On the nature of the infinite fall toward the EH

[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?

 

[zonde]

There is certain problem with the statement that falling clock will cross the event horizon in finite time. While proper time of the clock is invariant the concept of "event horizon" and therefore event of "crossing the event horizon" might turn out to be not so clearly defined and slightly more coordinate and assumptions dependant than proper time of the clock.

 

[PeterDonis]

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

No, pervect didn't do that. He said that people who think SC coordinates are privileged, do that.

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

He wasn't stating an assumption, he was stating a physical prediction of GR. That prediction doesn't involve any assumptions about whether, or where, static observers exist; you find that out by solving the EFE with the appropriate constraints. Again, it's the people who think SC coordinates are privileged who are begging the question, by assuming there have to be static observers everywhere instead of actually looking at the solution of the EFE to find out.

 

[PeterDonis]

While proper time of the clock is invariant the concept of "event horizon" and therefore event of "crossing the event horizon" might turn out to be not so clearly defined and slightly more coordinate and assumptions dependant than proper time of the clock.

Whether they "might" or not, they aren't; the event horizon is an invariant, global feature of the spacetime, and so are any events where particular worldlines cross the horizon. So this "problem" is not a problem.

 

[pervect]

CertainlyThere 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.

Actually, I think banishing the observer is a good idea. So I'd have to disagree with that "if the observer doesn't exist, we don't care about clocks". At least not in the sense that I'm talking about "an observer". "Observer" can have several meanings, the one you see to be suggesting is not at all the one I meant. I think the meaning I meant is made as clear as I can make it in the text. I''ll try to clarify - some.

In trying to make the exposition simple, entertaining, and easy to follow, I've probably sacrificed a lot of rigor. Quite possibly, even too much rigor. On the other hand, I've seen more rigorous explanations presented, which seem to just sail over everyone's head, or get ignored totally. (For instance when I mention Caroll's lecture notes. Or when I documented the historical shift in views on the topic in http://link.springer.com/article/10.1023/A:1022919909683

, the noun immediately recalls to the mind this
puzzling circumstance: during more than four decades since the discovery of the “Schwarzschild solution,” the overwhelming majority of the relativists harbored the conviction that the region within the “Schwarzschild radius” was physically meaningless, and strove to show that it could not be accessed from the outer space. During the subsequent four decades, after a seminal and nearly forgotten paper [1] that Synge wrote in 1950, an equally overwhelming majority of them
came to the conviction that the same region was physically meaningful and accessible “without a bump” along geodesics

If this doesn't convince people that the practicing view that the event horizon is "inaccessible" is outdated, I don't know what will. This quote does take the approach of "appealing to authority", though.

So - I thought I'd try something else...to see if I could explain, not just quote the literature, but to explain the logic. Furthermore, to explain in a way that didn't require math. (If people did follow the math, in my opinion we wouldn't be having this argument. It's the math, IMO, that convinced all those physicists to change their position - not the words.)

Apparently, however, the result from my experiment was not very successful - at least to date.

I will give an example in the literature about the merits of "banishing the observer" - demonstrating that the idea is possible, that it exists in the literature, and providing the rigor and dryness that I did not provide.http://arxiv.org/abs/gr-qc/9508043 "Precis of General Relativity"

A method for making sure that the relativity effects are specified correctly
(according to Einstein’s General Relativity) can be described rather briefly.
It agrees with Ashby’s approach but omits all discussion of how, historically
or logically, this viewpoint was developed. It also omits all the detailed
calculations. It is merely a statement of principles.

One first banishes the idea of an “observer”. This idea aided Einstein
in building special relativity but it is confusing and ambiguous in general
relativity. Instead one divides the theoretical landscape into two categories.
One category is the mathematical/conceptual model of whatever is happening
that merits our attention. The other category is measuring instruments
and the data tables they provide.

I would note that the author doesn't claim that the method presented is "the one true and exclusive way" to understand relativity. Their claim is more along the line of it's a way that works, and gets you to the right answers.

The second point: Misner (and I) put coordinates in the first category, the category of the mathematical model of what is going on. This is the "map" not the "territory". We put proper time in the second category, the category of measuring instruments and what they measure.

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

It _was_ a big jump.

