Are flowing space models compatible with GR?

[harrylin]

Are "flowing space" models compatible with GR?

Recently papers have been published with new "flowing space" models for GR. In particular a "flowing river" model by Hamilton:
http://ajp.aapt.org/resource/1/ajpias/v76/i6/p519_s1?
http://arxiv.org/abs/gr-qc/0411060

"In this model, space flows like a river through a flat background, while objects move through the river according to the rules of special relativity. "

I had the impression, years ago, that such models had been disproved because of giving predictions that do not match GR nor experiment; but perhaps this new one is different in a subtle way that escapes me.
In Einstein's GR, space, although of free choice, is taken as stationary reference, relative to which bodies are moving; it's a bit surprising for me if GR is equally compatible with a flowing space model in which a kind of ether flows like a river or waterfall relative to space.

Before starting a test example I'd like to be sure to understand it correctly:

- although Hamilton applies the model to black holes, it should work in general (such as near the Earth) if valid
- he pictures gravitation like an ether flow towards the mass
- an object at rest in the river is entirely unaffected by the flow

Is that correct?

This topic came up in another thread:

[..] Hamilton's river model's are [..] just a conceptual aid. They change not a single equation or rule for computing an observable.

That is for me the question!

 

[PAllen]

As I read this paper it is just about providing a conceptual interpretation of GP coordinates for spherically symmetric spacetime, and the Doran metric for Kerr-Newman spacetime. Everything here is interpretation of a geometry via particular coordinates and associate metric; more specifically, what these coordinates say about the local measurements of a particular class of observers. Since the geometries are well known exact solutions of GR, the coordinates and associated metrics are well known, unless there are gross mathematical errors, I don't understand how one can even talk about 'different predictions' or 'right versus wrong'. There is only the question of helpful vs. non-helpful, which is personal choice.

 

[Dale]

To further what PAllen said, my understanding is that this specific interpretation is limited to the coordinates mentioned above. It does not necessarily apply to other spacetimes in general. So I don't think that you can consider this model to be any kind of an alternative to GR, just a nice conceptual aid for certain coordinates.

 

[harrylin]

As I read this paper it is just about providing a conceptual interpretation of GP coordinates for spherically symmetric spacetime, and the Doran metric for Kerr-Newman spacetime. Everything here is interpretation of a geometry via particular coordinates and associate metric; more specifically, what these coordinates say about the local measurements of a particular class of observers. Since the geometries are well known exact solutions of GR, the coordinates and associated metrics are well known, unless there are gross mathematical errors, I don't understand how one can even talk about 'different predictions' or 'right versus wrong'. There is only the question of helpful vs. non-helpful, which is personal choice.

The issue is GR-compatible interpretation; does that mean YES to my three questions?

 

[harrylin]

To further what PAllen said, my understanding is that this specific interpretation is limited to the coordinates mentioned above. It does not necessarily apply to other spacetimes in general. So I don't think that you can consider this model to be any kind of an alternative to GR, just a nice conceptual aid for certain coordinates.

Then it is supposed, as I assumed, to work with the Earth's field - right?

 

[Dale]

Yes, neglecting any small deviations from the ideal symmetry.

 

[PAllen]

The issue is GR-compatible interpretation; does that mean YES to my three questions?

I don't understand what you mean by GR-compatible interpretation. If equations and predictions are the same, what would be a non-GR compatible interpretation?

Yes, to the first of your questions. Any spacetime that can be sufficiently closely modeled by SC geometry or Kerr-Newman geometry can use this interpretation. Near Earth qualifies, as does near sun.

I refuse to answer the second because I don't sufficiently understand what you mean by aether; Hamilton makes one aside reference to this in the text, and refers to one paper in the notes. Thus, I don't know the overalap between his and your concepts.

On the third question: yes for a sufficiently small object. The model, as I understand it, accounts for tidal forces by different river velocity in different places. So an object of any finite size will undergo tidal stresses, as required by GR.

