I received an email today that I thought was a copy of a message that
the author had posted to the PHYS-L archives. I responded to it thinking
that my messages would be posted to the archives. My answers to the
questions posed by the author, I think, might help clarify some issues,
so I'm posting my responses, here.
In response to a question asking if it's a fair statement that I expect
a line drawn from E1 to E2 to "coincide" in different frames, I replied:
No, I don't expect the line to coincide in different reference
frames. In the case I gave, the lines don't coincide in F and
F', but the point I'm trying to make is that they don't coincide
in spacetime, either. When I say they don't coincide in
spacetime, I mean, they don't coincide independently and apart
from either reference frame.
In response to a claim that the location of E1 will change in any
reference frame besides the one where you "fix" E1, as a function of
time, and that contrary to my first post, this will be true of E2, also,
I replied:
Right, that's true for E2, also, if you consider times later
than the occurrence of E2, but I was only considering times up
to the occurrence of E2.
Then, in a later email response to the same question, I replied:
Sorry, I misunderstood what you were saying, here. The Lorentz
transformations definitely indicate that the (assigned) spatial
location of E1 will _not_ change in _any_ reference frame. It's
position is fixed at x = 0 in F, and at x' = 0 in F', at all
times after its occurrence. What you said above is the way it
_should_ be, but in SR that isn't the way it is.
In response to a claim that this is true for Galilean relativity also, I
replied:
I think even Galileo would agree that the spatial position of E1
should always be the origin of the unprimed frame, in _both_
frames, for the direct transformation (for t >= 0).
It's a rule of mine that I won't respond to personal emails regarding
physics of any kind. From now on, please don't email me, since I will
only respond to messages that are posted to the PHYS-L archives, due to
bad experiences I've had in the past with personal emails. Had I known
that this author's email was not a copy of a post to PHYS-L, I would
not have answered it. Thanks.