However, the whole notion of the "clocks and rods" thing was intended to be a quick and non-rigorous summary of the traditional classical notions of the observer and his coordinate system, drawn from memory. (I suspect one can find some discussion along similar lines by Einstein, certainaly one can in MTW).

I intended it to be familiar, not something new. Since this particular observer - and - coordinate based approach doesn't actually work in this case, I didn't and don't really want to put in a lot of effort in justifying it. I'm trying to say"I think this approach is basically what you are doing, and while the idea has a lot of classical history to it, it will always fail to explain black holes, because the fundamental approach contains some false assumptions.

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

[/quote]

I just reviewed that, and I don't think I'm doing that.

[add]
Something else I should probably explain in greater detail, which is why there isn't any such thing as a stationary obserer at the event horizon. The reason is simple. The event horizion is a trapped, lightlike surface. So you can't have an "observer" there any more than you can have an "observer" sitting on a light beam.

THere's a PF Faq on why you can't have an observer ride along on a light beam. I hope this much is accepted by all, the only other thing you need to know then is that you can mark the event horizoin with a beam of light that sits there.

 

[harrylin]

FYI, concerning my post https://www.physicsforums.com/showpost.php?p=4193313&postcount=259 , PAllen insisted:

And again: I claim, along with others here, that there is no classical claim in the 2007 paper inconsistent with mathpages. This is based on understanding the math and background.[..]

I wrote to prof. Vachaspati to clarify if the classical findings in his paper are consistent with mathpages as PAllen thinks, while it is for me an obvious disagreement. His reply may be useful for some. I cited mathpages to him as follows:

"unavoidably [..] matter from the outside must reach the interior" because "an empty region around which matter "bunches up" outside an event horizon isn't viable", and "we arrive at a contradiction unless the value of m inside the horizon increases [..] in finite coordinate time." - http://www.mathpages.com/rr/s7-02/7-02.htm

Prof. Vachaspati comments (cited here with his permission):

Thanks for the interest. The issues you are discussing do seem to be all classical. Then, as you say, it is quite simple -- if you solve Einstein equations for the collapsing shell, it gives R=R_S only at infinite t.

I also asked him about his interpretation of t, and he answered:

It is true that t is a coordinate time but it is also the natural time coordinate for the asymptotic observer. In particular, the human life span is say ~100 years as measured in t. More to the point, however, is that the total energy of the collapsing body is emitted in some finite t, while the gravitational collapse takes infinite t.

Tanmay

 

[PAllen]

FYI, concerning my post https://www.physicsforums.com/showpost.php?p=4193313&postcount=259 , PAllen insisted:

I wrote to prof. Vachaspati to clarify if the classical findings in his paper are consistent with mathpages as PAllen thinks, while it is for me an obvious disagreement. His reply may be useful for some. I cited mathpages to him as follows:

"unavoidably [..] matter from the outside must reach the interior" because "an empty region around which matter "bunches up" outside an event horizon isn't viable", and "we arrive at a contradiction unless the value of m inside the horizon increases [..] in finite coordinate time." - http://www.mathpages.com/rr/s7-02/7-02.htm

Prof. Vachaspati comments (cited here with his permission):

Thanks for the interest. The issues you are discussing do seem to be all classical. Then, as you say, it is quite simple -- if you solve Einstein equations for the collapsing shell, it gives R=R_S only at infinite t.

I also asked him about his interpretation of t, and he answered:

It is true that t is a coordinate time but it is also the natural time coordinate for the asymptotic observer. In particular, the human life span is say ~100 years as measured in t. More to the point, however, is that the total energy of the collapsing body is emitted in some finite t, while the gravitational collapse takes infinite t.

Tanmay

Interesting, but it still leaves many question muddy.

Nothing he says about the classical solution is new or unusual, per se. Even, for example: "It is true that t is a coordinate time but it is also the natural time coordinate for the asymptotic observer" is also similar to statements in mathpages (see below), for example. I see no claim that the classical part is new, in result or interpretation, by itself. Then, the key point he makes to attach more fundamental meaning to the coordinate time result is: " More to the point, however, is that the total energy of the collapsing body is emitted in some finite t, while the gravitational collapse takes infinite t." . This is strictly a quantum claim - classically there is no emitted energy. This is precisely the statement that Padmnabhan disputes in the 2009 paper.

