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Relativity and the Unforeseen Error

The notion of relativity, born with Galileo and formalized by Newton, remained as such until Einstein. When he published his work in 1905, what would later be called the theory of special relativity completely overturned what was believed to be known about relativity. Distance, time, and simultaneity, previously considered as invariant or absolute in classical physics (Galileo/Newton), henceforth became relative concepts. Where only speed was considered relative, it was now the speed of light "c" along with the Lorentz transformations that became the absolute reference for judging the relationship between reference frames, i.e., the necessary clock for measuring events between reference frames. As there is a vast literature concerning the work on relativity by these three protagonists (Galileo, Newton, and Einstein) we will not elaborate further on the said works. It will be immediately understood that this is not a training or a complement of information aiming to teach the different theories of relativity.

Although the theory of special relativity is universally accepted, its origins nevertheless rest on a strange paradox or a curious misunderstanding. It is, moreover, from this misunderstanding that the inspiration for this present publication was born.

The Origins

Galilean relativity postulates the existence of inertial reference frames allowing the observation and quantification of movements, thereby implying that time and space are absolute references. A beach near a body of water or a park bordering a railway line are fixed, and by definition, inertial reference frames. The same applies to a boat, an aircraft, or a train in uniform rectilinear motion, provided that no other force or acceleration alters the reference frame considered. It is based on this postulate that Galileo asserts that " motion is as nothing " after he observed that the fall of an object was completely identical whether from a fixed reference frame or a reference frame in uniform rectilinear motion. Comparative observations made from these different reference frames proved this. Thus, the comparison of comparable elements allowed Galileo to support his postulate. The notion of relativity can now emerge from the moment when the position of the observer in a distinct, obviously inertial, reference frame must be taken into account to measure and quantify any movement. From this was born the law of composition of velocities, with the so-called Galilean transformations, as well as the notion of relativity. It is on this basis that Newton would state his laws of motion while confirming Galileo's relativistic logic.

The Paradox of Light

At the beginning of the twentieth century, among the unresolved mysteries, there was, among others, the constancy of the speed of light. As established by Maxwell's equations and confirmed in the Michelson-Morley experiment, it did not fit with what the laws of relativity then prescribed. In addition to lugging around an ether that could not really be identified or defined to justify the propagation of electromagnetic waves, including light, these waves did not conform to the law of composition of velocities deduced from the Galilean transformations. By substituting the Lorentz transformations for the Galilean transformations, Einstein resolved this paradox, incidentally getting rid of the concept of the ether, which led to nothing concrete. But did this paradox truly exist?

According to some interpretations, special relativity was born as an echo of the principles of Galilean relativity that could not explain the constant nature of the speed of light. Einstein, based on Maxwell's equations, supported his theory on these two postulates: the constancy of the speed of light and the non-existence of the ether. With this new theory of relativity, any conjecture induced by this paradox could now fall into oblivion.

Yet, there is a detail here that deserves examination and seems to have foolishly escaped the scientific world. Under specific conditions, as will be demonstrated, like light, sound and waves on water do not respond to the law of composition of velocities. If sound waves or waves on a liquid manage to conform to it, it is primarily due to the observation criteria or mechanisms rather than relativity itself. The paradox in question here, therefore, does not concern only light. If the theory of special relativity led us to believe that all paradoxes were now resolved, all the confusion surrounding what is, in fact, a simple misunderstanding, is not totally resolved.

Definition of Inertial Reference Frame

Let us first specify that there will be regular mention of a Galilean reference frame or Galilean relativity. Because Galileo was the first to put forward this notion and initiate a scientific movement on which future work and discoveries would be based, it is in these terms that it will be referred to. Most of the principles and rules that will be alluded to were mostly specified later by scientists other than Galileo himself.

Now, concerning the rules of relativity and their formulations, let us only recall that all inertial reference frames (Universal, Galilean relativity, or special relativity), to be considered as such, conformant, and valid, must respect the following conditions:

They must not undergo any acceleration, change of direction, or be subjected to external forces, or these must cancel each other out. They are, therefore, at rest or in uniform rectilinear motion.
The experiments conducted and their results are the same.
All the laws of physics must apply.

