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.

--
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