Quantum Theory has solved a lot of problems but there are some problems that are unsolved hoping that one day will be solved

To many questions at once. Ok for 1) and 2). From 3), there begin to be some conventions and assumptions. The current paradigm is, let try a group, write all possible lagrangians with all possible representations, thus defining a 'class of theories,' and let's eliminate most of them through general principles. The expected result is the only remaining theory is necessarily true, but the actual one is, surprisingly, one more Langrangian, aka quantum, theory invariant under the group, which doesn't prove that every possible theory is a quantum theory invariant under some group.

Yes Claude, you have the exact point: We are slaves of the optimization process and cannot even think out of the box. Is there an ny kind of non Lagrangian life in science?

It is a joke that everybody blames Leibniz (and Laplace) who argued:

"Everything proceeds mathematically...if someone could have a sufficient insight into the inner parts of things, and in addition had remembrance and intelligence enough to consider all the circumstances and take them into account, he would be a prophet and see the future in the present as in a mirror."

[ http://www.informationphilosopher.com/freedom/history/ ]

since you know: we have new tools now, indeterminacy, statistical methods et al, but we are at the same point, that of the almost theological arguments of Maupertuis about action! I don't know...

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

"...Cartesian and Newtonian physicists argued that in their collisions, point masses conserved both momentum and relative velocity. Leibnizians, on the other hand, argued that they also conserved what was called live force or vis viva.

...

Today, of course, the concept of a ‘hard’ body is rejected. And mass times the square of velocity is just twice kinetic energy so modern mechanics reserves a major role for the inheritor quantity of ‘live force’.

...

Hence the principle of least action is not just the culmination of Maupertuis’s work in several areas of physics, he sees it as his most important achievement in philosophy too, giving an incontrovertible proof of God."

Lagrangian mechanics is so powerful that we forget that it has left many skeletons behind it. Dissipative system are not described, but they can be by taking into account more parts. The equations are then time invertible, but non holonom systems still resist. Holonomy is at the heart of integrability, and when there is a non nul electromagnetic field, that means non holonomy. Of course, there is a Lagrangian formulation of classical electrodynamics, but there remain paradoxes like the Bohm-Aharonov effect.

I fully understand your dissatisfaction. The most acclaimed standard model dates back to 1973. See what have been the progress in biology in 40 years !

Actually there are distinct issues.

1. QM proceeds from "axioms", which are taken at face value. They are worth some attention. Actually one can prove that all the basic axioms (Hilbert space, operators, eigen values, tensor product...) can be mathematically proven from some basic and general features met by almost all the models used in physics. Probability have also a very natural explanation, which does not require any random behavior from particles. So they are not a special feature of a quantic world, but just an artefact coming from how we represent the physical laws.

2. The second issue is about the duality particles / fields, which is, after all, at the foundations of most modern physics. We have to revisit the concepts of particles and fields. One specific feature of particles is that they have a motion, and indeed this comes from our visualization of solid bodies. The usual mathematical way of representing a motion is through the group of displacements (translation x rotation). Unfortunately it cannot be extended to the relativist context : an element of the Poincarré group needs 10 parameters and the translation (spatial speed) is linked to the boost. The right representation is through spinors, for good logical reasons. So the relativist motion of a body (whatever the scale) must be represented by a spinor. From there using basic QM axioms one can give some physical substance to the concept of fields of spinors, and this is easily extended to the GR context. The gravitational field is then incorporated in a usual Yang Mills model.

3. The issue which is left is then the combination of the gravitational field with the other fields. In a Yang Mills model it requires the introduction of a group which encompasses both the Lorentz group and SU(3)xSU(2)xU(1). That is a great unification. One possible approach is by Clifford algebras. But this does not seem impossible.

Over all my beliief is that too little attention has been devoted to the basic concepts, and too much credance to mathematical tools (or more bluntly, computational tricks).

Thznx Bernd

I do not know what is quantum motion. Motion refers to some "matter" thing, and, as opposed to a force field, a material body is assumed to have a location and a speed. Duality cannot be conceived without specifying opposites. The issue is that in the motion we have two components, translation and rotation. And motion in a relativist picture cannot be defined as in the euclidian picture. The Wingner's solution from the Poincaré group is, from my point of view, wrong. We have to represent motion in a different way, using Clifford algebra, and we get a consistent explanation for spinors. And we go from Special Relativity to General Relativity very easily. Spinors are necessary because of relativity. The scale does not matter. Actually one can represent the motion of stars in a galaxy in the same formalism. QM comes in the story only to restrict the possible representations for the spinors. The set of values of spinors is a 10 dimensional real manifold (which could be intriguing for strings experts) and the motion of a given particle, in a local frame, is represented by two 3 dimensional vectors, as in classic mechanics..

Dear jean claude, the symmetry project is well established in our every day life due to the rigid body concept of motion: translation and rotation are very well explained with many many ways and SU(3)xSU(2)xU(1) and other symmetries can arise from such a view. But what if reality is not so rigid and instead is like a porridge ('chyle'), so all those nice concepts cannot even be defined? I guess that as we go deeper and deeper we cannot apply 'rigid body' arguments and we probably cannot even define other concepts like velocity et al. Another question is that of Cartesian coordinates and parity: are we sure that this great thing (do you remember the CPT...) really exists?

Dear Demetris,

It is clear that the concept of rotation comes from our usual observation of rigid bodies. However there is a discrepancy between the view of mathematicians (transformation to go from one frame to another) and the view of physicists, which perceive translational and rotational momenta as fundamental. Luckily the two visions are compatible in euclidean space, but this is no longer true in relativity. So we have to admit that the kinematic charactristics of material bodies must be defined in another way, and this is here that enter the spinors. They are vectors, so that they are measured in local frames, which involve groups etc...This is very similar to the way one represents the "charges" of particles. There is no assumption about the rigidity of the body, only that we do not consider that its internal stucture matters (as it is always done in mechanics).

All this can be done in the General Relativity context, so there is no need for cartesian coordinates (except of course locally).

Just a remark : the use of the word symmetry everywhere in physics is misguided. The concept is of the transformation to go from the measure done by an observer to the measure done by another observer, which involves the representation of a group. Whatever the reality one must account for this basic requirement : if one cannot compare the measures done by two observers there is no science.

I have opened a new thread here:

https://www.researchgate.net/post/Does_the_reality_continue_to_act_like_as_a_rigid_body_when_we_go_deeper_and_deeper

where I am trying to investigate the limits of our 'rigid body' defined objects when we are going to smaller distances.