We strive to show that the complexity of the modern theories that we observe is linked, in part, to the description that we make of them with our concepts inherited from classical mechanics. We will come to the conclusion that we need to define a new paradigm.
Frequency vs geometric parameters (space, time) for representing spacetime
The argument invoked in the following development is that the formal mathematical structure of frequency (dual of the entities of time and space, as evidenced by the Fourier transform) is more representative of the structure of a spacetime, because more synthetic than time and space, always perceived as fundamental entities when they are not. Indeed the concept of frequency and the constant celerity of the electromagnetic waves, integrates in a more synthetic way the spatial and temporal characters of spacetime.
A new paradigm
Light should not be thought of, as in classical mechanics, as a wave (or even a photon) propagating in a (fictitious) space at the velocity (constant and relative to the reference frame where it is observed) of approximately 300,000 km /s but as a spacetime object, represented by a null worldline, as described by relativity.
Instead of considering, as in preliminary special relativity described by the Lorentz transformations, an inertial (Galilean) frame as a reference frame, in which the other Galilean frames of reference and light are evaluated, with the disadvantage that there is an infinity of them all equivalent, we will consider the reference frame associated with the light which is unique.
for a discussion on this.
In the language of preliminary special relativity, one tried to save the Newtonian concepts of time and space by marking out the Galilean frames of reference in time and space, needing a synchronization process for time.
The dynamic parameter used, was, in general, the proper time, resulting from the ds²; defined in this Galilean frame.
As on a null geodesic (hence its name) this proper time parameter is zero, one considered that one could not say that light may be used as a reference frame because the synchronization using proper time was not possible. Let us point out that a null worldline is always geodesic.
But the modern concept of null geodesic (introduced by Minkowski in 1907) shows that we can use null frames, without this constraint, and this without any restriction of generality.
We will then consider that the set of all null worldlines in a spacetime (the universe), which are defined, even when no physical radiation exists (this is a fundamental claim), will constitute the reference frame of the universe (spacetime), in place of Galilean frame in special relativity.
As the proper time cannot be used on a null geodesic, we generally use the relativistic momentum, proportional to the frequency of the photon, (or equivalently to the electromagnetic wave that we designate usually by light).
As frequencies are more familiar to our mind than null geodesics, we will call this reference frame formed by all the null geodesics of spacetime a reference background (or referential (by abuse of language) or even a “frequential” type base
This applies to special and general relativity.
But let us recall, once again, that the existence of this frame, formed by a set of null geodesics, does not prejudge the existence of any physical background radiation, even though this may be the case in some solutions of general relativity.
To illustrate the experiments, we may select an arbitrary value of a frequency on these null geodesics (a value of the momentum therefore of a frequency) which will constitute a gauge, associated to a scale factor.
Note that any frequency is arbitrary because the conclusions that we will draw will be purely relative to ratios of frequencies.
Let us add that with this description the mystery of the constancy of the velocity of light disappears.
. Light is not something that has velocity relative to timelike worldines, it is an object of a spatio-temporal nature represented by a null geodesic in the spacetime modeling the universe.
In the paradigm that we propose, we use a class of null geodesics made up of the set of null geodesics of this spacetime (the universe defined by Einstein’s equation) endowed with the same dynamical parameter (the momentum or equivalently the frequency ) to constitute a global frame in the universe.
A priori, this choice of this common momentum can be arbitrary. But one could consider more than one class if it is useful, and refer to the considered class then.
It is the projection of such a null geodesic on a timelike worldline that will determine the momentum (the frequency and also the energy by the relation E = h.f) observed and measured on this timelike worldline.
Note the relative nature of this measurement, due to the arbitrary choice of the dynamic parameter of the class of null geodesics, which will give relative values of frequencies f1/f2 on two different timelike worldlines.
This approach does not claim to allow everything to be explained, but to better understand at least what we know, thus offering a strong basis for improving this knowledge;
Does the frequency representation allow a way towards a relation of indeterminacy and consequently a possible quantification?
Formally, mathematically, the relation between the representation by continuous geometric values of space and time and the representation by waves is done by using Fourier transforms, direct or inverse according to the direction of the transformation. One of the well-known properties of this transformation is indeterminacy. Assuming that, to characterize a photon and its propagation, one uses a wavelet, its position and its frequency cannot be known simultaneously with infinite precision.
