section_path: Relation to other physical theories/Special relativity
section_name: Special relativity
paragraph_text: Special relativity
  
  In special relativity, the rule that Wilczek called "Newton's Zeroth Law" breaks down: the mass of a composite object is not merely the sum of the masses of the individual pieces. Newton's first law, inertial motion, remains true. A form of Newton's second law, that force is the rate of change of momentum, also holds, as does the conservation of momentum. However, the definition of momentum is modified. Among the consequences of this is the fact that the more quickly a body moves, the harder it is to accelerate, and so, no matter how much force is applied, a body cannot be accelerated to the speed of light. Depending on the problem at hand, momentum in special relativity can be represented as a three-dimensional vector, p = m γ v {\displaystyle \mathbf {p} =m\gamma \mathbf {v} }, where m {\displaystyle m} is the body's rest mass and γ {\displaystyle \gamma } is the Lorentz factor, which depends upon the body's speed. Alternatively, momentum and force can be represented as four-vectors.
  
  Newton's third law must be modified in special relativity. The third law refers to the forces between two bodies at the same moment in time, and a key feature of special relativity is that simultaneity is relative. Events that happen at the same time relative to one observer can happen at different times relative to another. So, in a given observer's frame of reference, action and reaction may not be exactly opposite, and the total momentum of interacting bodies may not be conserved. The conservation of momentum is restored by including the momentum stored in the field that describes the bodies' interaction.
  
  Newtonian mechanics is a good approximation to special relativity when the speeds involved are small compared to that of light.