TO ALL: Thanks to the help of many dedicated forum members, I have learned that this problem can be explained by understanding Minkowski diagrams. Here is a consolidated list of helpful links: https://www.khanacademy.org/science/physics/special-relativity/minkowski-spacetime-2016-01-18T22:56:14.718Z/v/starting-to-set-up-a-newtonian-space-time-diagram https://www.physics.byu.edu/faculty/allred/222%2011/minkowski%2011.pdf
How can the speed of light remain constant in reference frames that experience time differently?
Maybe some context would be helpful, so let’s do a quick thought experiment: Imagine that you are standing on the platform of a railway station. A train approaches you at 99% the speed of light. It’s headlight flashes when the locomotive is directly in front of you*. At that instant, what do you see?
- Note: The fact that the headlight is directly in front of the observer when it flashes is crucial to this version of the thought experiment. The light source is not moving away from the observer in any direction, thus simplifying things by eliminating the relativistic doppler effect.
Although an overall analysis of this thought experiment would be greatly appreciated in the comments, there is a specific question that I am trying to answer: Is the absolute, (as opposed to observed) speed of light truly constant? Let’s take two perspectives to examine this scenario from. An engineer in the locomotive would observe that the photons emitted from the headlight are traveling at the speed of light, C, relative to him. He is also experiencing time at the same rate, or is in the same “time bubble” so to speak, as the light source because they are both moving at the same velocity. On the other hand, at what speed would the photons appear to be traveling from the perspective of the (relatively) stationary observer on the platform? This person is in a different time bubble than the engineer and the light source, since he is traveling at a different velocity. If the observed speed of light is constant, then the person on the platform would observe that the photons are traveling at C, relative to him. However, wouldn’t this mean that light was traveling at two different absolute speeds? In fact, it seems as though the absolute velocity of the photons would be greater for the observer on the platform than for the engineer, since the person on the platform observes the photons traveling away from the moving train at the same velocity that the engineer observers them when moving along with the train.
Essentially, how can time dilation explain why the observed speed of light remains constant in a scenario where the observer experiences time at a different rate than the light source which is being observed?