires 3 dimension. I need to supply an x, y, and z coordinate. A fourth dimension is merely a statement that to fully define where something is requires a fourth value. It does not necessarily follow that it is a place, as represented in science fiction movies, where you can go.

thanks

It is regularly stated by cosmologists that there is "nothing outside the universe". What is "nothing". Can one not define it as (1) timelessnes: i.e "nothing can change when there is nothing"; therefore "nothing" should (2) have zero entropy and thus zero temperature. A four-dimensional Euclidean space-time will have these properties because the time axis is perpendicular to the space axes. This implies that any differential within three-dimensional space with respect to time will have to be zero. Maybe our universe is flying apart to unbend space-time towards a state of zero entropy; as it had been before creation?

JB:"It is regularly stated by cosmologists that there is "nothing outside the universe". What is "nothing"."

The nothing in your quote means that there is nothing else besides our universe. Or in other words that there is no "outside" for our universe, only the "inside".

JB:"A four-dimensional Euclidean space-time will have these properties because the time axis is perpendicular to the space axes. This implies that any differential within three-dimensional space with respect to time will have to be zero."

Nah, it ain't working that way. First of all, the spacetime is not euclidean, is lorentzian, so time is pseudo-orthogonal on the space, so to speak.
Second of all, the time derivative in a foliation is not vanishing, unless you really don't know mathematical analysis. The difference being that you do not calculate d/dt[a(t_fixed)] but d/dt[a(t)]|t=t_fixed.


Maybe our universe is flying apart to unbend space-time towards a state of zero entropy; as it had been before creation?

Hi Pasti,

How can a geometry be Lorentzian? Either you have a "flat space" with linearly independent coordinates or you have a bent space whatever shape you call it. Even Einstein's equations of general relativity describes a "bent space-time field" relative to a four-dimensional Euclidean space. In a Eucildean space of any dimension derivatives calculated relative to a change along one of the axes are always zero. Thus within such a space one cannot calculate any change with time (the so-called fourth dimension); If nothing can change there must be nothing.

JB:"How can a geometry be Lorentzian?"

Huh?Come again? Lorentzian geometry (and not Riemannian geometry) is the basis of both special relativity and general relativity. How can you have such a geometry? Well, in lorentzian geometry you have a metric given by

(ds)^2= -(dt)^2+(dx)^2+(dy)^2+(dz)^2

instead of

(ds)^2=(dt)^2+(dx)^2+(dy)^2+(dz)^2

I am not exactly sure that I seee the problem.


JB:"Either you have a "flat space" with linearly independent coordinates or you have a bent space whatever shape you call it."

Well, the Riemaninan flat space (i.e. the Euclidean space) is given by a (global) metric g^ab=diag(+,+,+,+) while the Lorentzian flat space(i.e. the Minkovski space) is goven by a (global) metric g^ab=diag(-,+,+,+,). What is your point? I am not sure I follow.

JB:"Even Einstein's equations of general relativity describes a "bent space-time field" relative to a four-dimensional Euclidean space."

No, they originally have been developed for Lorentzian spacetimes. However, for certain applications where certain technicalities become annoying, you can have Euclidean/Riemanian GR.

JB:"In a Eucildean space of any dimension derivatives calculated relative to a change along one of the axes are always zero."

By no means. If what you say were true, you wouldn't have mechanics (classica) nor would you have differential geometry.

JB:"Thus within such a space one cannot calculate any change with time (the so-called fourth dimension); If nothing can change there must be nothing."

I would suggest that you take a look at lagrangean and hamiltonian mechanics. Also at quantum mechanics. Also differential equations and partial differential equations (specifically the initial value problem). I can give you refs on these issues if you so like.

Of course such a chnge in time can be calculated, that is why you have what is called the evolution equations (the equations of motion).

Hi Pasti,

You have good arguments and they are mostly correct in terms of the accepted framework.
The problem is the what you call the Lorentzian metric seems to indicate that one can represent the time axis as an imaginary axis perpendicular to the space axes; whereas it is known that space-time is bent. Although the Lorentzian metric also represents an inherent bending, I believe that it is not the whole story. Spaces could exist within which a time derivative is not possible and within which time then cannot exist. In fact I believe that an entangled mass-wave ("multi-particle" wave) represents such a space. I know you will now say that mass-waves are probability distributions and thus do not constitute an entity within space on their own. This is where I differ from Born; because Born's interpretaion of mass-waves violates the conservation of energy.

Rob:"The problem is the what you call the Lorentzian metric seems to indicate that one can represent the time axis as an imaginary axis perpendicular to the space axes; whereas it is known that space-time is bent."

You are confusing local flatness with global flatness (in both the Riemannian and Lorentzian case). A spacetime can be curved (not bent-use the appropriate terminology) and yet, locally it is always flat. This is quite straightforward to understand (the lower dimensional equivalent are that at any point of a curve you can construct a tangent, at any point on a surface you can construct a tangent plane,etc).

Alternatively, the quadratic form that represents the metric can always be diagonalized locally, but not always globally.

Rob:"Although the Lorentzian metric also represents an inherent bending, I believe that it is not the whole story. Spaces could exist within which a time derivative is not possible and within which time then cannot exist."

Well, then how about you construct it? Give me a spacetime metric in which time does not exist!

Rob:"In fact I believe that an entangled mass-wave ("multi-particle" wave) represents such a space."

You mean that a wavefunction can be represented on such a curved functional space, right? A wave is not a space, it either "exists" in a space, or is represented in a space.

Usually, such wavefunctions from a Hilbert space, and it is possible that this Hilbert space be not globally flat, but I won't ask you for an example.

Rob:"I know you will now say that mass-waves are probability distributions and thus do not constitute an entity within space on their own."

Once again, you mean that the squared magnitude of a wavefunction is distribution of localization probability in a space, right? Let's make a deal: if you want to dicuss such a topic, use the appropriate terminology, so that we can understand each other.

Rob: "This is where I differ from Born; because Born's interpretaion of mass-waves violates the conservation of energy."

First of all, you mean Bohr, right? Born was a physicist too, got a Nobel prize too, "discovered" the photon and quantum absorption of light, but he did not develop the Copenhagen interpretation of quantum mechanics. Bohr did.

So you say that this is where you disagree with Bohr. Fine with me. Now how does the Copenhagen interpretation of the wave-function violate energy conservation? This I am really interested to see (you realize why, right?)

Wnderful response Pasti!
You know the present paradigm well; so you have raised so many questions that it requires a book.
Go to my website.

Nonetheless, if you have linearly independent coordinates you cannot differentiate them relative to each other. If time is one of the coordinates it means that nothing can change within the remaining 3 coordinates. This is where mathematics predicts unequivocably what will happen in such a 4 dimensional (Euclidean)space. So I will leave it there for you to ponder.

The statistcal interpretation of the wave function is accredited to Born; not Bohr. In fact Born was belatedly given the Nobel Prize for it in 1954. It is based on Heisenverg's Uncertainty Relationship, which, according to Born implies that one cannot know the position and momentum of an electron at the same time. If this is true, then all the calculations to design electron microscopes and electron accelerators MUST be wrong. The statistical interpretaion of the wave function has NOTHING to do with experimental difficulties. This has been the mistake made by Heisenberg, and even Pauli, and blindly folloed by Einstein. The fact is that even if one could make perfect measurements Heisenberg's Uncertainty Relationship should still hold. Thus let us apply Born's interpretaion by using "perfect" measurements. This means that when measuring the position of an electron with momentum p, one will get a position but the momentum will become indeterminate. When now again measuring the momentum of the electron you get another value which can be larger than the original value p. This implies that the electron's energy has increased even though one has made perfect measurements. This not possible. You might want to argue that perfect measurements are not possible and walk away. This is correct in all cases (also clasically), but this does NOT remove the fact that the Born interpretation of the Heisenberg's Uncertainty Relationship has NOTHING to do with acuuracy of measurement. Thus the Born interpretation has to be wrong because it violates the conservation of energy.

