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In LIGO, a photon beam travels in two perpendicular direction and time taken by each beam is noted. Non zero time difference is a signature of GWs here. What if I use electron beam travelling at velocity (say, 0.8c) instead of photons? Will I be able to detect GWs? I think this will not work since electrons dont travel along null geodesics. But I am not sure.

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    $\begingroup$ Electrons dont always travel at a constant velocity relative to aby observer. The LIGO experiment only works with the constant speed of c. $\endgroup$ – Jaywalker Feb 23 '16 at 7:18
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In LIGO, a photon beam travels in two perpendicular direction and time taken by each beam is noted. Non zero time difference is a signature of GWs here.

Not correct, see this description and this video, at about 27', of the web cast . It is the interference pattern, the phase difference, that generates the signal.

gravdet

Simplified operation of a gravitational wave observatory

Figure 1: A beamsplitter (green line) splits coherent light (from the white box) into two beams which reflect off the mirrors (cyan oblongs); only one outgoing and reflected beam in each arm is shown, and separated for clarity. The reflected beams recombine and an interference pattern is detected (purple circle).

Figure 2: A gravitational wave passing over the left arm (yellow) changes its length and thus the interference pattern.

The LIGO set up is made so that phases at the light detector cancel out (see video at 27'), no light arrives, unless the relative distances of the two arms change, then an interference pattern will appear in the detector.

Electrons do not build up a space wave the same way photons build an electromagnetic wave, due to the charges introducing repulsive forces and magnetic fields attractive, the probability wave describing an electron beam would need a density matrix, not a coherent sinusoidal beam with phases. Thus this experiment could not be done with electrons with any velocity.

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  • $\begingroup$ Other than being charged, is there any other reason for which it fails to solve the purpose? Can you please elaborate "why photons only". $\endgroup$ – seeking_infinity Feb 23 '16 at 14:40
  • $\begingroup$ I will repeat : the setup depends on phase differences. One cannot set up an electron beam in a coherent probability wave so as to have the corresponding phase interference.( It is also the magnetic field of a moving electron which will attract the one next to it while the same charge is repulsive, a complex problem) $\endgroup$ – anna v Feb 23 '16 at 16:44
  • $\begingroup$ I understood why we cant use electrons. But I want to know whether photons moving along null geodesics also plays a role or not? What if our beam is made up of massive but neutral particles? $\endgroup$ – seeking_infinity Feb 28 '16 at 5:28
  • $\begingroup$ To get accurate interference fringes one needs plane waves, which are provided by the lasers in LIGO. A beam of massive neutral particles will give interference fringes to the probability distribution on the screen, but their direction and momentum cannot be controlled for four kilometers, let alone no method of reflection and beam spliting will work , as they are neutral. The reflections of laser light increase the path length to thousands of kilometers. It is already hard to have four kilometer vacuum for the laser light. $\endgroup$ – anna v Feb 28 '16 at 6:13
  • $\begingroup$ " a beam of massive neutral particles will give interference fringes" needs a qualification, if it is entangled, i.e. the phases between each neutral particle is fixed in the method of generation of the beam. I cannot see an experimetal method that can do this. Maybe using magnetic moments. $\endgroup$ – anna v Feb 28 '16 at 6:23

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