Q-reeus said:
Ah - you may be right about a 'blip' type Doppler shift if this is referring to a dynamical aspect, where one is bouncing radar off say an orbiting planet as it passes behind the sun, or where a massive object passes across the line of sight between 'fixed' source and receiver. That should give a very small and brief kind of 'FM modulation' that symmetrically cancels as per a full sinusoidal cycle (modulation cycle that is - not one cycle of emitted radiation!). It would not exist though if source, receiver, and gravitating mass are in a fixed relation. So was that your idea?
OK, no one is yelling at me for being off topic so here goes:
Tell me if you can spot any logical errors in my thought experiment.
You have two spaceships traveling far apart form each other, but at the same velocity/direction.
They each use sophisticated celestial navigation to remain exactly the same distance from each other at all times (pretending they are in "flat" space at all times during the experiment).
Ship One
continuously (no pulses) broadcasts an ordinary, spherically radiating microwave signal set at an extremely precise fixed frequency as monochromatic as possible.
Ship Two (the observer) receives the signal and measures the frequency with extreme precision.
They both pass by the sun perfectly
tangentially, with the sun in between, so eventually the signal is blocked.
As the ships approach the sun, the apparent distance between the ships should increase at a rate which is mostly (but not a simple calculation as it is in "flat" space) proportional to the tangential velocity of the two ships with respect to the sun because the signal now has to pass through a region of space where the signal follows geodesic lines.
The two ships have to be far enough apart at all times from the sun to be in "flat" space and at
exactly the same respective gravitation potential, to eliminate any "ordinary" gravitational red-shift.
If that rate of change of apparent distance is reasonably constant, there should be a Doppler shift in the received signal which remains about the same until the sun blocks the signal.
As they regain the signal after passing the sun, the Doppler shift should still be there exactly the same as before they passed the sun.
Once the two ships get far enough away for the sun to be in "flat" space again, the Doppler shift disappears.
The key is that the ships HAVE to use celestial navigation at all times to remain the exact same distance from each other, ignoring GR space-time distortion that the radar signal passes through.
If the apparent distance change includes an apparent acceleration, then the Doppler shift should also change as the ships approach and depart the area near the sun.
The experiment then can be repeated, with Ship Two now merely reflecting the signal back to Ship One. Now, Ship One is both the source and observer. The observed Doppler shift should be exactly twice as large, no matter if there is just an apparent constant velocity OR acceleration.
Of course, the Doppler shift will be tiny, probably unmeasurable even by the finest interferometer techniques available presently. I'm also assuming that any possible gravitational lensing will be far lower in intensity than the apparent Doppler effect and that the observer ship can completely eliminate the effect of any microwave signals coming from the Sun during the experiment. That could be the fly in the ointment.
As far as relating this experiment to the thread topic, I think it is safe to assume that both ships would experience the "same now" as an abstract construct, while their instruments are
simultaneously telling them otherwise.
ha, ha, get it?
simultaneously telling them they are not in the "same now." LOL
