Oppenheimer-Snyder model of star collapse

[harrylin]

This looks cool, thanks for the link!

Yes I also think that it's cool, The orbiter can be repositioned and double-clicking on it gives the energy. Seeing such nice programs encourages me to get back to doing some programming . Regretfully I don't know Java.

Now that I finally got an understanding of the "inside region" arguments, I can zoom in on the real issues - which did not go away. But before continuing I want to make sure of one thing:

[..] For the portion of the spacetime that is vacuum (i.e., outside the collapsing matter), yes. For the portion of the spacetime that is not vacuum (i.e., inside the collapsing matter), no: that portion of the spacetime is not vacuum (of course), it's [not]stationary (it's collapsing), and the boundary between it and the vacuum region is not stationary either (it's shrinking). [..] .

I think that you misunderstood. What I meant is that O-S are developing further Schwartzschild's model, which uses stationary space coordinates. That is consistent with Einstein's 1905 purpose ("the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place").
Like me, you seem to relate the motion of matter with respect to such a reference system in which space does not have a velocity vector; and my impression is that the O-S model that they presented is consistent with that.

 

[PeterDonis]

I think that you misunderstood. What I meant is that O-S are developing further Schwartzschild's model, which uses stationary space coordinates.

They use these coordinates in the first part of the paper; but in the second part of the paper they use different coordinates, ones which are comoving with the collapsing matter.

However, I wasn't making a statement about coordinates; I was making a statement about physics. The original Schwarzschild model was of a spacetime that is entirely static--nothing changes with time. The O-S model is of a spacetime that is only partially static; the region containing the collapsing matter is not static, it changes with time, and so does the radius of its boundary with the vacuum region. So if I am at a certain radius that is greater than the radius r_0 (what we would now call the horizon radius), the metric in my vicinity only becomes static once the collapsing matter falls past me to a smaller radius. That's true regardless of what coordinates I use.

That is consistent with Einstein's 1905 purpose ("the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place").

I don't have any particular problem with this, but I don't see how it's relevant to what we're discussing here. A coordinate system that is comoving with the collapsing matter doesn't have to "assign a velocity-vector to a point of the empty space", any more than a stationary coordinate system does.

 

[harrylin]

Atyy gave a for me useful reference about a nearly equivalent system with accelerating rockets, http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html#FREEFALL

The interesting phrase for me is:
"Eve could claim that Adam never reaches the horizon as far as she's concerned. However, not only is it clear that Adam really does cross the horizon".

I agree with that, but it appears for different reasons than some others.

In fact, according to 1916 GR, Eve's point of view is equally valid as that of Adam; according to that, acceleration and gravitation are just as "relative" as velocity, and their coordinate systems are valid GR systems.
However, the interpretation of what "really" happens is very different, even qualitatively; and in modern GR many people reject "induced gravitation" and agree that we can discern the difference between gravitation and acceleration.

We thus distinguish in that example that Eve's acceleration is real, and that her gravitational field is only apparent because the effect is not caused by the nearby presence of matter. For that reason I think that we should prefer Adam's interpretation. Similarly, in case of a real gravitational field that we ascribe to the presence of matter, it is Eve's interpretation that we should prefer.

Now, it is still not clear to me if O-S used what Einstein called a Gaussian coordinate system, or if they fitted two such systems together that correspond to the same interpretation, or with conflicting interpretations. So, I want to make sure that their model is self-consistent. I guess that it is; the only difference between their inner and outer region modelling is the presence of matter - correct?

 

[Dale]

However, the interpretation of what "really" happens is very different, even qualitatively; and in modern GR many people reject "induced gravitation" and agree that we can discern the difference between gravitation and acceleration.

We thus distinguish in that example that Eve's acceleration is real, and that her gravitational field is only apparent because the effect is not caused by the nearby presence of matter. For that reason I think that we should prefer Adam's interpretation. Similarly, in case of a real gravitational field that we ascribe to the presence of matter, it is Eve's interpretation that we should prefer.

The problem with this whole statement is not the different perspectives or interpretations, but the ambiguous term "real" which makes both paragraphs rather handwavy. What definition of "real" are you using, and can you demonstrate that Eve's acceleration indeed qualifies as "real" under that definition?

 

[PeterDonis]

In fact, according to 1916 GR, Eve's point of view is equally valid as that of Adam; according to that, acceleration and gravitation are just as "relative" as velocity, and their coordinate systems are valid GR systems.

For the region of spacetime that both coordinate systems cover, yes, this is true. However, if Adam's coordinate system covers a portion of spacetime that Eve's does not (in the scenario on Egan's web page, Adam's coordinates cover the entire spacetime, but Eve's only cover the wedge to the right of the horizon), then Eve's "point of view" will be limited in a way that Adam's is not.

in modern GR many people reject "induced gravitation" and agree that we can discern the difference between gravitation and acceleration.

