Suppose a person is moving with a very high speed which is close to that of light. Will the person notice any change in wavelength of any wave which we generally notice in ground frame? Let me add a little more context to it.
Let's assume a photon of $f$ frequency is incident on a metal surface of work function $W$. After $W$ amount energy of photon is expended,the rest is acquired by electron. So, A person in ground frame will make this observation: $hf=W+mc^2(\gamma-1)$ where gamma symbolizes $\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ with $v$ being the velocity of electron from ground frame . What gets me thinking is that the person in the high speed frame doesn't have any choice apart from making the same observation since $hf$ and $W$ are constant implying equal kinetic energy of electron in both frames of reference. But that can't possibly be true,since their measured velocity of electrons must differ in accordance with their frames of reference. So, I am conjecturing that $f$ or frequency and hence wavelength must be different in both frame of references. Is my conjecture plausible?
