Speed of Light
A New Perspective
This page presents a reflection on the physical status of the speed of light. The central question is not only what value observers measure, but whether light itself truly possesses, in its propagation between two points, an invariant speed for all inertial frames.
The Physical Meaning of the Second Postulate
The second postulate of special relativity, as formulated by Einstein in 1905, did not merely state that observers measure the same value for the speed of light. The original text states more precisely that light “is always propagated in empty space with a definite velocity c, independently of the state of motion of the emitting body”.
This formulation therefore seems to attribute a physical property directly to the propagation itself, and not merely to the results of measurements performed by observers.
Modern interpretations of the postulate are nuanced:
- “Every inertial observer measures the same value for the speed of light”;
- “The speed of light is the same in all inertial frames”;
- “The round-trip speed of light is constant and equal to c”.
But these formulations do not have exactly the same conceptual meaning. Some mainly concern measurements performed by observers, while others tend to attribute a physical property to the propagation itself.
The difficulty appears especially when considering one-way propagation between two spatially separated points. Indeed, the speed of light can only be directly measured experimentally in a round-trip configuration. A one-way measurement would already require the prior synchronization of distant clocks, and such synchronization itself uses light within the relativistic framework.
From that point on, the question becomes the following: does the observed invariance of the speed of light reflect a real physical property of light propagation, or only an invariance of measurements and observables? This question directly concerns the physical status — or lack thereof — of the relativity of simultaneity.
A Partially Incorrect Reasoning at the Origin of Special Relativity ?
“ It was once thought that the speed of light was invariant with respect to the ether, and that therefore it could not be invariant with respect to the Earth. The Michelson–Morley experiment was supposed to confirm this. Surprisingly, it seems instead to indicate that the speed of light is invariant with respect to the Earth. From there, Albert Einstein probably arrived at approximately the following reasoning: if the speed of light is invariant with respect to the Earth, even though the Earth is itself a moving body, then it must also be invariant with respect to any body in an inertial state. If one takes into account the train thought experiment, this amounts to saying that if the speed of light is invariant with respect to the station, then it is also invariant with respect to the train moving at constant speed relative to the station. This reasoning, as one may realize by reading this book, is partially incorrect. We shall see that it is probably more accurate to think — even if the origin is not immediately discovered — that there is a constant adaptation of the speed of light to the spatial configuration.” ” Extract from the book "Paradox of the invariance of the speed of light".
Three Possible Interpretations
There are not necessarily only two possible solutions regarding the speed of light.
1. Einstein’s Interpretation
The speed of light is considered invariant in all inertial frames. This position leads to relativity of simultaneity.
2. Lorentz’s Interpretation
The speed of light would be isotropic in a privileged frame, often associated with the ether, but anisotropic in other frames. Inertial frames would therefore not be physically equivalent.
3. The Hypothesis of Locally Privileged Frames
There exists a third possibility: the speed of light could be locally invariant relative to certain inertial observers, not because it would be absolutely invariant for all frames, but because it would depend on the local and global spatial configuration.
Towards a Speed Depending on Spatial Configuration
In this perspective, the issue is not simply to oppose Einstein to Lorentz. Another possibility must be considered: the propagation speed of light would depend on the spatial configuration. This hypothesis leads to a relational conception of space-time and motion.
“I am only trying to show that, from a theoretical point of view, the physical invariance of the speed of light implies relativity of simultaneity at the physical level. Yet the latter, leads to contradictions, makes it possible to eliminate the first possibility with certainty. And since the Lorentz interpretation can probably also be eliminated, only the interpretation I propose remains: a speed of light locally invariant relative to certain inertial observers because the speed of light depends on the spatial configuration. Moreover, this aspect could probably be measured...” — Idea extract from the book "And He Was Hovering Over the Waters: Towards a New Vision of the Physical World ?"
This point may notably be connected with the Shapiro effect, where the propagation time of light is modified by the presence of a gravitational field.
Round-Trip Time and Interferometer (FR) Click here
From conceptual reflexion to experimental verification Click here
Video Resource
The following video by Marc Lachièze-Rey provides an interesting discussion about speed, velocity, and the relativistic speed limit. It serves here as a starting point for extending the reflection toward a more relational approach to motion.
Is There Really a Limit to Velocities? — Marc Lachièze-Rey (FR)
The following remarks extend the reflection initiated from this video. They concern in particular the distinction between time, the rate of clocks, simultaneity, speed, and velocity.
April 28, 2028: Thank you for the explanations on velocity; however, a few remarks on related topics. The fact that clocks do not tick at the same rate depending on their position in space or their motion in no way implies that time does not exist. It simply means that the rate of physical processes depends on spatial conditions, which is very different from a denial of time itself. One cannot arbitrarily rule out the possibility that two ‘identical’ clocks, placed in different spatial conditions — for example on two different floors of the same building — may run simultaneously at different rates. Likewise, the fact that one cannot determine the simultaneity of two distant events independently of any measurement convention does not in any way imply that simultaneity does not exist. This is a limitation of our measurement procedures, not an ontological property. Furthermore, the fact that we only measure proper durations — that is, local times associated with particular physical processes — does not imply that time as such does not exist. Here again, one confuses an operational constraint with a conclusion about the nature of reality. Marc Lachièze-Rey overlooks these distinctions, moving from a statement about experimental limitations to a much stronger ontological interpretation, which nevertheless remains open to debate.
April 29, 2028: That being said, I find Marc Lachièze-Rey’s explanations of velocity very interesting. Replacing the notion of speed with that of velocity seems to open up an interesting line of thought. One might see in this a way to more finely relate the propagation of light to the structure of space.
April 30, 2028: Speed measures only how fast motion occurs, whereas velocity also specifies its direction. However, this direction is generally defined within an abstract space. One can go further by considering that velocity expresses an orientation within the real spatial structure, that is, within the set of relations that constitute physical space.
The energy–momentum four-vector unifies energy and motion within a geometric framework. A possible extension would be to define them as depending on the relational configuration, both local and global, which would amount to replacing a purely geometric description of motion with a relational one.
This is a line of reflection; I do not yet master its technical aspects, but it seems to me worth exploring.
May 4, 2028: Carlo Rovelli has made it possible for Aristotle’s definition of time to become non-circular, although this was probably not his primary intention. For Aristotle, time is the number of motion with respect to before and after, where ‘number’ is understood as that which allows counting. Now, Carlo Rovelli points out, from within Aristotle’s perspective, that one can count a motion by using another motion. From this point on, it becomes sufficient to replace “before and after,” which are temporal notions, with the idea of going from one point to another for a given moving body. Indeed, if an obstacle is placed, one can clearly see in which direction the motion proceeds, without needing to rely on these temporal notions. This means that Aristotle’s definition of time, clarified by the precision brought by Carlo Rovelli, can very well still be considered valid.
From there, instead of speaking of four dimensions—three of space and one of time—one can envisage a description based solely on spatial dimensions, by integrating temporal variations into the very structure of the relations between bodies. Such a perspective becomes possible within a fully relational approach to space and motion.
Philippe de Bellescize