Part V: The Relational Nature of the Speed Limit

The Conventional Understanding

Special relativity asserts that nothing can travel faster than light. This is presented as an absolute, frame-independent law: if you cannot exceed c in one reference frame, you cannot exceed it in any frame. The relativistic velocity addition formula guarantees this algebraically. No matter how you combine velocities, the result is always less than c.

The explanation typically given involves relativistic mass or the Lorentz factor γ. As an object approaches c, its effective mass increases, requiring ever more energy to accelerate further. At c, the mass would be infinite, requiring infinite energy — therefore c is unreachable.

This framing treats the speed limit as geometric, built into the structure of spacetime itself.

The PSK Reframe

PSK proposes that the speed limit is not geometric but causal — and crucially, not absolute but relational.

The constraint is this: you cannot accelerate something past c relative to yourself. Beyond c relative to you, you lose causal connection with it. State-mapping between you and the object ceases. You have nothing to push on.

But you can freely exceed c relative to others by accelerating yourself, because you are always at rest relative to yourself. You never approach your own horizon. The constraint applies to what you can do to other things, not to what you can do to yourself.

Two Scenarios

Consider two scenarios that illustrate this asymmetry.

Scenario 1: The Rocket. You are in a rocket accelerating at 1g — a comfortable, sustainable acceleration. From your frame, nothing changes as time passes. Your engine produces the same thrust, consumes fuel at the same rate, and you feel the same force pressing you into your seat.

After approximately one year of proper time at 1g, your velocity relative to Earth approaches c. In conventional relativity, this is where external observers would see your acceleration diminishing asymptotically, your relativistic mass increasing, your clock slowing dramatically.

In PSK, nothing special happens at c. You continue accelerating at 1g. Your velocity relative to Earth exceeds c. You cross Earth’s causal horizon — Earth can no longer receive state-mapping from you. But you notice nothing. You keep accelerating. Your velocity continues to increase: 1.5c, 2c, 10c relative to Earth. There is no barrier.

The "infinite energy" requirement dissolves because it was never about acceleration itself. It was the energy required to maintain causal connection with your origin frame while accelerating away from it. If you abandon that requirement — if you accept crossing the horizon — there is no infinite energy barrier. Your engine continues to produce 1g, and you continue to accelerate.

Scenario 2: The Particle Accelerator. You are operating a particle accelerator, attempting to push a proton to higher and higher velocities. As the proton approaches c relative to you, something changes.

How do you push a proton? With electromagnetic fields. Those fields are state-mapping — causal connection between your apparatus and the proton. State-mapping propagates at c.

As the proton approaches c relative to your accelerator, the causal connection between you and the proton becomes increasingly tenuous. The fields you generate have diminishing ability to interact with the proton because the proton is approaching the edge of your causal horizon.

At c, the proton would cross your horizon. You could not interact with it. You would have nothing to push on.

This is why particle accelerators asymptotically approach c but never reach it. Not because the proton "gains infinite mass," but because the accelerator loses the ability to interact with the proton. You cannot push something past your own horizon, because past your horizon, you cannot push.

The Asymmetry

The speed limit is asymmetric. You cannot accelerate an object past c relative to yourself — you lose causal connection, leaving nothing to push on. But you can exceed c relative to others by accelerating yourself — you are always at rest relative to yourself.

In the rocket, you accelerate with your reference frame. You are always stationary in your own frame, always fully causally connected to yourself and your immediate environment. There is no horizon you approach from the inside.

In the accelerator, you attempt to accelerate something away from your frame while you remain stationary. The object approaches your horizon. Interaction weakens. At c, interaction ceases.

This is why the same acceleration — say, 1g equivalent — that would eventually push a rocket past c relative to Earth cannot push a proton past c in an accelerator. In the rocket, you are accelerating yourself — you never approach any horizon. In the accelerator, you are accelerating something else — it approaches your horizon.

Energy Reconsidered

The "infinite energy to reach c" in conventional physics can be reinterpreted.

In a particle accelerator, the energy cost does increase dramatically as the particle approaches c. But this is not because the particle is "gaining mass." It is because the interaction between the accelerator and the particle is becoming geometrically inefficient. The state-mapping connections are stretched thin. More energy is required to achieve less effect because the causal coupling is weakening.

At c, the coupling would be zero. No amount of energy could accelerate the particle further, not because infinite energy is required, but because energy transfer requires causal connection, and causal connection has ceased.

For a self-propelled rocket, the situation differs entirely. The rocket’s engine interacts with the rocket locally — they share a reference frame, fully causally connected. The efficiency of this interaction does not diminish with velocity relative to external observers. The energy cost of continued acceleration remains constant in terms of fuel consumed per unit of proper acceleration.

The rocket pilot experiences no infinite energy barrier because they experience no weakening of causal connection with their own engine.

Implications

If this analysis is correct, several consequences follow.

Interstellar travel beyond c is possible. A spacecraft accelerating continuously could exceed c relative to its origin. It would cross the causal horizon, losing contact with home, but the crew would notice nothing unusual. They could travel to distant stars at arbitrarily high velocities relative to their origin, limited only by fuel supply and the willingness to sever causal connection with their starting point.

The twin paradox extends further than conventionally thought. A twin who accelerates past c relative to Earth does not merely age more slowly — they become causally disconnected. Whether they could ever return by decelerating and re-entering Earth’s horizon remains an open question.

Particle physics retains its limits. Accelerators will never push particles past c because the accelerator-particle interaction degrades as the particle approaches the accelerator’s horizon. This matches observation.

Communication limits remain. You can travel faster than c, but you cannot send a message faster than c. If you send a message by pushing matter — a probe, a particle, a letter — you cannot push it past your own horizon. If you send a message electromagnetically, you are not pushing anything at all. Light is not a projectile but state-mapping, the causal connection itself unfolding at c. State-mapping operates at c by definition because c is the densification rate. You cannot signal faster than causality propagates.

The universe is more traversable than conventionally believed, but horizon-crossing is consequential. Exceeding c does not violate physics — it severs causal connection with your origin. This may be acceptable for one-way journeys to distant destinations. It is not acceptable if you wish to return home and find it still there.

The Principle

The speed of light is not a speed limit in the conventional sense. It is the speed of causal connection.

You cannot interact with, observe, or influence anything beyond your causal horizon. Your horizon is defined by recession at c — anything receding from you faster than c is beyond your ability to affect.

You can exceed c relative to others because doing so simply means crossing their horizon, not your own. You remain fully causally connected to yourself and your local environment. The universe you can interact with travels with you.

The speed limit is real, but it is relational. It governs what you can do to other things, not what you can do to yourself. It is a limit on interaction across distance, not a limit on motion through space.

One way to state it: you cannot outrun your own causality, but you can outrun someone else’s.