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Re: A Geometrical Proof of the Non-invariance of the Spacetime Interval



I think the Galilean example helps avoid confusion. Do I understand
correctly, then, that you are simply interested in the distance between the
points where events E1and E2 occur? Do I further understand correctly that
you would like that distance to be the same in both reference frames?

If my understanding is correct, then please explain why you seem to choose
to give priority to frame F, by wanting the distance measured in F' to not
be zero. That seems to violate the basic principle of relativity, either
Galilean or special. Maybe the stake driven in at event E1 has moved
according to F', but the event of the stake-driving does not "move". The
distance between the stakes at the time of E2 is not given by transforming
E1, since E1 is an event that occurs at a specific time (zero). If you
want the distance between the stakes at the time of E2, you need an event
E3 that occurs at the location of the first stake at that time, and you
must determine that time.

Michael Burns-Kaurin
Spelman College




David Rutherford
<drutherford@SOFT To: PHYS-L@lists.nau.edu
COM.NET> cc:
Sent by: Forum Subject: Re: A Geometrical Proof of the Non-invariance of
for Physics the Spacetime Interval
Educators
<PHYS-L@lists.nau
.edu>


01/15/2003 03:15
AM
Please respond to
Forum for Physics
Educators






Bob LaMontagne wrote:

David Rutherford wrote:


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.


If E1 is a an event in spacetime, and E2 is a separate event in
spacetime,
how is there more than one unique "line" connecting them? F and F' may
have
different descriptions for that line, but there's nothing to "coincide
independently" since there's only one line being referred to.

You certainly wouldn't ask if E1 "coincides independently" in F and F'
because it's only one event. Likewise for E2. Why then ask that question
of
the line from E1 to E2?

Maybe I can show the way I think it should be by using Galilean
relativity as an analogy. I know that the Galilean transformations
aren't used to find the spacetime interval between events, but I think
they can be used to make my point.

Say the situation is the same as before, so that event E1 occurs at the
coincidence of the origins of F and F'. Then at time t = t, event E2
occurs at x = vt. The Galilean transformations give the coordinates of
E2 in F', in this situation, as

x' = x - vt = vt - vt = 0
y' = y = 0
z' = z = 0
t' = t

Now suppose that observers in F' are asked to give the distance between
E1 and E2. Should they say that x' = 0 (which is what the analogous
Lorentz transformations say), or should they say x' = x = vt = vt'? I
say they should say the latter.

For example, think of E1 as being the driving of a stake into the ground
at x = y = z = t = 0 in F, and E2 as the driving of a second stake at
x = vt, y = 0, z = 0, t = t. I say that a valid set of transformation
equations should give a comparison of the measurements of the distance
between those stakes at the time of E2 (that is, at t' = t), and the
time between the driving of the stakes at the time of E2 (that is, at
t' = t) in F and F'.

--
Dave Rutherford
"New Transformation Equations and the Electric Field Four-vector"
http://www.softcom.net/users/der555/newtransform.pdf

Applications:
"4/3 Problem Resolution"
http://www.softcom.net/users/der555/elecmass.pdf
"Action-reaction Paradox Resolution"
http://www.softcom.net/users/der555/actreact.pdf
"Energy Density Correction"
http://www.softcom.net/users/der555/enerdens.pdf
"Proposed Quantum Mechanical Connection"
http://www.softcom.net/users/der555/quantum.pdf