QED

JB:?You know the present paradigm well; so you have raised so many questions that it requires a book.Go to my website.?

Don?t insult me, will you. While I am open to new descriptions of superconductivity without cooperons, the internet is clogged with websites like yours where people claim to have discovered things that will revolutionize physics, philosophy and you name it and prove that whatever knowledge has been developed up to date is entirely wrong.
I will assume that at least you know the author of the book, if you are not him. So a few pieces of advice. I believe that you are aware of the fact that such a book can never have the general audience as a marketing target. In which case, the lack of a list of publications on the topic, as well as reviews by people working in solid state physics don?t exactly qualify the book as more than a hoax. The author should be aware of that, given his academic pedigree. So as I said before, I will wait for the published papers.

JB:?Nonetheless, if you have linearly independent coordinates you cannot differentiate them relative to each other. If time is one of the coordinates it means that nothing can change within the remaining 3 coordinates. This is where mathematics predicts unequivocably what will happen in such a 4 dimensional (Euclidean)space. So I will leave it there for you to ponder.?

You can leave anyplace until it gets rotten. Mathematics does not unequivocally predict such a nonsense (at least that is what comes out from what you say). And until you clear this up in a more cogent manner, I wil treat it as a nonsense, and I will send you back to learn calculus, differential geometry and theoretical mechanics.

JB:?The statistcal interpretation of the wave function is accredited to Born; not Bohr. In fact Born was belatedly given the Nobel Prize for it in 1954. It is based on Heisenberg's Uncertainty Relationship, which, according to Born implies that one cannot know the position and momentum of an electron at the same time.?

You are right, my bad. I apologize. It was Born who stumbled upon the ideea that the square of the amplitude is the localization probability distribution.

JB:?If this is true, then all the calculations to design electron microscopes and electron accelerators MUST be wrong.?

Eppur si muove?

JB:?The fact is that even if one could make perfect measurements Heisenberg's Uncertainty Relationship should still hold. Thus let us apply Born's interpretaion by using "perfect" measurements.?

Then let?s.

JB: ?This means that when measuring the position of an electron with momentum p, one will get a position but the momentum will become indeterminate. When now again measuring the momentum of the electron you get another value which can be larger than the original value p. This implies that the electron's energy has increased even though one has made perfect measurements. This not possible.?

I agree it isn?t possible, but there is an error in your nicht gut gedankt experiment screaming at me. If you measure the position precisely, say you get x1, the measurement error for the momentum is indeterminately large, via Heisenberg uncertainty relations. This means that the momentum can be anything, and you don?t know what it is, since you didn?t measure it. Let?s say it was p1.
If you then measure the momentum precisely, you get a value, say p2. But since you don?t know what p1 is, from the first measurement, you cannot actually say that p2 can be larger than p1. You?ve introduced this assumption ad hoc, and of course that if you consider it valid, you get a violation of energy conservation. The problem is that you cannot introduce it as you please, unless you have some very heavy observational evidence for it. Which you don?t have such evidence. Au contraire.


JB:?You might want to argue that perfect measurements are not possible and walk away. This is correct in all cases (also clasically), but this does NOT remove the fact that the Born interpretation of the Heisenberg's Uncertainty Relationship has NOTHING to do with acuracy of measurement. Thus the Born interpretation has to be wrong because it violates the conservation of energy.?

I won?t argue that perfect measurements do not exist in fact. For the time being it isn?t necessary for the example you gave to figure out where and how experimental/instrumental errors come into play. Not even principialy.
And while I am open to arguments about Born being wrong in its interpretation, yourr example hardly qualifies as that. For the time being, it qualifies only as a not so well thought experiment. But then I am sure you won?t agree with my conclusion.

Pasti: Don?t insult me, will you. While I am open to new descriptions of superconductivity without cooperons, the internet is clogged with websites like yours where people claim to have discovered things that will revolutionize physics, philosophy and you name it and prove that whatever knowledge has been developed up to date is entirely wrong.
I will assume that at least you know the author of the book, if you are not him. So a few pieces of advice. I believe that you are aware of the fact that such a book can never have the general audience as a marketing target. In which case, the lack of a list of publications on the topic, as well as reviews by people working in solid state physics don?t exactly qualify the book as more than a hoax. The author should be aware of that, given his academic pedigree. So as I said before, I will wait for the published papers.

I agree that there are numerous books published by individuals who claim they have solved the problems of physics which qualified scientists have not been able to do up to now. The latest one that I am aware of is "The Final Theory". It usually does not take long to determine the wrong premises that have led such an author astray. In the latter book it is clear that the author became stuck in the time before Galileo. He does not understand the role that relativity (Galilean and Einsteinian) plays when analysing dynamical systems. It is a pity that such books are published. They muddy the water so that people ignore other books which are truly adding to our knowledge. You should at least have been opnminded enough to read the prologue to the book on "superconduction without Cooper pairs". The reason why the author was forced to publish a book is explained in detail. The book is at present being reviewed by competent scientists and these reviews (posistive or negative) will be posted on that website as they become available. There are already some reviews. The author of that book also challenges the whole scientific community to prove him wrong (in writing). Furthermore on the website it is clearly argued why the BCS theory is not a theory at all, and what the actual mechanism for superconduction must be. So I challenge you to read that and point out the flaws.

Pasti: Mathematics does not unequivocally predict such a nonsense (at least that is what comes out from what you say). And until you clear this up in a more cogent manner, I wil treat it as a nonsense, and I will send you back to learn calculus, differential geometry and theoretical mechanics.

Consider a four-dimensional Euclidean space with coordinates x(1), x(2), x(3) and x(4). these coordinates are lineraly independent so that
dx(i)/dx(j)=0 for all i not equal to j. Thus if the fourth axis relates to time in any way nothing can change within three-dimensional space defined by the first three coordinates. What I speculated on is that this might be why space-time must be curved; i.e. neither special relativity or general relativity can be described by an Euclidean metric. I further speculated that a Euclidean space-time might thus be considered as "nothing" because if it exists nothing can change with time within the three space coordinates. I just thought it might be an interesting idea, and did not expect that I will be sent back to relearn calculus!

Pasti: I agree it isn?t possible, but there is an error in your nicht gut gedankt experiment screaming at me. If you measure the position precisely, say you get x1, the measurement error for the momentum is indeterminately large, via Heisenberg uncertainty relations. This means that the momentum can be anything, and you don?t know what it is, since you didn?t measure it. Let?s say it was p1.
If you then measure the momentum precisely, you get a value, say p2. But since you don?t know what p1 is, from the first measurement, you cannot actually say that p2 can be larger than p1. You?ve introduced this assumption ad hoc, and of course that if you consider it valid, you get a violation of energy conservation. The problem is that you cannot introduce it as you please, unless you have some very heavy observational evidence for it. Which you don?t have such evidence. Au contraire.