It is indeed this property which is the source of this relation of indeterminacy in quantum mechanics.
Here in relativity could we also use this property to open a way towards the quantification of the theory? It seems that this track has not been yet explored….
After these remarks, let’s continue by questioning our knowledge in the current status.
Real or apparent complexity?
Note: This post includes an excerpt from the page: Spacetime. Coordinates: those of null type, lead to a new paradigm. Null principal geodesics. What physical reality revealed?
One can only be struck by the mathematical complexity that must be implemented to establish theories that attempt to account for phenomena as they are observed.
The example given in the preceding chapters gives only a pale image of this.
Theories such as strings, twistors, loop gravity and to a lesser extent relativity, quantum mechanics and quantum field theory require very deep knowledge of mathematics to understand anything about them, which is not the case of “the layman”.
Yet the layman, like all the others, is submitted to these laws in a natural way. A glaring disproportion.
What flagrant disproportion!
One wonders why the laws of nature applying to us seem so complex!
Is there a reason for this? Wouldn’t they be just as effective if they were much simpler? Should we attribute this to the intrinsic complexity of nature itself, at least as it appears to us (the phenomena), or to the relative indigence of our mind  and our senses, since this complexity is appreciated by them.
It would be like looking at an object with a very bad instrument that would give exploded, distorted and blurry images of it.
Indeed, we are « optimized » to live, reproduce and prosper in a well-defined world which is our planet with the Sun.
Thus, our senses that provide information to our mind are adapted. For sight, for example, its maximum sensitivity is for the majority yellow radiation of our star in the sky.
This, which is not fortuitous, is well described by Darwinism. As for our brain, its primary function has been to manage “vital”, namely, survival, reproduction and so on.
If mutations of our brain allowing more elaborate and efficient strategies have occurred and persisted, it is because of the advantage that they conferred on those who had inherited them.
This evolution has made our mental structures evolve towards greater complexity and first, probably marginally, it turned out that these structures could have served other purposes that went well beyond the vital minimum.
Artistic representation, contemplation of nature and awareness of seasonal movements, admiration of the starry sky and recognition of useful star structures for finding their way, recognition of regularities and rules in nature as it presented itself to them.
These phenomena, first attributed to “deities”, ended up giving rise to another representation which must be related to the birth of a scientific method.
All this has developed well until it reaches a high level of sophistication, but mainly in the limited context of our environment, which we will qualify here as a mesocosm.
So, it is not surprising that when we extend our field of investigation to the macrocosm (universe) or microcosm (quantum world) our brain and the tools it has forged were not adapted and that these worlds seem very mysterious, distorted and strange to us when seen by some tools of our mind.
Note that mathematics remains however the most powerful tool of our mind. The very concise mathematical representation of spacetime in general relativity, an incomprehensible concept for us because it destroys our concepts of time and space conceived as immediate idea of our consciousness.
Ditto for quantum mechanics and quantum field theory where a formalism, which Feynman described as incomprehensible, describes the phenomena rather well, shaking up other a priori of our understanding (determinism).
We must therefore realize that if the macrocosm and the microcosm are not familiar to us and upset our ideas, it is mathematics that is probably right and that it is our a priori ideas (which would only be habits of thought) that needs to be reviewed.
For example, the superposition of states in quantum mechanics which seems strange to us, is not necessarily so, because if one is tempted by a mechanistic description of the microcosm (well-identified objects in a well-known spatio-temporal context ) which would be the extrapolation of the mesocosm, it is difficult to see how some properties of the mesocosm could result from it.
Everything would risk being so deterministic that the possible world would be “frozen”. It is also difficult to see how consciousness could emerge from such a deterministic world.
For the macrocosm, some paradoxes are inexplicable if we consider time and space as independent and objectively physical entities.
This is not said to discourage us but on the contrary to make evolve a part of our brain in order to put its concepts in agreement with what mathematics teaches us, in other words to make this part of the brain to be coherent with another part of itself
The entanglement of the knowledge process
Being part of the universe, we are subject to these laws, including our mind and our senses, they are the ones that are at work in our mind and the “physical” validations that we can make of them.