References, please? In "modern GR", people recognize that the word "gravitation" can refer to multiple things. If it refers to "acceleration due to gravity", then "modern GR" agrees with "1916 GR" that "gravitation" can be turned into "acceleration" by changing coordinates, so both are "relative" in that sense. I don't know of anyone in "modern GR" who claims we can distinguish between "gravitation" in this particular sense and acceleration.

But if "gravitation" refers to "tidal gravity", then "gravitation" in that sense is *not* relative; it is spacetime curvature, which is a coordinate-independent thing. "Modern GR" *does* claim that "gravitation" in the sense of spacetime curvature can't be removed by choosing coordinates. However, it can be made negligible in a sufficiently small patch of spacetime by choosing coordinates appropriately. "1916 GR" said the same thing, so again "modern GR" is no different than "1916 GR" in this sense.

We thus distinguish in that example that Eve's acceleration is real, and that her gravitational field is only apparent because the effect is not caused by the nearby presence of matter. For that reason I think that we should prefer Adam's interpretation. Similarly, in case of a real gravitational field that we ascribe to the presence of matter, it is Eve's interpretation that we should prefer.

But Eve's interpretation doesn't cover all of the spacetime. That's obvious in the scenario given on Egan's web page, but you still don't appear to realize that exactly the *same* reasoning applies to the case of a black hole.

In the Adam-Eve scenario, Eve can easily compute that the proper time along Adam's worldline from when he steps off the ship to when he reaches the Rindler horizon is finite. She can also easily compute that there is nothing physically present at the Rindler horizon that would cause Adam's worldline to end there. Finally, she can compute that, once Adam reaches the Rindler horizon, he can't get back out into the region of spacetime "above" it, because to do so he would have to move faster than light. So Eve can conclude that there must be a region of spacetime beyond the Rindler horizon, where Adam's worldline goes, even though she can't see it (light rays from it can never reach her).

If Eve were hovering above a black hole, and Adam stepped off the ship and fell in, *exactly* the same reasoning would apply. You can even draw a spacetime diagram of that scenario that looks almost identical to Egan's diagram; I did it in a recent post in the other thread that we have running on this topic. So just as in the case of Egan's scenario, in the black hole scenario we can see that Adam's coordinates cover a region of spacetime that Eve's don't. *That* is the reason that Adam's interpretation is "preferred", to the extent that it is--in the region of spacetime that both Adam's and Eve's coordinates cover, neither one is "preferred"; they can both be used to describe events and calculate physical quantities, and both will give the same answers. But Eve's is limited in coverage in a way that Adam's is not.

Now, it is still not clear to me if O-S used what Einstein called a Gaussian coordinate system

Every coordinate system that I've ever seen in any relativity paper is a Gaussian coordinate system by Einstein's definition; it's a very general definition. All of the coordinates used in the O-S paper are certainly Gaussian.

So, I want to make sure that their model is self-consistent. I guess that it is; the only difference between their inner and outer region modelling is the presence of matter - correct?

Yes. The key constraint that needs to be enforced to make the model consistent is basically that the metric and its derivatives match at the boundary; the technical term is "junction conditions". (I'm not sure that specific term appears in the paper; I think it was coined later on. But I think they talk about matching at the boundary.)

 

[Mike Holland]

How can one determine the difference between gravitation and acceleration from inside a spaceship/lift? In Eve's case, she could experiment and find that the gravitation force is uniform, not focussed on a point below her, but that just means the mass is very great and very far away - within the limits of her measurements.

If we throw out the principle of equivalence, doesn't most of GR goes with it?.

Mike

 

[PeterDonis]

How can one determine the difference between gravitation and acceleration from inside a spaceship/lift?

One can't.

In Eve's case, she could experiment and find that the gravitation force is uniform, not focussed on a point below her, but that just means the mass is very great and very far away - within the limits of her measurements.

Actually, even the word "uniform" has to be carefully defined in this case. If we consider a family of observers who are at rest at different spatial locations in Eve's coordinates, they will not all feel the same acceleration; observers further away from the Rindler horizon than Eve is will feel less acceleration than Eve, while observers closer to the Rindler horizon will feel more.

The correct way to distinguish the case of Eve from the case of an Eve-like observer who is accelerating above a gravitating body is by looking at spacetime curvature. Eve can compute the components of the curvature tensor in her coordinates just as Adam can in his; both of them will get zero, indicating that the spacetime they are in is flat, so no gravitating mass is present. An Eve-like observer accelerating above a gravitating body will compute a non-zero spacetime curvature; so will an Adam-like observer who is falling towards the body. This indicates that gravitating mass is present. But these computations can't be made "locally"; that is, they can't be made just using data acquired at one event (or in a small local patch around one event). They have to be made based on measurements made at different spatial locations, and/or at different times, so that the data covers a large enough portion of the spacetime for curvature to show up (where "large enough" depends on the accuracy of the measurements).

