Peter Christensen wrote:
Just asking for some opinions, as some good inputs are always
valuable...
[...]
Simply using "Proper Time" on the axis, which is usually considered as
the "Time Axis". That's different, unusual and it will "probably look
very wrong" for most people, at least at a first glance. But honestly,
I think, that I can get something useful out of it. And it's the same
with the momentum-energy vectors: I simply use m (mass) instead of E
(energy) on the main axis, and of course, I also know that this is
very unsual, I know that.

To be very short: I'm trying with vectors like this: (c*"proper
time",x,y,z) and (m*c,p_x,p_y,p_z) instead of the usual representation
with (c*t,x,y,z) and (E/c,p_x,p_y,p_z).

Have you "pro's" seen something simiar earlier, and if so, then what
was the outcome? -Could it be used for something, and if not, then why
not?

First of all, Tom Roberts' coments in post
is very valuable.

However, there is another point to consider. Proper time is defined as
the time that passes on the object when it is free of gravitational
fields and not moving. So using c*proper_time rather than c*t would
restrict the coordinate to only object that are not in gravitational
fields and not moving.

Furthermore, the term p_t=E/c comes from the topology of space-time
and the invariance of lengths, and also that the theory should also
apply to photons. To say that p_t=m*c implies that the objects are not
photons and also must be at rest, since in your version
p_t=p_old_t/gamma and gamma=1.

Aside from these two differences, your theory is basically GR
restricted to non-moving objects that are not in a gravitational field
and not photons.

--
// The TimeLord says:
// Pogo 2.0 = We have met the aliens, and they are us!

The TimeLord wrote:
Proper time is defined as
the time that passes on the object when it is free of gravitational
fields and not moving.

Not true. the proper time of an object is the time elapsed on an ideal
clock that remains collocated with and comoving with the object. Whether
or not someone thinks it is "moving" [#], and whether or not there is
gravitation present, does not affect this definition (though they can
affect the relationship between the object's proper time and other
clocks). Indeed, it is essential to GR that the proper time of an object
be related to that object only, completely independent of its environment.

[#] Proper time is that of the object itself. The object,
of course, does not consider it (itself) to be moving.


Tom Roberts

Tom Roberts wrote:
The TimeLord wrote:
Proper time is defined as
the time that passes on the object when it is free of gravitational
fields and not moving.

Not true. the proper time of an object is the time elapsed on an ideal
clock that remains collocated with and comoving with the object. Whether
[...]
[#] Proper time is that of the object itself. The object,
of course, does not consider it (itself) to be moving.

Yeah, I stated what I wanted to say very poorly. The sad thing is I
really can't think of a way to clean it up. What I was trying to avoid
is the situation where someone would argue that proper time is the
same as observed time for all points and times of observation when v=0
but a/=0. I guess I'm trying too hard to anticipate those who hate
Relativity without understanding it.

At any rate you're right and I've messed up in the way I said what I
was trying to think of.

--
// The TimeLord says:
// Pogo 2.0 = We have met the aliens, and they are us!