It is most convenient for establishment of causality if the contrasting material states of affairs are precisely matched, except for only one variable factor, perhaps measured by a real number. Physics
One has to be careful in the use of the word cause in physics. Properly speaking, the hypothesized cause and the hypothesized effect are each temporally transient processes. For example, force is a useful concept for the explanation of acceleration, but force is not by itself a cause. More is needed. For example, a temporally transient process might be characterized by a definite change of force at a definite time. Such a process can be regarded as a cause. Causality is not inherently implied in equations of motion, but postulated as an additional constraint that needs to be satisfied (i.e. a cause always precedes its effect). This constraint has mathematical implications such as the Kramers-Kronig relations. Causality is one of the most fundamental and essential notions of physics. Causal efficacy cannot propagate faster than light. Otherwise, reference coordinate systems could be constructed (using the Lorentz transform of special relativity) in which an observer would see an effect precede its cause (i.e. the postulate of causality would be violated). Causal notions appear in the context of the flow of mass-energy. Any actual process has causal efficacy that can propagate no faster than light. In contrast, an abstraction has no causal efficacy.
Here the notion of causality is one of contributory causality as discussed above: If the true value 
  
    
      
        
          a
          
            j
          
        
        ≠
        0
      
    
    {\displaystyle a_{j}\neq 0}
  , then a change in 
  
    
      
        
          x
          
            j
          
        
      
    
    {\displaystyle x_{j}}
   will result in a change in y unless some other causative variable(s), either included in the regression or implicit in the error term, change in such a way as to exactly offset its effect; thus a change in 
  
    
      
        
          x
          
            j
          
        
      
    
    {\displaystyle x_{j}}
   is not sufficient to change y.