 

[Mike Holland]

Thanks. That's what I thought. I would be really upset if anyone disproved the principle of equivalence - I think it is the most brilliant insight ever! But I am quite happy with it only working for observations made in small lifts and spaceships (including observations through the windows).

Mike

 

[harrylin]

For the region of spacetime that both coordinate systems cover, yes, this is true. However [..]

I introduced here a primer of what I want to discuss in the parallel thread to make myself understood; I will continue that part of our discussion there (and there is almost too much to catch up with there!). What I wanted to get clarified here, as it is precisely the topic:

[..] Yes [= their model is self-consistent [..]; the only difference between their inner and outer region modelling is the presence of matter]. The key constraint that needs to be enforced to make the model consistent is basically that the metric and its derivatives match at the boundary; the technical term is "junction conditions". (I'm not sure that specific term appears in the paper; I think it was coined later on. But I think they talk about matching at the boundary.) [..]

OK, thanks for that clarification - it tells me that my first impression of their paper was correct.

How can one determine the difference between gravitation and acceleration from inside a spaceship/lift? In Eve's case, she could experiment and find that the gravitation force is uniform, not focussed on a point below her, but that just means the mass is very great and very far away - within the limits of her measurements. If we throw out the principle of equivalence, doesn't most of GR goes with it?
[...] I am quite happy with it only working for observations made in small lifts and spaceships

In fact, nowadays "blind" Earth sensors can be made (detecting the field non-uniformity) that fit inside a "picosatellite" of 10x10x10cm.

GR does not depend on technical limitations of measurement nor does it forbid people to measure on more than a single point - that would make it an invalid theory from the outset.
Schwartzschild and Oppenheimer used non-local coordinates because GR does not require a "local" reference system. That does in no way affect the Einstein equivalence principle. As I cited earlier:

"K' [..] has a uniformly accelerated motion relative to K [..] [This] can be explained in as good a manner in the following way. The reference-system K' has no acceleration. In the space-time region considered there is a gravitation-field which generates the accelerated motion relative to K'."
- https://en.wikisource.org/wiki/The_Foundation_of_the_Generalised_Theory_of_Relativity

Also:
"This is by no means true for all gravitational fields, but only for those of quite special form. It is, for instance, impossible to choose a body of reference such that, as judged from it, the gravitational field of the Earth (in its entirety) vanishes.
[..]
Even though by no means all gravitational fields can be produced in this way [= from acceleration], yet we may entertain the hope that the general law of gravitation will be derivable from such gravitational fields of a special kind. "
- starting from section 20 of: https://en.wikisource.org/wiki/Rela...ument_for_the_General_Postulate_of_Relativity

 

[Mike Holland]

I had no idea we had such sensitive instruments! OK, so all we need is an infinite mass an infinite distance away. No problem!

Thanks for the references.

Mike

 

[pervect]

I ran across this on the springerlink site I mentioned in another post. The link will turn into a pumpkin - I mean get hidden behind a paywall - after Nov 30, however.

I thought it gave a good overview. My short summary & interpretation of the main point. "We know better now".

http://dx.doi.org/10.1023/A:1022919909683

One of the great conundrums in the history of general relativity is certainly constituted
by the “Schwarzschild solution.” Also to a person with a marginal interest
in the history of this discipline, 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] [Synge, J. L. (1950). Proc. R. Irish Acad. 53A, 83.] 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. This major theme, for the time span
1915–1955, has undergone a very accurate historical scrutiny [2, 3, 4].
{
[2] Eisenstaedt, J. (1982). Arch. Hist. Exact Sci. 27, 157.
[3] Eisenstaedt, J. (1986). Arch. Hist. Exact Sci. 35, 115.
[4] Eisenstaedt, J. (1987). Arch. Hist. Exact Sci. 37, 275.
}
The subsequent years, in particular the crucial sixties, still await for a like historical work.

I should add that after this introduction, the authors go on to look at a different issue, the differences between Scwarzschild's original paper and the usually quoted "SC" coordinates. The two are not the same.

 

[PeterDonis]

I should add that after this introduction, the authors go on to look at a different issue, the differences between Scwarzschild's original paper and the usually quoted "SC" coordinates. The two are not the same.

I had seen mention of this before, but this paper does a good job of explaining what was going on.

