I need someone to resolve this paradox for me.(adsbygoogle = window.adsbygoogle || []).push({});

Before I start, here are the basic ideas:

Okay, so every moving particle has a DeBroglie wavelength: E=hc/[tex]\lambda[/tex].

This also means that each particle has a frequency: E=hf

So it also has a period: E=h/[tex]\tau[/tex]

So any given mass has a DeBroglie period of [tex]\tau[/tex]=h/mc^2

Consider the train problem with the light clock. The guy on the train sees the light clock ticking normally. Now an outside observer sees the train moving and thus will see the light clock ticking slower. This is due to time dilation: t' = t[tex]\gamma[/tex].

Okay, so here is the paradox: Now imagine you have an electron on the train instead of the light clock and you are monitoring it's DeBroglie period. Now since it is a time period, it should appear to increase in duration to the observer outside of the train. This cannot happen however, because if the time period increase, the frequency would decrease meaning the energy would decrease. A moving particle must have more energy than it does at rest.

What is the deal here?

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# DeBroglie and Time Dilation Paradox

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