These are the essential conditions allowing the definition of one or more reference frames from which observations can be conducted and compared. Note that these same conditions apply within the framework of the theory of special relativity.

However, within the framework of Galilean relativity, for its principles to be respected in accordance with Newton's laws of motion, although distinct from special relativity, the following observation rules are prescribed:

For any change of reference frame, the Galilean transformations apply.
Velocities are relative and respond to the law of composition of velocities according to the aforementioned transformations, v = v' + U.
Distances and durations are invariant.
The simultaneity of events is absolute.

Inertial reference frames and the accompanying observation rules form this whole that is called Galilean relativity. Building on this definition, let us now specify which observations can be apprehended with waves of all natures. Notwithstanding the nature of the reference frames and the rules of relativity, it is possible to observe and measure the following phenomena:

There are movements whose speeds are measurable depending on an observation point, whether it is in motion or not.
A measurable Doppler effect, whether the observation point is in motion or the reference frame itself.
A difference in time can be observed according to the point of view and the chronology of the events considered, a priori, simultaneous.

To this, let us add the observation conditions themselves. The distinction must be made because the observation conditions prevailing in the observed reference frame and that of the observer must be the same. It only remains now to ensure that these observations and the experiments conducted remain consistent with the laws of relativity. It then becomes relevant to ask the following question:

Do the reference frames involved share something common between them, and, if so, does this interfere with the interpretation of the results?

Reference Frame Test (Waves on Water)

In a first exercise, let's take the case of a wave on the water. Better yet, a stylus that, with a regular movement, generates a series of waves. A first, in a basin near a railway line, and a second in a basin located inside a wagon of the train circulating at constant uniform speed on the said railway line. The two basins are of the same depth and, need it be specified, both contain water. An observer is positioned in each of the reference frames. Each of these reference frames is considered inertial and corresponds to the validity criteria cited previously. From this exercise, we obtain two scenarios: a static basin and a moving basin, from which the present observers will draw observations and conclusions.

Scenario 1 (Reference frame proper to each observer):

Each of the observers measures the speed of propagation of the waves in their respective basin. Since, in accordance with their reference frame, the water is at rest in each of the basins, they will both obtain the same speeds. The frequency of the waves observed is the same regardless of the direction in each of the reference frames, and no Doppler effect can be noted.

Scenario 2 (Reference frame proper to the other observer):

Each of the observers measures the speed of propagation of the waves in the basin of the other reference frame with the formula v = v’ + U or v = v’ – U according to the direction of the waves. Again, each of the observers obtains the same results. Likewise, each will observe a difference in the frequency of the waves depending on the direction of propagation and will obtain the same frequency measurement results.

Considering only the speeds and applying the Galilean transformations, the speed difference between the measured waves is entirely explained by the composition of velocities. The experiment is therefore entirely consistent with Galilean relativity. Up to this point, there is neither misunderstanding nor contradiction with the classical laws of relativity.

Let's now repeat the same exercise, but this time with a single basin for both reference frames. To avoid confusing the measurements, this is done in two stages.

In a first step (Fixed reference frame):

The stylus on the ground reproduces the same waves as those observed in Scenario 1 of the first exercise. The observer on the ground will thus obtain exactly the same results as before, the same propagation speed with no Doppler effect. As everything is static, they only take the measurements and have no need to perform any calculation taking into account the movement of the train.
As for the observer aboard the train, they will arrive at the same results as in Scenario 2 when observing the basin on the ground. Here we still have the same conditions where the Galilean transformations apply, and the measured Doppler effect remained the same.

