Motor Daddy:
I have re-drawn my diagram to include a picture showing how things would look in the Motor Daddy universe in the frame of the train/box.
Notice that in the Motor Daddy universe the light spreads out in a sphere in "space" around the point of emission of the light. In the frame of the box, that point in "space" moves backwards with respect to the box.
Compare the Einstein train/box frame, in which the light sphere spreads out from the source at the centre of the box at an equal speed in all directions. This is in accordance with Einstein's 2nd postulate.
I see the redrawn diagram in post #1137. Let me test my understanding. This is a depiction of a single flash of light emitted from the center of the train and the light flash is observed by a passenger on the train and by an observer on the embankment. The left hand column and the center column are two frames of reference according to SR. One frame is from the embankment, and the other is inside the train. You have drawn three time lapse pictures of the light sphere expanding for each of the two Einstein frames in accordance with the postulates of SR.
Einstein’s Embankment Frame
On the left we have the three time lapse pictures of the light sphere expanding from the instant of the event. The first time lapse picture shows the light sphere as a circle with the point of emission as a point in the center of the light sphere, and the rectangle represents the train position as it passes the observer. I think you have shown the train length contracted
. The first frame is just an instant after the light flash and the radius of the light sphere is small and hasn’t reached the sides of the train and hasn’t reached the observer yet.
On the left, the second and third pictures show the train rectangle passing the observer and the light sphere continuing to expanding. I am assuming that the third time lapse picture which shows the light flash reaching the side of the train is also the point in time when the observer on the embankment sees the flash. It is as if the observer on the embankment has his nose right up to the side of the passing train. Is that right or close enough?
There is a time delay from the instant of the flash until the observer on the embankment sees it. To clarify, I think you are depicting a time delay from the perspective of the observer on the embankment so he sees the flash when the light sphere expands out to him at c from his frame as if his nose was at the side of the train.
Einstein’s Train Frame
The Einstein train frame, the middle set of time lapse pictures is from the train frame. The three pictures show the light sphere expanding within the train in accordance with Einstein’s second postulate:
Special Relativity
2. Second postulate (invariance of c)
As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.
The light sphere expanding in the train frame moves with the train according to the perspective of the observer on the train and the observer on the train sees the light sphere expanding relative to the inside of the train car. If he is sitting at the middle of the train in a window seat with his nose up to the window he sees the light on a time delay as the light sphere expands from the middle of the train car to his perspective at the side window. He sees the embankment moving past the windows.
Comparison between the two Einstein frames:
From the embankment the light sphere expands from its point of emission toward the observer on the embankment who would testify that he saw the flash just before the train has passed but after the center of the train has passed. He probably knows that there was a time delay between the flash and the time the light sphere from the flash reached him, but when the sphere reached him, as shown in the third time lapse picture in the left hand column, the train was almost past him when he saw the light. The nose of the passenger sitting by the window had already passed the observer on the embankment, right.
From inside the train the light sphere expands from its point of emission toward the sides of the train car. When the passenger sitting with his nose to the window sees the light flash as the light sphere expands to reach him he would testify that the observer on the embankment who had his nose right up to the train had already passed outside his window.
In other words, the light sphere moved in accordance with SR in each frame and the description of the light sphere and the physical location of the observers implies that there was a separate light sphere in each frame.
MD’s view from the moving box.
MD from his moving box which we can call the train car for all intents and purposes initiates a light flash from the center of the box. According to MD’s postulate:
Light propagates at c from the absolute point in space where it is propagated.
Thus from inside MD’s box the light sphere expands as the box moves away from the point of emission. The light reaches an observer sitting at the side and toward the rear of the box at the same time that it reaches an observer outside the box who has his nose right up to the box. They both see the same light sphere and would testify that they also saw the nose of the other observer pass at the same time as the light reached them.
Have I got a grasp of how the two different postulates would change the description of the observations from inside and outside the box, i.e. the train?