 

[PeterDonis]

In Einstein's GR, space, although of free choice, is taken as stationary reference, relative to which bodies are moving

What (I think) you mean by "space" here is not what the river model means by "space" as in "space is flowing into the black hole." The "space" in the sense of "the spatial coordinates in the Painleve chart" is not flowing inward; a given radial coordinate r refers to the same 2-sphere (i.e., the same "distance from the hole") at all times. The "space" that is flowing inward is something different, a "space" constructed from the frame fields of Painleve observers.

- although Hamilton applies the model to black holes, it should work in general (such as near the Earth) if valid

Yes. It works for the exterior vacuum region around any static, spherically symmetric gravitating body. Of course, in the case of the Earth, the inward "river velocity" never gets anywhere close to the speed of light.

- he pictures gravitation like an ether flow towards the mass

Kinda sorta; the term "ether flow" may have lots of undesirable connotations.

- an object at rest in the river is entirely unaffected by the flow

Except in so far as the flow "carries" it inward.

That is for me the question!

The river model is an *interpretation* of GR, not a different theory. (More specifically, it's an interpretation to help you visualize the gravity of a static, spherically symmetric body, based on using Painleve coordinates to describe the field.) All of the equations are the same as for Painleve coordinates (since they *are* the equations of Painleve coordinates), and all the observables are the same as GR (since they *are* the observables predicted by GR).

 

[pervect]

I'm not terribly fond of the "flowing river of space-time" model that Hamilton has. But - it is a better alternative than the time stops at the event horizon" model. Which I gather was his main intention. (I had an opportuity to talk to him over a wiki article some time back. As I recall he complained he had some trouble getting it published).

The main reason I'm not fond of the model is that there isn't any way to build a "space-flow-o-meter" to detect flowing space-time. So it's really more of a mental crutch or visual aid, not something you can measure. It's probaby a better visual aid than "stopping time" though.

 

[Pierre007080]

As a "popular physicist" I find the Flowing Space model extremely useful. It ties in with Einstein's insistence that the free falling frame is inertial. With the modern developments ascribing energy and various fields to "vacuum" I cannot understand the way everybody treads so lightly around the aether issue.
The concept that EVERYTHING (including space with it's structural fields, Higgs field, dark matter and dark energy) is being attracted by a massive body and all moving at the same velocity seems a fact that cannot be reasoned away and a better place to start understanding gravity than the complicated equations of GR that only a few can make sense of.
What are the simplistic issues that disproves this model? Be gentle Guys!

 

[harrylin]

I don't understand what you mean by GR-compatible interpretation. If equations and predictions are the same, what would be a non-GR compatible interpretation?

Yes, to the first of your questions. [..] Near Earth qualifies, as does near sun.
[..] the second because I don't sufficiently understand what you mean [..]
On the third question: yes for a sufficiently small object. [..]

Thanks. My purpose with this thread is to understand how such a model can give GR predictions, by means of a simple example in a post later today. For the second question, PeterDonis gives some valuable feedback:

What (I think) you mean by "space" here is not what the river model means by "space" as in "space is flowing into the black hole." The "space" in the sense of "the spatial coordinates in the Painleve chart" is not flowing inward; a given radial coordinate r refers to the same 2-sphere (i.e., the same "distance from the hole") at all times. The "space" that is flowing inward is something different, a "space" constructed from the frame fields of Painleve observers. [..]
It works for the exterior vacuum region around any static, spherically symmetric gravitating body. Of course, in the case of the Earth, the inward "river velocity" never gets anywhere close to the speed of light. [..]

This may be the issue; however as you next formulate it, sounds exactly as I understood it.

To elaborate, I understood it as an imaginary inward flow relative to a static coordinate background, such that SR can be applied relative to that imaginary inflowing medium. According to an observer on Earth the total effect is then the combined effect of "inflow" plus SR effects relative to the "river".

 

[harrylin]

I'm not terribly fond of the "flowing river of space-time" model that Hamilton has. But - it is a better alternative than the time stops at the event horizon" model. Which I gather was his main intention. [..]

