Its mathematical expression does not propagate in the ordinary sense of the word, though it may refer to virtual or nominal velocities with magnitudes greater than that of light. For example, wave packets are mathematical objects that have group velocity and phase velocity. The energy of a wave packet travels at the group velocity (under normal circumstances); since energy has causal efficacy, the group velocity cannot be faster than the speed of light. The phase of a wave packet travels at the phase velocity; since phase is not causal, the phase velocity of a wave packet can be faster than light.Causal notions are important in general relativity to the extent that the existence of an arrow of time demands that the universes semi-Riemannian manifold be orientable, so that "future" and "past" are globally definable quantities. Engineering
A causal system is a system with output and internal states that depends only on the current and previous input values. A system that has some dependence on input values from the future (in addition to possible past or current input values) is termed an acausal system, and a system that depends solely on future input values is an anticausal system. Acausal filters, for example, can only exist as postprocessing filters, because these filters can extract future values from a memory buffer or a file. Biology, medicine and epidemiology
Austin Bradford Hill built upon the work of Hume and Popper and suggested in his paper "The Environment and Disease: Association or Causation?"
A "recovery" algorithm was developed by Rebane and Pearl (1987) which rests on Wrights distinction between the three possible types of causal substructures allowed in a directed acyclic graph (DAG):

  
    
      
        X
        →
        Y
        →
        Z
      
    
    {\displaystyle X\rightarrow Y\rightarrow Z}
  

  
    
      
        X
        ←
        Y
        →
        Z
      
    
    {\displaystyle X\leftarrow Y\rightarrow Z}
  

  
    
      
        X
        →
        Y
        ←
        Z
      
    
    {\displaystyle X\rightarrow Y\leftarrow Z}
  Type 1 and type 2 represent the same statistical dependencies (i.e., 
  
    
      
        X
      
    
    {\displaystyle X}
   and 
  
    
      
        Z
      
    
    {\displaystyle Z}
   are independent given 
  
    
      
        Y
      
    
    {\displaystyle Y}
  ) and are, therefore, indistinguishable within purely cross-sectional data.