As for mathpages, I have addressed what are superficial readings of Keven Brown's sometimes complicated presentations style. For example, in addition to statements like the following (but note the point "paradox to be resolved"):

"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). To resolve this apparent paradox requires a careful examination of the definition of a black hole, and of the behavior of the Schwarzschild time coordinate near an event horizon."

You have statements like:

"We saw that the radial position of a test particle starting at radius r = 10m and t = 0 (for example) as a function of the particle’s proper time is a simple cycloid right down to r = 0, whereas if the same trajectory is described in terms of Schwarzschild coordinate time, the infalling object traverses through infinite coordinate time in order to reach the event horizon"

and: "The event horizon is in the future of every locus of constant Schwarzschild coordinate time, all the way to future infinity. In fact, the event horizon is part of future null infinity"

"Also, the Schwarzschild time coordinate is physically significant in the sense that it is the unique time coordinate in terms of which the spherically symmetrical solution is static, i.e., the metric coefficients are independent of time. In other words, the time coordinate is a Killing vector field. The existence of a singularity in a Killing vector has global significance, being a one-way causal boundary."

There are a number of specific statements in the mathpages description that I might take exception to as poorly worded, stretching a point, etc. But, I still see nothing either in mathpages or Vachaspati's strictly classical claims inconsistent with how I summarize the mainstream (which is also similar to how textbooks and Padmanabhan summarize it):

"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."

[Edit: consistent with the above, is that other researchers interpret the only significant content of the 2007 paper is the quantum claim that "evaporation completes before collapse". Either this is true, or there is nothing to the 2007 paper.]

 

[zonde]

Actually, I think banishing the observer is a good idea. So I'd have to disagree with that "if the observer doesn't exist, we don't care about clocks". At least not in the sense that I'm talking about "an observer". "Observer" can have several meanings, the one you see to be suggesting is not at all the one I meant. I think the meaning I meant is made as clear as I can make it in the text. I''ll try to clarify - some.

I am not sure I understand in what sense do you mean "observer". Your quote from http://arxiv.org/abs/gr-qc/9508043 "Precis of General Relativity" does not contain any explanation. It only says: 'One first banishes the idea of an “observer”.'

So let me explain in what sense I mean "observer" and why you can't banish "obsever" in the sense I mean it.
To do science we relay on scientific method. But how can we relate statements made about spacetime as a whole with scientific method? And as I see it we have to view worldline of someone who is using scientific method to build the model of the things he observes. And the question is what he can (and can't) observe according to the theory.

Besides we want worldline of an observer who is maximally similar to Earth observer so that we can compare our observations with theoretical predictions and potentially falsify the theory.

If this doesn't convince people that the practicing view that the event horizon is "inaccessible" is outdated, I don't know what will. This quote does take the approach of "appealing to authority", though.

This just demonstrates how unreliable is "appeal to authority" in this field.

It _was_ a big jump.

However, the whole notion of the "clocks and rods" thing was intended to be a quick and non-rigorous summary of the traditional classical notions of the observer and his coordinate system, drawn from memory. (I suspect one can find some discussion along similar lines by Einstein, certainaly one can in MTW).

I intended it to be familiar, not something new. Since this particular observer - and - coordinate based approach doesn't actually work in this case, I didn't and don't really want to put in a lot of effort in justifying it. I'm trying to say"I think this approach is basically what you are doing, and while the idea has a lot of classical history to it, it will always fail to explain black holes, because the fundamental approach contains some false assumptions.

Not sure that you understood me. You said:
A. The single reading on a single clock is about as simple as you get.
B. An "observer" is a much more complicated mental construct [than A].
C. B is much more demanding assumption than assuming basically that "clocks exist, and you can use them to measure time".

The way you say it it seems like you are implying that "single reading on a single clock exists" is as simple as "many clocks exist, and you can use them to measure time".

Well, NO.

I just reviewed that, and I don't think I'm doing that.

If you argue for possible existence of black hole then assuming that black hole (EH) exists is begging the question fallacy.

 

[Mike Holland]

Austin0, I gather that I did not reply to this post of yours. I have poseed this reply under the original topic, and am repeating it here.

Quote by Austin0
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.
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 answer here is that all points on the two time scales ARE related by the SC metric, all the points from 0 to infinity on the distant observer's clock are related to the points from 0 to T on the faller's clock, where T is his local time when he gets to the horizon. Obviously it is not a linear relationship, more like a tangent graph where tangent goes to infinity as angle goes to 90 degrees, and so they don't agree on relative elapsed times. Each sees the other's clock ticking at a different rate to his own, an ever increasing difference.

 

[Mike Holland]

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.

Yes, in their local proper time they all run at the same rate.

But consider the following thought experiment.

I will make two clocks that emit light pulses every second, and then place one at the bottom of a deep hole and one at the top. For convenience, I will assume that the Earth is not rotating, and that its mass is concentrated near the centre, so that gravity is a lot stronger at the botton of the hole.

Now I observe the light pulses coming from the two clocks, and find that they are not synchronised. I get 99 pulses on the bottom clock for every 100 on my local clock. So I infer that I have 1% gravitational time dilation present. In what way is this conclusion dependent on a coordinate system? If I position myself next to the bottom clock, I will see the same difference in rates. If I position myself 100 miles above the top clock, I will again get the same result. All I have done is count light pulses. If I am moving towards the two clocks or away from them, I may see them both pulsing faster or slower, but I will still see this 1% difference - every 100 flashes of the top clock the photons from the two clocks will arrive side by side, wherever I am along the line joining the two clocks.

So where have I assumed a simultaneity convention?

 

[PAllen]

Yes, in their local proper time they all run at the same rate.

But consider the following thought experiment.

I will make two clocks that emit light pulses every second, and then place one at the bottom of a deep hole and one at the top. For convenience, I will assume that the Earth is not rotating, and that its mass is concentrated near the centre, so that gravity is a lot stronger at the botton of the hole.

Now I observe the light pulses coming from the two clocks, and find that they are not synchronised. I get 99 pulses on the bottom clock for every 100 on my local clock. So I infer that I have 1% gravitational time dilation present. In what way is this conclusion dependent on a coordinate system? If I position myself next to the bottom clock, I will see the same difference in rates. If I position myself 100 miles above the top clock, I will again get the same result. All I have done is count light pulses. If I am moving towards the two clocks or away from them, I may see them both pulsing faster or slower, but I will still see this 1% difference - every 100 flashes of the top clock the photons from the two clocks will arrive side by side, wherever I am along the line joining the two clocks.

So where have I assumed a simultaneity convention?

This is direct observation. However, now Let's ask what Einstein's 1915 equations predict about a clock in inertial free fall towards a collapsing body of sufficient mass (inertial clock), that is engaged in communication with a distant clock. As the inertial clock nears the surface:

- The signals it gets from the distant clock may show the same rate as its own clock, be moderately slower than its own clock, or be faster - all depending on where it's fall started from, and any initial radial speed it had. This remains true all the way to the singularity - there will never be infinite blue shift measured by the the free fall clock based on signals it gets from the distant clock - right up to the singularity.

- The distant clock sees the inertial clock slow down, effectively stop, and suffer infinite red shift.

There is no contradiction because the distant observer can calculate that GR says the latter is due to gravity's effect on light and all other possible signals; and GR makes a completely unambiguous prediction about what the inertial clock will measure (even if the distant clock can never access those measurements). The ability to define gravitational time dilation disappears on approach to (and past) the horizon because there are no static (hovering) observers in reference to which it can be defined and separated from Doppler.

 

[Dale]

Now I observe the light pulses coming from the two clocks, and find that they are not synchronised. I get 99 pulses on the bottom clock for every 100 on my local clock. So I infer that I have 1% gravitational time dilation present. In what way is this conclusion dependent on a coordinate system?

This is an illogical inference. The same observed facts fit with other coordinate systems where the gravitational time dilation is not 1%.

 

[PeterDonis]

If you argue for possible existence of black hole then assuming that black hole (EH) exists is begging the question fallacy.

He didn't assume the EH exists. The existence of the EH is not assumed, it's derived by solving the EFE. What pervect was doing was pointing out an assumption made by people who deny that the EH exists: they assume that there must be a static observer everywhere in the spacetime. If you actually work through the solution of the EFE for a spherically symmetric vacuum spacetime, you find that that assumption is false. But that's not *assuming* anything; it's *deriving* it.

 

[PeterDonis]

Each sees the other's clock ticking at a different rate to his own, an ever increasing difference.

I commented on this in the other thread, but I'll repeat it here: this isn't quite correct. SC coordinates can be thought of as the "natural" ones for the distant observer, but they are not the "natural" ones for the infalling observer. So it's not really correct to equate SC coordinate values to anything the infalling observer "sees".

 

[PeterDonis]

So where have I assumed a simultaneity convention?

You've implicitly adopted one, because you've specified that both clocks are at rest relative to each other. For that special case, there is a common simultaneity convention that is "natural" to both clocks, and you've defined "gravitational time dilation" as being relative to that convention.

But as soon as you have one clock moving relative to the other, you no longer have a common simultaneity convention that's "natural" to both of them, so your definition of "gravitational time dilation" no longer works.

 

[pervect]

So let me explain in what sense I mean "observer" and why you can't banish "obsever" in the sense I mean it.
To do science we relay on scientific method. But how can we relate statements made about spacetime as a whole with scientific method? And as I see it we have to view worldline of someone who is using scientific method to build the model of the things he observes. And the question is what he can (and can't) observe according to the theory.

Besides we want worldline of an observer who is maximally similar to Earth observer so that we can compare our observations with theoretical predictions and potentially falsify the theory.

I would call the things one can measure along a single worldline "measurements". An example of what I am calling a measurement would be something similar to this. "At a proper time of xx.xxx by my clock, a signal of frequency yyy was recorded , identified as being from object zzz. The signal was decoded as having a timestamp (from object zzz) of uu.uuu.

Without going completely into the definition of an observer, I'll relate one quantity of interest that's relevant to the discussion that is not in the form of such a measurement.

This is "Event P is simultaneous with event Q".

Making such a statement requires more than just a "measurement" as I have described it. One could say that one received a signal (as above) from P and a signal from Q at the same time, but it's easy to see that this does not imply that P and Q are simultaneous - for instance P might be further away from you than Q, in which case the simultaneous receipt of signals would show that Q occurred before P.

I'm saying that making such a statement requires more structure than a "measurement" does. I was going a bit into the detail of what sort of extra structure was required - I'll repeat myself on this point a bit later.

This just demonstrates how unreliable is "appeal to authority" in this field.

It certainly doesn't demonstrate that to me! I'm not quite sure what you are thinking here. I will try to resist the obvious interpretation of "I don't like it when you bring up things that are contrary with my position."

Not sure that you understood me. You said:
A. The single reading on a single clock is about as simple as you get.
B. An "observer" is a much more complicated mental construct [than A].
C. B is much more demanding assumption than assuming basically that "clocks exist, and you can use them to measure time".

Yes. I hope the example I've given above explains the specific point in mind. I'll take the opportunity to describe in detail the set of measurements and the extra structure needed to say that "event P is simultaneous with event Q" beyond specifying the worldline of a single observer.

The particular suggestion I made (which is more or less the standard way of defining simultaneity) was that one had a chain of observers, all synchronizing their clocks by exchanging signals and using the Einstein Convention. This process of synchronzing also in general requires rate-adjusting in GR. When, according to this chain of observers , the adjusted reading for the observer in the chain co-located with P is the same as the adjusted reading for the observer in the chain colocated with Q is the same, the events are simultaneous.

The sub-point is that this statement is NOT in general independent of what chain of observers you use between P and Q. So one way of defining this extra structure, needed to talk about simultaneity, is to define this chain of observers. Which requires more than specifying the worldline of a single observer.

The way you say it it seems like you are implying that "single reading on a single clock exists" is as simple as "many clocks exist, and you can use them to measure time".

Well, NO.If you argue for possible existence of black hole then assuming that black hole (EH) exists is begging the question fallacy.

I don't feel like I should or have to argue for the "possible existence of black holes". Black holes are a part of the understanding of physics of GR. If you think that's what I am, or should be doing, that I'm "debating the existence of black holes", it may be time for me to abandon the thread.