Another interesting thing I saw in this paper is the claim that restricting the range of the standard Schwarzschild r coordinate to 0 < r < infinity is an "arbitrary restriction". They reference a 1989 paper by Abrams. The argument goes like this: we start with the general line element (in slightly more compact notation than the paper uses)

ds^2 = H(r) dt^2 - F(r) dr^2 - G(r) d\Omega^2

with 0 < r < infinity because the "r" here is supposed to be the "standard" r of spherical polar coordinates with its standard range. Then we rescale the r coordinate to eliminate the function G(r), by defining r^* = \sqrt{G(r)}, so that we can rewrite the line element as

ds^2 = H(r^*) dt^2 - F(r^*) {dr^*}^2 - {r^*}^2 d\Omega^2

But the paper claims that, since G(r) was an arbitrary function, we can no longer be sure that the range of r* is 0 < r* < infinity, since we can't assume that G(0) = 0.

The reason this jumped out at me is that it is not the derivation I'm used to seeing of the standard Schwarzschild line element. The standard derivation (as given, for example, in MTW) starts by *defining* the r coordinate such that the area of a 2-sphere at r is given by 4 \pi r^2. That definition ensures that the angular part of the line element is r^2 d\Omega^2, with no other factors present.

The only reason I can see to work with a more general form of the line element with an extra function G(r) in the angular part would be if one wanted to use a *different* radial coordinate, such as the isotropic radial coordinate, for which the area of a 2-sphere at "r" is *not* 4 \pi r^2. But if you are just trying to derive the standard Schwarzschild line element, I don't see the point of doing that; it's easy to show (as MTW do) that there is no loss of generality in defining the radial coordinate as I described above as long as the spacetime is spherically symmetric, and that definition obviously requires 0 < r < infinity. I haven't seen anything in any other literature I've read about that being an "arbitrary restriction"; has anyone else?

 

[harrylin]

I had no idea we had such sensitive instruments! OK, so all we need is an infinite mass an infinite distance away. No problem!

Thanks for the references.

Mike

You're welcome - but I wonder if you understood the references. Why do you think that you would need an infinite mass an infinite distance away? It's a bit similar to an inertial reference system (with which I mean a system in uniform rectilinear motion): we do not need any literal reference body like that. Theory relates to idealizations.

 

[harrylin]

[...] I thought it gave a good overview. [..]
http://dx.doi.org/10.1023/A:1022919909683

Thanks that looks interesting!

The author seems to answer an unanswered question that I posed here:
I guess that "extension "a la Synge" means that it was Synge who proposed the inside model.

 

[pervect]

Thanks that looks interesting!

The author seems to answer an unanswered question that I posed here:
I guess that "extension "a la Synge" means that it was Synge who proposed the inside model.

There's some related stuff at:
"Schwazchild and Synge once again"
"More on the early interpretation of the Schwarzschild Solution" (Arxiv, appaently published as well)
"On the Singularities of a Riemannian Manifold", Szerkes

Synge's paper is behind a paywall still (JSTOR). Some of the above will be behind a paywall soonish.

 

[Mike Holland]

You're welcome - but I wonder if you understood the references. Why do you think that you would need an infinite mass an infinite distance away? .

The idea is to get a uniform, linear gravitationan field, so that these very sensitive instruments cannot tell the difference between it and an accelerating frame. But I was joking - that's why I said "no problem" tongue-in-cheek.

I admit the maths in the first reference is way beyond me. The second one is largely what I have read in many popular books on GR.

 

[harrylin]

The idea is to get a uniform, linear gravitationan field, so that these very sensitive instruments cannot tell the difference between it and an accelerating frame. But I was joking - that's why I said "no problem" tongue-in-cheek.

I admit the maths in the first reference is way beyond me. The second one is largely what I have read in many popular books on GR.

The first reference does not only contain math, but also a clarification of the intended physical meaning of the math. And I still wonder why you continue to get the wrong idea... One last try (as it is off-topic):

"Principle of Equivalence: If in a space free from gravitation a reference system is uniformly accelerated, the reference system can be treated as being "at rest," provided one interprets the condition of the space with respect to it as a homogeneous gravitational field. - Einstein et al, Physical Review 1935

Now tell me, how does the equivalence principle pretend that gravitational fields must be uniform or linear?

Note: Interestingly he adds the footnote that It is worth pointing out that [the resulting] metric field does not represent the whole Minkowski space but only part of it. That could be fitting for discussion in a parallel thread.

 

[pervect]

Synge's paper is behind a paywall still (JSTOR).

I should add that if one's interest is in the actual physics, rather than just history, there are plenty of modern textbooks that explain the same thing Synge's paper did - and they're probably be easaier to read and written at greater length, as well.

Some can even be found online, e.g. Caroll's lecture notes.

 

[Mike Holland]

Now tell me, how does the equivalence principle pretend that gravitational fields must be uniform or linear?