In a second step (Moving reference frame):

It is in the basin located on the ground that the train's stylus now moves. Note, however, that the experiment in time will be limited to the time the train takes to travel the basin. The stylus thus moves from one end of the basin to the other. When it starts generating the waves, it is immediately noted that the speed of each of the wave crests is the same as those generated by the stylus on the ground.
For the observer on the ground, although the measured speeds remain the same as if it were their own stylus, they immediately notice a Doppler effect comparable to that observed in Scenario 2 of the first exercise. What is confusing here is that it is not possible for them to apply the law of composition of velocities as they had done previously.
A different, but equally troubling observation for the observer aboard the train: when the stylus and basin were on their own side, where no composition of velocities applied, they are now obliged to proceed with the Galilean transformations to cross-check their wave propagation speed measurements. Whether the latter is positioned in front, behind, or facing the stylus, the same measurements and calculations remain. This is not the case, however, when it comes time to measure the frequency of the waves. While no Doppler effect can be measured when facing the stylus, in the other cases, a different and measurable frequency will be noted. There will therefore be a Doppler effect that the first exercise did not predict in Scenario 1.

If it is a little early to make a precise comparison of what has just been observed with what is known about the behavior of light, a correlation can already be established. By sharing the same propagation medium, the observed propagation speed was the same, regardless of the observation point. This is the same finding as during the observations made with light during the nineteenth and twentieth centuries. Therefore, it is permissible to postulate that in the second exercise, assuming that the law of composition of velocities is intrinsically linked to the theoretical framework of Galilean relativity, one or the other of the reference frames can no longer be considered conformant. Both share the same propagation medium. In fact, it is the train itself or the wagon, to be more precise, that no longer corresponds to the validity criteria since the chosen propagation medium does not entirely form a body with it. Also, note that during the first exercise, it was not the stylus following the movement of the wagon that imparted additional speed to the generated waves, but the speed of the basin itself and its contents. As just specified, the whole formed a body with the reference frame. It was not necessary to quantify the observations or to put everything into an equation; the logic itself was sufficient to explain why, under these conditions, it was impossible to apply the law of composition of velocities.

Regarding Sound

To support the arguments put forward, what about sound? It was discussed earlier, but if the Doppler effect is a phenomenon that requires explanation, unless one is hard of hearing, everyone has experienced this effect. We have all had the opportunity to note the sound difference when comparing the noise of a car approaching us to that of one moving away. This is a difference in the frequency of the sound waves perceived by our hearing. It is the same effect that was discussed earlier with the waves, but visually and measurable in space. The distinction will have been noted between wave crests approaching each other and those moving away in the opposite direction.

That said, the speed of sound propagation depends directly on the medium in which it propagates. In the air, the speed is approximately 340 meters per second, or 1224 km/h. A loudspeaker, the sound of which can be heard from outside, in a train speeding along versus another in a railway station, regardless of the tests and observations carried out, the speed of sound will remain unchanged. Thus, an auditor aboard the train, whether they are at the front of the train or the rear, will not be able to note any difference according to their position since this auditor is speeding along at the same speed as the train, while an auditor located on the station platform can note the sound difference as the train passes. Only the Doppler effect will make a distinction since the speed of the sound waves itself will be the same for both. Proof of this is the sonic boom of jet planes when breaking the sound barrier, demonstrating that movement does not alter the speed of sound itself in any way. Here again, the law of composition of velocities cannot be applied. If a train and a station can be considered valid as reference frames to judge the launch of a projectile in each of them, this is not the case for sound or any other phenomenon that can behave like a wave if it cannot be confined to the observed reference frame.

Let's not conclude too quickly, because if we limited ourselves to considering only the sound emitted from a loudspeaker inside one of the train wagons, it then becomes possible to apply the principles of relativity to it. The propagation medium being isolated from the outside world, we can thus apply the law of composition of velocities. Although sound waves cannot be seen, there are ways to measure their impact on any fixed mobile inside the wagon, which would allow us to visualize them and perform the appropriate calculations. By doing so, it can be seen, in such a context, that the reference frame constituted by the wagon will be valid. Moreover, if the train in question were to break the sound barrier, while for people outside only a sonic boom from the train would be perceived, the auditors inside the wagon would simply continue to be soothed by the sound as if nothing had happened.