One understands that this implies structural limits on our knowledge:
We seek to understand the laws by a process which itself is subject to them.
We can then be surprised that we can make such elaborate mathematical constructions which go well beyond the immediate data that daily experience presents to us and which seem, for some, even to be unrelated to them.
This is possibly related to the phenomenon of consciousness which involves a self-questioning process: the « abstract » model of the physical world built by our mind for the purpose of effective decision-making can, itself, be taken then as an object to question.
In the examples we will show that this ability can give us access to a more synthetic knowledge of our world than that available by the phenomena.
Witnessing that, the heuristic power of theories that predict phenomena that we have not observed and not even imagined. But it is suspected that this process can only provide incomplete information.
A partial view of the world
From these considerations, it seems reasonable to ask, like Plato, if the phenomena, shadows of a “perfect” reality, are not the source of this complexity. They would be fragments, probably incomplete and distorted and, as such, appearing very mysterious, of the puzzle representing a supposed “physical reality”.
This point has been the subject of an abundant literature, let us point out Majid’s article ““Principle of Representation-Theoretic Self-Duality”, which endeavors to show that from these shadows, for certain types of phenomena, it is possible to describe the source.
An opening to a world that is not physically accessible?
The complex mathematical constructions of our theories would therefore not necessarily be linked to the complexity of nature itself but to the fact that we only have scattered and distorted fragments of it.
They then aim to try to reconstitute (apparently with some success) a better image of nature from these disparate and degraded scraps according to coherences or supposed laws.
Let us point out that this is a remarkable advance, because it is a construction that goes beyond the “shadows” (phenomena) that we observe, in other words a knowledge, undoubtedly incomplete, of a “reality” more synthetic than its shadows.
We live in a certain physical context from which we cannot escape. The fact that certain theories (general relativity based on spacetime and quantum mechanics upsetting our principles most anchored in our minds) flout our understanding should not be considered devastating.
On the contrary, if this opens a window to a world that surprises us, history has shown that we have adapted our paradigms to describe them and even if we are troubled by what we have had to do, we did it.
And, taking as object, the theories that we had to build, by analyzing them, we still improve our knowledge of the world, in regard to the supposed morphisms between the physical world and these theories.
These mysteries should therefore not upset us since they are the manifestation of a possible ability to understand or at least imagine the unimaginable.
We may hope that knowing more than the shadows is not lost! It is a mystery of thought which, although exerted by certain material processes (assemblies of atoms) is capable of producing formal constructions that this type of assembly did not allow to be predicted.
The biggest mystery for us is us!
How did we get here ?
If the Darwinian approach offers a description, a posteriori, it shows that it could have been very different and one can wonder, for other planets what could well happen and result?
We must all the same keep in mind that what is called the validation (in fact the non-rejection) of a theory can only be based on these fragments (phenomena) which are the only objects which are accessible: the theory must predict these fragments.
The scientist will look for laws that could give a coherent meaning to the production of these fragments, without necessarily being able to discover the image of the complete puzzle which may be simple (but we do not know it)!
Another question then arises: what kind of laws, a priori, to try to give meaning to the fragments he observes, does the scientist have and what is their source?
Symmetry as ultimate or fundamental knowledge.
For example, symmetries are increasingly invoked, which can manifest themselves through geometric aspects or more formally through invariants through transformations (groups of symmetries) in physics (quantum field theory, for example). It is true that when we probe nature in its ultimate entrenchments, there are hardly any more than relationships from which we can only extract symmetries! H. Weyl who was interested in the subject suggests that we draw this interest for symmetries from the observation of nature (mineral world, crystals, plants, animals, ..): they are omnipresent.
Nature loves symmetry.
Failing to describe totally the nature in, the scientist can hope to improve his knowledge of nature by diversifying and acquiring new experimental means that will allow him to have other fragments or even all the pieces of the puzzle, which does not mean that we will know how to put them together to discover the image they represent!
This induces that the structure of the mathematical formalism which have been implemented with success, inform us about the laws of nature because we are entitled to claim that this success results from a morphism between the structure of the laws of nature and the structure of the formalism which correctly predicts the phenomena depending of these laws that the nature proposes to us.
This shows the interest represented by these formalisms, which must be interpreted in the context of what they produce: the imprint of the key adapted to the lock representing the physical “reality”!