No you misunderstood: you first measure p1, then the position x1 and then p2 using perfect measurements. Now Shroedinger's equation is a statement of the conservation of energy. Thus if you start of with a momentum p1, then measure x1, and then p2, one must have that p1=p2 or else you violate the conservation of energy. After all there was no potential energy term involved. Furthermore it is a perfect measurement which, owing to its perfectness does not inject energy when making the measurement. Thus if p1 and p1 are different where did the energy come from or go to? I hope I have expressed myself more cogently.

Pasti:I won?t argue that perfect measurements do not exist in fact. For the time being it isn?t necessary for the example you gave to figure out where and how experimental/instrumental errors come into play. Not even principialy.
And while I am open to arguments about Born being wrong in its interpretation, yourr example hardly qualifies as that. For the time being, it qualifies only as a not so well thought experiment. But then I am sure you won?t agree with my conclusion.

The mistake that Born and Heisenberg made was to equate the wave-function in k-space as relating to de Broglie's wavelength and thus to the momentum of the electron. Now accept for arguments sake that you can model a single stationary electron in space by a localised time-independent field that does not spread with time and that you are within the same inertial framework in which the electron is stationary. The localised field lives in position space as well as in k-space. How do you measure the De Broglie wavelength of the electron? You cannot, because the De Broglie wavelength is a relativistic paramter. You will measure different values for it when you move at different velocities relative to the time-independent stationary field representing the electron. Thus the De Broglie momentum-wavelength relationship has nothing to do with the uncertainty in k-space. The uncertainties in position an k are determined, as for any other wave, by the boundary conditions. It is for this reason that an electron can spread out and go through both slits when it encounters the boundary conditions set by the slits. It is also for this reason why it can again become a localised wave when it encounters the boundary conditions set by the detector. You will now probably ask what the boundary conditions are which localises the electron wave in "free space". This relates to the mass of the electron. There is not enough space to treat it further in this forum. I hope that my discussion above might now convince you. Thanks for your responses it helped me to think more clearly.
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JB: ?The author of that book also challenges the whole scientific community to prove him wrong (in writing). Furthermore on the website it is clearly argued why the BCS theory is not a theory at all, and what the actual mechanism for superconduction must be. So I challenge you to read that and point out the flaws.?

You see, JB, your academic pedigree should have taught you long ago that it is not the others burden to prove you wrong, but it is your burden to prove to the others that you are right (with all the pain this actually implies). If you are wrong, most of the scientists will just ignore you, with all of the unfortunate consequences of this attitude. And believe it or not, I sympathize with you more than you will ever be able to know. I am however not impressed by the close-mindedness of peer reviewing, although it can be pigheaded. There are alternatives to it that allow you to actually publish your papers for the entire scientific community to be able to read and judge them. For example, you can upload your work, both experimental and theoretical on www.arxiv.org. And you?d better do that soon, because you know how this is, if the papers are there, chances for you to be vindicated by someone are larger. You should be able to do it quite fast, since I understand that you already have the rejected drafts. As I said previously, I will be waiting for the papers first. Then I will form my own conclusion, whichever that might be.

JB:?Consider a four-dimensional Euclidean space with coordinates x(1), x(2), x(3) and x(4). these coordinates are lineraly independent so that dx(i)/dx(j)=0 for all i not equal to j. Thus if the fourth axis relates to time in any way nothing can change within three-dimensional space defined by the first three coordinates. What I speculated on is that this might be why space-time must be curved; i.e. neither special relativity or general relativity can be described by an Euclidean metric. I further speculated that a Euclidean space-time might thus be considered as "nothing" because if it exists nothing can change with time within the three space coordinates. I just thought it might be an interesting idea, and did not expect that I will be sent back to relearn calculus!?

Oh boy, now I think I understand what you want to say by all this. See why clear communication is preferable? In a certain way, you are right, but it seems to me you have forced particular conclusions into a general context.

You are right about the fact that indeed an euclidean, respectively minkowskian space is an absolutely empty space with nothing happening in it (but not based on the arguments that you made, see below). This doesn?t mean, formally at least, that time does not exist. It exists, but you have simply nothing evolving in time into the same thing, i.e. into nothing. Just take my word for it, this is not related to the traditional issue of time in field theory (if you want I can give you refs on this issue, for gravity at least).

For your arguments to become generally valid (i.e. the derivative relations involving the Kronecker delta to give the information about the spacetime), you need a theory where the spacetime geometry is intimately related to the phenomenology, and for this reason, it would only apply to general relativity. It isn?t working for any other theory.

If you are not talking of gravity, then your conclusion is erroneous. This is straightforward to understand, if you accept the concept of ?background?. In special relativity, the minkowski space is the background in which everything happens, all phenomenology takes place in this background. Consider a point P in the background spacetime, with coordinates
xP1,?xP4 (index 1 usually stands for time). Now consider a phenomenon/event (say a moving particle) at the same point P in the spacetime (at least at a certain moment), and label the coordinates xPE1,?xPE4. Then at say xP1=xPE1, you will have xPi=xPEi, i=2-4, i.e. the event coincides with your point. You see where I am going with this? While in time nothing happens with the point P of the minkowskian spacetime, not the same is the case with the coordinates of the events, which will generally evolve in time.
This means that nothing happens with the spacetime, and yet something happens in the spacetime. In GR, the spacetime point is the ?event?, roughly speaking. This is the difference, and this is why your equations do not imply that nothing happens in that space. They only mean that nothing happens with the space itself, but the space doesn?t have too be empty! This is basically why I sent you back to lagrangean mechanics, differential geometry and calculus. You have unwillingly extended automatically what happens to the space to what happens in the space. Which in 8 out of 10 cases is incorrect (the remaining correct cases are QFT in curved spacetimes and GR)

JB:?No you misunderstood: you first measure p1, then the position x1 and then p2 using perfect measurements.?

JB, this is not what you said. You said just measure first x1 and then p2. But OK, suppose that I misunderstood.

JB:?Now Shroedinger's equation is a statement of the conservation of energy. Thus if you start of with a momentum p1, then measure x1, and then p2, one must have that p1=p2 or else you violate the conservation of energy. After all there was no potential energy term involved.?

We agree, even if potential energy were involved.

JB:?Furthermore it is a perfect measurement which, owing to its perfectness does not inject energy when making the measurement. Thus if p1 and p1 are different where did the energy come from or go to? I hope I have expressed myself more cogently.?

Yes, you exposed the issue in a clearer manner. I might have even understood what you wanted to say. So to summarize (perfect measurements): you measure first p0, then you measure x1. Due to the Heisenberg inequalities, after you measure x1, the momentum p1 has become indeterminate. Then you measure the momentum again, and due to the fact that you measured x1 previously and p1 had become indeterminate, the value p2 that you will measure now (the third time) can be anything, including the case where p2>p0. This is your thought experiment right? Please confirm if this is what you indeed wanted to say, before we go any further.


JB:?The mistake that Born and Heisenberg made was to equate the wave-function in k-space as relating to de Broglie's wavelength and thus to the momentum of the electron.?

OK?

JB:?Now accept for arguments sake that you can model a single stationary electron in space by a localized time-independent field that does not spread with time and that you are within the same inertial framework in which the electron is stationary.?

OK, let?s say for argument?s sake that I do accept your assumptions. What is a localized field, and what is the localized field describing the electron?

JB:?The localized field lives in position space as well as in k-space.?

