I have provided some very simple arguments here that clearly indicate a specific problem in relativity. It is very straight forward and fundamental, but it requires an equally straight forward and fundamental solution. 100 years have passed and nobody has solved it. Perhaps someone here might do so.

First, concerning some basic requirements of special relativity. Mathematically, it is defined by the Lorentz Transformations:





where


(x is position, t is time, c is the speed of light and v is the relative velocity)

Note that the Lorentz Transformations are based solely on relative velocity. This is very important, because there is nothing mathematically wrong with the equations, but as a physics formula, each variable relates to something physical and therefore has physical implications built into the equation. The implications here are that two observers using this equation can say nothing about their intrinsic motion. All the equation tells them is how they are moving relative to each other. Note also that these equations are very limited (and not very practical) since they apply only in the case of constant relative velocity. But no worry, we can derive a differential form and get:



We do not even have to do any work since one can simply copy it out of a text book (I used Jackson). Now this formula turns out to be very practical and is commonly used to determined the life-times of particles moving at high velocities. Note that this equation incorporates acceleration. It is important to understand to which acceleration it refers. The acceleration here, since it directly correlates to the relative velocity of the Lorentz Transformations is a relative acceleration. That is, it is the change in relative velocity over time. It is a purely kinematic value. It tells us nothing about what forces are present. It tells us only that the relative velocity between the two observers is changing.

So far I have made no argument against relativity and have only spoken of relativity exactly by the book. So, if you have found yourself disagreeing with anything mentioned so far, then you do not understand relativity... so you can stop reading.

Now lets consider a specific physical situation. I am not claiming any contradictions, but will only set up the situation and see how the above equations can be used in relation to it. (e.g. Be used completely, be used in part, or used in a modified form.)

Now imagine that there are two observers, observer A watches observer B accelerate straight away from him to a certain distance and then return to him by the same route. Observer A uses equation (3) to determine the time that has passed for observer B relative to his own time and he finds that less time has passed for observer B....exactly as the equation has predicted.

Now observer B sees observer A kinematically accelerate away from him and return in exactly the same fashion as observer A had seen him do. Observer B uses the same equation (3) giving the same velocity and change in velocity to observer A. His result is that less time has passed for observer A relative to his own time. (This by definition is a physical contradiction.) But it turns out in reality that equation (3) gave him the wrong result! observer A had in fact experienced more time.

As everyone knows by now, observer B apparently had experienced a force which caused his acceleration (which was observed by A) and it caused B to see observer A accelerate (change his relative velocity) in relation to him.

Now was it wrong for observer B to try and use equation (3)? It turns out that observer B had, in fact felt the force that accelerated him, but since there was still the same relative acceleration created and since there was no term or factor in the equation (3) indicating a force, there was no reason to assume that he would get a wrong answer. In fact, it was not the wrong choice by observer B, it was the inaccuracy of the formula when being applied by an observer being accelerated.

So far then there is not necessarily a contradiction (since special relativity is a limited theory). What we have learned is that the equations of special relativity are wrong when being applied by an observer who is accelerating (they still work if only the observed object is accelerating).

Thus special relativity causes a contradiction which is only resolved by special relativity's failure to be accurate when used by an accelerating observer.

Now since special relativity involves only relative velocity and relative acceleration (change in relative velocity) there is no possible way it can resolve the contradiction, since it contains no reference to the dynamic state of the observers. Thus it cannot distinguish which actually accelerated. Of course, the observers would know, but since the equations do not contain the information, they are wrong when applied in this case.

Thus if someone says that the reason there is no contradiction is because one of the observers is accelerating, he may possibly be right. BUT if he claims that special relativity can give the correct times for both observers and thereby resolve the contradiction (right after he stated that special relativity is invalid for one of the observers) then he is hopelessly insane. If you are one of these people, you can stop reading now.

For relativity to survive, it thus requires that general relativity supply an answer. What exactly do we need from general relativity for this problem?

Equation (3) needs to be adjusted so that it has terms or factors relating to the forces on each observer in such a way that the formula gives the correct time as observed by each, not just observer A (the non-accelerating observer). When the force is zero, then it should reduce to equation (3), but only for the non-accelerating observers. Thus in this example observer A, having experienced zero force, would be able to use equation (3), but observer B would use a modified version of equation (3) which included factors or terms based on the force he has experienced. This equation, on integration, would then yield the correct passage of time of observer A as seen by observer B.

General Relativity would have to be able to provide the necessary corrections.

Until such corrections have been provided (not just claimed).....Relativity remains self-contradicting.