Relativity claims that if two events are simultaneous in an inertial frame of reference, then they cannot be simultaneous in another inertial frame of reference which is moving uniformly and rectilinearly at a velocity v relative to the first inertial frame of reference.

But if the Lorentz transformation equations are correct, this claim results in a clear contradiction, as follows:

1. Let there be an inertial frame of reference -- which we shall designate as I -- in which there are two clocks C₁ and C₂, separated from one another spatially, and synchronised: so that whenever the clock C₁ indicates a moment in time t₁, the other indicates a moment in time t₂ such that t₁ = t₂ = t.

 
2. Let there be another inertial frame of reference -- which we shall designate as I' -- also moving rectilinearly and uniformly at a velocity v relative to I, in which there are two more spatially separated clocks C'₁ and C'₂, which are also synchronised: that is, whenever the clock C'₁ indicates a moment t' coinciding with the moment t indicated by the clock C₁, the clock C'₂ also indicates the same moment t' indicated by the clock C'₁.

 
3. Now when the clock C₁ indicates any particular moment t₁, the moment t₁ must be related to the moment t'₁ indicated by the clock C'₁ by the Lorentz transformation equation

 
t'₁ = (t-vx/c²)/(1-v²/c²)^0.5


... where x is the distance, as measured by an observer in I, between clock C₁ and clock C'₁, and the moment t = t₁ is that indicated by the clock C₁ ... and c is of course the speed of light.
 

4. So when C₁ and C₂ both indicate a particular moment t = t₁ = t₂, C'₁ indicates a particular moment t'₁.

 
5. And when the clock C₂ indicates the same moment t₂ = t = t₁ as is indicated by Clock C₁, the moment t₂ must be related to the moment t'₂ indicated by the clock C'₂ by the Lorentz transformation equation

 
t'₂ = (t-vy/c²)/(1-v²/c²)^0.5


... where y is the distance, as measured by an observer in I, between clock C₂ and clock C'₂, and the moment t is, again, that indicated by the clock C₂ ... and c is again the speed of light.
 

6. So when the clocks C₁ and C₂ both simultaneously indicate a particular moment t = t₁ = t₂, the clock C'₂ indicates a particular moment t'₂.

 
7. Now unless x = y above -- which is highly unlikely, though of course not impossible -- it is clear that t'₁ will not be equal to t'₂ above: both of them being indicated, of course, when both the clocks C₁ and C₂ indicate the single moment in time t = t₁ = t₂.

 
8. But this contradicts Point No. 2. above, according to which whenever C'₁ indicates any particular moment t', C'₂ must also indicate the same moment t', since both C'₁ and C'₂ are synchronised.

Or expressed in table form: 
 
 

It is of course abundantly clear that the above two tables contradict one another in their fifth columns.
 
 
 
 

Any comments? e-mail me.
 
 

* At least, not necessarily.