My point was simply that with these very refined instruments, an observer in a lift could detect the differences in a gravitational field from the top of the lift to the bottom, and as a result he would know he as in a gravitational field and not accelerating. To make these differences too small for him to measure, we would need a very uniform field, which is why I suggested a very large mass a very large distance away.

As long as you are observing/measuring at one point, the principle works, but when you can take measurements at two or more separate points with sufficiently sensitive instruments you can tell the difference.

Mike

 

[PeterDonis]

To make these differences too small for him to measure, we would need a very uniform field, which is why I suggested a very large mass a very large distance away.

Or we could restrict measurements to a much smaller length scale. 10cm sounds pretty small by everyday standards, but it's still 14 orders of magnitude larger than an atomic nucleus and 34 orders of magnitude larger than the Planck length.

As long as you are observing/measuring at one point, the principle works, but when you can take measurements at two or more separate points with sufficiently sensitive instruments you can tell the difference.

Yes, that's true. But conversely, given a fixed sensitivity of instruments there will be some length scale small enough that we can make measurements at two points separated by that length scale and not detect the difference.

 

[Mike Holland]

Yes, agreed. That simply means my mass need not be infinite nor infinitely far away.

But you've forgotten we are discusing an observer in a lift or spaceship! A bit more than 10cm.

 

[PeterDonis]

Yes, agreed. That simply means my mass need not be infinite nor infinitely far away.

Right.

But you've forgotten we are discusing an observer in a lift or spaceship! A bit more than 10cm.

So what? GR does not say that gravity must be indistinguishable from acceleration on length scales that are significant by our everyday standards. It only says that there is *some* length scale, however small, at which they are indistinguishable.

 

[harrylin]

I should add that if one's interest is in the actual physics, rather than just history, there are plenty of modern textbooks that explain the same thing Synge's paper did - and they're probably be easaier to read and written at greater length, as well.

Some can even be found online, e.g. Caroll's lecture notes.

In view of the discussion in the other thread, that subtopic appears to be not what people nowadays would call "actual physics" but "philosophy" or "metaphysics" - and for such, the development of thought is certainly relevant. Yesterday I found a paper by Finkelstein who also refers to a certain "Kruskaal"(sic). That may be an interesting discussion topic.

 

[harrylin]

[..] As long as you are observing/measuring at one point, the principle works, but when you can take measurements at two or more separate points with sufficiently sensitive instruments you can tell the difference.
Mike

I fully agreed with your point. We can apply the equivalence principle only as approximation for what I call real gravitational fields - such as from planets and stars. And I pointed out to you that, contrary to what Peter suggests, the Einstein equivalence principle is not concerned with that (see again my post #117).
If this remains unclear then it will need a separate thread - discussions here show that in such cases like this usually >10 posts are required, often more than 100.

 

[PeterDonis]

And I pointed out to you that, contrary to what Peter suggests, the Einstein equivalence principle is not concerned with that (see again my post #117).

So you are saying that the Einstein equivalence principle has nothing to do with real gravitational fields? Please read my post #122, in which I briefly stated how GR applies the Einstein Equivalence Principle to real gravitational fields; do you disagree with anything I said there?

 

[PeterDonis]

In view of the discussion in the other thread, that subtopic appears to be not what people nowadays would call "actual physics" but "philosophy" or "metaphysics"

In my case, at least, I've said explicitly at least once that I am only interested in the actual physics, not the history. The only reason I've been trying to pin down what you think Einstein actually said is that you appear to agree with Einstein about the actual physics, and I don't.

 

[harrylin]

In my case, at least, I've said explicitly at least once that I am only interested in the actual physics, not the history. The only reason I've been trying to pin down what you think Einstein actually said is that you appear to agree with Einstein about the actual physics, and I don't.

You misunderstood. Most people call "actual physics" that what we can verify by means of experiments.

 

[harrylin]

So you are saying that the Einstein equivalence principle has nothing to do with real gravitational fields?

Obviously I am not saying that; I do think that the explanations that I cited can't be clearer on that. Thus I cannot make sense of such a question, sorry.

Please read my post #122, in which I briefly stated how GR applies the Einstein Equivalence Principle to real gravitational fields; do you disagree with anything I said there?

While I don't disagree with it, it risks to give the wrong and ridiculous impression - as happened to Mike - of a principle that only works in a point.

 

[PeterDonis]

You misunderstood. Most people call "actual physics" that what we can verify by means of experiments.

Plus what we can conclude indirectly based on the theories that are confirmed by direct experiments. Nobody has directly observed quarks, and the standard model of particle physics says quarks can't be directly observed (and explains why this is the case); yet I doubt if any particle physicist would say that quarks aren't part of "actual physics".