A few examples illustrating this
Special Relativity (SR)
We know the quarrel over the authorship of special relativity, Einstein having been described by some as a copycat! It is true that Lorentz found empirical transformations for SR
Poincaré by the group of transformations of the space of special relativity that he identified, contributed to the genesis of this theory, which “was in the air” at the time, following the problem posed by electromagnetism and the Morley-Michelson experiment.
But it must be recognized that it was Einstein, in 1905, who gave it its foundation by giving it a physical meaning through the principle of “relativity”.
All physical phenomena (apart from gravitation) obey the same laws in all inertial reference frames which are only differentiated by a relative (constant) velocity.
This is enough, with the parameter of the velocity of light which is a constant in all frames of reference  , to constrain and derive the equations of special relativity.
Indeed, these “Galilean frames” are characterized by the fact that we feel no constraint (the objects “float and we float).
In these Galilean frames having the same phenomenology, the physics must be the same.
None are privileged.
In 1905 we had all the pieces of the puzzle, but that it was Einstein who showed what they should represent and therefore how to put these pieces together.
Note that in this presentation of the beginning of the history of special relativity, the « Newtonian » conception is still very present, via the inertial reference frames, marked out in time and space, a desperate process, to preserve these concepts of time and space. in relativistic mechanics.
The concept of the velocity of light (velocity of a wave relative to a frame of reference where it is measured) is a remnant of the Newtonian approach.
The correct description in relativity is a spacetime null worldline.
It is this description that contains all her attributes in relativity.
Let us recall that this worldline is always a geodesic and that its notion of relative velocity with respect to a reference frame is inadequate in relativity.
The velocity of light is always the same, only the frequency of the « associated wave » (or the momentum of the photon) matters and then how to define it in relativity since the proper time of a null geodesic is zero: we generally take another parameter which is associated with the momentum, therefore with the frequency.
We know that in general relativity, in some solutions, (the standard model of modern cosmology for example: Big Bang) the radiation, in a general way, can form a physical reference frame (CMB) common to all the observers, where any “observer” can be located.
The Micheson-Morley experiment
Let us add that if we consider a « stationary » radiation which « fills » all of spacetime, that only the observed frequency will vary according to the observer, the result of Michelson Morley’s experiment is perfectly explained.
Due to Doppler effect, the redshift of the light towards the mirror in the direction of the motion is compensated by the blueshift of the reflected light in the opposite direction.
Note the similarity with the explanation given by Lorentz where he supposed a (mysterious) contraction of physical rigid objects.
The frequency description gives another version without assuming a contraction of rather rigid equipment!
Around 1907, Minkowski gave it a more formal and more synthetic description by defining the spacetime, reducing time and space to shadows..
This considerable conceptual progress makes it possible to understand paradoxes like that of Langevin’s traveler, incomprehensible in Newtonian mechanics.
It is still difficult to understand today, because we still try to consider this journey in a space provided with a fixed structure on trajectories (lines in this fixed space between points of this fixed space) on which a rocket accelerates in a Newtonian way.
This does not allow an understanding of the phenomenon.
We must abandon Newtonian space and time, which do not exist in relativity, and consider only spacetime, where there is no fixed space, to understand the phenomenon!
It is necessary to consider the worldlines followed by the 2 protagonists (twins or not) and to measure the associated proper times for understanding the phenomenon.
Compared to the stationary frequency frame filling the universe, the traveler observes a spectral blueshift compared to the sedentary. This means that the number of periods per unit of its proper time is greater for it than for its counterpart on Earth.
In the complete round trip, the traveler and the sedentary person will have counted the same number of periods of the background radiation, (just draw a diagram to be convinced of this: the background radiation oscillates synchronously, it provides a frame reference time) but as the traveler has counted more periods per unit of his own time, he is younger than him.
Of course, this supposes that we forget our usual concepts of space and time in favor of that of spacetime which is not familiar to us.
This is a typical example where our understanding is blurred by habits of thought which penalize us in the apprehension of a deeper physical nature: that which is underpinned by spacetime, of which one of the deepest mysteries is the role of light (electromagnetic waves) whose velocity is finite in Newtonian like approach.
This is what gives to spacetime its peculiar and strange (hyperbolic) nature.
