[Halc]

I see a semantic problem. We know that there is a black hole around 1600 lightyears away from us. That is well within the radius of the universe about which we can make meaningful statements (48,000,000,000 ly or thereabouts) so it is within the observable universe, even though its contents are not observable.

This statement is fairly meaningless since it mixes coordinate systems. In cosmic coordinates, the observable universe relative to Earth currently has a radius of around 48 BLY. In various different coordinate systems, that size might be a lot more or a lot less. Point is, if you're using that coordinate system, black holes don't exist. All events within black holes have no coordinates in that coordinate system. They're all in some kind of causal future of the events which comprise the current state relative to those cosmic coordinates. No black hole event can have a causal effect on an event outside, but the outside events can have a causal effect on the events inside. That puts them all in the future, and thus the problem becomes no different than being able to see Earth, 2024.

So you're right, there are events nearby (e.g. Earth 2024) which are not part of the current observable universe, but one doesn't need to invoke black holes to demonstrate this. Only events before the current time are part of it. By definition, not just events in our past light cone. The universe would be a lot smaller if restricted to only those.

It is also probably true to say that we are not observable from inside a black hole

That's quite wrong. One can observe the outside just fine from in there. You can still measure the CMB for instance, but it will be even more redshifted than what we see here.

Now if we were inside a BH, we would be subject to an incoming rain of photons from spaghettified stuff crossing the event horizon.

It's tidal forces that spaghettify you. Jump into a large enough black hole and you'd not notice the crossing of the event horizon at all. Nothing of particular note happens to you there, even if you're looking out of the window. Yes, the tidal forces would eventually kill you (inside or outside the BH) before you reach the end of time singularity.

Concerning observation of the inside of a rock, the word 'observe' in 'observable universe' uses the physics definition of observation, not the street definition. The physics definition has nothing to do with humans, eyes, or specifically light.

[Eternal Student]

Hi.

    You've got to start feeling a little concerned for @alancalverd.  It should be made clear that a lot of what they said was right, spelt correctly and quite well written.   All of it was valued.

Best Wishes.   

[alancalverd]

In cosmic coordinates, the observable universe relative to Earth currently has a radius of around 48 BLY. In various different coordinate systems, that size might be a lot more or a lot less. Point is, if you're using that coordinate system, black holes don't exist.

But we know where some of them are, in our cosmic coordinate system. Knowing the position of something that you know doesn't exist is, to say the least, inconsistent with most definitions of sanity.

No black hole event can have a causal effect on an event outside, but the outside events can have a causal effect on the events inside.

True for events inside the black hole, but haven't we detected the collision of two black holes?

[Eternal Student]

Hi.

   First of all, I think I've made a mistake.   I can only apologise.

   In post #17 I said something like this:

I'm not going to bore everyone with the integration but it'll be enough to note what the metric is telling us.    It says, that when  r ≈ rs    then  a small change in the radial co-ordinate  dr     is worth an infinite amount of distance,  ds.    To say that another way, even if we take a small step across the event horizon  (change r from  rs-dr   to  rs+dr ) that is an unbounded amount of physical distance.

    I really should have bored everyone with the integration, then we'd have got it right.   Sorry, it was too late at night when I wrote that post.  If you do it carefully,  then although we do have  ds = f(r) dr   and  f(r) → ∞   when  r → r_s    it doesn't race off to infinity too fast,  recall that for integration we have dr → 0 and overall  this integral   



remains finite.

   Anyone who's interested can find the details here:
https://physics.stackexchange.com/questions/85975/how-much-extra-distance-to-an-event-horizon

Fortunately it doesn't change too much of the spirit of what was said.   That integrand becomes imaginary when  r<r_s  which makes the distance from something inside the interior of a black hole to something outside of the event horizon an imaginary number,  i.e.  it's not an ordinary physical distance (it's a time separation).   So we still have the assertion that nothing in the interior of a black hole is included in the Observable Universe (from plant earth).

I have edited the earlier post to show I was an idiot.

Best Wishes.

[Halc]

I have edited the earlier post to show I was an idiot.

We all make mistakes. You're not an idiot for having done one, else I'd be well onto the moron end of the spectrum.
Perhaps the rest of us are the idiots for not spotting the error first (or ever had you given us time).

[evan_au]

No black hole event can have a causal effect on an event outside

haven't we detected the collision of two black holes?

The gravitational field of a black hole extends well outside the event horizon.
When two black holes are in close orbit, the rapidly changing gravitational fields shake the fabric of spacetime, radiating away angular momentum in the form of gravitational waves.
Once the two black holes have merged, and the event horizon is a single ellipsoid, the gravitational radiation abruptly ceases.

