Regarding 3): I don't think that waves were abandoned, recall the famous wave-particle duality (http://en.wikipedia.org/wiki/Wave–particle_duality) to begin with.

Hello Demetris

My answers to yours questions:

1) NO.

2) The searching for absolute accuracy is a problem of the paradigm of modernity, we are now in contemporary times.

3) DO NOT have left the waves. Quite the contrary. The whole universe is wave energy, thought.

Wait, and soon I will upload my second article translated in english (Are Quantum Theory Questions Epistemic?).

Thanks.

Viviana

Because all of you, even Feynman, analyze quantum phenomena from classical mechanics. But the Quantum phenomena are outside of classical mechanics. The quantum is not mechanic.

Wait, and soon I will upload my second article translated in english (Are Quantum Theory Questions Epistemic?).

Thanks.

Viviana

I write in spanish and then translated to english. Sorry.

Thanks.

Viviana

Hello Martin.

YES !! I'm agree with you.

and thank you Demetris.

Viviana

When I was in high school I had been tought the concept of Force Field: " a section of space where if we put a testing quantity, a force will be applied to it", roughly speaking.

When I was in University I learned about Linear Algebra fundamentals and saw the concept of a linear operator with eigenvalues λ (lambda) as the physical observables and eigenvectors as the new term of wave-function |ψ> ( |psi> ). There existed two almost equivalent representations, that of Schroedinger (with differential equations) and the Heisenberg one (with matrices). Later after I learned that we could quantize the operators and form the Quantum Field Theory. But, when taking the formal power series they told me that the series divergences! So, we had to do the trick of 'renormalisation' process in order to remove the infinities. That was not sound 'proper' to me. It is like we want to build a skyscraper and put wood for the foundations...

Martin, the same is true for me: I escaped in Economics, but I found so many 'assumptions' there... I agree, life has its own laws!

The Hamiltonian: this procedure has started from classical mechanics and is still alive. But don' t you think that we maybe have to escape from Hamiltonian systems which always need a symmetry? OK, the supersymmetric theories have been released faster than windows versions, but do you think that everything has to be tighted with a conservation law? Why we cannot create a theory that explains particle interactions without a Hamiltonian?

Lagrangian dynamical systems: We have accepted that all interesting systems in Nature are of that kind. Is it true or is it just another linearization of the truth? Please read carefully next wiki:

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

[The only thing that the above wiki does not mention is the foundamental role of lagrangian formalism in modern Economics]

So, dear colleagues, if you want to escape from mainstream Physics here is the rule: Try to build a theory that does not use Action and Calculus of Variations anymore. Is it possible?

The concept of Force: Is Force actually a Field or is it a holistic (Johan I borrow your notation :) ) concept? Is the potential to act to a test particle isolated from the position of it or it is apparent like a holistic chord or string or something else since the creation of the source? For example when we have a twin genesis from an electron and a positron this seems to be reasonable but what about other charges? Get away from charges and go to masses: Is the gravitational force field really a field or is it a space-time curvature like GR manifests? If we accept the latter, then force is able to applied only due the so called geodesic lines. So, we have to accept the same for electromagnetic forces? And who are the geodesic lines in empty space? The lines of the electric field? OK, I posted two many questions, thus I summarize:

1)Is the apply of a force an isolated event or a holistic one?

2)Is the apply of a force instantaneous (like a global chord connecting source and test particle) or it 'travels' with the speed of light (if so why with a smaller speed?)

3)Is the line of force application a proper geodesic line and if so why has to be so?

@Charles, you don' t use Lagrangian but you use Hamiltonian. For me Hamiltonian and Langrangian are parts of the same coin. Besides this I post some quotes from your work and I' d like from you to expand them a little bit more.

For example:

1)Why to accept the conservation of probability?

2)Why are we able to count particles, to measure position and to measure the relative measure of every frequency?

@Charles, you have done a quality work and I mean it. Probably you may take a decision: either you will continue the mainstream road or you will take an alternative one. Have in mind that the second road will not give you so many publications like the first one, but you have the qualifications to find something new.

At our topic now: You have made this sequence of implies:

Higher Level Theory ==> QED ==> Classical Quantum Mechanics.

But, at the end above, we know that integral of over a distinct volume gives the probability that the particle on state |psi> is inside that volume. This probability of course is time dependent. So, I think, you cannot start by the Axiom of probability conservation. Even if you can (maybe), you cannot escape from something mysterious like Action which you have already avoid by not taking a Langrangian.

My point is that we need something outside the 'trap' of energy-time dualism, the symmetries involved and the breaking of them and all those things. Only then we should be able to formulate a different particle Physics.

OK, Charles, you have made your choice! But let me intrigue you :)

Imagine that there exist a theoretical representation, still unknown, such that:

1)Does not have any point singularity problems at all

2)Can explain all 'strange' quantum phenomena like entangled particles

3)Can be decomposed in lower level theories simply like SR gives Newtonian motion for v

Let us accept that nature can be explained with a variety of ways and with the same accuracy. Then we have to choose among competing theories those that can explain the observed phenomena under:

1)the smallest set of initial assumptions or Axioms

2)the smallest set of final corrections due to approximations

Of course we always must remember that our science is almost every time a linear approximation of the truth, so it is necessary to try for theories that do not use the trick of keeping a few terms in the relevant Taylor expansion series.

