Here is a thought experiment: Alice is traveling in a ship towards a BH. Alex, well outside the reach of BH, is recording her progress with a detector. Will he see Alice headed to BH ever disappear?

No black holes anywhere, so who cares. Not I.

Regards

Arindam:

Anyway, suppose we have a lossless tunnel of light from Earth to an object - say a working clock - moving away.
At the speed of light, whatever time the clock shows remains fixed so far as we on Earth are concerned. It is like, frozen. For the same image (phasefront) is coming at us. it is not that the clock has got stuck. It is that it appears to have got

stuck.

Beyond the speed of light, the clock vanishes, for the clock is travelling faster than light and light from the clock cannot reach us.
Below the speed of light, the clock slows down to some value between rest and speed of light.

This has nothing to do with Einstein's relativity, just practical matters.

I don't understand the relativity part in your last sentence. When clock is moving at c, and the observer is moving at c then the clock works fine when the relative velocity is zero.

okay.

However if the observer is at rest, all bets are off.

Why should that be?

Arinda:

I don't understand the part the clock appears frozen when it is moving at c.

And the observer is at v=0, yes?

Look at it this way.
Light comes to you at speed c normally.
When the object is receding at c, information via light won't come to you, or keep on coming to you.
Just one frame will be seen in a lossless pipe type scheme, say.
That is the time information, frozen.
When it is going beyond c, then not even that frame will come to you as the clock is travelling faster than light so the information via light can never reach.

Still don't get it. So if a star is moving at light speed, its light will never reach us?

Yes, yes, yes. The light from that star going away from us at the speed of light will never reach us.
Light from a star coming towards us will have a higher speed, so there will be the blueshift Doppler phenomenon.
Light from a star going away from us will be redshifted.
The Einsteinians, ignore the blueshift, such as from our neighbour Andromeda. They see only the redshift to "prove" the universe is expanding. They totally ignore the blueshift.
The Sanatana stand is the universe is eternal, and an eternal universe is naturally infinite.

Perhaps its arrival on earth will be delayed by some factor. But me thinks it will sure arrive.

Cheer up, to scientific knowledge there is no large body that travels anywhere near the speed of light.
Anyway, mathematically if s is the distance away from us of the star going away at the speed of light, then the time for light from that star to come (t=s/v) will by the distance s divided by the relative velocity, which in this case v= is c - c =0. So
time for arrival t is s/0 or infinity. No light from that star, ever. Hope this helps.

This is like saying if a source of sound moves faster than sound, its sound waves will never reach us, which is not true. For example when the concorde used to fly above us, its sound got to us much after it has flown away from us.

Good point.
The sound can only come to you when the relative velocity is above 0, is positive, going by the above example.
The concorde was supersonic, but that was only at high altitudes.
When measured by some say high rise balloon at that same altitude, there would be no sound when Concorde goes past the balloon. As the Concorde comes, there is a huge roar of very high and increasing frequency, that is, from (v_sound+v_concorde)/modS()
to (v_sound-v_concorde)/modS() - that is very very high pitched to just no sound at all.
But if you measure it from below, not at the same level, then the case is different.

To hear it, near ground its flight could not be supersonic, though nearly so, for now v=v_sound - v_concorde = something positive, so t is s/v, a high value, takes long to come, quite as you say, much after it has flown away from us.
Also, the inclination angle in this case has a bearing, but that is a longer story, for in this case the relative velocity gets affected by the angle causing increased distancing. Just as we see a plane for long in the air, but not for long if its low
flying.

Pray, enlighten me, O Master!

Hope you are satisfied, disciple.

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