Final answer:
The most useful technologies for helping to prove or disprove Einstein's special theory of relativity among the provided options are rockets and cellular phones with GPS capability. Rockets can reach high velocities where relativistic effects occur, and GPS needs to account for relativity to function correctly.
Step-by-step explanation:
To determine which of the following technologies could be most useful in helping to prove or disprove Einstein's special theory of relativity: X-ray machines, Rockets, Plastics, or Cellular Phones, we must consider the abilities of these technologies to operate under conditions relating to the theory's principles. Concerning Einstein's theory, one of the key tenets is the effect of high speeds on time and space, particularly phenomena such as time dilation and length contraction. Global Positioning Systems (GPS), a technology embedded in devices like cellular phones, are practical examples of technology that must account for the effects predicted by special relativity, such as time dilation, due to the high speeds at which their signals travel.
Therefore, among the options provided, rockets are most closely associated with practical applications of Einstein's theory because they can achieve the extreme velocities necessary to demonstrate relativistic effects. Moreover, GPS technology, typically found in cellular phones, directly employs the principles of special relativity to ensure its accuracy and functionality. X-ray machines and plastics are not directly involved in testing or applying the principles of special relativity. Since rockets and GPS-enabled cellular phones are capable of dealing with relatvistic speeds and can observe the time dilation as predicted by Einstein, these would be the most useful in helping to prove or disprove the concepts within the theory.