If you want to say that black holes aren't part of *directly confirmed* physics, I agree. But I have been understanding you to be making the much stronger claim that black holes can't be part of actual physics period, including all the things we can indirectly conclude. We can indirectly conclude that black holes are part of actual physics because if they weren't, the Einstein Field Equation would have to stop being valid at the horizon, for no apparent reason.

If you want to say that black holes aren't part of "actual physics" because quantum effects prevent horizons from forming in the first place, that is possible, but not established. But if that is your position, it's pointless to talk about classical GR at all if we want to talk about actual physics, since you're saying that classical GR isn't the correct description of actual physics. Which means that all the talk about coordinate time going to infinity at the horizon is beside the point; that's part of the standard classical GR model. In any quantum model where the horizon is prevented from forming by quantum effects, the analog of "coordinate time" would never go to infinity at all.

So I guess I'm confused about exactly what your position is.

 

[pervect]

In view of the discussion in the other thread, that subtopic appears to be not what people nowadays would call "actual physics" but "philosophy" or "metaphysics" - and for such, the development of thought is certainly relevant. Yesterday I found a paper by Finkelstein who also refers to a certain "Kruskaal"(sic). That may be an interesting discussion topic.

A lot of the thread undoubtedly has been metaphysics. Arguing about which parts of the thread are physical and which are metaphysical is one of the parts of this sprawling thread that is metaphysical.

Meanwhile, back to my point. One doesn't need to dig up Synge's original paper to understand the actual physical predictions of GR. One only needs to read a modern textbook. The physics is very widely available, presented in a pedagogical manner.

It's not vital to see this one particular paper to understand the arguments. If one wants to understand the history, the paper would be very valuable. The history is an interesting topic - hints as to the modern solution were available as early as 1923 by LeMaitre. So why did it take so long to come to the modern understanding? But I'm afraid I don't know the answer to that. History isn't my field.

One way to get the thread back on track to physics (and out of the metaphysical morass that it appears to be bogging it down) would be to talk about and study the general properties of horizons - which occur in SR as well as GR, as a few posters have noted. (Dr. Greg, I believe.

If people actually WANT to talk about the physics, this is probably the way to go. But mostly I see entrenched positions, and a lot of debating tactics, not an actual discussion where people are trying to learn the modern view.

 

[PeterDonis]

Obviously I am not saying that; I do think that the explanations that I cited can't be clearer on that.

Ok, at least that makes your position clear.

While I don't disagree with it, it risks to give the wrong and ridiculous impression - as happened to Mike - of a principle that only works in a point.

Huh? I explicitly said that there is always some length scale--i.e., some scale larger than a point--at which the curvature can't be detected. This is because our measurements always have some finite sensitivity.

 

[Mike Holland]

In my defence :

"Principle of Equivalence: If in a space free from gravitation a reference system is uniformly accelerated, the reference system can be treated as being "at rest," provided one interprets the condition of the space with respect to it as a homogeneous gravitational field. - Einstein et al, Physical Review 1935

Now tell me, how does the equivalence principle pretend that gravitational fields must be uniform or linear?

From Wiki:
homogeneous

1.Of the same kind; alike, similar.
2.Having the same composition throughout; of uniform make-up.
3.(chemistry) in the same state of matter.
4.(mathematics) Of which the properties of a smaller set apply to the whole; scalable.

Mike

 

[harrylin]

Plus what we can conclude indirectly based on the theories that are confirmed by direct experiments. Nobody has directly observed quarks, and the standard model of particle physics says quarks can't be directly observed (and explains why this is the case); yet I doubt if any particle physicist would say that quarks aren't part of "actual physics". [..]

I meant with "actual physics" the verifiable predictions. Surely all particle physicists would agree that quarks belong to "actual theory of physics". Next we could ask to which theory or model they belong; and thus:

[..] We can indirectly conclude that black holes are part of actual [theory of] physics because if they weren't, the Einstein Field Equation would have to stop being valid at the horizon, for no apparent reason.

That is the part that I thought would be answered in this thread. However we discovered that Oppenheimer-Snyder did not get that far, and that the current answer to that question is based on additional modelling. I will therefore start a new topic on that if no-one else does.

[..] So I guess I'm confused about exactly what your position is.

I have no position about the physical reality of fully formed black holes, that is too esoteric for me. I doubt that fully formed black holes can be consistent with Einstein's GR and I suspect that GR is like beer, coming in different brands and flavours; but I think that it will require a longer discussion than this one to get to the bottom of this. Therefore I intend to start a new thread with better focus, on the compatibility of the(?) extended star collapse solution with Einstein's GR.