The simple logical exercise just demonstrated here: the fact that two reference frames share the same propagation medium automatically discredits them when it comes to measuring wave phenomena. In such cases, whether it is sound or light, we generally compare reference frames sharing the same propagation medium where the observed phenomenon depends on this same medium. Consequently, when two reference frames share a common element intrinsically linked to the phenomenon being observed, they are no longer distinct, relativity as normally understood no longer exists, and the law of composition of velocities can no longer be applied. It is immediately apparent that an essential rule is missing from the definition of a reference frame. That a reference frame is considered inertial is not sufficient in itself to judge and gauge the relativity of what is being observed. The observable and measurable relationship of the considered events must also take into account the total distinction between the reference frames involved.

Simultaneity of Events

To avoid making things too complex concerning the rules governing the principles of relativity, the simultaneity of events has not been raised until now. Let's now consider two projectiles launched at the same moment and with exactly the same velocity criteria. Both will fall to the ground at the same moment. Whether on the ground or in any vehicle in uniform rectilinear motion, the result will be the same. The same will apply if the two reference frames are compared with each other; if the launch of projectiles is synchronized, all projectiles will reach the ground at the same moment. So far, everything seems fine, and the integration of the rule into the definition of a reference frame cannot be questioned.

However, as in the cases mentioned previously, considering only events involving wave phenomena, the results are no longer the same. With waves on the water in the two basins considered in Scenario 1 of the first exercise, there is indeed simultaneity. In the case of Scenario 2 and the second exercise, one cannot conclude the existence of simultaneity. Indeed, if the movement of the waves in a basin on the ground is observed from the train and the limits of observation are set at the limits of the wagon in which one is located, it will be noted that the first waves will reach the back of the wagon before a single one has reached the front. No need to lend oneself to new exercises with the other wave phenomena, the results will be the same as here. This is one of the aspects of relativity on which the theory of special relativity relies to preserve the invariance of the speed of light, even though no distinction relative to the propagation medium is made.

In view of the demonstrations that have just been carried out on reference frames and their relationships, i.e., relativity itself, can the simultaneity of events really be rejected as one of the rules defining an inertial reference frame? The question can be asked, and the answer is simply relative. Nothing that has been put forward so far tells us that simultaneity cannot be verified. It has only been shown that from non-conformant reference frames, the simultaneity of events could not be visually verified. By setting the right calculation benchmarks to determine the occurrence of the considered events, it is then possible to determine whether there is simultaneity or not. Before rejecting this rule, it must reject itself in a context where the reference frames are genuinely conformant beyond any doubt. The invalidity of the reference frames regarding the law of composition of velocities considered so far does not, therefore, allow us to reject this rule in the context of Galilean relativity. This should be taken with a certain lightness; the different situations and observation conditions will at all times require judging the relativity of the events among themselves to determine if the latter are indeed simultaneous. Like special relativity, we are forced to conclude that the simultaneity of events is not absolute, but relative.

Additional Clarifications on Reference Frames

To fully grasp the nature of a reference frame and judge its interaction with another, as well as its validity, a distinction must be made as to whether the observed phenomenon depends on the propagation medium or how the comparisons made depend on it. It is also necessary to establish whether the propagation medium itself is in motion or not according to the reference frames.

The movement of a ball thrown in two distinct reference frames does not depend on the medium in which the ball is projected. Its movement is only affected by it. Whether it is in the air or in the water, the conditions must simply be the same in each of the reference frames to compare the same things. Since the movement of the ball does not rely in any way on the propagation medium, but rather on what generates its movement, it is only necessary to distinguish whether this medium is in motion or not and, consequently, linked to the reference frame concerned.

Let's specify that what drives the ball cannot depend on the medium in which it propagates. It is on its source of impulse, the element that projects it, and its mechanical link with the reference frame in question that generates its movement. This movement can only be altered by the nature of the medium, unlike a wave in the water or sound waves in the air, which depend directly on the medium itself to propagate, a medium which is, in fact, their propagation support. As for light, from what we know to date, it does not depend on any medium and does not possess a propagation support. If light has a defined speed in a vacuum, it varies, however, depending on the medium in which it propagates and not according to the vehicle from which it is emitted or the movement or non-movement of the latter.