Unfortunately in Billiard-Physics that is the case.

I think the problem comes from the small distances involved in particle physics. If we accept the superposition of waves (|ψn>) then they all are inside a very small volume, so we probably treat the wave-packet as a single object, ie a particle. But if that wave-packet passes through a double slit, then its wave nature is again apparent. Of course we have already made a heroic assumption, that of the physically representability of every term in our Fourier series expansion, probably Johan could argue that we just have a unique holistic wave, not a wave packet.

By the other hand, electromagnetic waves have roughly been examined and with a small exception for the Ampere Law (where there are some objections) everybody agree for its theoretical basis.

It is interesting to notice that Einstein spent the last part of his life by trying to unify EM wave theory with GR gravity theory, without success.

So, dear Johan, could you finish what Albert didn't manage to do? We are waiting.

Back to our Billiard now. I have already posted a Proposal:

"Let us insert to the Lagrangian density of the quantum field theory particle field another propagating term which is Lorentz invariant and so on.... Then we will demand to build a CERN version 2.0 in order to search for the existence of our theoretically predicted particle after many years and after many $bn have been spent... Who knows, probably they will give us a Prize after many years..."

Is it seems like a joke? Then, please tell me what is the difference with Higgs mechanism?

So, our Billiard still remains on the table and is waiting us...

@Charles, if I tell you that I have added a term like a geometric series:

1/(1+x)=1-x+x^2-x^3+...

but it is also holds that x>2, then every conclusion that I have made using the above expansion is an illusion... since it does not converge for |x|>1.

I think that one crucial point is if a Fourier series expansion in waves ('k') is apparent in real existence or it is just a convinient mathematical construction based on the (in principal correct) superposition property of waves. Here is the chance: To plan experiments where we can falsify the above superposition summation over k's.

Has anybody in mind experiments like that?

@Johan, I think you have to expand your arguments about contraction of the electron wave on an atomic detector at the double slit experiment.

@Charles, I think that you would probably explain more the guidance of the electrons from photons when they pass through the double slits.

Let's take a turn to classical Physics now: I want all of us to think about the motion of a drum. The total solution is not a pure harmonic superposition solution but it is a direct application of Fourier Analysis:

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

But, how many modes of vibration are really exist inside an oscillating drum? Or, how many in principle can exist without damaging it?

I ask this question just for the Fourier series expansion: although it is from 0,1 to infinity, are we sure that all modes can exist?

Practically, when the above series is terminated?

Dear Johan, I think the esensse is your quote:

"Since there are billions of linearly independent function-spaces which you can use to obtain the same solution. "

That' s exactly my point: Since we have so many competing interpretations, why do we choose one specific (for example the sinusoidal) in order to describe reality? It is the same problem I face in my working field, everybody chooses a function a priori and then, after curve OLS fitting, differentiates twice in order to find the inflection point.

How can we rule out all those a priori chosen models in Physics?

[Even in the Higgs resonance the scientists have chosen a polynomial interpolation in order to fit the data, so many $bn spent and they chose the simplest interpolation scheme that they could use...]

@Charles, the use of complex numbers is very convinient for every electrical engineer, if you look up the EM waves you will see them to be complex vectors, with real part=E and imaginary part=B. So, our problem is not the complex nature of |ψ>. The problem is how is justified the choice of the form in the Fourier series expansion and how are we sure that all those (in principle OUR choice) terms reperesent real particle or wave or chord properties?

If we answer that question, then we can proceed further.

@Charles, there is nothing mythical at the existence of a Hilbert space, instead that we need the class of squared integrable functions in order to be able to compute the Fourier coefficients by an integral fo proper inner products.

@Charles, I am answering your question:

'So the actual question to ask is "why do we have a Hilbert space".'

We have a Hilbert space in order to do the calculations relevant to our Fourier series.

I think that the so 'wild' debate about particles has to do a little with:

1)the non common sense definition of a particle in such a way that no infinities arise at all

2)the total denial of every alternative wave like represantation

3)the fact that current paradigm in Quantum Physics works at least for the first terms at every relevant series

So, the particle lovers say: My theory is accurate, while the wave lovers say: This is something like Epicycles.

My question is this:

"How can we decide about the true nature of an electron without any ambiguity?"

Dear Johan, thank you for your detailed definition of electron. The only part that I think is not so obvious is Deduction 6(ii),(iii). Although I could agree with you for the electron as a wave just described by you, I cannot agree that this description implies that an electron is also an EM wave. This point needs further arguments.

@Johan, if we accept your conclusion then it is like accepting the next principle:

"When an interaction occurs and something is absorbed, then the material of the two entities should be the same".

I think this assumption is very weak.

@Charles: "Heisenberg, Scrhoedinger, de Broglie et al." were no experimentalists.

@Johen: You idea of an electron circulating around proton seems flawed. Namely at least one of the reference frames cannot be inertial, so the Lorentz transformation does not apply here.