Of course they would.
Would you agree that it is reasonable to describe the distance between ourselves and the other observer, divided by the time between our observations, as the speed at which the signal is sweeping the circumference?
Yes, I imagine so.
And so for a circumference that is maybe 6,000 lightyears in length (for a pulsar 950+ ly away), and with that 6,000 ly circumference being swept more than once per second, the speed is greater than c, right?
Remember, no object is moving around the circumference; just a continuous succession of illumination events (which are followed by non-illumination, which might as well be called a shadow)
Pulses from pulsars are not redshifted.
At the risk of being socially graceless I’ll just say this.
I’m out.
This is what I mean about this thread not being serious. Instead of conceding that the example of pulsars demonstrates that shadows can move faster than c (if we want to quibble between a pulse moving and a shadow moving, note that a shadow is following behind the pulse), you pivot to new claims about redshifting and detectability.
Well, regarding detectability, the furthest detected pulsar to date is 50 million light years away and pulses once per second. That’s a circumference of 314 million light years, so the pulse is moving at ~10,000 quadrillion times c. So yeah, regardless of whether there is some maximum distance of detecting pulsars, the distances we can already see to, illustrate that pulses absolutely do sweep a circle much faster than c.
Regarding redshift, who cares? Detectability is at least relevant to the argument, the wavelength is not.
I am not sure about the pulsar thing, there may be something else to it, but I will concede that it does seem to represent a distinct shadow exceeding c.
Thank you. I know it’s tough to say that at this point in a thread. 
Thank you.
I realise that it’s maybe not completely straightforward to consider it light and shade when it’s gamma rays or X rays, but that is just different wavelengths of radiation that our meat-eyes can’t pick up (although I think there are visible light pulsars too possibly).
I think it’s important to underline that when we see something like a laser pointer dot moving on the wall and we consider two positions A and B from different times, there isn’t anything at position B that was present at position A - nothing has moved from A to B; all there is, is:
- photons illuminating A at one moment
- different photons illuminating point B later
We see it as the dot moving, but it’s just a continuum of brand new dots being made over and over in different positions - and we would still perceive it as movement if the photons at A and B were projected from different sources with whatever timing was convenient to make it look like movement (like the chasing lights on a fairground ride)
I think maybe one thing that needs to be (re-)emphasized is that relativity absolutely has no problem with a shadow appearing to move from A to B at a speed exceeding that of light. Relativity reigns in the propagation speed of influences between distinct regions of space; often, this is glossed as ‘transmission of information’, but really, it’s just putting a boundary on when something you do here can first influence what happens over there.
A shadow passing from A to B does not transmit any influence from A to B. There’s nothing anybody at A could do that, by means of the shadow passing over them, could influence what happens at B. Rather, the source of the shadow could influence things both at A and B—but that influence patently travels at most at c. The same reasoning applies for spots of light, or the spots of sequential incidence of other particles, such as droplets of water—if you’re splashed by water at A, and someone at B is getting splashed by water emanating from the same source an amount of time shorter than the propagation time of a beam of light between A and B later, there’s nothing you can do to your droplets of water that influence anything about B’s droplets. Hence, Einstein don’t care.
So, no contradiction exists, as far as relativity is concerned, between the apparent speed of a moving shadow and the cosmic speed limit. There is thus nothing to reconcile.
This is entirely separate from the question of whether we can observe a shadow appearing to move faster than light. Of course there will be challenges to such observation, because of sizes, distances, or time scales involved. But those challenges are not due to restrictions imposed by the speed of light-limit, as no such restrictions exist for this case.
That said, we can again look at the rotating half-shell occluding the sun. Yes, the shadow’s edge may be an imprecisely defined boundary, but that doesn’t mean the shadow’s propagation speed is likewise imprecise. We might imagine a ring of solar collectors (or another kind of photodetectors) arrayed around the sun at sufficient distance. For each, there will come a moment where they register zero (or, only background fluctuations). Taking account of that event, and plotting its ‘propagation’ around the perimeter, will yield an apparent speed greater than c, perfectly unambiguously.
There is no problem at all with that, as again the darkening of one detector can’t be used to influence anything at (‘send a signal to’) the point of darkening of another faster than light.
Absolutely; I’ve heard weather forecasters talking about rain in one area that will ‘move’ to another area; the clouds producing the rain might have moved (or not), but the rain didn’t; some rain fell in one place, then some other rain fell in another place; movement is a convenient way to think about change sometimes, even when the thing we’re talking about moving, isn’t.
It is pretty straightforward to send pulses of light through an appropriate medium and have their group velocity be faster or slower than the speed of light, e.g.
https://www.researchgate.net/publication/224043148_Observation_of_Superluminal_and_Slow_Light_Propagation_in_Erbium-Doped_Optical_Fiber
Yet another instance of a “spot” moving at a different velocity to the light itself.