In the context of the theory of special relativity, it is common to use drawings, graphs, and animations of all kinds to demonstrate how to apprehend distances and time based on a light or laser beam emitted from a moving vehicle compared to the same device located in a totally inert environment. Although rather eloquent demonstrations are achieved¹ , in most, if not all, cases, the emitted beam is presented as if it absolutely had to take part in the movement of the vehicle, which is not accurate, even if it is not totally false. Despite the admirable efforts of mathematical conjugations, where distances are contracted on one side and time is dilated on the other, to make the events corroborate with each other; although the final result seems convincing, it is in fact a loss of effort and energy. We are naively seeking to compare the incomparable. Since the propagation medium of light is the same for both reference frames, they cannot be compared in this way to explain the composition of velocities in special relativity or Galilean relativity.

Note, however, this distinction. Although it is essential that the propagation medium is exactly the same for the validity of the experiment, it must be independent of any other reference frame, which is not the case here. The two reference frames are bathed in the same medium. Moreover, even if the emission source follows the movement of the vehicle, the light itself is not affected in its course. Only a Doppler effect can be measured depending on the speed of the vehicle. By slowing down a photon to the point that its speed would only be a fraction of the vehicle's speed (something modern science has the capacity to do), its projection would be observed not in front of its emission source, but behind it. It would then be noted that its propagation would be exactly the same as that of the photon generated in the totally inert reference frame, provided, of course, that the propagation medium remains the same for the two reference frames.

Two lasers projecting their beams into a sodium basin whose state allows the progression of the beams to be slowed down; one laser in a fixed position and the other in motion. The progression of the beams will be the same for each of the lasers. On the other hand, by placing the lasers in two distinct basins, one fixed and the other in motion, a difference in the speed of progression of the light beams can be noted in such a way that the law of composition of velocities will then apply. This last example highlights that although there is similarity between the propagation media, they are totally distinct from each other.

Redefining What an Inertial Reference Frame Is

Throughout the arguments presented so far, the existence of a problem in the rules of validity for observations and measurements relative to the interpretation of the definition of an inertial reference frame will have been noted. To remedy this deficiency that has just been discovered, it appears essential that one or more corrections be made. What has already been postulated at the origin cannot be questioned and must therefore remain as is. It is simply necessary to add new conditions that will allow the true nature of an inertial reference frame to be clarified with precision within the framework of any observation or experiment subject to the principles of relativity. Here, therefore, are all the conditions to be respected:

They must not undergo any acceleration, change of direction, or be subjected to external forces, or these must cancel each other out. They are, therefore, at rest or in uniform rectilinear motion.
The experiments conducted and their results are the same.
All the laws of physics must apply.
The conditions of the medium and the medium itself in which experiments and observations take place must be absolutely identical. In other words, the ambient medium in each of the reference frames must possess exactly the same physical properties.
The ambient medium or support in which experiments and observations are carried out must be completely distinct from one reference frame to another for the law of composition of velocities to apply. Otherwise, this law does not apply, and the speeds are considered as measured.

As for distances, durations, and the simultaneity of events which were then considered absolute, they must now be apprehended differently.

Distances and durations are invariant insofar as the masses and speeds involved remain within the realm of the reasonable, where the Galilean transformations apply, meaning that the reference frames are perfectly distinct.
The simultaneity of events is determined. It must be demonstrated with the appropriate mathematical conversions when visualization cannot confirm it.

The two new conditions stated concerning the medium will now allow any experiment or observation carried out to be validated to target the real relationship between the observed, measured, and quantified events with accuracy. Note in passing that the new added conditions are not limited to a specific medium, as is required for waves, sound waves, or electromagnetic waves. They concern all types of media, whether it is delimited or not, or yet to be discovered.

And Special Relativity?

