Natural Science Forum / Physics / Relativity / October 2006

Relativity - Affine Geometry ?
Abstract:

Einstein addressed the twin paradox in special relativity in a relatively
unknown, unusual and rarely cited paper written in 1918, in the form of a
dialogue between a critic and a relativist. Contrary to most textbook
versions of the resolution, Einstein admitted that the special relativistic
time dilation was symmetric for the twins, and he had to invoke,
asymmetrically, the general relativistic gravitational time dilation during
the brief periods of acceleration to justify the asymmetrical aging.
Notably, Einstein did not use any argument related to simultaneity or
Doppler shift in his analysis. I discuss Einstein's resolution and several
conceptual issues that arise. It is concluded that Einstein's resolution
using gravitational time dilation suffers from logical and physical flaws,
and gives incorrect answers in a general setting. The counter examples imply
the need to reconsider many issues related to the comparison of transported
clocks. The failure of the accepted views and resolutions is traced to the
fact that the special relativity principle formulated originally for physics
in empty space is not valid in the matter-filled universe.
Einstein's special theory of relativity is about measurements between frames
of reference in a state of non acceleration. It is an observation that the
velocity of light is independent of the relative velocity between observer
and the source. From this Lorenz postulated a length contraction to allow
for this. Einstein derived the same equation from the observations.
If you look at this equation there is no special frame so any frame may be
taken as the reference frame.
Let us consider the passage of mesons from the origin in the upper
atmosphere to their arrival at a counter on the earth's surface. The
observer "sees" the origin from his frame and since he is "looking" at the
meson then this point is only a few feet above the laboratory roof because
of the Lorenz contraction. Thus accounting for the short passage time. The
"meson" "sees" the path it travels from the upper atmosphere to the surface
as the same few feet as it is "looking" at the observer's reference frame.
It seems to me that there is no real contraction, only an effect similar to
perspective as a result of the way light travels and is only an appearance.
Relativity is 4-space perspective.
This would mean that a journey in a very fast space craft to a nearby solar
system (say 10 light years) would take a time given after the length
contraction and time contraction had been allowed for. (This is called the
4-velocity) I suggest that the 4-velocity is the "real" velocity and what we
see is the result of 4-space perspective.
V=v/sqr(1-(v/c)^2) V is the 4-velocity and the velocity in all frames.
It would therefore be possible for deep space journeys with a fast
spacecraft in normal time spans. (By fast I mean velocities close to that of
light - say closer than 99%c).
It also strikes me that since all frames are equivalent the "Twin Paradox"
does not occur, the two brothers will agree both about the time and distance
travelled.
Since perspective is the projection of 3-space to 2-space then relativity is
the projection of 4-space to 3-space.
Hello,

So even the man himself admitted his idea had been misinterpreted by his
followers.  The general theory relativity that deals with acceleration does
not map well into special relativity because the forces on the objects do
not influence signal exchanges in any way.

If you think of the star ship journey in terms of a two dimensional space
time diagram (other massive objects are too far away to be of any influence)
then you have a hill.  Now in normal hills the distance over the hill is
longer than the distance along the flat, but in the relativity case the
distance over the hill is shorter than the flat because it is a negative
hill.

That is because one of the dimensions is jct and the other is x now using
Pythagoras the hypotenuse for this negative hill, which is really just a
wobbly 'v' is 2*( x^2-(ct)^2)^0.5 and that is less than 2x.  This is because
we are in hyperspace. x is the "rest" distance and "t" is the time
calculated at the x/v where v is the velocity. So the distance travelled is
2*(x^2-(c(x/v))^2)^0.5.  and that takes (that distance)/v in real time.

The precise shape of the curve only means we need to do an integration along
the curve VIS differential geometry, I get it now, with my brand new brain,
fitted after they took out my old one a couple of months ago.

Get it! So space travel is really very easy you just have to fast enough.

"The faster you go, the quicker you get there" just like running a race!

I didn't win!

My understanding of special relativity is limited. However my opinion is
that the contraction effects are a 4-perspective effect due to the constancy
of the velocity of light, there is no physical contraction at all.

My mind forms a concept of a ^ shaped hill of the space-time trajectory of a
return particle path where the path over the hill is shorter that the path
taken at rest or very slowly, so the higher the velocity the shorter the
path over the hill. It is a metric space.

The other related point is the relativistic momentum now since the path
depends on the velocity then there is the notion of a real or true velocity
v/gamma. In the momentum of a particle the momentum as measured by collision
is m v/gamma so as the velocity increases the mass remains the same.

In the derivation of the kinetic energy the formula:
   mv/sqr(1-(v/c)^2)

may be separated into to partial fractions
   m x v/Sqr(1-(v/c)^2)
When you integrate with respect to v from 0 to a number less than c to find
the kinetic energy.

This gives the solution mc2 for the rest mass energy as with the older
Einstein version. He chose his method because of theological augment to make
the maths easier, he said "God would not choose such a complicated
mathematics". God is not stupid either.

This method gives the idea of a true or real velocity of v/sqr(1-(v/c)^2).

I am aware that this in not original but unfortunately theologians kill
people who come up with this (several times a month) along with the doubters
of Gauss.

Such is the evil of man (I disagree with you so your brain has gone wrong, I
will remove it) - Doctor your head has gone wrong it needs amputating!

However the time taken for a round trip works out different from the usual
relativity theory, as in a Metric space.

The general theory is a metric space where the distance shortest between
adjacent points is given by a metric resulting from the sum mass + energy
nearby. It could be represented by a matrix which could include the special
theory as terms in the matrix to work out the distance between adjacent
points.

Again there is no real contraction it caused by 4-perpective due the metric
caused by the constancy of the velocity of light.