 

[harrylin]

A lot of the thread undoubtedly has been metaphysics. Arguing about which parts of the thread are physical and which are metaphysical is one of the parts of this sprawling thread that is metaphysical.[..]
why did it take so long to come to the modern understanding? But I'm afraid I don't know the answer to that. History isn't my field. [..]
If people actually WANT to talk about the physics, this is probably the way to go. But mostly I see entrenched positions, and a lot of debating tactics, not an actual discussion where people are trying to learn the modern view.

I can't get a clear picture of what you mean with "the modern view of physics"...
Which do you mean:
1. modern understanding of things that cannot be verified ("metaphysics")
2. modern understanding of things that are verifiable for humans on Earth ("physics")
3. ?

I expect a physics discussion forum to put the emphasis on option 2, but also permitting some discussion of the different theories and models. Insofar as any related metaphysics emerges in such a discussion, its origins should be clearly and correctly identified without indoctrination tactics - I think that that is necessary in order to keep the discussion objective.

For example, the following type of discussion can go on forever (Berne:P-A transaction) but is a waste of time:
Eve: Marx held that God doesn't exist, and he argued that religion is opium for the people.
Adam: You are wrong, just read any religious book: you should learn that they all say that God exists.

 

[Dale]

That is the part that I thought would be answered in this thread. However we discovered that Oppenheimer-Snyder did not get that far, and that the current answer to that question is based on additional modelling.

What additional modeling are you referring to? The question can be answered unambiguously with the EFE and the dustball matter distribution.

 

[harrylin]

What additional modeling are you referring to? The question can be answered unambiguously with the EFE and the dustball matter distribution.

That is the additional modelling that I am referring to, and the discussion of which I foresee as going over 100 posts.

 

[Dale]

I don't see how that is "additional", it is exactly what O and S used. Even if OS "did not get that far" in their analysis of their solution there is nothing "additional" added to the model for the modern analysis.

 

[pervect]

I can't get a clear picture of what you mean with "the modern view of physics"...
Which do you mean:
1. modern understanding of things that cannot be verified ("metaphysics")
2. modern understanding of things that are verifiable for humans on Earth ("physics")
3. ?

First of all, I don't think it's "impossible" in principle to verify. The fact that you'll almost certainly die shortly after verifying (or not verifying) the predictions that GR makes when falling into a black hole doesn't mean they can't be tested. Or calculated. It just means that you'll die shortly after verifying (or not verifying) the predictions - unless something really really unexpected happens.

Secondly , there's opportunity to apply the exact same arguments to other situations involving event horizons that don't involve black holes. Specifically, the Rindler horizon. These would be difficult to test with our current technology, though. The experiment is interesting, so I'll spell it out in more detail, since I've been alluding it to some time in the belief it was obvious (but perhaps it isn't to you? )

The experiment involves launching a spaceship that accelerates at 1g for a year shiptime - or .1g for 10 years shiptime - or .001 g for 1000 years shiptime.

The spaceship observes the Earth through a telescope. The prediction of SR in this case (you don't even need GR) that the Earth appears to fall behind an event horizon There will be some last event that the spaceship sees - say year 2100 exactly on the new years day celebration in Grenwich.

The metric from the accelerating spaceship looks like this, assuming the spaceship accelerates in the z direction. (There are some variant forms of the metric, this version is normalized so that g_uv = diag(-1,1,1,1) at the origin.

ds^2 = -(1+ gz)^2 dt^2 + dx^2 + dy^2 + dz^2


http://en.wikipedia.org/w/index.php?title=Rindler_coordinates&oldid=522511984 has the details if you're interested (but you may see minor details differ, these could be confusing).

As the observer on the spaceship watches the Earth approach New Years 2100,, the spaceship sees the image grow dimmer and dimmer, and the Earth's clocks appear to slow down. Just as it would if the Earth were falling through the event horizon of a very large black hole, as g_00 falls towards zero at the critical value z = -1/g. (In non-geometric units, that's z = c^2/g). This is the critical value because g_00 goes to zero. I believe you call it something like "time stopping?" I forget how you referred to this condition.

Now, if we apply your argument, the Earth ceases to exist in the year 2100 at new Years in some philosophically meaningful sense. At the very least, something dramatic happens on that date, as "time stops".

My position is that it's pretty obvious the Earth won't cease to exist at New Years day on the year 2100 in any sort of meaningful sense. And that the people on Earth won't even notice this, or notice anything about "time stopping" or anythign like that. In fact, they'll find New Years day 2100 quite unremarkable.

As far as modern goes, the reason I say that is the following quote that I gave earlier.

One of the great conundrums in the history of general relativity is certainly constituted
by the “Schwarzschild solution.” Also to a person with a marginal interest
in the history of this discipline, 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] [Synge, J. L. (1950). Proc. R. Irish Acad. 53A, 83.] 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.