With this I kind of start having problems. Due to Fourier reasons, you cannot have a localized field in both spaces. Which is what I assume you are saying above.

JB:?How do you measure the De Broglie wavelength of the electron? You cannot, because the De Broglie wavelength is a relativistic parameter.?

Not the way I know it. The de Broglie wavelength is also present in classical mechanics. The particle wave duality applies for any moving particle, and as far as I know, it was tested also for slow (nonrelativistic) electrons.

JB:?You will measure different values for it when you move at different velocities relative to the time-independent stationary field representing the electron.?

Sure, but this a reference frame issue, not a measurement issue. What is your point?

JB:?Thus the De Broglie momentum-wavelength relationship has nothing to do with the uncertainty in k-space.?

It never did. Exactly for the reason that it is a reference frame issue and not a fundamental issue, in your example. The uncertainty in the reciprocal space will also change with the reference frame. As far as I know, it is not Lorentz invariant.

JB: ?The uncertainties in position and k are determined, as for any other wave, by the boundary conditions. It is for this reason that an electron can spread out and go through both slits when it encounters the boundary conditions set by the slits. It is also for this reason why it can again become a localized wave when it encounters the boundary conditions set by the detector. You will now probably ask what the boundary conditions are which localizes the electron wave in "free space".

No, I am asking how boundary conditions (in the sense of partial differential equations) can determine the uncertainties (any uncertainties)in position and momentum (as in measurement uncertainties). I am willing to give you the benefit of the doubt that once again, your formulation of the issue is not very clear. So maybe you would like to elaborate.

JB:?This relates to the mass of the electron. There is not enough space to treat it further in this forum. I hope that my discussion above might now convince you.?

It hasn?t convinced me yet, not even by a long shot, but I agree with you that the discussion is limited on this forum. Any suggestions?

Johnny Boy Johnny Boy ... are you sure you made it to post-graduate work?

If so please explain why this doesn't just make you lose your cookies?

"The author of that book also challenges the whole scientific community to prove him wrong (in writing)."

What a blivet.
(feel free look up the definition of the word at wikipedia.org)

Pasti: You see, JB, your academic pedigree should have taught you long ago that it is not the others burden to prove you wrong, but it is your burden to prove to the others that you are right (with all the pain this actually implies). For example, you can upload your work, both experimental and theoretical on www.arxiv.org. You should be able to do it quite fast, since I understand that you already have the rejected drafts.

Thanks, that is good advice, and I would have followed it if I were still publishing only for academic merit. Unfortunately I could not find sponsorship over the last three years and had to go into debt to do my reseach and file patents. Thus I am forced to make ends meet by selling my book. It is, however, the burden of peer reviewers to prove you wrong if they can. The problem is that I had trouble finding peer reviewers even when I published my original experimental results. By the way these papers have been in the public domain for nearly three years and nobody could point out an obvious mistake in them. Furthermore the results has recently been independently confirmed and this will be published soon. Fortunately, for the mechanism responsible for superconduction, peer reviewers have now come forward. These reviews will be posted on the relevant website when they become available.

Pasti: Oh boy, now I think I understand what you want to say by all this. See why clear communication is preferable? In a certain way, you are right, but it seems to me you have forced particular conclusions into a general context.

That is all I wanted to hear. I just raised the point to get some reaction from people like you who who are better qualified in Relativity than I am. From my "stupid" viewpoint it seemed attractive to speculate that the "nothing outside the universe" is a four-dimensional Euclidean space which became locally curved for our universe to initiate. What I like of this idea is that our universe is then "surrounded" by an infinite zero-entropy reservoir and that this means that our universe is flying apart to go back to zero entropy, instead of to maximise entropy.

Pasti:This doesn?t mean, formally at least, that time does not exist. It exists, but you have simply nothing evolving in time into the same thing, i.e. into nothing.

How can you have time when nothing is evolving? There is then no mechanism to even measure time!

Pasti: For your arguments to become generally valid (i.e. the derivative relations involving the Kronecker delta to give the information about the spacetime), you need a theory where the spacetime geometry is intimately related to the phenomenology, and for this reason, it would only apply to general relativity. It isn?t working for any other theory.

You are correct. This is why I raised the issue of the electron being a time-independent field within a inertial reference frame; i.e. it is not a particle within a space but a piece of warped space within which time does not exist. I will elaborate further below.

Pasti: If you are not talking of gravity, then your conclusion is erroneous. This is straightforward to understand, if you accept the concept of ?background?. In special relativity, the minkowski space is the background in which everything happens, all phenomenology takes place in this background. Consider a point P in the background spacetime, with coordinates
xP1,?xP4 (index 1 usually stands for time). Now consider a phenomenon/event (say a moving particle) at the same point P in the spacetime (at least at a certain moment), and label the coordinates xPE1,?xPE4. Then at say xP1=xPE1, you will have xPi=xPEi, i=2-4, i.e. the event coincides with your point. You see where I am going with this? While in time nothing happens with the point P of the minkowskian spacetime, not the same is the case with the coordinates of the events, which will generally evolve in time.
This means that nothing happens with the spacetime, and yet something happens in the spacetime. In GR, the spacetime point is the ?event?, roughly speaking. This is the difference, and this is why your equations do not imply that nothing happens in that space. They only mean that nothing happens with the space itself, but the space doesn?t have too be empty! This is basically why I sent you back to lagrangean mechanics, differential geometry and calculus. You have unwillingly extended automatically what happens to the space to what happens in the space. Which in 8 out of 10 cases is incorrect (the remaining correct cases are QFT in curved spacetimes and GR).

I may be wrong, but this argument seems to me to be only valid if time exists separate from three-dimensional space. It also rests on the assumption that is now generally accepted, that particles exist "in space"; i.e. are seperate to space. I am not saying I will be proved correct in the end, but it is exactly these two assumptions I am trying to challenge.

JB, this is not what you said. You said just measure first x1 and then p2. But OK, suppose that I misunderstood.

I am sorry, I am a bit dyslexic and my mind sometimes races ahead of what I am writing.

Pasti: We agree, even if potential energy were involved.

I am happy we are in agreement on this point; even when potential energy is involved.

Pasti:Yes, you exposed the issue in a clearer manner. I might have even understood what you wanted to say. So to summarize (perfect measurements): you measure first p0, then you measure x1. Due to the Heisenberg inequalities, after you measure x1, the momentum p1 has become indeterminate. Then you measure the momentum again, and due to the fact that you measured x1 previously and p1 had become indeterminate, the value p2 that you will measure now (the third time) can be anything, including the case where p2>p0. This is your thought experiment right? Please confirm if this is what you indeed wanted to say, before we go any further.

Yes you have got it! This is exactly my thought experiment.

Pasti: OK, let?s say for argument?s sake that I do accept your assumptions. What is a localized field, and what is the localized field describing the electron?

Great question. An atomic orbital is a localised time-independent field. What I am proposing is that the orbital is the electron; and not a magically mysterious point particle. It is my opinion that point paerticles can only exist in Plato's mathematical universe; not in ours.

Pasti: quoting JB:?The localized field lives in position space as well as in k-space".With this I kind of start having problems. Due to Fourier reasons, you cannot have a localized field in both spaces. Which is what I assume you are saying above.

