The Gedanken Experiments:

Here we will look at two thought experiments that combine relativity with quantum theory. Both experiments suggest inconsistent observations for observers traveling at relative velocities.

Written 2000

Formatted 2010

 

[1] Diffraction vs. Relativistic Observers

Single Slit Diffraction

 

Imagine the standard single slit diffraction experiments from optical physics. To know how our light will diffract, all we need to know is the wavelength of the incident light, and the size of the hole in the barrier. Longer wavelengths will produce a wider spread, and narrower holes will produce a wider spread.

For our explanation we will forgo the rigorous procedural mathematics of physics and simply describe the experiment (conceptual mathematics.) Imagine 3 observers to this experiment:
  • Observer 1: sits with the apparatus in the same frame of reference
  • Observer 2: travels at relativistic speeds towards the light source
  • Observer 3: travels at relativistic speeds perpendicular to the apparatus

Observer 1 sees the light in the experiment diffracted in a SINC(X) pattern. This can be found in any basic text on physics. The distribution of light on the panel depends on the wavelength of the light and the width of the slit, as well as the distance between the slit and the panel.

When we consider the relativist Doppler shift, Observer 2, it would seem, should see a different spread to the diffraction pattern. He will see the light as a shorter wavelength (blue-shifted) and the apparatus Lorentz contracted. Both of these affects imply that the diffraction should spread less than it does for observer 1.

Diffraction pattern

Similarly, Observer 3 should see the diffraction slit as Lorentz contracted. This implies he should see the light as more spread out than the other two observers. So were is the light really? Or do the diffraction equations become invalid for relativistic observers?

 

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[2] Pair Production vs. Relativistic Observers

This problem is similar.

According to quantum physics light can spontaneously transform into matter if only its energy is high enough. This will occur when the frequency of the light has an energy (E=hv) that is higher than the energy of an electron-anti electron pair (E=mc^2).

Again, Imagine three relativistic observers.

  • Observer 1: transmits a beam at that critical frequency.
  • Observer 2: travels towards the light source
  • Observer 3: travels away from the light source

By the Lorentz-Doppler shift, Observer 2 should see a higher frequency hence greater pair production, and Observer 3 should see a lower frequency hence less, or even no pair production. How can there be more electrons (for observer 2 to see) and no electrons (for observer 3 to see) at the same time? Can the observations of all three observers be made consistent?

 
 

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