It's exactly that issue that triggered this thread; for me it is evident that the two models are first of all incompatible as interpretation goes, and I don't get how they can give the same predictions.
Einstein's model gives that, as interpreted from a distant system, the resonance frequency of an object in free fall near a black hole goes to zero. As a matter of fact, Einstein's GR corresponds to a modified Lorentz ether (as long as one stays away from extremes such as black holes).
In contrast, Hamilton's "flowing river" model gives that, as interpreted from a distant system, the resonance frequency of an object in free fall near a black hole is completely unaffected (correct?). If the river model is like I think, then it can't work and the experts are stupid for not having noticed (or more nicely put: I would be much smarter than them). Much more likely is that I misunderstand it, and I want to know what.

As a "popular physicist" I find the Flowing Space model extremely useful. It ties in with Einstein's insistence that the free falling frame is inertial. [..] The concept that EVERYTHING (including space with it's structural fields, Higgs field, dark matter and dark energy) is being attracted by a massive body and all moving at the same velocity seems a fact that cannot be reasoned away and a better place to start understanding gravity than the complicated equations of GR that only a few can make sense of.
What are the simplistic issues that disproves this model? Be gentle Guys!

What Einstein argued is not at all like a free falling space if I understand what Hamilton means with that. It's a bit subtle; for example Hamilton's "river" can exceed the speed of light near a black hole in our galaxy. But I think that it's time to grab the bull by the horn and discuss a simple example (next post; I now came up with an extremely simple test case, but later today as I must work now).

PS. For a really simple model that doesn't match GR exactly (but it should match all experiments so far), see my new thread here: https://www.physicsforums.com/showthread.php?t=647616

 

[PAllen]

It's exactly that issue that triggered this thread; for me it is evident that the two models are first of all incompatible as interpretation goes, and I don't get how they can give the same predictions.
Einstein's model gives that, as interpreted from a distant system, the resonance frequency of an object in free fall near a black hole goes to zero. As a matter of fact, Einstein's GR corresponds to a modified Lorentz ether (at least far away from black holes).
In contrast, Hamilton's "flowing river" model gives that, as interpreted from a distant system, the resonance frequency of an object in free fall near a black hole is completely unaffected (correct?). If the river model is like I think, then it can't work and the experts are stupid for not having noticed. Much more likely is that I misunderstand it, and I want to know what.

Somehow, you need to be more precise about what incompatibility you see (perhaps in your upcoming post). As I see it, we have the same solution under discussion (the SC geometry). For this, we have multiple coordinates we can place on it (like rectilinear and polar on a flat plane). For one of these coordinates (GP coordinates), you can use an analogy to describe the experience of specific class of local frames as flowing in a river, and describe other local frames in relation to these (via SR). There is only one set of physical laws involved: the EFE globally; SR locally. I remain unable to conceive of conflict.

Maybe the key is here: "Einstein's model gives that, as interpreted from a distant system, the resonance frequency of an object in free fall near a black hole goes to zero. As a matter of fact, Einstein's GR corresponds to a modified Lorentz ether (at least far away from black holes)"

This is wrong. Or, at best, it takes approximate treatment of one solution as the whole theory. Only in your mind have I ever seen Einstein so maligned as to confuse an approximate treatment of a special case of his own theory as the whole thing.

What you say about distant regions is an approximation. Useful, perhaps, but not = to the theory as a whole.

What you say about resonant frequency is nonsense. Even for earth, we don't talk about the resonant frequency of hydrogen in a valley being different from the resonant frequency on a mountain top. We say they are locally unchanged. However, hydrogen emissions, decay rates etc. for an object in the valley observed from a mountain are reduced. This is of the same character as Doppler, and, in fact, the mathematical basis of all Doppler in GR is the same [I have described the math to you in another thread; I will repeat here if you request]. Treated in an exact manner, there are not two (or three) types of Doppler, but only one. Separating them is purely a computational convenience for special cases. Special case does not equal general case.

