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"
