According to special relativity, the momentum (mv) of an object at relativistic speed is actually: more, less or no different than if it were at rest

More.

since at rest it has no momentum, it will have more at any old speed.

According to special relativity, the momentum (mv) of an object at relativistic speeds is actually more than if it were at rest. This phenomenon is known as relativistic momentum.

To understand why relativistic momentum increases, we need to consider the theory of special relativity, which was developed by Albert Einstein in 1905. According to special relativity, the laws of physics remain the same for all observers in inertial reference frames moving at constant velocities relative to each other.

One of the key principles of special relativity is that the speed of light in a vacuum is always constant and the same for all observers, regardless of their relative motion. This principle has profound consequences for how we understand the behavior of objects moving at high speeds.

In classical Newtonian physics, momentum is defined as the product of an object's mass (m) and its velocity (v). However, special relativity introduces a modification to this definition to account for the effects of high velocities.

According to special relativity, the relativistic momentum (p) of an object is given by the formula:

p = γmv

In this equation, γ (gamma) represents the Lorentz factor, which depends on the velocity of the object relative to the speed of light (v/c) and is given by:

γ = 1/√(1 - (v^2/c^2))

Here, c represents the speed of light in a vacuum.

When an object is at rest, its velocity is zero, and the Lorentz factor becomes 1. Therefore, the relativistic momentum reduces to the classical momentum, as we expect.

However, when an object approaches the speed of light, the Lorentz factor becomes larger, and as a result, the relativistic momentum increases. This means that the momentum of an object moving at relativistic speeds is greater than if it were at rest.

So, according to special relativity, the momentum of an object at relativistic speed is more than if it were at rest. This is one of the counterintuitive and fascinating aspects of the theory of special relativity.