Let us add that this results from considerations dealing with the coherence of knowledge and causality (linked to information). Indeed, it is to have an invariant available to all observers (spacetime interval) that confer to this invariant a physical character, on the conviction that the phenomena had an “objective” character (coincidences of Einstein), what the theory had to respect.
Moreover, an event B cannot have been caused by another A if the information linked to this event A did not reach event B when it occurs. This is a model; however the character and role of light is certainly not fully understood.
There was a small paternity dispute between Einstein and Hilbert which was settled amicably, Hilbert acknowledging that most of the analysis of the problem was due to Einstein, his contribution on the equation was simply solving of a mathematical problem (brilliantly, because he proposed a much more general method than that of Einstein by defining an action, Hilbert’s action, for general relativity).
Einstein, who for his part had endeavored to transpose gravitation into a relativistic form, had established his equation well before Hilbert, but in a less elegant way.
The geometric form of the theory of general relativity which is a theory of gravitation shows that we can describe, for example the universe, by its geometry which depends on what constitutes the universe.
The great interest of this formulation is that it makes it possible to take into account a “non-linearity” which seems necessary: all the objects contribute to defining the geometry of the universe to which, in return, all these same objects will be coupled (they will follow geodesics of the geometry of this universe).
The circle is complete. Magnificent solution implementing this recursion where the object (the one who rules) is also the subject (the one who submits). A model that could serve as a paradigm for phenomena like consciousness?
Another beauty of the solution, the universe thus defined is “self-sufficient”, (spacetime is defined by what is called a manifold in mathematics) in other words, it does not need anything other than itself to exist and be totally defined. This eludes the problem of a creation and “reduces” it to that of an existence.
Many scientists have contributed to this theory, so bizarre that its physical interpretation is still open to debate, even if the Copenhagen School’s interpretation is the reference.
Faced with the strange nature, very different from what the world of classical physics and mechanics presented to us, that scientists were discovering, it is interesting to note the approach of W. Heisenberg who proposed to abandon all the concepts of classical mechanics and to consider only the “observables” (the phenomena) as elements of the theory. They were presented in matrices, associated with a formalism that allowed calculations to be made.
On the other hand, Schrödinger was developing a solution with an equation of a wave function, allowing to define the state of a system. We know that this following formalism also included operators, associated with the physical quantities, which applied to the wave function allows to predict the probabilities of measurement results. These two formalisms turned out to be equivalent, which is interesting, because it shows that two fundamentally different approaches could just, as well, describe what we could know about nature.
Theory, experience and information
Physics being an experimental science, we often oppose theory, supposed to be a pure production of our mind to model and try to make intelligible the physical phenomena and experience which is the counterpart of the model, applicable to the physical world.
Bachelard who in his book, “the new scientific spirit” develops this supposed antagonism, links theory to “rationalism” (the reason of the mind), and experience to “realism” (the physical world). He tries to show that, these two aspects are not totally separable and therefore more than an opposition, we are dealing with a kind of unique dual entity of which realism and rationalism are not totally separable and independent characters.
Sometimes it is rationalism which leads science and realism follows (experiments are carried out to validate new elements what the new theory predicts), sometimes it is realism which, through unexplained experiments, will stimulate the minds of scientists in order to build a new theory that explains them.
The most uncompromising rationalist cannot avoid taking experience into account, and the most determined realist, in constructing his experiments, cannot ignore theory, an experience being according to him a materialized theory.
He concludes: “Physics is an impure metaphysics because it must be accountable to experience”.
An experiment provides information on the state of a system via “measurements”. These measures generally involve instruments that can be sophisticated, in order to adapt to the phenomenon to be studied, hence Bachelard’s remark (an experiment includes a part of materialized theory).
In classical mechanics this has not raised any notable philosophical debate on the role of the experimenter. We considered a system to be studied. It contains information that one wishes to acquire via an experimenter equipped with his equipment. These two systems will interact during the measurement. They are generally thought of as two independent systems that resume their own “life” after interaction.
In quantum mechanics it is quite different. Measurement, taking information from the system, disrupts, reduces, or even destroys, fundamentally the information in the system. It is not a passive act (or very weakly active) without consequences on the system but on the contrary very active. The information is not only acquired but also taken (therefore removed from the system) and therefore will reduce the degrees of freedom of the system to the point that, from indeterminate, it can pass into a known state.
