The Bobs are helping to conduct Gedanken(Thought)-Experiments, that demonstrate five key concepts underlying Einstein’s Special theory of Relativity. Click on each link below to view the experiment and rationale for each concept:
- Constant c: The speed of light in vacuum is constant regardless of the motion of the light source or the observer.
- Relativity of Simultaneity: Constant c leads to the strange result that simultaneous events on the platform are not simultaneous when observed from the train (and vice-versa).
- Time dilation: Specifically, a moving clock runs slower when observed by someone at rest.
- Length contraction: As time is dilated, length of the train and all objects on it are contracted when measured from the platform (and vice-versa).
- Lorentz transformations: Time dilation, length contraction and in general, transformation of space and time coordinates between moving reference frames can be performed using the Lorentz transformation equations.
Some (optional) reading before you proceed...
- It is important to note the difference between the Principle of Relativity and the Einstein's Theory of Relativity. The former is based on Newton's laws of motion and pre-dates Einstein. The Principle of Relativity grandfathers in some postulates (such as equivalence of intertial reference frames, invariance of the Laws of Physics etc.) that we accept without proof. Some of these postulates are changed, but not disproved by Special Theory.
- As you consider each concept and its experiment, it is important to ask and answer the 4 Ws.
- What happened? The point of each experiment is to analyze one or more events that occur somewhere in space and time.
- Who was watching? We take apart each event to understand how they appear to different observers.
- Where did it happen? The space coordinates of the event as measured by each observer. We assume that a rigid coordinate system is attached to the train and platform. In each experiment, we assume that the train is moving at a constant velocity $v$ relative to the platform. As motion is constant, Newton's law of inertia applies, and so these systems are also called inertial reference frames.
- When did it happen? The time coordinate specifies the time of the event as measured by each observer. The whole point of Special Relativity is to prove that, just like Where, When also depends on What and Who.
- As the relativistic effects become apparent only when objects move at speeds close to $c$, we invoke the lazy, good-for-nothing, physicist principle and use a very low value of $c$. Just remember that the relativistic effects are experienced by the Bobs and not by you - the big observer in the sky. Where appropriate, we alter lengths and time intervals (but not the entire scene) to account for relativistic effects in each reference frame.
Einstein. A. (1915). Relativity: The Special and General Theory. In Gutfreund H. and Renn J. (eds) Relativity - 100th Anniversary Edition. Princeton University Press.
Taylor, E. F., Wheeler, J. A. (1991). Spacetime physics: Introduction to special relativity (2nd ed.). New York: W.H. Freeman and Company.
Libretexts. 5: Relativity. Physics LibreTexts, Libretexts, 5 Nov. 2020.