To sum:

1) GR, in no form, or coordinates, says the resonant frequency of hydrogen changes as it approaches an EH. The axiom of 'locally SR physics' is built into the mathematical framework of GR (that the tangent plane at every point has Minkowski metric).

2) There is no upper bound to Doppler factor between source and target, and in a variety of ways you can get infinite Doppler, and horizons: a uniformly accelerating rocket will have a horizon with infinite Doppler. A distant observer will see infinite Doppler for an object approaching an EH. There is a great similarity between these two cases. In both cases, that one observer (accelerating rocket; observer away from BH) sees a horizon has no bearing on what a different observer sees (in both cases, the 'horizon observer' observer has no specific awareness of the horizon seen by the other, and sees no sudden change in light frequency as they cross the horizon; this fact can be derived in all coordinates, even SC coordinates using limiting arguments).

3) There is no difference in character between mountain to valley Doppler on Earth versus approach to an EH. There is only difference in degree. We don't require that that valley dweller consider time to be truly slower for them.

 

[PAllen]

What Einstein argued is not at all like a free falling space if I understand what Hamilton means with that. It's a bit subtle; for example Hamilton's "river" can exceed the speed of light near a black hole in our galaxy. But I think that it's time to grab the bull by the horn and discuss a simple example (next post; I now came up with an extremely simple test case, but later today as I must work now).

The "river" exceeding the speed of light is analogous to an expanding universe solution with > c recession velocity between co-moving observers. In no way is it inconsistent with GR as Einstein understood it.

Again, it seems you have a personal theory (not just interpretation) that you derive from over-interpreting selected Einstein approximate computations for special cases; and you seem to believe this is the 'real GR' per Einstein.

 

[PAllen]

Let me be even clearer on what seems a key point:Gravitational time dilation is a computed, coordinate feature that can be defined only in near static spacetime regions. It if very useful computationally, but is not a physical observable at all, ever.

What is an observable, and never requires the concept gravitational time dilation to compute, is Doppler. The Doppler factor in GR as in SR affects both signal frequency (and therefore, any other distantly observed clock rate as well) and wavelength.

Note that these statements apply almost verbatim to frame dependent time dilation versus Doppler in SR.

 

[harrylin]

Sorry, I made it too simple: originally I had in mind something like Gravity probe A, but now simplified it to a high tower with clocks.

However, with a high tower it is clear to me that such a river flow model should work: If I correctly understand it, in Hamilton's model the ground clock will have more SR time dilation than the top clock (correct?).

It should be an example that is more like gravity probe A but still simple enough for a forum discussion. I'll be back!

 

[PAllen]

Sorry, I made it too simple: originally I had in mind something like Gravity probe A, but now simplified it to a high tower with clocks.

However, with a high tower it is clear to me that such a river flow model should work: If I correctly understand it, in Hamilton's model the ground clock will have more SR time dilation than the top clock (correct?).

It should be an example that is more like gravity probe A but still simple enough for a forum discussion. I'll be back!

Correct.

If you are planning on bringing in rotation effects, you will need to understand the Doran metric part of Hamilton's article. I have not read this part through, myself yet. The 'river' gets complicated for the rotating case.

Also, recall Dalespam pointed out in #3: this is the limit of Hamilton's interpretation. He has not proposed any way to apply it to a more general scenario than an ideal rotating, massive gravitational source.

[edit: wait, it was probe B that was about rotational effects. Probe A was just a precise, scaled up, version of the tower scenario (using rocket and maser). I see it as exactly the same case. ]

 

[zonde]

This is wrong. Or, at best, it takes approximate treatment of one solution as the whole theory. Only in your mind have I ever seen Einstein so maligned as to confuse an approximate treatment of a special case of his own theory as the whole thing.

Well you see, in SR any inertial frame is valid and it does not come into conflict with any other inertial frame. We can relate this with global one-to-one mapping.

This does hold for different coordinate maps for black holes.