Illustration by Young’s slits
The mechanism which leads to this has been the subject of different interpretations, but, for example in the Young’s two slits experiment, the fact of knowing (by a detector on a slit) through which slit a photon has passed will modify, even if the detector does not detect anything (in which case it is assumed that it has passed through the other slit) the observed phenomenon.
The fact of acquiring information even when nothing is happening is called contra-factuality in some works (see note ).
It is understood that, when the detector attached to a slot detects something, it takes a quantity of information on the state, this modifies the phenomenon, compared to that where there is no detector, because a part of his information was taken from him and transmitted to the experimenter.
Overall, the information seems to have been preserved if we consider a system that includes the experimenter (it has been transferred from one subsystem to another)
On the other hand, when it does not detect anything, but it does provide, the same amount of information (the opposite information on the condition) is less obvious.
Curiously, since nothing was detected, it would seem that no information was taken and that, as we have the same result as when we detect the passage through a slit, we could think that the information of the global system has increased, but in view of the end result, which is the same in terms of information (although the latter is different) this does not appear to be the case. Perhaps the activity of the detector should be taken into account in the balance sheet?
Either way, this result seems odd.
Anyway, it is clear that it is the fact that there is a detector in the instrumental device which is important and which differentiates the situation from the case where there is not: The experimental device is different therefore the associated information also !
The interaction between the experimenter equipped with his instrumentation with the system is different. This is what, a priori, even if the experimental device detects nothing, because the experimenter, who built the experimental device, foresaw this case in his quest for information, will change the observed phenomenology!
The role of the experimenter, relying on a theoretical model, cannot be ignored. It is therefore indeed an interaction between a physical system and the mind of the physicist equipped with a theory via his experimental device.
Some, like Wigner, see the phenomenology of observed quantum mechanics as the essential imprint of the mind of the physicist.
In quantum mechanics it would then seem more adequate to evaluate and consider the information, not to the system studied and to the experimenter separately, but globally associated with the global system made up of the physical subsystem to be studied and the subsystem linked to the experimenter in interaction, because at the moment of the interaction they form only one system! If we neglect errors during the experiment, the information therefore the entropy  of the global system, considered isolated, (including the experimenter), before the experiment and after the experiment should be identical (we have since the contra-factuality seems to raise a doubt). Information that has been transferred from one subsystem to another subsystem remains in the overall system. 
A formalism, to be developed, which could take this into account would perhaps allow certain very disturbing aspects of the theory to be removed …
 We can lend our mind a structural indigence, however note that by its ability to learn and evolve we cannot make a final judgment on the state of the knowledge made today. We must also take into account that certain concepts, such as space and time, concepts inherent to our existence, are so significant, and that despite all our efforts to detach from them, they are still often still present, in the background, in our mind, which burdens its meaning. See example of Langevin’s traveller’s paradox, for example, in special relativity.
 This structurally very important point, this limit being involved in causality, resulting from the principle of relativity which reveals a velocity invariant but does not specify its value. The value of this constant is an experimental data. see again: https://astromontgeron.fr/SR-Penrose.pdf
 Entropy and information are two presentations of the same concept.
 This transfer of information is even more evident in the illustration of Young’s slits problem by Elitzur-Vaidman cited by R.Penrose (Nobel Prize 2021) in his book “The two infinites and the human spirit – Fields Flammarion ”where it is a question of recognizing in a batch of atomic bombs equipped with a detonator constituted by an ultra-sensitive mirror such as a photon activates it by making me move (mobile), those which are operational from those which are faulty where the mirror is blocked, which is indistinguishable without destroying it. We insert a bomb whose mirror detonator serves as a mirror in an experimental quantum device, without knowing whether it is operational or defective. The authors show that their quantum device makes it possible to select operational bombs without destroying them, by using the mechanism of contra-factuality. In other words, while when we insert the bomb into the device we do not know if the mirror is mobile or blocked, the information is in the object, but not in the knowledge of the experimenter, the experience will reveal to him this information, by means of a protocol, without removing this information from the bomb (which would be the case by its destruction for operational bombs).
For more information, see for example: