On the nature of the infinite fall toward the EH

[PAllen]

"My finger never ends because the foobar coordinate goes to infinity on approach to my finger tip".

That is the sum total of so many debates here. Yes, foobar length of my finger is infinite. Yes, my finger is not very long; foobar length has a limited meaning. These are compatible, not contradictory statements.

 

[rjbeery]

"My finger never ends because the foobar coordinate goes to infinity on approach to my finger tip".

That is the sum total of so many debates here. Yes, foobar length of my finger is infinite. Yes, my finger is not very long; foobar length has a limited meaning. These are compatible, not contradictory statements.

OK it's rare that I literally laugh out loud at my computer screen...

 

[Dale]

So, if anyone else here expresses any doubts that Vachaspati found as "classical GR" solution an infinite Schwarzschild coordinate time for black hole forming whereas (according to me as well as this forum in 2010) Brown argues on his pages that this is impossible, I will ask Vachaspati to clarify this point in view of the pedagogical value.

I have doubts.

 

[PAllen]

I have doubts.

About which part?

 

[Austin0]

Everyone agrees on infinite Schwarzschild coordinate time for black hole formation. Brown, and mainstream GR since 1960 supplements this statement with the understanding that this coordinate time has a limited meaning, and that if you ask what is predicted for the infalling matter you must conclude BH formation in finite clock time of the infalling clocks. And that there are many way besides SC coordinate time by which these events can be correlated with external events. This keeps circling back to the same misunderstanding explored with you in several threads and hundreds of posts here. Except in this context, you project your misunderstanding onto others.

So everyone agrees on infinite coordinate time on a static clock at infinity for BH formation or infalling approach to EH but you all keep reiterating that this coordinate time has no physical meaning and that any of us who think there are questions here are attributing incorrect meaning to this evaluation.
That the proper time of the falling clock is a finite value.

But are you not attributing equal physical meaning to the subjective time of the infaller??
Time dilation is inherently a relative evaluation. What difference does it make what the elapsed time on the falling clock is.

These were addressed to Mike Holland in the original thread but I would like your response as he didn't address them.

you say the falling observers clock is never stopped in either frame because the distant observers clock never reaches infinity.
I agree. but you seem to ignore the fact that this is only true in the region where the faller has NOT reached the singularity (The EH.)
you then want to magically have the faller PASS the horizon without ever having reached it.

It appears you interpret time dilation in a way that creates alternate contradictory realities.
If your premise that reaching the horizon requires infinite coordinate time for the distant observer is correct, that means that at all points in that interval the times at the two locations will be related by the SC metric. Both observers will agree on these relative elapsed times and both observers will agree that the faller has not reached the horizon.

the fact that the time subjectively passes normally for the faller does not affect this relationship.

Would you disagree with this?

Austin0

An analogous scenario:
As system passes that is accelerating from the distant past that now has a gamma factor of 10²⁰ At this point we "observe" a passenger starting to walk from one end to the other. A stroll requiring 10 sec of ship time.
We jump ahead an interval on the order of the age of the universe 10¹⁰ Earth years. A future observer would see the passenger in virtually the same point in the walk with an elapsed time on his watch of 0.0018 secs.
Ahead another 10¹⁰ years etc.etc.

In fact the 10 seconds on the ship would equate to approx 5.5 x 10¹³yrs.
even without factoring in the increased gamma from the acceleration over this time.

SO for the next 3,500 ages of the universe both frames will agree the passenger has not reached the far end of the ship. The fact that time appears to be passing normally for the passenger does not mean that he will ever complete his trip in the real universe.

Which is what you are suggesting here . One universe where the passenger never completes his walk (reaches the horizon) and another where he finishes his walk and moves on (reaches the horizon and moves past it)

 

[PAllen]

So everyone agrees on infinite coordinate time on a static clock at infinity for BH formation or infalling approach to EH but you all keep reiterating that this coordinate time has no physical meaning and that any of us who think there are questions here are attributing incorrect meaning to this evaluation.
That the proper time of the falling clock is a finite value.

But are you not attributing equal physical meaning to the subjective time of the infaller??

It is proper time (= time on clocks; progress of physical processes) that is the observable quantity. Coordinate time and time dilation are not measurements or observables at all.

GR gives no preference to any observer or clock. It makes the specific predictions:

- distant observer never sees anything cross 'cross' a computed radius called the event horizon. If isolated, there is a black surface infinitesimally larger than this radius.

- infalling observer crosses horizon in and reaches singularity in finite time time on their clock.

These are the unambiguous, physical predictions. They are not contradictory.

Time dilation is inherently a relative evaluation. What difference does it make what the elapsed time on the falling clock is.

No, you confuse time dilation which is not an observable at all, with the most direct physical prediction of GR: proper time = progress of any physical process that evolves. Proper time is invariant not relative. Time dilation, the non-observable quantitiy, is what varies by observer and even convention.

These were addressed to Mike Holland in the original thread but I would like your response as he didn't address them.


Would you disagree with this?

Austin0

Obviously, I disagree with almost all of it. It is just wrong.

 

[PeterDonis]

But are you not attributing equal physical meaning to the subjective time of the infaller??

No, we are attributing physical meaning to the directly observable proper time on the infaller's clock. That is not "subjective", except in the trivial sense that it's that particular observer who directly observes it. But that directly observable number is an invariant; anyone can calculate it using any coordinate chart they like that covers the appropriate portion of the infaller's worldline, and they will get the same answer.

Furthermore, the proper time on the infaller's clock is only being used to make assertions about what happens along the infaller's worldline, i.e., along the worldline where that proper time is directly observable. The coordinate time is being used, by those who make assertions about what it "means", to make assertions about what happens *elsewhere* than on the worldline of an observer "at infinity", for whom coordinate time = proper time. It's the fact that something that can only be observed on one particular worldline (and on an idealized one at that, since it's the worldline of the observer "at infinity") is being used to make assertions about the entire spacetime, that creates the problem.

Time dilation is inherently a relative evaluation. What difference does it make what the elapsed time on the falling clock is.

The assertion that's being made is not about "time dilation". It's not relative. It's an assertion that the infaller's worldline continues all the way down to the singularity, because the infaller's proper time is finite and the spacetime curvature in the infaller's vicinity is finite all the way down to the singularity. Those are physical invariants--direct observations that the infaller can make. For the claim not to be true, physics along the infaller's worldline would suddenly have to start working differently at the horizon, for no apparent reason. That's why it makes a difference what the elapsed time on the falling clock is.

Would you disagree with this?

The relationship between the elapsed time on the infaller's clock and the coordinate time is fine for the portion of the infaller's trajectory that is above the horizon. And yes, both observers will agree that the infaller has not yet reached the horizon, *on that portion of his trajectory*.

But when the infaller reaches the horizon, he "disappears" from the distant observer's coordinates, and from his "line of sight", since light rays emitted at or inside the horizon can't get back out to the distant observer. The problem arises when people try to translate "the infaller disappears from the distant observer's sight at the horizon" into "the infaller never reaches the horizon, period". That's not a valid translation.

 

[Nugatory]

But are you not attributing equal physical meaning to the subjective time of the infaller??
Time dilation is inherently a relative evaluation. What difference does it make what the elapsed time on the falling clock is?

Use a sample of radioactive material, steadily decaying according to whatever its half-life is, as your clock. Now it's easier to see that the "reading" on this clock, namely the fraction of the original material that has decayed, has real physical significance; it's not in the least bit subjective. That's proper time.

Time dilation is the ratio of proper time on a given world line to proper time on some other world line. Neither of these proper times are subjective or relative, but the ratio between them depends on which "some other world line" you choose to calculate this ratio.

 

[Dale]

But are you not attributing equal physical meaning to the subjective time of the infaller??

No. GR attributes MORE physical meaning to proper time than to coordinate time. Proper time is an invariant and objectively measurable quantity, coordinate time is a frame variant mathematical convention. They are not given equal meaning.

 

[PeterDonis]

the ratio between them depends on which "some other world line" you choose to calculate this ratio.

And also on what simultaneity convention you adopt, so that you can pick out "corresponding" events on each worldline between which you are going to calculate the proper time elapsed, for comparison.

 

[pervect]

So everyone agrees on infinite coordinate time on a static clock at infinity for BH formation or infalling approach to EH but you all keep reiterating that this coordinate time has no physical meaning and that any of us who think there are questions here are attributing incorrect meaning to this evaluation.
That the proper time of the falling clock is a finite value.

But are you not attributing equal physical meaning to the subjective time of the infaller??
Time dilation is inherently a relative evaluation. What difference does it make what the elapsed time on the falling clock is.

I'd say we've responded at length. It's just that the explanations have to all appearnces not been understood. Is it worth another try? I don't know for sure, but I'll give it One More Go.

The reading on a clock is a physical measurement. It's something you can observe directly. It's about as simple as you get. It's a good thing to take as a primitive axiomatic element, one that you can't make simpler.

One probably does idealize things a tiny bit to assume there is such a thing as a "perfect clock". Or if not "perfect", at least one "good enough" so that you can take any given measurement you desire to whatever accuracy you desire. Possibly there are hidden deep waters here (especially if you start to drag QM into the picture rather than try to view the whole affair classically) but it's really not a terribly demanding assumption.

An "observer" is a much more complicated mental construct. You not only have one physical clock (which you still assume keeps perfect time, or at least good enough time, as above), but you start imagining a whole network of virtual clocks. These clocks don't actually exist, but you imagine them as if they do. It's much more demanding assumption than assuming basically that "clocks exist, and you can use them to measure time".

You also typically assume that all the clocks are "not moving" with respect to one another. So now you imagine imaginary rigid bars connecting all the imaginary clocks.

Then you imagine that you synchronize all these clocks. Well, you immediately run into the problem that they don't all run at the same rate. You can see this from actual measurements here on Earth (as well as theoretical predictions form GR). So you start adjusting the actual clocks reading in such a way that you can synchronize them, according to some agreed-upon scheme (which generally boils down to the Einstein clock synchronization convetion) and start calling this adjustment that you need to impose "time dilation".

And you call this mental construct "reality". But it's really a rather complex structure that you've built up in your mind. And there are a lot of assumptions that go into making it all work an hang together.

When you start assuming that this mental structure is "more real" than the reading you can take on what you can imagine as a single, physical, clock, is where you start to get into trouble. One way that happens is when you start taking the "time dilation" that you had to posit to account for the fact that the clocks all ticked at different rates, as being "real" , "more real" than the actual clock reading somehow. But actually, the time dilation depends on a lot of tiny little details, involving how you set up your infinite array of non-existent mentally imagined clocks in the first place. It depends on how you set up your mental construct, it's a property of the map of reality you're trying to construct, it depends on your choice of coordinates.

But if you step back and look at the bigger picture, at least one of the implicit properties (that you can create a rigid structure of imagiary clocks that fill all of space),a property that you've just ASSUMED can be satisfied, isn't satisfied by black holes.

We've said this before, but it mostly gets ignored. Possibly because of the language used.

So, I'll repeat it with emphasis, in the hope it get's through. (Though if the problem is linguistic, rather than one of attention in such a huge, meandering thread) the emphasis might not help.

There are no static observers at the event horizon of a black hole

So, you really can't extend the "infinite stationary clocks connected by rods" sort of mental structure to encompass a black hole. The mental structure isn''t compatible.

But, having (apparently) given this rather complex mental structure "reality", the nay-sayers put it, beyond reproach, and don't think about it's flaws. And thus they say - there is no reality at the event horizon.

Some of us / many of us point out that the more primitive structrues - the idea that clocks "exist" and you can measure time with them - doesn't have any such problems, but this observation just gets pushed aside. How, I don't know. Wishful thinking is my diagnosis, to be honest.

So in short people wind up so attached to their big, complicated mental sturcture underlying the idea of "an observer" that they throw out the much simpler point about being able to use clocks to measure time, and ignore the simpler results (that don't need any such big assumptions) as being in conflict with what they want to believe.

Furthermore, the fact that you can't "see" beyond the event horizon has a significance that's generally overstated. If you can take the limit of a function you can exactingly say "the limit of proper time as you approach the event horizon is finite and can be measured by an external observer - but only in the limit".

Anyway, this turned out to be longer than I thought. I hope writing it is not as big a waste of my time as I fear it might be.

 

[pervect]

A question I thought I had answered 6 times already (in other threads), and immediately answered yet again.

Only six?
.

 

[pervect]

Is it really true that "Everyone agrees on infinite Schwarzschild coordinate time for black hole formation"? It sure seems that Brown is arguing otherwise.


http://www.mathpages.com/rr/s7-02/7-02.htm

I don't think the mathpages is peer reviewed. Not that it's awful, but even the author notes that his views are unconventional on this page.