As has just been demonstrated, the paradox from which special relativity was born comes from a misinterpretation of the observation rules between inertial reference frames. Scientific rigor obliges, as soon as it was noted that light had a finite speed, the best thinkers immediately set about verifying its compatibility with Galilean relativity. Unable to verify the compatibility, a hypothesis was put forward, giving birth to the luminiferous ether to try to explain the invariance of this speed. In parallel, to overcome the problem of velocity transformations, some alternatives appeared, such as the one known as the Lorentz transformations. First formulated by Hendrik Lorentz and formalized by Henri Poincaré in his draft of special relativity to be consecrated within the framework of the theory of special relativity as popularized by Albert Einstein by presenting it as follows:

The ether is an arbitrary notion that is not useful for the expression of the theory of relativity.
The speed of light in a vacuum is equal to c in all inertial reference frames. It depends neither on the movement of the source nor the observer.
The laws of physics respect the principle of relativity.

This approach is extremely correct and remains current in the context of Galilean relativity as it has just been redefined. In the first assertion, real or not, the ether remains arbitrary as soon as it is considered as the same propagation medium in each of the reference frames and that an adequate distinction is established between them. The second assertion concerning the speed of light was consecrated in the preceding demonstrations concerning the movement of the source or the observer. As for the respect of the principle of relativity, this remains the constant premise to be observed since the first theses in this sense were put forward. As correct as these assertions are, the framework of observations is never explicitly questioned within the framework of special relativity.

However, as mentioned in the introduction, if Einstein's work on relativity had only aimed to resolve the paradox of light, it might not have been perceived in the same way. But these are only hypotheses. Let us only recall that his work does not mention it directly. At most, one finds an allusion to emphasize that there is no absolute rest space. It is rather on the simultaneity of events that the first sketches of the developing theory concentrate first. Although debatable according to some, the different translations or interpretations of how to shed light on the nature of the simultaneity of events, its publication nevertheless provides sufficient proof of its relativity. It is from this first observation that the relativity of distances and time itself is subsequently highlighted.

The theory of special relativity states the respect for the basic principles of reference frames. Without questioning this theory, one is entitled to ask whether it still respects the principles now that we have new statements concerning Galilean relativity. Let us first note that if the theory does not explicitly use the notion of a reference frame, it refers to it through stationary systems in which the Newtonian equations are true after stating the idea that there could not be an absolutely rest space. This pushes us to interpret that Einstein does not question the acquired notions of a reference frame and that he develops his theory around the known and admitted principles of a reference frame.

Let us now focus on the question we have raised. If we already know that special relativity agrees with the basic principles of an inertial reference frame, we must now verify whether it is still in agreement with the two new rules proposed. Regarding the statement that "The conditions of the medium and the medium itself in which experiments and observations take place must be absolutely identical," we have nothing to say against it. Indeed, the exercises presented by Einstein are all carried out in the same medium (vacuum) and are in agreement with this statement.

As for "The medium must be completely distinct from one reference frame to another," this is where the question really arises. Indeed, the required distinction is not made, the medium being the vacuum and, therefore, common to all reference frames. Since the law of composition of velocities cannot be applied, it is the subterfuge of the Lorentz transformations that serves as a workaround here.

In the kinematic portion of the theory, light is used as an absolute reference to determine the simultaneity of events first and then to judge the relativity of lengths and time. Since light is not the object of the measurement and serves, on the contrary, as a measurement tool, the principle concerning the homogeneity of the medium is respected, while the calculations and exercises presented are the tools used to consecrate the independence of the media between reference frames. The use of the speed of light as a tool to measure events, although appropriate, seems here to only serve to distort reality since the distinction of the medium is not proven between reference frames.

So, why introduce and stick to the Lorentz transformations in special relativity? Obviously, the misunderstanding about the framework of observations had still not been noted. Their introduction, however, led to unexpected conclusions about spacetime that Galilean relativity does not reveal so far. Despite experimental confirmations on which great technological advances rest and whose predictions (time dilation, mass-energy equivalence) are validated daily (GPS, particle accelerators), special relativity is consequently an established theory that does not, however, highlight the distinction of the medium between reference frames. This suggests that supplementary studies and work are required and necessary to go beyond the theory stage. This is, however, not the subject of the current discussion and largely exceeds its scope.

