I read through DeBroglie's original paper - and also a modern explanation on the same (attached). The first contradiction that DeBroglie arrives at is simple enough - he considers the 'wave-particle' as observed from a stationary frame - and from a moving frame. The 'inner frequency' of the wave-particle is v' = v SQRT (1-Beta^2) Equation (1) Now, he looks at the Energy transformation - and arrives at - v' = v / [SQRT (1-Beta^2)]. equation (2) (1) and (2) are different - that is plain to see. To explain this difference, de-Broglie assumes ANOTHER fictitious wave associated with the particle. This is the part I am having trouble with - can anyone shed light on this second wave - and how it resolves the dilemma? Page 2 in the attached article discusses this fully.