Let us again consider an atomic orbital. In terms of Heisenberg's terminology such an orbital has an uncertainty in position and an uncertainty in k-space. Thus in my terminology, the orbital exists in both spaces and one can go from one representation to the other by means of a Fourier transform. Obviously the more localised the orbital is in postion space the less localised it becomes in k-space and vice versa.

Pasti: Not the way I know it. The de Broglie wavelength is also present in classical mechanics. The particle wave duality applies for any moving particle, and as far as I know, it was tested also for slow (nonrelativistic) electrons.

I agree for non-relativistic. What I meant by relatavistic incles Galileo's statement of relativity as a subset.
I can only agree with you if you accept the validity of Bohr's priniple of complemetarity; which I believe is totally wrong. There is no duality. The electron is a localised wave-field which seems to us to be a particle when it is "viewed" from outside the field; it seems to be a particle because such a field has a centre of mass and a centre of charge.

Pasti: Sure, but this a reference frame issue, not a measurement issue. What is your point?

The point I am trying to make is that in order to measure the De Broglie wave-length the electron has to interact with a measurement apparatus that is moving relative to the stationary time-independen electron wave. By this interaction the electron wave has to become part of the framework within which the apparatus (say a double slit) resides; i.e. the electron also now has kinetic energy within the framework of the apparatus. By interacting with the apparatus the boundary conditions change and this changes the relationship between the "uncertainty" in position and the "uncerainty" in k. Thus the electron wave can then spread out in position space and move through both slits. If you now want to determine through which slit the electron has moved, you must have another apparatus behind the double slit screen. This apparatus again changes the boundary condition. The electron wave becomes localised and cannot interfere with itself.

Pasti:It never did. Exactly for the reason that it is a reference frame issue and not a fundamental issue, in your example. The uncertainty in the reciprocal space will also change with the reference frame. As far as I know, it is not Lorentz invariant.

Exactly my point above!

Pasti: No, I am asking how boundary conditions (in the sense of partial differential equations) can determine the uncertainties (any uncertainties)in position and momentum (as in measurement uncertainties). I am willing to give you the benefit of the doubt that once again, your formulation of the issue is not very clear. So maybe you would like to elaborate.

There are no measurement uncertainties as implied by the Copenhagen interpretation. The electron is a wave-field that can morph from one form into another. And these forms can be directly calculated from the Shroedinger equation. Schroedinger did not realise that he has solved the whole problem, because he was misled by the arguments he had with Bohr and Heisenberg

Pasti:It hasn?t convinced me yet, not even by a long shot, but I agree with you that the discussion is limited on this forum. Any suggestions?

After thinking about it I have come to the conclusion that I should try and elaborate a bit further using this forum:
Let us start by comparing photons and electrons. The difference between an electron and a photon is that one has mass and the other not; but mass is also energy. Why this discrepancy? It of course relates to relativity. A photon can never be stationary within an inertial reference frame. The fact that the electron has mass means that it can be stationary within an inertial reference frame. So if the latter reasoning is correct, then it implies that you can know both the position and momentum for an electron at the same time. This is also borne out by the fact that we can accurately calculate and predict the trajectory of an electron in free space by knowing using both its position and momentum at any point along the trajectory.
Now what is mass? We know it relates to inertia; i.e. once in rest within an inertial reference frame it will remain at rest unless a force is applied. Even when applying a force, the electron resists this force because it has mass. To be at rest, such a particle must be in equilibrium; and because it resits being forced out of rest it must be in STABLE EQUILIBRIUM. Thus there must be a restorin force acting. Accordingly, the assumption that a free electron in space has zero potential energy must be wrong. Where does the restoring force come from? It can only be a virtual positive charge which comes into action. By using Coulomb's law one can derive such a charge and one then finds that one can describe the restoring force by a harmonic force; i.e. "the electron "perfoms harmonic vibrations" through its equilibrium point. Using a wave equation one can then calculate the localised wave which is the electron. The electron is then a time-independent localised field with a Gaussian shape. The frequency relates to the "virtual" positive charge being seperated by a distance over the fourth dimension. Within the wave the space is Euclidean four-dimensional. Time only exists outside the wave.
By postulating this model (which I agree is still speculative) it does give new insights; for example, it implies that matter and antimatter is separated over the fourth dimension by a three-dimensional interface (our space). It also indicates that the muon and the tau are excited states of the electron. It also indicates that within such a wave time does not exist, even though the wave can morph from one form to another when the boundary conditions it encounters change; because time does not exist it also does not exist within a properly entangled wave (this explains the EPR paradox); however, there are "multiparticle waves" within which time interactions can occur (the latter are not entangled and therefore I have called them enmeshed waves); etc.


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JB, sorry for the delay. I will get to your message as soon as I can.

Once again, sorry it took me so long. But with this long postings, it is bound to happen.

JB:?The problem is that I had trouble finding peer reviewers even when I published my original experimental results. By the way these papers have been in the public domain for nearly three years and nobody could point out an obvious mistake in them.?

As I said, I sympathize with you regarding the peer reviewing process. More often than not, a rejected paper signifies not that something is wrong with a paper as much as either the fact that the reviewer is either really unfamiliar with the topic, or that he is really uncomfortable (for one reason or another) with it. And even more unfortunately, due to phenomena like Pons and Fleischman (I am sure you remember the ?cold? fusion hysteria that was sparked by them in the 80?s), very few of the peer reviewers do not want anymore to take a stand in any controversial issue.
The only effective way to counteract this most unfortunate tendency of peer reviewing is to make papers and research public before the peer-reviewing process, hence the utilities of e-print archives like arxiv, spires, etc.

BTW, could you provide me a list of the refs that are already public? It will only make my search shorter.

JB:?Furthermore the results has recently been independently confirmed and this will be published soon. Fortunately, for the mechanism responsible for super-conduction, peer reviewers have now come forward. These reviews will be posted on the relevant website when they become available.?

Well, I can only whish that were you right, you should be vindicated so to speak. All the best of luck with that.

JB:?That is all I wanted to hear. I just raised the point to get some reaction from people like you who are better qualified in Relativity than I am. ?

It took me a while to understand what you wanted to say, because your basic argument was flawed. But somehow you got a rather correct ideea, even if it was based on incorrect arguments.

JB:?From my "stupid" viewpoint it seemed attractive to speculate that the "nothing outside the universe" is a four-dimensional Euclidean space which became locally curved for our universe to initiate.?

If we are talking about GR (general relativity) the Universe is the Lorentzian (not euclidean) spacetime. There is nothing ?outside? it, it has no outside. Only inside. And if you want to pay tribute to the Big Bang, the Universe was not created in this Lorentzian space, but the entire spacetime was created as the Universe. And BTW, it is globally curved and locally flat. Not locally curved.

JB:?What I like of this idea is that our universe is then "surrounded" by an infinite zero-entropy reservoir and that this means that our universe is flying apart to go back to zero entropy, instead of to maximize entropy. ?

Nope. For several reasons. First one is even if GR does allows such a view (but the background is curved, you have something in it) it will hardly be a zero entropy reservoir. In short, it ain?t working that way. And in SR (special relativity where the background is flat) energy cannot be exchanged with the background, simply because the background has nothing in it that could take such energy.

JB:?How can you have time when nothing is evolving? There is then no mechanism to even measure time!?

I said formally. You simply have a time axis, that is all. It is the same issue as with a chamber containing ?perfect vacuum?, just that now you have a 4-dimensional chamber. Does it make physical sense to have an entirely empty Universe? Hardly, in my opinion, unless you consider this empty space as a background (i.e. you are talking about perturbative GR). But nevertheless, such an empty space satisfies Einstein?s equations.