And yet another thing is that these BH coordinate maps describe highly symmetric eternal objects i.e. their past is symmetric with their future. This is very special case. And basically not interesting as we believe that all BH have formed in finite past.
How many of these BH coordinate charts will fail miserably when applied to BH with finite past?

 

[zonde]

As I see the river model I don't see how it can work.

First to talk about river model we map GR curved spacetime to flat spacetime and introduce some medium who's properties cover up for effects described by curvature of spacetime.
So we have that some property (let's assume it is density) determines coordinate speed of light.
And as we talk about river model we have flux of that medium. But in order to have constant density we have to have dynamic equilibrium and that means that we have the same flux as we go closer and closer to gravitating object. And flux per surface unit increases as inverse square law.

So we have coordinate speed of light changing as a function c=k*(1/r^1/2) while flux changes as k*(1/r²).
And I just don't really see how to connect these two function in physically meaningful way.

Please note that I don't say it's impossible. I just don't see a way.
Actually it feels like one possibility should still be explored. When we map curved spacetime to flat one we take coordinate r from GR coordinate charts and carry it over to flat coordinates i.e. we take projection of curved spacetime to flat one. But maybe we can use conformal map from curved spacetime to flat one? And that even seems mathematically more justified.

 

[PAllen]

Well you see, in SR any inertial frame is valid and it does not come into conflict with any other inertial frame. We can relate this with global one-to-one mapping.

This does hold for different coordinate maps for black holes.

And yet another thing is that these BH coordinate maps describe highly symmetric eternal objects i.e. their past is symmetric with their future. This is very special case. And basically not interesting as we believe that all BH have formed in finite past.
How many of these BH coordinate charts will fail miserably when applied to BH with finite past?

On your last question, none of them.

On your observations, I genuinely don't understand your point. What I was arguing against was apparent claim that free faller and distant observer represented two disconnected 'realities' rather than two equally valid observational points of view for the same overall universe. The SR analogy clearly favors the latter point of view.

 

[PAllen]

As I see the river model I don't see how it can work.

First to talk about river model we map GR curved spacetime to flat spacetime and introduce some medium who's properties cover up for effects described by curvature of spacetime.
So we have that some property (let's assume it is density) determines coordinate speed of light.
And as we talk about river model we have flux of that medium. But in order to have constant density we have to have dynamic equilibrium and that means that we have the same flux as we go closer and closer to gravitating object. And flux per surface unit increases as inverse square law.

So we have coordinate speed of light changing as a function c=k*(1/r^1/2) while flux changes as k*(1/r²).
And I just don't really see how to connect these two function in physically meaningful way.

Please note that I don't say it's impossible. I just don't see a way.
Actually it feels like one possibility should still be explored. When we map curved spacetime to flat one we take coordinate r from GR coordinate charts and carry it over to flat coordinates i.e. we take projection of curved spacetime to flat one. But maybe we can use conformal map from curved spacetime to flat one? And that even seems mathematically more justified.

I don't understand how what you say above relate to the river model. The river model says the speed of light for frame carried with the flow is always c. Behavior for a local frame moving relative to a 'carried' frame is given my SR formulas.

The apparent slow down of light emitted near horizon as perceived by a distant observer comes from this light 'fighting the river flow' to get the the distant observer.

Can you explain what you mean about flux? I see nothing about this in Hamilton's paper.

Further, I note that this model really cannot be wrong because it is just geometry using GP coordinates; any observable comes out the same as SC coordinates by pure mathematical construction. Please don't bring into this thread your rejection coordinate independence of GR observables.

 

[harrylin]

As I see the river model I don't see how it can work.[..]
Please note that I don't say it's impossible. I just don't see a way.
Actually it feels like one possibility should still be explored. When we map curved spacetime to flat one we take coordinate r from GR coordinate charts and carry it over to flat coordinates i.e. we take projection of curved spacetime to flat one. But maybe we can use conformal map from curved spacetime to flat one? And that even seems mathematically more justified.

