Suppose a universe exists that contains only a single pulse of light.
No particles, clocks, observers, atoms, stars, or ambient temperature. The universe contains nothing except this one photon, an isolated pulse of electromagnetic radiation, a wave suspended in perfect conceptual emptiness.
So, what can we say about this situation?
Of course, this is not a real physical scenario, but as a conceptual stress test, designed to probe the coherence and limits of our understanding of reality.
Light, we are told, travels at a fixed speed, which we call c. Imagine a single particle moving forward in time as an electromagnetic wavefront. Yet, as soon as we do this, we hit a subtle wall. Just like before, when there is nothing else in space as a reference, then there is no motion at all. Again, the problem isn’t that we can’t measure, but that motion itself is only a relationship between objects or systems.
However, beyond mere motion, we need to pay attention to something even more fundamental: direction. In this universe, there is no “forward.” In fact, there is no up, down, left, right. Because there are no other objects, no reference points or coordinate system can be established, making direction inherently undefined. To say the light is “moving toward x direction” is meaningless.
So if there is no motion or direction, how can we understand the speed of light still being constant?
Velocity is the complete description of motion that includes both how fast something is moving (which we call speed) and the direction it is going. A car moving 60 mph north has a different velocity than one moving 60 mph east, even though their speeds are identical. Velocity is not just speed. That direction or orientation is called a vector. Speed is a type of quantity we call a scalar, since it only has size (we call this magnitude) but no direction. Temperature is also a scalar, since it tell us “how much” but not “which way.”
In the case of our empty universe with a single photon, the directional component of velocity (the vector) is physically absent and undefined as a concept. If direction itself doesn’t exist, then neither does velocity. This reveals a rarely noticed asymmetry. Physics and math necessarily treats the two components of velocity (speed and direction) differently. This leads to a critical question about the foundations of relativity.
This began as a nagging question for me years ago, something that just didn’t sit quite right. There is a simple formula that expresses the velocity of light as v = c·v̂ (velocity is the speed of light multiplied by its vector/direction). But what happens to that expression when the vector v̂ becomes zero or just vanishes?
This is the problem: Physics takes the speed of light as an axiom. An axiom is a starting principle that is accepted as true without proof (often because it cannot be proven). Axioms serve as a foundation for building a theory. In physics, they are the basic assumptions we don’t question when developing mathematical models. An axiom of Special Relativity is that “the speed of light is for all observers”. This postulate is usually understood in the sense of measurement. It tells us how different observers measure the speed of light relative to themselves.
But doesn’t this axiom also say something about reality? After all, the conclusion of Special Relativity is that spacetime itself changes because of it. What is relativity actually saying about the nature of light? Can we still conceive of it as a thing traveling through space? The lonely photon forces this question.
What the axiom really means is that the speed is constrained to be c, no matter the frame of reference. But notice the strangeness. It says the speed of light is constant, not the velocity of light. That’s because the direction vector of light changes depending on your frame of reference.
Here lies the conceptual tension: Special Relativity elevates c, the magnitude of the velocity, to an absolute constant, unchanging across frames. Yet, the direction component, essential for velocity to exist conceptually, remains relative and, in our limit case, vanishes entirely. Physics treats the two components of velocity asymmetrically: one absolute, one relative.
This isn’t merely a feature of math. It presents a philosophical challenge. While classical physics treats velocity as a unified concept (a vector where magnitude and direction are inseparable parts of the same relational description), Special Relativity seems to grant the magnitude (c) an independent, absolute existence detached from the possibility of defining a direction. If direction truly vanishes conceptually in our lonely photon universe, how can velocity itself exist? And if velocity is conceptually impossible, what does it mean if we say its magnitude, ‘speed’ still persists? Does a “speed” retain meaning if the possibility of direction doesn’t exist?
Modern physics developed powerful mathematical tools, like four-vectors and the Minkowski spacetime metric, to handle these kinematics consistently with observation. This mathematical machinery, prompted by experimental results inconsistent with classical notions, successfully ensures Lorentz covariance and makes calculations work. However, one could argue that this formalism, while calculationally effective, achieves consistency by fundamentally redefining concepts like distance and time into the spacetime interval, effectively embedding c into the geometry itself. This mathematical success might obscure rather than resolve the underlying conceptual question: Is it coherent to treat speed (c) as an absolute constant when its necessary counterpart, direction, is relative and can conceptually vanish? Does embedding c into the geometry implicitly reify spacetime, giving it an absolute background structure that pure relationalism, taken seriously, would deny?
This asymmetry, this tension between the absolute nature ascribed to c and the relational nature of direction, isn’t merely a technical distinction or philosophical curiosity. It suggests a potential vulnerability in the conceptual bedrock of physics.
Exploring the ramifications of this tension has led me to ideas that cascade throughout physics. The mathematics of our current theories may remain largely intact as descriptive tools, but their interpretation, the questions they permit, and their potential limitations might change profoundly. Acknowledging this foundational tension offers a new perspective, suggesting that puzzles like quantum non-locality, certain cosmological models, and the unification quest might be intertwined with, or even artifacts of, how we’ve conceptualized motion, speed, and spacetime based on assumptions that this thought experiment calls into question.
Our most basic understanding of the universe may rest less on a simple error, and more on a deep-seated conceptual tension brushed under the mathematical rug. Reframing our approach based on this insight doesn’t just aim to solve existing problems; it suggests some might dissolve entirely by removing the assumptions that created them in the first place. The remainder of this work explores these consequences in detail.