JB:? This is why I raised the issue of the electron being a time-independent field within a inertial reference frame; i.e. it is not a particle within a space but a piece of warped space within which time does not exist. I will elaborate further below.?

You are principially right, but this means that you need to unify gravity with electromagnetism. Only gravity curves spacetime, electromagnetism does not.

JB:?I may be wrong, but this argument seems to me to be only valid if time exists separate from three-dimensional space.?

It is in SR and GR. Not in say regular electromagnetism.

JB:?It also rests on the assumption that is now generally accepted, that particles exist "in space"; i.e. are separate to space. I am not saying I will be proved correct in the end, but it is exactly these two assumptions I am trying to challenge. ?

Yes, particles exist as separate entities from the background in everything but GR. Formally at least. But as I said before, in order to challenge these assumptions, and to have the picture you envision, you have to unify gravity with electromagnetism, and this is energetically way, way beyond the range of regular electromagnetic interaction (what you usually have in solids and in plasmas).

JB:?Yes you have got it! This is exactly my thought experiment.?

Well, once we?ve cleared this issue, let?s see. We assume perfect measurements, a la Born. If we do that, the interpretation of the Heisenberg uncertainty relations cannot be but that if you measure accurately the position, the measured value for the momentum has huge errors. And not that the momentum becomes indeterminate. The measured value for the momentum will have huge errors, but the momentum of the particle remains unaffected (perfect measurements). Which of course, doesn?t make sense when you start thinking about how you could actually measure ?simultaneously? two quantities (that would be related to Heisenberg?s uncertainties for simultaneous measurements of conjugate variables), and what a perfect measurement a la Born means (beyond a formal definition)
Alternatively, if you would assume that after the measurement the conjugate quantity becomes indeterminate (the other way to interpret Heisenberg uncertainty relations- imperfect measurements), this would mean that you wouldn?t even be able to measure the position after first measuring the momentum simply because you wouldn?t know where your particle is.
So anyway, NOW indeed I am starting to have problems with the measurement process. Not to mention with this picture which is quite semiclassical. But as far as I am aware, Born?s perfect measurement assumptions/models have long been abandoned, ever since von Neumann toyed with this issues (not that he actually solved it unequivocally).


It would be a rather a forced conclusion to state that Heisenberg?s inequalities violate energy conservation (not to mention incorrect if you assume perfectmeaurements). Not because I am encroached in the traditional paradigms, but because as far as I know, the issue of measurement has not yet been given a satisfactory explanation. To me it makes much more sense to first understand better the measurement issue/process, and then draw any conclusions on the violation of energy conservation by Heuisenberg?s uncertainty relations.



JB:?Great question. An atomic orbital is a localized time-independent field. What I am proposing is that the orbital is the electron; and not a magically mysterious point particle. It is my opinion that point particles can only exist in Plato's mathematical universe; not in ours.?

Now I am again having problems. An orbital is not a localized object. It is exactly the opposite, a delocalized object. Extending spatially to infinity (just think of the fact that the s-orbital for the H atom decreases exponentially with the radius).

And the orbital ?is? basically the electron, in the sense that say, for the case of the H-molecule, the strength of the ?bonds? are given by the overlap of the valence orbitals. The ionic or covalent character of the bond (a la Pauling) is based on the degree of overlap of valence orbitals so in materisl structures you can pretty much say that the electron is the orbital. But the risk is high to get stuck into syntax rather than physics.The problem is that you do not have such structures for the free electron, as you well know.

As for the electron not being a point particle, the only answer I can give is ?duh!?. Point particles are a classical abstraction. But the electron not being a particle at all, that is an entirely different issue. Because then you have to explain (differently) all the classical phenomena where the electron behaves exactly like a particle. Including the Stern-Gerlach experiment, including the trajectories of charges in electromagnetic fields (mass-spectrometers, accelerators, multipliers etc). You have to admit that the body of evidence in favor of the electron being some sort of volume limited blob of mass and charge is quite large and quite consistent, in the (semi)classical regime.


JB:?Let us again consider an atomic orbital. In terms of Heisenberg's terminology such an orbital has an uncertainty in position and an uncertainty in k-space.?

No, the electron in the orbitals has the uncertainty in position and momentum. The orbitals are related to the wavefunction and hence to the localization probability in the position representation.

JB:?Thus in my terminology, the orbital exists in both spaces and one can go from one representation to the other by means of a Fourier transform. ?

True.

JB:?Obviously the more localized the orbital is in position space the less localized it becomes in k-space and vice versa.?

Nope. The electron does this, not the orbitals. By the electron now I mean the operators associated with it, which act on the wavefunction/orbital.

JB:?I can only agree with you if you accept the validity of Bohr's priniple of complemetarity; which I believe is totally wrong. There is no duality. The electron is a localized wave-field which seems to us to be a particle when it is "viewed" from outside the field; it seems to be a particle because such a field has a centre of mass and a centre of charge.?

OK, and what is this field? Because for the time being, you have practically restated Bohr?s complementarity principle in a slightly different from.

JB:?The point I am trying to make is that in order to measure the De Broglie wave-length the electron has to interact with a measurement apparatus that is moving relative to the stationary time-independent electron wave.?

OK?!?!

JB:?By this interaction the electron wave has to become part of the framework within which the apparatus (say a double slit) resides; i.e. the electron also now has kinetic energy within the framework of the apparatus.?

OK?!?! I mean, up to this moment you are not saying anything new.

JB:?By interacting with the apparatus the boundary conditions change and this changes the relationship between the "uncertainty" in position and the "uncerainty" in k. ?

If by this you mean that the spectrum of the operators (and of course the corresponding wavefunction for the electron) changes ? and hence the explicit expression of the Heisenberg relations ? because the boundary conditions for solving the Schroedinger equation change, then I agree.

JB:?Thus the electron wave can then spread out in position space and move through both slits. If you now want to determine through which slit the electron has moved, you must have another apparatus behind the double slit screen. This apparatus again changes the boundary condition. The electron wave becomes localized and cannot interfere with itself.?

I am not sure I see the point. Sure, each (non-perfect, in the Born sense) measurement will change the momentum and the position of the electron in its trajectory, but so what? If the electron continues to propagate, then you solve the Schroedinger equation picewise, each time with the appropriate boundary conditions. This does not mean the electron cannot interfere with itself. It can if you leave it continue its way until it is absorbed by the screen. And we are back to the issue of how you actually do the measurements. If you absorb it immediately after the slit, or if you strongly perturb it with your measurement, of course you won?t get the diffraction pattern on the screen. Or you will get it very distorted.

You cannot make such considerations and just ignore the influence of the measurement. Here, the details of the measurement become essential, and you cannot actually idealize so easy the measuring apparatus. But again, this is nothing new on this issue. If you really have the time for that, try a Monte Carlo simulation.


JB:?There are no measurement uncertainties as implied by the Copenhagen interpretation. The electron is a wave-field that can morph from one form into another. And these forms can be directly calculated from the Shroedinger equation. Schroedinger did not realise that he has solved the whole problem, because he was misled by the arguments he had with Bohr and Heisenberg.?

