What if there is a single lightning strike at midpoint M?

In Einstein's train thought experiment he has the lightning strikes
occurring at Point A and Point B simultaneously relative to the
embankment. Einstein goes on to state for the Observer on the train:

"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 on 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."

What happens if we change where the lightning strike occurs in
Einstein's train thought experiment? What happens if there is now just
a single lightning strike that occurs at midpoints M (relative to the
embankement) and M' (relative to the train)?

Using Einstein's reasoning we can falsely conclude:

"Now in reality (considered with reference to the railway embankment)
Point A on the train is hastening towards the beam of light coming from
M, whilst Point B on the train is riding on ahead of the beam of light
coming from M. Hence the light from the lightning strike will reach
Point A on the train earlier than Point B on the train."

Since the speed of light is constant regardless of direction of travel
in the train reference frame, the light from the lightning strike at
Point M must reach Point A on the train and Point B on the train
simultaneously.

The problem with Einstein's train thought experiment is he draws
conclusions from one reference frame for events which occur in another
reference frame. Einstein cannot state, "Now in reality (considered
with reference to the railway embankment) (the Observer on the train)
is hastening towards the beam of light coming from B."

For Einstein's train thought experiment, the following is a more
appropriate conclusion: From the embankment reference frame, both
lightning strikes will reach the Observer on the embankment
simultaneously. From the train reference frame, both lightning strikes
will reach the Observer on the train simultaneously.

Any conclusion based upon one reference frame determining when an event
occurs in another reference frame is derived from a faulty premise.

.

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