AnssiH has been very helpful in showing me how my presentations are misunderstood. With Anssi's help I have now composed a third version of my presentation and arranged for it to be published as a standard book soon to be available on Amazon.com.

On the other hand, it has come to my attention that one very serious aspect of my presentation has been overlooked by Anssi. I have been thinking about that aspect and have decided to present it here as I am sure that if it wasn't clear to Anssi, it was probably overlooked by everyone else also. It is a direct consequence of special relativity (both my presentation and Einstein's) and, when examined from the perspective of my presentation, applies directly to general relativity also.

It has to do with how things actually appear to an observer; an issue seldom examined carefully by the professionals. Let me construct a subtle thought experiment worth examining.

Suppose we have an individual making some careful examinations from a spaceship traveling at a high enough velocity to make special relativity an important issue in the examinations I am about to describe. I want to exactly represent the following examinations from both the rest frame (the frame in which the spaceship is traveling at a high velocity) and the frame within which the space ship is at rest. Dimensions in the frame of the space ship will be primed.

First of all, the correct transformations between the two frames are expressly given by the following well known special relativistic relationships:

[math]

x'=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}[x-vt]

\;\;\;\;

and

\;\;\;\;

t'=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}[t-\frac{vx}{c^2}]

[/math]

Regarding the other relationships, y'=y and z'=z so these coordinates do not require a careful analysis. On the other hand, any measurements involving x and x' must be carefully looked at.

In this thought experiment, there will be a metal panel at the rear of the spaceship orthogonal to the path of the ship. In that panel, there will be two holes each a specific distance from the center line of the ship. Note that both the rest observer and the observer on the ship will agree as to the separation of those two holes (they are no more than measurements in the y-z direction).

At the front end of the ship, on a plane also orthogonal to the path of the ship and on a line directly represented by same y-z direction used to specify the two holes above (once again symmetric to the center line of the ship) there will be two photon detectors which can be moved to any desired position along that line. Note that once again, both the rest observer and the observer on the ship will agree as to the separation of those detectors (their positions are again no more than measurements in the y-z direction).

For any star viewed directly to the rear of the ship, those two detectors may be set to a position to detect that that star simultaneously: i.e., [math]t_{1}'[/math] must exactly equal [math]t_{2}'[/math]

Since those two detectors are in exactly the same y-z plane at the moment of that detection the x separation of the two events is exactly zero in both reference frames and thus, though t' may not be the same as t, the difference between [math]t_{1}[/math] and [math]t_{2}[/math] must also be zero: i.e., these two specific events are seen as exactly simultaneous in both frames.

Now this posses a seriously interesting geometric issue.

Let us now examine the triangle formed by the two detectors and the star being detected. Clearly the rest observer will observe that the photons pass through the two holes at the rear of the ship and impact the detectors at the front of the ship and as such define a very specific geometric construct.

If that ship were actually at rest at t=0, that geometric construct would provide a means of measuring the distance to the star being detected. However, if the ship were moving at a high velocity, as measured in the ships frame of reference, the geometric construct is exactly the same as that which would have been measured if the ship were at rest. This implies the distance to the star as calculated on board the moving ship would be exactly the same as that calculated were the ship at rest.

That result implies a rather astounding consequence. Using their observations both the rest observer and the moving observer would map the universe with identical separations between the stars. This is not at all what is implied by the standard interpretations of special relativity. What is important here is that we have avoided bringing in the issue of general simultaneity, the central complication of any relativistic calculation.

If anyone can see an error in this presentation, please put forth a logical argument which defeats the conclusion.

Thanks for your attention -- Dick

**Edited by Doctordick, 17 May 2014 - 03:51 PM.**