So I don't think that these two statements are contradictory.

Inside a black hole...You can still measure the CMB for instance, but it will be even more redshifted than what we see here.

Scenario 1
I think that if you were able to maintain a constant distance just outside the event horizon, the infalling CMB photons from all directions would be blue-shifted? (or equivalently, your clock would tick slower than a distant clock=Einstein shift?).
- This same effect would occur if you were just inside the event horizon (only "maintaining position" becomes impossible)

Scenario 2
If you are free-falling into the black hole from infinity, you would reach a significant fraction of the speed of light by the time you reached the event horizon, and CMB from behind you would be strongly red-shifted (=Doppler Shift). But CMB from the sides would not be red-shifted by the same amount in classical physics.
- But the time dilation would still occur, so photons from the side would be blue-shifted?

This is a horrible mish-mash of classical and relativistic physics - can you clarify these two scenarios, please, Halc?

[Halc]

No black hole event can have a causal effect on an event outside

haven't we detected the collision of two black holes?

Yes, but what we detect is radiation originating outside them. None originate from an event inside.

Keep in mind I'm not an expert, but you asked for my input.

The gravitational field of a black hole extends well outside the event horizon.

Well yes, but the gravitational field of an apple extends just as far. A field is by definition 'everywhere', but the influence on that field of said BH extends no further than that of the apple. It arguably stops at the edge of the visible universe, but it also arguably doesn't.

Once the two black holes have merged, and the event horizon is a single ellipsoid, the gravitational radiation abruptly ceases.

Fairly abrupt in terms of our ability to measure it, but technically the radiation continues 'forever' just like the radiation of a light dropped into a black hole. So it fades to immeasurability very quickly.

Inside a black hole...You can still measure the CMB for instance, but it will be even more redshifted than what we see here.

Scenario 1
I think that if you were able to maintain a constant distance just outside the event horizon, the infalling CMB photons from all directions would be blue-shifted? (or equivalently, your clock would tick slower than a distant clock=Einstein shift?).
- This same effect would occur if you were just inside the event horizon (only "maintaining position" becomes impossible)

First of all, from either of these two observation points, all of the CMB would be visible regardless of the direction from which it comes, in contrast to a telescope on Earth where Earth blocks half of it. But to the observer in question, all the light from anywhere would appear to come from a finite angle of view. If you're hovering like that, it would appear to come from the direction of acceleration, and yes, it would be blueshifted in both cases due to your near infinite acceleration rate. It would be redshifted relative to any inertial observer. Somewhere in between I suppose there's a rate of moderate acceleration where the CMB would appear the same frequency as we see here on Earth.

Yes, a clock hovering just outside the black hole runs much slower than a distant clock, just like a clock at the rear of an accelerating rocket runs slower than another clock attached to the front of it.

As for the falling clock with no proper acceleration, which one runs faster is a frame dependent thing.

Scenario 2
If you are free-falling into the black hole from infinity, you would reach a significant fraction of the speed of light by the time you reached the event horizon

Depends how you measure it. Your coordinate speed falls to zero as the EH is approached, which is a lot less than the coordinate speed of light, but still slower than the light falling in with you. So I guess one must ask 'the speed of which light?'.

and CMB from behind you would be strongly red-shifted (=Doppler Shift). But CMB from the sides would not be red-shifted by the same amount in classical physics.

The CMB is visible only from a limited angle of view as the EH is approached. I think (not sure) that CMB light coming from the side (or even from the direction you're falling) would appear just as redshifted as the stuff in the middle.

The angle of view of the outside CMB gets narrower the deeper you fall, and only shrinks to zero degrees at the singularity. They have several really nice simulations of this on youtube.

But the time dilation would still occur, so photons from the side would be blue-shifted?

Nothing blueshifted if it's freefalling.

[yor_on]

Hi.

An alternative way of stating things:

   "The observable universe" is something we can see.   We're all fairly sure that it's a real thing.

   "The Universe" is just a word with various definitions, no-one has seen it.   It's generally understood to mean  "everything, absolutely everything".    This concept on its own is not a simple one.  Can we say it's a set of things, a really big set that has everything in it?   In Mathematics, most set theories are incompatible with the existence of such a set (see  Wikipedia's entry  if you're interested     https://en.wikipedia.org/wiki/Universal_set  ).   To say this more strongly, the  ZFC system of Mathematics - which is what you would have studied at school whether you knew it by the name ZFC or not -   this does not allow the existence of such a set.

Best Wishes.

Interesting as well as funny ES, as it made me think of  https://plato.stanford.edu/entries/goedel-incompleteness/