 

[pervect]

I can't make anything else of it; but everyone can make mistakes. So, if anyone else here expresses any doubts that Vachaspati found as "classical GR" solution an infinite Schwarzschild coordinate time for black hole forming whereas (according to me as well as this forum in 2010) Brown argues on his pages that this is impossible, I will ask Vachaspati to clarify this point in view of the pedagogical value.

While you're asking Vachaspati to make clarifications, since it appears he might be the rare person you might actually listen to (I'm sorry, but I don't think you've actually listened to any of the 3-4 SA's on this thread), you might ask him if he agrees that the proper time it takes for a free-falling observer starting at rest at a large (but finite) distance away from a black hole to reach the event horizon is finite.

You might also ask him if said proper time can be observed, not directly, but as a limit, by an external observer.

 

[Mike Holland]

Then you imagine that you synchronize all these clocks. Well, you immediately run into the problem that they don't all run at the same rate. You can see this from actual measurements here on Earth (as well as theoretical predictions form GR). So you start adjusting the actual clocks reading in such a way that you can synchronize them, according to some agreed-upon scheme (which generally boils down to the Einstein clock synchronization convetion) and start calling this adjustment that you need to impose "time dilation"..

Just a little quibble. Why don't the clocks all run at the same rate? I thought that is was the time dilation that caused this situation. Time dilation is what causes the discrepancy, not what we invent after the fact to correct it. I suppose it amounts to the same thing, though.

 

[harrylin]

I have doubts.

OK! I'll keep you informed.

 

[harrylin]

While you're asking Vachaspati to make clarifications, since it appears he might be the rare person you might actually listen to (I'm sorry, but I don't think you've actually listened to any of the 3-4 SA's on this thread), you might ask him if he agrees that the proper time it takes for a free-falling observer starting at rest at a large (but finite) distance away from a black hole to reach the event horizon is finite.

You might also ask him if said proper time can be observed, not directly, but as a limit, by an external observer.

I'm very sorry as I'm not aware of any disagreements about such questions and I even explained that according to me everyone agrees on the answer to your first question above - on top of that I gave twice a link to a simulation program that nicely illustrates the same. And of course I will only ask him about the results as presented in his paper.

 

[stevendaryl]

I just read that whole link and I see nothing contradicting the statement that it takes infinite Schwarzschild coordinate time for a black hole to form. He goes to great lengths to explain exactly what this does and doesn't mean, physically, but never states anything different. He describes this as a mysterious fact that warrants explanation in light of other facts. People may be over-interpreting the following:

"Nevertheless, if mass accumulates near the exterior of a black hole's event horizon the gravitational radius of the combined system must eventually increase far enough to encompass the accumulated mass, leading unavoidably to the conclusion that matter from the outside must reach the interior, and it must do so in a way that is perceptible in finite coordinate time for a distant observer, which seems to directly conflict with Item 2 (and certainly seems inconsistent with the "frozen star" interpretation)."

However, note that he doesn't use Schwarzschild here, and calls this a paradox to be resolved.

What do you mean by "he doesn't use Schwarzschild here"? Do you mean he doesn't use Schwarzschild coordinates? That was certainly how I interpreted his statement:

...leading unavoidably to the conclusion that matter from the outside must reach the interior, and it must do so in a way that is perceptible in finite [Schwarzschild] coordinate time for a distant observer...

He doesn't say Schwarzschild coordinates, but what else would he mean by "coordinate time for a distant observer"?

It seemed to me that his whole paper was from the point of view of Schwarzschild coordinates. The issue is this: You have a black hole of mass M, and a thin spherical shell of dust, also of mass M, falling inward. The question put by the author is how the position of the shell changes as a function of Schwarzschild time coordinate t. As t → ∞, the location of the shell asymptotically approaches the Schwarzschild radius, but which Schwarzschild radius? That of the original mass M, or the eventual mass, 2M?

It's a more complex problem than the usual sort of question about things falling into a black hole, because in the usual treatment, the mass of the infalling object is considered to be negligible compared with the mass of the black hole, and so the location of the event horizon isn't changed significantly.

I seem to remember seeing an analysis once of a mass falling into a black hole which included the change in the event horizon, but I don't remember where.

 

[stevendaryl]

No. GR attributes MORE physical meaning to proper time than to coordinate time. Proper time is an invariant and objectively measurable quantity, coordinate time is a frame variant mathematical convention. They are not given equal meaning.

