Suffice to say that when you use the Lorentz transformation correctly, you will find that the following statement by Einstein, which can be found in his little book entitled RELATIVITY: The special and General Theory, page 26, is not correct: "Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding ahead of the beam of light coming from A, Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.".
No, Einstein got that right. The highlighted qualification is key.
To explain where
johanfprins and/or his friend went wrong, I'll need to talk about Einstein's two observers:
- Observer M' is on the train, exactly halfway between the points A and B at which lightning strikes the train.
- Observer M is on the embankment beside the railroad track, watching the train travel from his left to his right. In observer M's frame of reference, the lightning strikes at A and B are simultaneous, and observer M deduces that observer M' must have passed observer M at the instant of those lightning strikes (because M' is exactly halfway between the points A and B at which those simultaneous lighting strikes damaged the train).
To make my presentation a little more concrete than Einstein's, I'm going to assume that observer M' is situated at the exact middle of a train car, and that points A and B are the rearward and forward ends of that car.
I'm also going to assume that the train-bound observer M' is a conductor, with instantaneous reflexes, who's about to punch a ticket that some passenger is moving at a constant rate across the punch. Furthermore, I will assume that M' is so sensitive to bright light that he punches that ticket (instantaneously) whenever light from a nearby lightning strike reaches him.
With those assumptions, the question of simultaneity reduces to this: Does the observer M' punch just one hole in the ticket, or does he punch two?
Now when using the Lorentz transformation directly you will find that within ANY inertial reference frame, the light beam from B as well as the light beam from A are both still approaching the observer with speed c.
That sentence is correct. In particular, it is correct for both M and M'.
What
johanfprins and/or his friend are forgetting is that, within the inertial frame of the observer M on the embankment, observer M' is moving away from the light at A and toward the light at B. Since the speed of light is finite, observer M sees that M' has travelled some distance to the right of M before M' sees the light from either A or B. In the frame of reference of observer M, therefore, the light from A (at the rear end of the car) must travel farther before it reaches M' (at the exact middle of the car) than does the light from B (at the front of the car). Hence observer M sees the light from B reach observer M' a little before the light from A.
So observer M sees M' punching two separate holes in the ticket.
If the observer could have rushed into the light beam from B, and away from the light beam coming from A, the light speed from B relative to the observer would be larger than c, and the light speed relative to the observer from A would be less than c.
No. That is where
johanfprins and/or his friend go wrong. To draw the conclusion stated in that sentence,
johanfprins and/or his friend must assume that the lightning strikes at A and B are simultaneous
in the frame of observer M' as well as in the frame of observer M.
That's not true. Indeed, the relativity of simultaneity is the whole point (and the title!) of Einstein's chapter 9, in which this example appears.
In effect,
johanfprins is arguing that M' punches only one hole in the ticket.
But we already know that, as seen by observer M, M' punches two separate holes. We can assume that observer M' puts the ticket in his pocket after punching the holes, and has dinner with observer M later. When observer M tells M' that there are two holes in the ticket, M' can verify that fact by pulling the ticket out of his pocket.
Because there are two holes in the ticket, the light from A must have reached observer M' after the light from B. That refutes
johanfprins while confirming Einstein. According to observer M, the lightning flashes at A and B were simultaneous. According to observer M', they were not simultaneous; the flash at B happened before the flash at A.
Simultaneity is relative.
Try the derivation yourself if you are competent; which I, however, doubt. I also reasoned like you before it was proved to me by my colleague that Einstein's reasoning was defective: I was just as astonished, but fortunately I am not a dogmatically ossified person like you are.
johanfprins and his friend are mistaken.
johanfprins made a much more serious mistake when he decided that he and his friend were right, while Einstein and everyone else were wrong.
johanfprins compounded his errors by congratulating himself on not being "a dogmatically ossified person" like the tens of thousands of physicists and millions of laypersons who actually understood Einstein's argument.
Nowhere have I or my friend said that the two simultaneous events will also be simultaneous within another inertial reference frame. All that is claimed, and which follows directly from the Lorentz transformation is that this is NOT CAUSED by an observer "hastening into a light beam and riding ahead of the other light beam" The latter is not possible since the speed of light is always the same relative to any object no matter how fast the object is moving!!!
As explained above,
johanfprins and/or his friend have misinterpreted the passage to which they are objecting. That took some doing, because they had to ignore Einstein's parenthetical remark, which I highlighted at the top of this post.
As seen by observer M, observer M' really is "hastening into a light beam and riding ahead of the other light beam."
johanfprins and/or his friend appear to be assuming that Einstein's remark applies also to what is seen in the inertial frame of observer M'. That's a rookie mistake.