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How will relativistic effects affect the interference pattern?

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  • $\begingroup$ You need to define what is moving relative to what in any relativistic problem. $\endgroup$ – StephenG Aug 17 at 7:36
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    $\begingroup$ Why should that make a difference, since the double slit experiment can be done with photons, which obviously move at the speed of light? $\endgroup$ – PM 2Ring Aug 17 at 9:03
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    $\begingroup$ @StevenG The OP means the speed of electrons with respect to the slit. $\endgroup$ – my2cts Aug 17 at 10:14
  • $\begingroup$ @my2cts I'd prefer the OP clarify what they mean that other people guess. There is a difference between the equipment moving together at relativistic speeds relative to an observer an observer but the electrons at "normal" speeds relative to the slit and the case where electrons are moving at some high relativistic speed relative to the slit (a case you cover yourself). $\endgroup$ – StephenG Aug 17 at 16:30
  • $\begingroup$ How near is near? A 200keV electron, typical in a TEM, already has to be treated relativistically to get the correct momentum. And, there were various 1MeV and higher TEMs made. They all got diffraction patterns just fine. $\endgroup$ – Jon Custer Aug 17 at 17:17
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The wavelength of relativistic electrons is very short, about $\lambda_{Compton}/\gamma = 2.2 pm /\gamma $. If you had a slit system of this dimension you would see the same pattern as for nonrelativistic electrons or light. Note that ordinary light is fully relativistic. However, an atom has a typical size of 100 pm so it would require neutron star conditions to create such a slit system. Never say never.

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