Just a little comment about that. I would say that proper time and Schwarzschild coordinate time are both physically meaningful, but for different reasons. Proper time is always physically meaningful, for any geometry. Schwarzschild coordinate time is physically meaningful in the context of black holes because it is a Killing vector field. Of all possible time-like coordinates in the exterior of a black hole, only the Schwarzschild time allows a time-independent metric. That's physically meaningful.

 

[stevendaryl]

What do you mean by "he doesn't use Schwarzschild here"? Do you mean he doesn't use Schwarzschild coordinates? That was certainly how I interpreted his statement:

He doesn't say Schwarzschild coordinates, but what else would he mean by "coordinate time for a distant observer"?

It seemed to me that his whole paper was from the point of view of Schwarzschild coordinates. The issue is this: You have a black hole of mass M, and a thin spherical shell of dust, also of mass M, falling inward. The question put by the author is how the position of the shell changes as a function of Schwarzschild time coordinate t. As t → ∞, the location of the shell asymptotically approaches the Schwarzschild radius, but which Schwarzschild radius? That of the original mass M, or the eventual mass, 2M?

Actually, this question has a very easy answer, from the point of view of the distant observer. Outside of the infalling shell, the effective mass is 2M, and so the usual Schwarzschild coordinates can be used with that mass. Those coordinates say that the outer surface of the shell must approach radius r = 4GM/c² asymptotically as t → ∞. So there is never a finite coordinate value for t at which the shell is inside its own event horizon.

So I don't know what the author meant when he said that "matter from the outside must reach the interior, and it must do so in a way that is perceptible in finite coordinate time for a distant observer".

 

[Dale]

Just a little quibble. Why don't the clocks all run at the same rate? I thought that is was the time dilation that caused this situation.

In an invariant sense clocks do all run at the same rate. They all run at a rate of 1 second/light-second, in an invariant sense.

In order to make a statement that they run at different rates you already have to introduce a coordinate system with a simultaneity convention. Only then can you get clocks running at different rates (1/γ) proper-second/coordinate-second.

 

[Dale]

Just a little comment about that. I would say that proper time and Schwarzschild coordinate time are both physically meaningful, but for different reasons. Proper time is always physically meaningful, for any geometry. Schwarzschild coordinate time is physically meaningful in the context of black holes because it is a Killing vector field. Of all possible time-like coordinates in the exterior of a black hole, only the Schwarzschild time allows a time-independent metric. That's physically meaningful.

But even in this case it is the invariants*, not the coordinates which are important. The Killing vector field exists in all coordinate charts and is the same geometric field in each expressing the same symmetry in each. It is only easier to calculate in the Schwarzschild coordinates.

I think what I said in 176 still holds:

That is easy. There is NO physical interpretation of ANY coordinate system (incl. SC and all of the other coordinate systems that we have discussed); what has physical interpretations are the invariants.

The purpose of any coordinate system is simply to make calculations possible or even easy. In some coordinate systems the calculation of specific invariants becomes particularly easy, but even then it is the physical invariants which are easily calculated from the coordinates which have a physical interpretation, not the coordinates themselves.

*maybe I should say "covariants" instead of "invariants", but that sounds weird

 

[PAllen]

What do you mean by "he doesn't use Schwarzschild here"? Do you mean he doesn't use Schwarzschild coordinates? That was certainly how I interpreted his statement:


He doesn't say Schwarzschild coordinates, but what else would he mean by "coordinate time for a distant observer"?

Kevin Brown has a writing style where he often poses statements shows are wrong (partly or completely) in an extended dialog. Further along on the page he not only arrives at the conclusion of infinite SC exterior time but has some nice pictures of how it looks in a representation of complete spactime. You see that the event of the horizon passing each particle is on 'sheet' of infinite SC coordinate time.

 

[stevendaryl]

But even in this case it is the invariants*, not the coordinates which are important. The Killing vector field exists in all coordinate charts and is the same geometric field in each expressing the same symmetry in each. It is only easier to calculate in the Schwarzschild coordinates.

The Schwarzschild time coordinate is the integral of the Killing vector field. So whether you're using Schwarzschild coordinates or not, the Schwarzschild time t is physically meaningful as the integral of the Killing vector field.

 

[Dale]

The Schwarzschild time coordinate is the integral of the Killing vector field. So whether you're using Schwarzschild coordinates or not, the Schwarzschild time t is physically meaningful as the integral of the Killing vector field.

