Relativity - Affine Geometry ?

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.

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.

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.

I made a mistake when I changed the co-ordinates from linear to exponential to look inside a black hole. You see the scale is similar to the Kelvin scale. By using a linear scale we can see 0 but it cannot be reached. We should really be using a log scale so 0 is – infinity so cannot be reached.

To understand it you need the theory of metric spaces and the Einstein’s concept of sitting at the foot of a cliff. Now light is falling down towards you and it gains energy as it falls but since it cannot go any faster (or slower) it increases in frequency, so shortening the wavelength. This wavelength can be thought of as the shape factor of space at that point and the frequency as the local shape factor of time.

So space is smaller as you go towards a massive object (like your left index finger). Now as a small object goes near a big object the space gets changed in length, (it is not real, it is 4-perspective), so like a beam of light passes through a change in refractive index it is bend towards the region of space is shorter. It is as if light moves more slowly.

Now to do the sums, you need a tensor (this is a matrix) now a position in space-time is a 4 vector. This is a column of 4 numbers.

The matrix operation x takes you from the column vector (now) to the column vector (soon).

The matrix is a square 4 x 4 that is the result of taking each element of now to each element of soon.

gives you the translation event now to soon. Which generally means you have moved and the velocity in the 3- subspace and is given by the 3 subspace numbers divided by the time subspace.

With curved space there are off diagonal numbers that mix the 4 dimensions thus making space linear but curved. (linear algebra).

Movement in the precense of matter.

the traslation from now to soon in the presence of matter needs a formula in the diagonal metric tensor to represent the change from now to soon,

if now is 15,000 km from earth's centre, and soon is 14,991 from the earths centre then a potential energy change takes place of Gm/15000-Gm/14991 G is the universal constant of gravity (mearurable) and mass is the mass+energy within the point.

So the metric means that as we do the translation the space shape factor changes

Now the shape factor of space is = Gm/r as far as I understand it.

so far away the factor is 0

The light here is of frequency f and wavelength L=cf

at a disdance r the shape factor is Gm/r so the energy of light will be higher.The energy of light is hf in flat space but as it goes closer to a mass+energy it is of higher energy, Gm/r the light gains potential energy (Gm/big to GM/less big)=hf to hf + small bit

so Gm/r2-Gm/r1=hf1-hf2 to put that into the diffential form for integration is not needed if we use the metric tenso. the shape has changed from (Gm/r2)/h to (Gm/r1/h) to get the length we have to use the wavelegth this is fL=c so L=c/f

So the length of space has changed from c/(Gm/r1/h) to c/(Gm/r2/h). So space can be mapped in shape according to the location relative to massive objects or areas of energy, includes light energy.

to make it simple the tensor is a series of sums so the column vector x1...x4 is for sums

x1 x a number >y2 now if y2 is r2 from a massive object and x1 is r1 from a massive object then the shape factor is included. x1 is a point the ordinate of the massive object is x0 and also y0 this is the same point, then the translation is from a shape of c/Gm/(x1-x0)/h to c/Gm/(y1-y0)/h.

Above is the calculation for the energy a 1 Kg mass requires to reach 0.9 c and under this is the calculation of the mass ratio for a photon rocket to acquire 0.9 c. Calculation by MathCad 14. It means that to reach 0.9 c the rocket with a 1 Kg payload needs to convert 2.064 Kg into light as the propulsion fluid. So its start up weight would be 3.064 Kg. Such a unit would require a matter burning engine. This would be a very hot plasma contained magnetically as in my thermonuclear reactor running at a higher temperature than required for proton fusion.

Relativity Geometry

Relativity - Affine Geometry ?