Sure, the Copenhagen interpretation is relatively simplistic when it comes to the picture of it, with perfect measurements and so on and so forth. But it is an idealized interpretation, for perfect measurements. Extension to actual measurements (and if you ever attempted that you know how difficult it is to model even the simpler detection apparatus) will not change the Heisenberg uncertainty relations (remember their derivation), you will only have to match them piecewise for each measurement.


JB:?Let us start by comparing photons and electrons.?

Let?s.

JB:?The difference between an electron and a photon is that one has mass and the other not; but mass is also energy.?

You mean the electron has rest mass (energy) while the photon doesn?t. And this is not all. One has charge, the other doesn?t, one is a fermion, the other is a boson, etc.

JB:?The fact that the electron has mass means that it can be stationary within an inertial reference frame.?

In principle? Now you have to devise an experiment where indeed you have a stationary electron?And to my best knowledge, there hasn?t been any such experiment.

JB:?So if the latter reasoning is correct, then it implies that you can know both the position and momentum for an electron at the same time.?

To know is not exactly the same as to measure. While you might get an electron like this (stationary somehow), a realistic measurement would immediately change this state (remember, the any measurement related to the electron must necessarily be of quantum nature!).

JB:?This is also borne out by the fact that we can accurately calculate and predict the trajectory of an electron in free space by knowing using both its position and momentum at any point along the trajectory.?

OK?

JB:?Now what is mass? We know it relates to inertia; i.e. once in rest within an inertial reference frame it will remain at rest unless a force is applied. Even when applying a force, the electron resists this force because it has mass. To be at rest, such a particle must be in equilibrium; and because it resits being forced out of rest it must be in STABLE EQUILIBRIUM. Thus there must be a restorin force acting.?

JB, it seems to me that you are mixing Newton?s principles in their idealized version with practice. First of all, in an inertial frame your particle can move with constant velocity, and the same description of inertia works if you attempt to change the particle?s ?state of motion?.

Seconf of all, if at rest, as you say, you don?t need stable equilibrium for it to be at rest, you can have also ?indifferent? equilibrium (particle on a flat potential vs particle in a potential well), and in this case, you don?t need any restoring force to act on it. It seems to me again that you are twisting the issue of centipetal/centrifugal force from mechanics. So maybe you can clarify your idea better.


JB:?Accordingly, the assumption that a free electron in space has zero potential energy must be wrong. ?

Not in an idealized environment, with everything electrically neutral and no image charges (no conductors, semiconductors or dielectrics) present. In practice, you can never have these idealized conditions (you can at best have a large UHV chamber, but you will have ?image? charges affecting the electron (even though these interactions will be probably negligible for any reasonable sizes of the chamber).

JB:?Where does the restoring force come from? It can only be a virtual positive charge which comes into action. By using Coulomb's law one can derive such a charge and one then finds that one can describe the restoring force by a harmonic force; i.e. "the electron "perfoms harmonic vibrations" through its equilibrium point. ?

Oh, JB, for God?s sake. The electromagnetic force between two attracting charges cannot give you a harmonic force (no echilibrium configuration for the system) unless you have also a repulsive force between them. And don?t quote me the Drude model, and the similar one for the dielectric permitivity due to bound electrons (I forget it?s name). The situations are entirely different.

JB:?Using a wave equation one can then calculate the localised wave which is the electron. The electron is then a time-independent localised field with a Gaussian shape.?

Any linear harmonic ?response? has a gaussian profile.

JB:?The frequency relates to the "virtual" positive charge being seperated by a distance over the fourth dimension. Within the wave the space is Euclidean four-dimensional. Time only exists outside the wave. ?

Now it gets better and better. It seems that you need a Kaluza-Klein type of theory, but with a lorentzian space. BTW, just for fun, in Kaluza-Klein theories (you have two ?time? axes and three spatial axes) you can recover the charge of the electron by projection onto the regular space, but don?t get excited, it is completely different than what you are talking about.

JB:?By postulating this model (which I agree is still speculative)

Still?? You have dismissed away by a handwave without too much consideration (or based on equally speculative arguments) classical mechanics, special and general relativity and the underlying experimental evidence at the same time and you say it?s speculative? OK.

JB:?it does give new insights; for example, it implies that matter and antimatter is separated over the fourth dimension by a three-dimensional interface (our space). It also indicates that the muon and the tau are excited states of the electron.
Oh, that?s peachy. So now out of the way goes also quantum electrodynamics and chromodynamics (with the appropriate supporting experimental evidene). Just peachy.

JB, I am sorry. In order NOT to explain much, and based on arguments which I can only hope I did not understand correctly, because if I did, most of them are incorrect, and without any shred of evidence you have just overthrown all the theories of physics (classical, and quantum) in favor of a wildly speculative theory unsupported by any experimental evidence.
As I said, I am open to such things (new thewories, new interpretations, etc). But not when even the theoretical argumentation lacks in validity. And in your particular case, not when also experimental evidence also lacks totally.

Dear Pasti,

Thank you for spending so much time. I really appreciate it. Thank you also for your understanding when it comes to peer reviewers. I agree Pons and Fleischman caused some havock. You ask for references. The following two papers:
Semicond. Sci. and Technol. volume 18, 2003 page S125 and page S131. Thank you also for wishing me luck with being vindicated. I am sure I will be. Unfortunately, I am not convinced by all your arguments. Fortunately we live in the 21st century; it is not a sin to differ with accepted dogma anymore. If I want to consider every argument you raised, my response will be far too long for this forum. Thus I am going to pick out a few points and respond. This does not mean that I necessarily agree with the arguments that I am not responding to.

Pasti: And BTW, it is globally curved and locally flat. Not locally curved.

I thought it is locally curved around a black hole, or a star, or even the earth?

Pasti: Nope. For several reasons. First one is even if GR does allows such a view (but the background is curved, you have something in it) it will hardly be a zero entropy reservoir. In short, it ain?t working that way. And in SR (special relativity where the background is flat) energy cannot be exchanged with the background, simply because the background has nothing in it that could take such energy.

I think we are using different semanitics and will not be able to solve it quickly here. I was of the opinion that even for special relativity space-time is curved (not space on its own I agree): see for example Feynman lectures vol. II chapter 42.

Pasti: You are principally right, but this means that you need to unify gravity with electromagnetism. Only gravity curves spacetime, electromagnetism does not.

I believe that gravity and electromagnetism have been unified via quantum mechanics. We just did not realise it. In my model of the electron the mass is purely electromagnetic in origin. Unfortunately I cannot present the model here, but am willing to e-mail you extracts from it. Is the e-mail address under your profile still correct?

Pasti: from JB:.. "this argument seems to me to be only valid if time exists separate from three-dimensional space." It is in SR and GR. Not in say regular electromagnetism.

I disagree but will leave it there for now.

Pasti: Well, once we?ve cleared this issue, let?s see. We assume perfect measurements, a la Born. If we do that, the interpretation of the Heisenberg uncertainty relations cannot be but that if you measure accurately the position, the measured value for the momentum has huge errors. And not that the momentum becomes indeterminate. The measured value for the momentum will have huge errors, but the momentum of the particle remains unaffected (perfect measurements). Which of course, doesn?t make sense when you start thinking about how you could actually measure ?simultaneously? two quantities (that would be related to Heisenberg?s uncertainties for simultaneous measurements of conjugate variables), and what a perfect measurement a la Born means (beyond a formal definition)
Alternatively, if you would assume that after the measurement the conjugate quantity becomes indeterminate (the other way to interpret Heisenberg uncertainty relations- imperfect measurements), this would mean that you wouldn?t even be able to measure the position after first measuring the momentum simply because you wouldn?t know where your particle is.
So anyway, NOW indeed I am starting to have problems with the measurement process. Not to mention with this picture which is quite semiclassical. But as far as I am aware, Born?s perfect measurement assumptions/models have long been abandoned, ever since von Neumann toyed with this issues (not that he actually solved it unequivocally).

