I have run into problems getting my head around the special theory of relativity, as my understanding of it causes parodoxical outcomes. I would much prefer to have a congruent understanding of the theory, rather than maintain my current perplexed perspective. It would be greatly appreciated, if you could help me escape confusion. Based on my assumption that Lorentz transformations affect a moving body by slowing down time and contracting length, in order to maintain the speed of light according to all observers, i have run into a problem. This problem does not exist in a situation where a moving observer, moves from point A to point B and the pulse of light in question that must be maintained to be the speed of light, is traveling in the same direction, that being from point A to point B. Although the relative speed between the pulse of light and the moving observer, is equal to the speed of the pulse of light minus the speed of the moving observer, according to a stationary observer. Lorentz transformations affect the measurement of speed by the moving observer and maintain that the speed of the pulse, is the speed of light. My problem emerges in the situation where the pulse instead of travelling from point A to point B, does the opposite and moves from point B to point A. In this situation a stationary observer would consider the relative speed between the pulse of light and the moving observer to be added together, resulting in a faster than the speed of light velocity. In this situation the problem arises due to the fact that time dilation( the slowing of the rate of time) and length contraction, would speed up the pulse of light, rather than slowing it down, which would be inconsistent with the theory. This problem does not arise when you consider the velocity subtraction formula U = (S-V)/(1-(SV/C^2)) U: The velocity of an object in question relative to a moving observer, according to the moving observer S: The velocity of the object in question relative to the stationary observer, according to the stationary observer V: The velocity of the moving observer relative to a stationary observer, according to the stationary observer (S-V): The velocity of the object in question relative to the moving observer, according to the stationary observer 1/(1-(SV/C^2): The converting factor, that converts (S-V) into U C: The speed of light If the object in question is a pulse of light then S=C in situation one and -C in situation two. According to the special theory of relativity U=C in situation one and -C in situation two U = (C-V)/(1-(CV/C^2)) = ((C^3)-(C^2)V)/((C^2)-CV) = C((C^2)-CV)/((C^2)-CV) = C U = (-C-V)/(1-(CV/C^2)) = ((-C^3)-(C^2)V)/((C^2)-CV) = -C((C^2)-CV)/((C^2)-CV) = -C As it can be seen no problem arrises when this formula is used and as this is official formula, my perspective is wrong. In order to rectify my perspective, attempting to understand how the formula is derived would be a good start, with my approach being a good old fashioned thought experiment. The flash and superman are on a high speed train, as they are too lazy to run or fly to a ten pin bowling contest. During this train ride the flash and superman get into an argument, over how fast they can bowl a bowling ball down an alley. Each of them states there case to one another but either one concedes. A scientist sitting across from them, sick of their bickering, suggests that they test the speed of their bowls in the observation carriage of the train, with a devise he has in his luggage. This device consists of laser sensors, spaced one meter apart, the lasers shine perpendicular to reflectors, which allow the sensors to know if something has passed between the sensor and reflector (the same as a shop sensor). When the first beam from the first sensor is broken, a stop watch is turned on. When the second beam from the second sensor is broken the stop watch is turned off. The value recorded on the stop watch in the unit seconds divided by 1, will give a determined speed in the units meters per second. The experiment is established in the observation carriage so that, the flash and superman will bowl from the back end of the carriage and have there balls move up the carriage until they come into contact with the first beam and then the second, allowing them to finally resolve there argument. In my minds eye I am able to witness this experiment, track side as the observation carriage is completely glass, allowing me to view a ruler in between the sensors, that sates the distance apart is one metre and the stop watch. As i am able to see the reading on the stop watch and the ruler stating that the distance between the sensors to be one meter. I will be able to determine the speed of the bowling balls, relative to the train according to the observers on the train. Qualitatively according to special relativity, the relative speed between me and the the train should determine the difference in what i consider to be a meter and a second and what the flash, superman and the scientist consider to be one meter and a second. If i was not able to see the meter ruler or the stop watch, i should by logic based on the speed of the bowling balls, relative to me according to me and the train relative to me according to me, what they will determine the relative speed is of the balls compared to the train, according to observers on the train. Without Lorentz transformations, what i would determine the relative speed to be between the balls and the train to be, would be the same for those on board, however Lorentz transformations contract length and slow time. My one meter is longer than the trains one meter and my stop watch runs faster than the one on the train. To obtain the relative speed according to the train, the length it appears to cover to me relative to the train, must be converted into the length it appears to cover to the train and the time it takes to cover that length, according to me must be converted into the time it takes to cover the length according to the train. Without knowing the formulas for length contraction and time dilation, one might come up with this formula: U = (S-V)*((M/T)/(B/P) U: The velocity of the bowling ball relative to the train, according to the observers on the train S: The velocity of the bowling ball relative to trackside me, according to trackside me V: The velocity of the moving observer relative to a trackside me, according to trackside me (S-V): The velocity of the bowling ball relative to the train, according to trackside me M: the length of one meter, according to trackside me T: the length of what the train says is one meter, according to trackside me B: the duration of what the trains stopwatch considers to be one second, according to trackside me P: the duration of one second according to trackside me If I now look up what the formulas are for M/T and B/P, i should arrive at the same formula as the official one. M/T = 1/(1-(V^2/C^2))^0.5 B/P= (1-(V^2/C^2))^0.5 Then the velocity subtraction formula should be U = (S-V)/(1-(V^2/C^2)) The formula above is not the official velocity subtraction formula and only produces the same outcome when the S=V or the relative speed one is trying to determine according to the moving observer, is the moving observer themselves (U=0) As you can see at this point, i was not able to derive the official formula and rectify my perspective. What assumptions are false in the thought experiment and what are the correct ones i should have made?