Given:

A light signal is emitted from a source toward a plate with a double slit (figures 1, 2 & 3). The light source is moving with respect to you the observer. The double slit is at rest.

Double Slit (at rest)

Light Source (moving)

Fig 1. Double Slit at Rest. Light Source moving down with respect to you.

Fig 2. Double Slit at Rest. Light Source moving down with respect to you.

Fig 3. Double Slit at Rest. Light Source moving down with respect to you.

The velocity of the source and the timing of the emission are such that the light signal passes through both slits at the same time according to the observer ridding with the plate. The times for the two events are recorded by red dots at the location of the clock hands (figure 4).

Fig 4. Double Slit at Rest. Light Source moving down with respect to you. Red dots at circumference of clock face indicates when the light signal was received.

Question:

What would an observer riding with the source observe?

Answer:

With respect to the source, it is the plate that is moving. That means the clocks at the two slits don’t show the same time (figure 5).

Double Slit (moving)

Light Source (at rest)

Fig 5. Double Slit moving up. Light Source at Rest with respect to you.

They are also running slower that the clock at the source. The light signal is emitted at the same time (figure 6) as before according to the source clock. Note the green dot at the location of the clock hand.

Fig 6. Double Slit moving up. Light Source at Rest with respect to you.

The plate passes the source so the light signal must “catch up to it” (figure 7). Note that the signal enters the lower slit (figure 6) and is recorded as entered by the lower clock (figure 8). Then the signal enters the upper slit and is recorded as such by its clock (figure 9). Note that both clocks ridding with the plate record the same time for the arrival of the signal (figure 10).

Fig 7. Double Slit moving up. Light Source at Rest with respect to you.

Fig 8. Double Slit moving up. Light Source at Rest with respect to you. One red dot at circumference of this clock face indicates when the light signal was received.

Fig 9. Double Slit moving up. Light Source at Rest with respect to you.

Fig 10. Double Slit moving up. Light Source at Rest with respect to you. Red dots at circumference of clock face indicate when the light signal was received.

If there was a gate on each slit and both were programmed to close at the same time, closure would either prevent or allow the signal to pass through both slits.

The geometry looks different to different observers. But if the observers get together and compare notes, they will all agree on what the three clocks recorded.