What I advocate is that Heisenberg's uncertainty relationship has nothing to do with a measurement problem for a particle; it simply states the average dimension of the wave (which is the actuality), and how it relates to the dimension of the same wave in k-space. This relationship can change when the boundary conditions change; which also happens when making a measurement.In other words delta(p) has nothing to do with the actual momentum of an electron; because if it does it would mean that an electron which forms an atomic orbital will be moving all the time. How can it do that without radiating em waves? The reason why this does not occur is that the electron is not a particle playing "hide and seek" but it is actually a non-changing distributed charge around the nucleus. Why do we not accept what the Schroedinger equation gives us as the reality?

Pasti: Now I am again having problems. An orbital is not a localized object. It is exactly the opposite, a delocalized object. Extending spatially to infinity (just think of the fact that the s-orbital for the H atom decreases exponentially with the radius).....And the orbital ?is? basically the electron, in the sense that say, for the case of the H-molecule, the strength of the ?bonds? are given by the overlap of the valence orbitals. etc.

Now that is a good argument!! But why are two hydrogen atoms not always bonded? After all their electron orbitals stretch to infinity and must thus always overlap. This is what my experiment solved. There is a critical radius for an orbital outside of which one experiences the orbital as a point charge; and therefore classical calculations can then be used; however, when the two electron orbitals overlap so that their critical radii overlap, quantum mechanics becomes applicable. For an orbital this radius is given by the "uncertainty in position" as calculated from the centre of charge of the orbital multiplied by the square root of 2.


Pasti:..... But the risk is high to get stuck into syntax rather than physics.The problem is that you do not have such structures for the free electron, as you well know.

This is where I differ. A free electron is also a localised orbital. This is the calculation I will send to you once you have confirmed your e-mail address.

Pasti: But the electron not being a particle at all, that is an entirely different issue. Because then you have to explain (differently) all the classical phenomena where the electron behaves exactly like a particle. Including the Stern-Gerlach experiment, including the trajectories of charges in electromagnetic fields (mass-spectrometers, accelerators, multipliers etc). You have to admit that the body of evidence in favor of the electron being some sort of volume limited blob of mass and charge is quite large and quite consistent, in the (semi)classical regime.

Your argument is correct; however, I have just (above) given you the limits when classical mechanics and quantum mechanics apply. The interface is given by the critical radii of the waves that interact (the spherical region within the wave defined by this radius is the localised wave or "blob" that is the electron).

Pasti: Nope. The electron does this, not the orbitals. By the electron now I mean the operators associated with it, which act on the wavefunction/orbital.

Yes the electron does it because the orbital IS THE ELECTRON!!

Pasti: If by this you mean that the spectrum of the operators (and of course the corresponding wavefunction for the electron) changes ? and hence the explicit expression of the Heisenberg relations ? because the boundary conditions for solving the Schroedinger equation change, then I agree.

We agree!

Pasti: I am not sure I see the point. Sure, each (non-perfect, in the Born sense) measurement will change the momentum and the position of the electron in its trajectory, but so what? If the electron continues to propagate, then you solve the Schroedinger equation picewise, each time with the appropriate boundary conditions. This does not mean the electron cannot interfere with itself. It can if you leave it continue its way until it is absorbed by the screen. And we are back to the issue of how you actually do the measurements. If you absorb it immediately after the slit, or if you strongly perturb it with your measurement, of course you won?t get the diffraction pattern on the screen. Or you will get it very distorted.

Yes but why do you get the diffraction pattern on the screen if the electron is a particle? To answer you fully is not possible in this forum. If you are interested I will send you another extract dealing with this situation in detail.

Pasti: In principle? Now you have to devise an experiment where indeed you have a stationary electron?And to my best knowledge, there hasn?t been any such experiment.

Any body with mass travelling with a constant speed is stationary within an inertial framework travelling with it. Galileo stated it and nearly lost his life; and Newton's first law formalised it. By shooting an electron from an electron gun to a screen one can calculate the trajectory classically (using Newton's laws). This implies that while the electron is travelling at a constant speed to the screen it is stationary within the inertial framework travelling with it QED.

Pasti: To know is not exactly the same as to measure. While you might get an electron like this (stationary somehow), a realistic measurement would immediately change this state (remember, the any measurement related to the electron must necessarily be of quantum nature!).

According to Born it is not possible to know the position and momentum at the same time. His interpretation has nothing to do with the problems assiciated with doing the measurements.

Pasti: JB, it seems to me that you are mixing Newton?s principles in their idealized version with practice. First of all, in an inertial frame your particle can move with constant velocity..

That is right, but it is stationary within the inertial reference frame travelling with it.

Pasti: Second of all, if at rest, as you say, you don?t need stable equilibrium for it to be at rest, you can have also ?indifferent? equilibrium (particle on a flat potential vs particle in a potential well), and in this case, you don?t need any restoring force to act on it.

If you have "indifferent" equilibrium you will not have inertia. Consider a ball on a flat frictionless plane. To move it requires nearly no force; in the limit zero force. The fact that a body with mass has inertia means that it resists being moved from being at rest. This is exactly the interpretation of mass.

Pasti: Oh, JB, for God?s sake. The electromagnetic force between two attracting charges cannot give you a harmonic force (no echilibrium configuration for the system) unless you have also a repulsive force between them.

It can as you will see from the extracts I am willing to send you. Consider the following thought experiment: assume an electron approaches a positive charge below a surface that it cannot penetrate (this is a possible scenario when you have a suitable n-type semiconductor surface). It can then not form an orbital around the charge but it still experiences a Coulomb interaction when it approaches the charge along a line going through the positive charge and which is normal to the surface. When the electron moves away from the normal line in a direction parallel to the surface it will experience a restoring force back to the normal line; i.e. the lateral wave function describing such an electron is Gaussian. Closed solutions can be derived from the Schroedinger equation. All I did for a "free electron" has been to extend this model to four dimensions.

Pasti: Now it gets better and better. It seems that you need a Kaluza-Klein type of theory, but with a lorentzian space. BTW, just for fun, in Kaluza-Klein theories (you have two ?time? axes and three spatial axes) you can recover the charge of the electron by projection onto the regular space, but don?t get excited, it is completely different than what you are talking about.

This has nothing to do with Kaluza-Klein.

Pasti: Still?? You have dismissed away by a handwave without too much consideration (or based on equally speculative arguments) classical mechanics, special and general relativity and the underlying experimental evidence at the same time and you say it?s speculative? OK.

I disagree with your analysis here.

Pasti: Oh, that?s peachy. So now out of the way goes also quantum electrodynamics and chromodynamics (with the appropriate supporting experimental evidene). Just peachy.

I do not believe in any theory that has to be renormilsed to get away from infinies. Such theories need a very close shave from Occam's Razor. Remember Ptolemy's model of the universe with its "epicycles" was also for hundreds of years supported by "appropriate supporting experimental evidence"

"Yes the electron does it because the orbital IS THE ELECTRON!!"
Very beautifully said.Please explain it more.
Thanks.