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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.
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.