According to Kepler laws, obtained from the motions of the planets of the solar system, and the Christiam Huygens law on the centrifugal force, Newton concludes that the force acting between the two bodies take place in straight line between the two bodies and is proportional to the inverse of the square of the distance between the two bodies [1]. Newton work on gravitation was published: the 5 July 1687in: Principia, thus, there is more than 300years.
To understand the atomic spectra Bohr has supposed a motion of the electron around the atomic nucleus, similar to that of the planets and an angular momentum equal to an integer number of the Plank constant h. This hypothesis has allowed a number of interpretations; however, in the study of the quantum state, it appears half-integer quantum numbers for the angular momentum and the hypothesis of spin-up or spin-down to explain these numbers is still questionable. In fact, it is possible to interpret the half-quantum number supposing that the interaction electron proton involve the three directions of the space see: “The spin and the angular momentum”.
Now each one of the two first quantum states 1s has just one quantum of action, as a result each 1s state has thus one half quantum of action ½h associated either to the rotation or to the linear component perpendicular to the motion of rotation. Each one of the other quantum states have one or several additional quantum, each one corresponding to just one degree of freedom, they are undividable. As a result, the half-quantum number of the angular momentum of the different quantum states is that of one of the two 1s states, the same for the linear component.
This approach is possible if the interaction is the result of exchanges of very small grains of mass. This hypothesis is suggested by the paper of Einstein on relativity “the law of the physics must be independent of the place of the observation”. Indeed describing the interaction from the electron or the proton the alone possible variable is the mass. Thus, the motion is the result of exchange of mass between the proton and the electron. The space being supposed isotropic les exchange take place in all the directions and the orbital motion implies a linear component perpendicular to the plan of the motion.
As a feedback of the quantum mechanics, we can suppose that interaction giving the motion of the planets must involve the three directions of the space. Certainly it is difficult aftre more than three hundred years during which we have worked with just an interaction in straight line, but one has to espect further progress, for example, the earth's magnetic field must probably be the result of the gravitation.
[1] Wikipedia: Gravitation, french version
Dear Xavier Oudet
I am not surprised why there are no comments because your question envelopes too much issues to give an adequate response. Nevertheless, I give it a try.
I have copied a comment of mine about gravitation. Maybe we first can get some consensus about the question: “What is gravitation?”
The term “gravitation” is dedicated to the observation that every object is “attracted” by all the other objects and visa versa. We know it because of the mutual changes of position of all the objects. Objects represent concentrations of energy (E = mc2) thus the difference between an object and vacuum space around is the local “density” of the energy within a large volume. If we propose that there is a magic trick to redistribute (expand) the concentrated energy of the objects it is easy to imagine that the expansion of the energy of all the objects in the universe will result in a universe with average amplitudes everywhere within the electromagnetic field. An imaginary situation that is part of the Standard cosmological model.
Suppose we can “roll back” the evolution of our universe till the moment that there is no matter to be find. Now there are only the continuous changing amplitudes of the electric field and the resultant vectors of the corresponding magnetic field. An amplitude of the electric field is a local amount of quanta (Planck’s constant) thus the amplitude generates vectors and the vectors generate the direction of the change of the "next" amplitude (law of conservation of energy and the law of the conservation of momentum). However, the electric and magnetic field are not the only 2 universal fields that fill the volume of our universe. There is also the universal scalar field (the Higgs field).
In vacuum space all the scalars of the Higgs field have exactly the same magnitude. In a universe without matter the whole volume of the universe is vacuum space thus the scalars of the Higgs field don’t change their magnitude. Energy is change of position and time (= the power to change position and time) thus in our universe the electric field is the cause behind the total amount of change (the magnetic field is a vector field and vectors don’t transfer energy because vectors are 1-dimensional).
Now, where is the force of gravitation? Einstein told his students (1920) that without matter in the universe there is no theory of General relativity and Eric Verlinde (2011) proved that Newtonian gravity is an emergent force field too. Thus the field of gravitation emerges at the moment that matter is created in our universe. And the mechanism behind the creation of matter – rest mass carrying particles – is the electromagnetic field (the local concentration of quanta).
The Higgs mechanism represents the local decrease of scalars at the moment the local concentration of the electromagnetic field (density) exceeds a certain threshold. The released energy of the decreased scalar becomes part of the local electric field. The flat scalars of the Higgs field get vectorized by the decreased scalar(s) of the rest mass carrying particle and at the same moment a local field of gravitation emerges.
Now the question is, which of both forced changes – the local increase of the electric field and the vectorization of the scalars of the Higgs field in vacuum space around – is what we have termed “the force of gravitation”?
Newtonian gravity is a vector field, it doesn’t transfer energy and it acts instantaneous, so this is in line with the vectorized scalars of the Higgs field in vacuum space (and an attracting force is identical to a push force).
Einstein’s curved spacetime is bound to the speed of light, it transfers energy and it is supposed to “curve” space itself (actually the electric field). This is partly in line with the local supply of energy from the Higgs field to the electric field. Although Einstein didn’t realize that the whole volume of the universe isn’t dynamical, only the part of the volume of the electric field (about 26% of the volume of the universe). Moreover, the transfer of energy by the decreased scalar(s) to the local electric field doesn’t change the local volume of the combined Higgs field and electric field. But without a local expansion of space itself there cannot be a geometrical curvature of space itself.