Synthesis and Perspectives

What conclusion can first be drawn from this thought experiment? It seems strange in the first place that no one stopped at this state of affairs, that is, that the observation rules between reference frames according to Galilean relativity have always been misinterpreted. The luminiferous ether, this attempt to formulate a hypothesis concerning a fabric or a propagation support mechanical carrier of electromagnetic waves, would never have seen the light of day if the observation rules in relativity had not been misinterpreted.

At the advent of the theory of special relativity, the success of its postulates and of its transformations legitimately focused the scientific community on the validation of the theory itself. In this momentum, all questioning about the very foundations of Galilean relativity and particularly concerning the fundamental observation rules seems to have been relegated to oblivion. The necessity of reconciling the constancy of the speed of light with the basic principles of relativity led to a mathematical solution (the Lorentz transformations), without, however, revising the interpretation of reference frames in the face of wave phenomena, which was at the origin of the misunderstanding.

The observations and thought experiments conducted here, whether concerning projectiles, waves on water, sound waves, or light waves, have revealed the existence of a deep misunderstanding at the heart of the understanding of reference frames. It was demonstrated that the basic principles describing any inertial reference frame remained immutable. It is in the interpretation of the laws of relativity, the observation rules to be more precise, that the confusion reigned at the origin of the misunderstanding. It was also demonstrated that the Galilean law of composition of velocities systematically fails when the two reference frames share the same propagation medium (such as water for waves, air for sound, or vacuum for light), because the speed of the wave is then determined by the support of propagation of the latter, i.e., this medium, and not by the movement of its source.

By proposing the addition of two fundamental conditions—"the identity of the physical properties of the medium and the necessity of a total distinction between the media of the reference frames for the application of the composition of velocities"—we formalize a missing validity rule. This clarification allows us to judge when the law of composition of velocities applies and to distinguish the conditions where the speeds must be considered as invariant values, thereby proving the failure of the Galilean model recognized to this day. It is in this momentum, demonstrating the relativity of velocities, that the relativity of simultaneity and the duration of events was affirmed.

Since all scientific processes or experiments must rely on postulates, working tools, and solid knowledge, we are entitled to question several theories, including those that mainly rely on an interpretation of reference frames and observation rules that were believed to be valid until now. Like the theory of special relativity, new deficiencies have been demonstrated in the study of the systems involved, namely the reference frames, the effect of which may cast doubt on several theories and known research to this day.

Without rejecting everything out of hand, let us note, however, that the correct use of appropriately defined reference frames paves the way for new hypotheses leading to new theories or even new laws of physics. We are entitled to believe that where scientific advances seem to be slowed down by phenomena still unexplained or theories that still cannot be validated or invalidated, they can be re-evaluated with a new perspective.

¹ You are invited to consult the various videos available dealing with the subject on YouTube, including the one from the "e’penser" channel, where a truly brilliant demonstration is made.

Boisleduc 2021-12-27 Rev:(25-11-13)

Relativity and the Unacknowledged Error

The notion of relativity, born with Galileo and formalized by Newton, remained as such until Einstein. When he published his work in 1905, what would later be called the theory of special relativity completely overturned what was believed to be known about relativity. Distance, time, and simultaneity, previously considered as invariant or absolute in classical physics (Galileo/Newton), henceforth became relative concepts. Where only speed was considered relative, it was now the speed of light "c" along with the Lorentz transformations that became the absolute reference for judging the relationship between reference frames, i.e., the necessary clock for measuring events between reference frames. As there is a vast literature concerning the work on relativity by these three protagonists—Galileo, Newton, and Einstein—we will not dwell further on the said works. It will be immediately understood that this is not a training or a complement of information aiming to teach the different theories of relativity.