The SC t coordinate additionally introduces a simultaneity convention between the different integral curves of the Killing field that is not present in the Killing field itself and which is an arbitrary convention. I stand by my previous statements: the Killing field is physically meaningful, the coordinates are not.

 

[PAllen]

Independent of the 'extra' killing vector field in the SC geometry (timelike -> static exterior; spacelike -> not static interior; 'extra' meaning in addition to the kvfs of spherical symmetry), there is a physical statement that can be made about spacetimes with horizons that is much more general than for just SC geometry (e.g. allows evolving and merging horizons, thus no timelike kvfs at all):

The union of past light cones along all timelike world lines that always include future null infinity in their future light cones, fails to cover all of spacetime. [Open universe required for this statement to be have meaning]

This can be physically interpreted as saying 'outside observers' never see or are influenced by any physical event on or inside a horizon. This observation also has a coordinate consequence: if your conventions for building coordinates requires an outside observer to receive a signal from an event in order to label it, any horizon and interior cannot be labeled at all in such coordinates (irrespective of where you assign infinite coordinate values). Exterior SC coordinates and generalizations of them for non-static exteriors happen to be of this class - they simply cannot assign coordinates to certain parts of spacetime.

If you allow building coordinates in such a way as to label events outside observers can either receive signals from or send signals to, then you can label horizons and interiors, as well as exterior, in a single coherent coordinate system [edit: there may be issues of global topology of spacetime preventing covering all spacetime, but horizons and interiors will be accessible to such coordinate conventions.]

 

[PeterDonis]

Schwarzschild coordinate time is physically meaningful in the context of black holes because it is a Killing vector field. Of all possible time-like coordinates in the exterior of a black hole, only the Schwarzschild time allows a time-independent metric.

This is not correct. As DaleSpam pointed out, Schwarzschild coordinate time uses the KVF plus a particular simultaneity convention. Other charts, such as Painleve and Eddington-Finkelstein, use the same KVF to define their time coordinates, so that the line element in all of them is independent of the time coordinate, but with different simultaneity conventions.

 

[PeterDonis]

The Schwarzschild time coordinate is the integral of the Killing vector field.

I assume you mean that integral curves of the KVF are also integral curves of the Schwarzschild time coordinate. That's true, but the Schwarzschild time coordinate imposes a particular parameterization of those integral curves which is only one of many possible ones. The Painleve and Eddington-Finkelstein charts have the same integral curves for the time coordinate, but with different parameterizations. (However, there *is* something about the Schwarzschild coordinate time parameterization which is special; see the response I'm about to post to DaleSpam.)

 

[PeterDonis]

The SC t coordinate additionally introduces a simultaneity convention between the different integral curves of the Killing field that is not present in the Killing field itself and which is an arbitrary convention.

This is true, but there is something about the SC t coordinate simultaneity convention which is special: it is the only one whose surfaces of constant time are orthogonal to the integral curves of the KVF. (Thus, the SC chart is the only chart with integral curves of the KVF as integral curves of its time coordinate, in which the line element is diagonal.) That is an invariant way of characterizing the simultaneity convention of the SC chart.

Of course, this doesn't fix any of the problems with the SC chart, such as the fact that it is singular at the horizon. It just points out that, in a curved spacetime, you probably won't be able to find a single chart that has all the properties you would like a chart to have, the way you can in flat spacetime.

 

[zonde]

The reading on a clock is a physical measurement. It's something you can observe directly. It's about as simple as you get. It's a good thing to take as a primitive axiomatic element, one that you can't make simpler.

Certainly

An "observer" is a much more complicated mental construct. You not only have one physical clock (which you still assume keeps perfect time, or at least good enough time, as above), but you start imagining a whole network of virtual clocks. These clocks don't actually exist, but you imagine them as if they do. It's much more demanding assumption than assuming basically that "clocks exist, and you can use them to measure time".

There is certain philosophical problem with your line of reasoning. If observer doesn't exist we don't care about clocks. If clocks don't exist we still care that observer exists.

Besides you jumped from single physical measurement of single clock to statement about many clocks and "measurement of time".

So, I'll repeat it with emphasis, in the hope it get's through. (Though if the problem is linguistic, rather than one of attention in such a huge, meandering thread) the emphasis might not help.

There are no static observers at the event horizon of a black hole

pervect, have you ever heard about Begging the question fallacy?