TheAlgorithms/Java · error · IllegalArgumentException

Speed must not exceed the speed of light

Error message

Speed must not exceed the speed of light

What it means

Thrown by Relativity.velocityAddition when Math.abs(v1) > SPEED_OF_LIGHT. The relativistic velocity-addition formula (v1 - v) / (1 - v1*v/c^2) only has physical meaning when the object's velocity in the lab frame does not exceed c; a superluminal v1 is invalid. This is the first of two velocity guards in velocityAddition, checked before the frame-velocity v guard.

Source

Thrown at src/main/java/com/thealgorithms/physics/Relativity.java:74

     * @return The time that has passed in the laboratory frame (s).
     */
    public static double timeDilation(double time, double v) {
        if (time < 0) {
            throw new IllegalArgumentException("Time must be non-negative");
        }
        return time * gamma(v);
    }

    /**
     * Calculates the velocity with respect to the moving frame.
     *
     * @param v1 The velocity of the object with respect to laboratory frame (m/s).
     * @param v The velocity of the moving frame (m/s).
     * @return The velocity with respect to the moving frame (m/s).
     */
    public static double velocityAddition(double v1, double v) {
        if (Math.abs(v1) > SPEED_OF_LIGHT) {
            throw new IllegalArgumentException("Speed must not exceed the speed of light");
        }
        if (Math.abs(v) >= SPEED_OF_LIGHT) {
            throw new IllegalArgumentException("Frame speed must be lower than the speed of light");
        }
        return (v1 - v) / (1 - v1 * v / (SPEED_OF_LIGHT * SPEED_OF_LIGHT));
    }
}

View on GitHub (pinned to fdfb9a395b)

Solutions

1. Ensure |v1| is in m/s and does not exceed 299792458 m/s.
2. Verify the unit of v1 matches the SPEED_OF_LIGHT constant (m/s in this file).
3. If v1 originates from a previous velocityAddition result, the prior call already enforces subluminal output, so a superluminal input here signals a unit error.

Example fix

// before
double u = Relativity.velocityAddition(4e8, 1e8);
// after
double u = Relativity.velocityAddition(2e8, 1e8);

if (Math.abs(v1) > SPEED_OF_LIGHT) {
    throw new IllegalArgumentException("|v1| must be <= c, got " + v1);
}
double u = Relativity.velocityAddition(v1, v);

When it happens

Trigger: Calling velocityAddition(v1, v) with |v1| strictly greater than SPEED_OF_LIGHT. A v1 of exactly ±c is allowed by this guard (it checks > not >=), though the formula denominator may still misbehave.

Common situations: Unit mismatch (km/s vs m/s) inflating v1, or composing velocities from a Galilean-addition step that already exceeded c before being passed here.

Related errors

• Speed must be lower than the speed of light
• Frame speed must be lower than the speed of light
• Length must be non-negative
• Time must be non-negative
• Orbiting mass and radius must be positive.

AI-assisted analysis of TheAlgorithms/Java@fdfb9a395b (2026-08-13). Data as JSON: /api/errors/11f33523974b832b. Report an issue: GitHub.