So, basically the position you've been trying to argue and debate (as nearly as I understand it) was discredited over 50 years ago.

 

[PeterDonis]

I meant with "actual physics" the verifiable predictions. Surely all particle physicists would agree that quarks belong to "actual theory of physics".

Ok, so by "actual physics" you mean "what's directly observed", and stuff that is only known indirectly, you call "actual theory of physics". That clarifies your terminology, thanks.

A quick comment, though: you seem very quick to jump to conclusions about what people would "surely" agree to. I don't think particle physicists would say that quarks are "theoretical"; particle physicists appear to me to believe overwhelmingly that quarks are as physically real as tables and chairs. (Some, the extreme reductionists, may even believe that quarks are *more* physically real than tables and chairs, since quarks are fundamental particles and tables and chairs are not. I don't agree with that view, but it's hard not to believe that at least some physicists hold it when you see what they say and read what they write. Eddington himself delivered a famous lecture, which I think got put into his book "The Nature of the Physical World", in which he argued that the table in front of him was not real, only the atoms making it up were. I can only guess what he would have said if he'd known about quarks.) The term "actual theory of physics" doesn't seem to me to match that very well.

Next we could ask to which theory or model they belong
...
That is the part that I thought would be answered in this thread. However we discovered that Oppenheimer-Snyder did not get that far, and that the current answer to that question is based on additional modelling.

If you want to call it that. I think most people would call it simply *completing* the model that O-S left incomplete. There's nothing in the "additional modeling" that O-S themselves couldn't have done if they had just continued their own model past the horizon. But by all means start a separate thread if you want to talk specifically about the modern, completed model.

I have no position about the physical reality of fully formed black holes, that is too esoteric for me.

Ok, that's fine.

I doubt that fully formed black holes can be consistent with Einstein's GR

Then this is the part you should focus on; why do you think this? (You might also want to clarify what you mean by "fully formed black holes"; do you mean that you don't think event horizons are consistent with GR?)

and I suspect that GR is like beer, coming in different brands and flavours

Every physical theory has multiple solutions; that is, the mathematics of the theory can describe multiple scenarios, which may or may not be physically reasonable. GR is no different. What look like "different brands and flavours" to you are just different solutions to the equations; some are physically reasonable, some are not. But that discussion can continue in a new thread, as you say.

 

[harrylin]

First of all, I don't think it's "impossible" in principle to verify. The fact that you'll almost certainly die shortly after verifying (or not verifying) the predictions that GR makes when falling into a black hole doesn't mean they can't be tested. Or calculated. It just means that you'll die shortly after verifying (or not verifying) the predictions - unless something really really unexpected happens.

If you read carefully, you see that I excluded that for obvious reasons: the physics community on Earth cannot know the information from the space traveller out of a black hole zone, just as they cannot know the information about heaven from people who died.

Secondly , there's opportunity to apply the exact same arguments to other situations involving event horizons that don't involve black holes. Specifically, the Rindler horizon. These would be difficult to test with our current technology, though. The experiment is interesting, so I'll spell it out in more detail, since I've been alluding it to some time in the belief it was obvious (but perhaps it isn't to you? ) [..]

I had the impression that Atyy was the first who referred to that illustration in recent discussions; I next referred to it in this thread and started elaborating on that excellent case in the "notions" thread. In this thread I also included a brief comment by Einstein on that example (in fact, why is it called "Rindler horizon"? He was still a schoolboy when Einstein mentioned it).
Regretfully more than ever the discussion is hindered by incompatible definitions based on different schools of teaching. I intend to do a "retake" of that illustration in the new thread, with a brief summary of comments by different people, including yours.

So, basically the position you've been trying to argue and debate (as nearly as I understand it) was discredited over 50 years ago.

Not at all, as far as I understand it; but even if that were the case, your last sentence resembles the useless argument of Adam to an "Adult" question in my illustration (a "Parent" reply). The scientific approach is to scrutinise the arguments.

 

[harrylin]

[..] there's opportunity to apply the exact same arguments to other situations involving event horizons that don't involve black holes. Specifically, the Rindler horizon. These would be difficult to test with our current technology, though. The experiment is interesting, so I'll spell it out in more detail, since I've been alluding it to some time in the belief it was obvious (but perhaps it isn't to you? )

The experiment involves launching a spaceship that accelerates at 1g for a year shiptime - or .1g for 10 years shiptime - or .001 g for 1000 years shiptime. [..]

[..] Regretfully more than ever the discussion is hindered by incompatible definitions based on different schools of teaching. I intend to do a "retake" of that illustration in the new thread, with a brief summary of comments by different people, including yours. [..].

The new thread: https://www.physicsforums.com/showthread.php?p=4181348