The mechanism behind the concentration of quanta by the electromagnetic field doesn’t stop at the moment local rest mass is created. So we have to conclude that there are 2 types of gravitational fields. A vector field responsible for the concentration of rest mass (Newtonian gravity) and a topological field (= electric field) responsible for the concentration of energy (Einstein’s “curved spacetime”). The latter is in line with the existence of Dark matter (mass without rest mass).
With kind regards, Sydney
dear friends, please tell me what do you understand by 'field'; huygens defined it as the 'carrier', a medium' of a force; as it is well known, there are four fundamental forces in the universe, at least till now; i'm very sorry, but i don't dealt with quantum mechanics, higgs bosons, etc; i'm a 'classical' man, and, i don't think at my age(61), i whish to start from the very beginning with this domain; i red in a book of popularisation written by hawking, that in order to verify all the 'interesting' hypotheses like teleportation, time travels, etc, a thousands billions km long accelerator would be needed; so, we must expect for a new revolutionary theory; maybe it will come soon, as demonstrated by the history of physics -:);
on the other hand, why nothing about the bohr's planetary model, at the first sight al least, after my oppinion you need no more to extend gravity(rotation) from classical mechanics to quantum one; of course, all it depends on what do you want to do, concretelly; yours, mircea
i'm back; mention that all you will do with the copenhagen interpretation will be for 'practical purposes', otherwise you need quantum gravity; it would be very interesting if you could avoid it, i'll think a bit about 'how' and 'aiming what'; yours, mircea
Dear Mircea Ciobanu
In 1934 Einstein stated in his new book that universal fields represent the properties of space itself. I don’t need Einstein to understand spatial fields but it shows that fields are not a new concept. Actually, even the ancient Greek philosophers (about 600 BC) used a concept that described observable reality as the creation of an underlying field structure (Parmenides). These ancient philosophers were not “unscientific dreamers”, see: https://www.nature.com/articles/s41598-021-84310-w.
Imagine a checkerboard. If we fill all the white squares with one checker (black) we can imagine that the checker board represents a homogeneous field. But of course we can redistribute the checkers. Some white squares will be empty now and some squares will hold one or more black checkers on top. But half the squares of the checkerboard have another colour (brown). If all these squares represent another field and every brown square gets a white checker, the checkerboard shows a nice similarity with fields in physics. Both fields have their own “space” within the surface area of the checker board and each field have its own properties (the amount of black checkers and white checkers in every square). Of course, our universe is a volume and not a surface area but the general concept is clear: space itself is “build up” by different spatial fields and the continuous redistribution of the properties of these fields are known as observable phenomena (particles, atoms, celestial bodies, etc.). Actually, it is the general concept of modern quantum field theory (see Art Hobson (2013): “There are no particles, there are only fields”. https://arxiv.org/ftp/arxiv/papers/1204/1204.4616.pdf).
With kind regards, Sydney
i believe that's all i can answer to the question of how equivaleting classical rotation with quantum one; considering the planetary solar system and the bohr's planetary atom, let's say we whish to to discretizes the 'orbits'; in quantum mechanics, they are already discretisized by the bohr's second postulate; when considering a satellitary planet, the gravitational force force is centripetal, kMm/r**2=mv**2/r (1); in the case of the atom, the inverse square law electrostatic atraction is centripetal too, but the angular momentum is quantifyied, being a multiple of (h/2*pi)*v*r; but in classical case, the otrbits are 'discretisezed' in a way, not by integer or rationale numbers, but by real ones, satisfying the condition the gravitational force being centripetal; so the 'r' is restricted to have only those values satisfying eq 1. I realize my answer is a bit ambiguous, but i think you understand what i meant; yours, mircea
Dear Mircea Ciobanu
The problem is that Christian Huygens didn’t know what the cause is behind the centrifugal force. The centrifugal force is an observation, related to the centrifugal motion of objects. We can compare the difference between centrifugal and linear motion to get some insight, but that doesn’t change the fact that we don’t know the underlying creating mechanism. And Isaac Newton didn’t know it either although he founded his theory of gravitation on the existence of the centrifugal force. Moreover, the problem about the origin of centrifugal motion still exists (e.g. the spin of sub-atomic particles).
So if I want to answer Xavier Oudet’s question I have to describe the mechanism behind the centrifugal force at the smallest scale of reality (quantum reality). But that’s not enough because in modern physics there is the conviction that gravity is the consequence of the curvature of space itself (Einstein’s theory of General relativity). Unfortunately the proposed curvature of space doesn’t need Christian Huygens centrifugal force to describe the properties of the “field of gravitation” in relation to the orbits of planets around a star. Moreover, at the quantum level time – like time in classical mechanics – is a constant (in conflict with Einstein’s curved spacetime).
That’s why Xavier Oudet’s question cannot be answered without solving this contradictions. So I have to start to get some consensus about the origin of the force of gravitation. At least, if the question is still "alive"...
With kind regards, Sydney
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