The distinction between a tachyon and a photon goes far beyond simple velocity. They exist in entirely different kinematic domains separated by the impassable boundary of the speed of light ($c$). One represents the absolute universal speed limit, while the other represents a hypothetical realm where that limit is the floor, not the ceiling.
1. The Nature of Mass: Luxons vs. Tachyons
In the framework of relativistic kinematics, all particles are classified by their invariant rest mass ($m₀$).
A photon is classified as a luxon. It has exactly zero rest mass ($m₀ = 0$). Because it has no mass, it cannot be at rest in any frame of reference; it must always travel at exactly $c$ in a vacuum. Its energy is entirely kinetic and related directly to its momentum via the equation $E = pc$.
A tachyon, on the other hand, possesses an imaginary rest mass ($m₀ = i\mu$). This mathematical quirk is required so that its total energy and momentum remain real observable numbers while traveling faster than $c$. Because its mass is imaginary, its squared mass is negative ($m² < 0$).
2. The Energy-Velocity Relationship
The most dramatic difference between photons and tachyons is how they respond to changes in energy.
- Photons: Adding energy to a photon does not change its speed. A high-energy gamma-ray photon and a low-energy radio photon both travel at exactly $c$ in a vacuum. Instead, adding energy increases the photon's frequency (and decreases its wavelength) according to the Planck-Einstein relation ($E = hf$).
- Tachyons: The energy-velocity relationship is inverted. Adding energy to a tachyon slows it down, pushing its velocity closer to $c$ from above. Removing energy causes the tachyon to speed up. A tachyon with exactly zero energy would be traveling at infinite velocity.
The Absolute Barrier
The speed of light ($c$) acts as a two-sided mirror. For ordinary matter (bradyons), $c$ is a ceiling that requires infinite energy to reach. For tachyons, $c$ is a floor that also requires infinite energy to reach. Photons live exactly on the mirror itself. Neither tachyons nor ordinary matter can ever cross the barrier to become the other.
3. Spin and Helicity
In Quantum Electrodynamics (QED), a photon is a gauge boson with a spin of 1. However, because it is massless and travels at $c$, its spin can only align parallel or anti-parallel to its direction of motion. It has only two polarization states (left-handed and right-handed helicity).
If a tachyon were a quantum particle with spin, the rules of the Poincaré group dictate it would have continuous spin (an infinite number of polarization states) due to its spacelike momentum vector. Because infinite polarization states are not observed in nature, theorists strictly model tachyons as scalar fields (spin-0) rather than vector bosons like the photon.
4. Causality and Spacetime
Photons follow lightlike (or null) trajectories through four-dimensional spacetime. A light signal connects cause and effect at the absolute fastest rate possible in the universe. All observers, regardless of their relative motion, will agree on the order of events connected by a photon.
Tachyons follow spacelike trajectories. This fundamentally breaks causality. If a tachyon transmits a signal, the order of emission and absorption depends on the observer's frame of reference. Observer A might see the tachyon move from Point 1 to Point 2, while a fast-moving Observer B sees the tachyon move from Point 2 to Point 1.
Summary
The photon is the deeply verified, massless carrier of the electromagnetic force that defines the geometry of spacetime. The tachyon is a theoretical construct—a mathematical exploration of what happens to the Lorentz transformations when velocities exceed the photon's invariant speed. While photons bind the universe together, tachyons represent the hypothetical instabilities that tear vacuum states apart.