I almost fully agree, but for a different reason which I will explain with a simple thought experiment. Einstein's GR is compatible with a modified Lorentz ether model just as he explained; with such a model one can use for experiments on Earth the ECI frame and SR, plus GR corrections for height. That is exactly the kind of mapping that Gravity probe A used and also what GPS uses for its satellites; it is not something that "should still be explored". Thus it was paradoxical for me that a kind of flowing ether model could give the same results. Of course, for example a voltage source can be replaced by a current source with the same effects, so I searched if I could come up with an example thought experiment where the effect is different according to my understanding; and I now came up with such a test case.

Please be a little patient as I have a life with a job and I want to do better than most posters who come with such questions by making it as simple as possible (without making it too simple, which I did yesterday) and plugging in numbers with (IMHO) correct calculations.

 

[zonde]

I don't understand how what you say above relate to the river model. The river model says the speed of light for frame carried with the flow is always c. Behavior for a local frame moving relative to a 'carried' frame is given my SR formulas.

The apparent slow down of light emitted near horizon as perceived by a distant observer comes from this light 'fighting the river flow' to get the the distant observer.

Can you explain what you mean about flux? I see nothing about this in Hamilton's paper.

Yes, the things about density where out of place. Sorry for my error.
But let me fix my error. Let's say we want to find out at at what speed the river is flowing. As time dilation is related to speed of river flow we can write time dilation as function of that speed using SR:
$$d=\sqrt{1-\frac{v^2}{c^2}}$$
But GR tells us what is time dilation as function of distance from gravitating body:
$$d=\sqrt{1-\frac{r_0}{r}}$$
So we can write speed of the river flow as function of distance from gravitating body:
$$\sqrt{1-\frac{v^2}{c^2}}=\sqrt{1-\frac{r_0}{r}}$$
$$\frac{v^2}{c^2}=\frac{r_0}{r}$$
$$v=c\;\sqrt{\frac{r_0}{r}}$$
But because the surface that the river is flowing trough is reduced as we approach gravitating body it should be speeding up. And that increase should follow inverse square law as speed of the river flow should be inversely proportional to the surface it is flowing trough.
$$v=k\;\frac{1}{r^2}$$

Two functions are obviously different as one contains r^-1/2 but the other one r^-2. Hence it doesn't work.

 

[PAllen]

Yes, the things about density where out of place. Sorry for my error.
But let me fix my error. Let's say we want to find out at at what speed the river is flowing. As time dilation is related to speed of river flow we can write time dilation as function of that speed using SR:
$$d=\sqrt{1-\frac{v^2}{c^2}}$$
But GR tells us what is time dilation as function of distance from gravitating body:
$$d=\sqrt{1-\frac{r_0}{r}}$$
So we can write speed of the river flow as function of distance from gravitating body:
$$\sqrt{1-\frac{v^2}{c^2}}=\sqrt{1-\frac{r_0}{r}}$$
$$\frac{v^2}{c^2}=\frac{r_0}{r}$$
$$v=c\;\sqrt{\frac{r_0}{r}}$$
But because the surface that the river is flowing trough is reduced as we approach gravitating body it should be speeding up. And that increase should follow inverse square law as speed of the river flow should be inversely proportional to the surface it is flowing trough.
$$v=k\;\frac{1}{r^2}$$

Two functions are obviously different as one contains r^-1/2 but the other one r^-2. Hence it doesn't work.

This is nonsense. The river is not a material fluid following fluid flow laws. It is a flow of imaginary (figurative sense, not √ -1) space, and its laws are as derived in the paper. In this regard, your first calculation is correct, and is consistent with equation (2) of the paper. Your second is something you made up that is wrong. You have refuted a nonsensical straw man.

 

[PAllen]

Einstein's GR is compatible with a modified Lorentz ether model just as he explained; with such a model one can use for experiments on Earth the ECI frame and SR, plus GR corrections for height. That is exactly the kind of mapping that Gravity probe A used and also what GPS uses for its satellites; it is not something that "should still be explored".

I am curious to see this claim of Einstein in context. I suspect I would interpret it quite differently from you. Do have a reference?

The rest of the context you are discussing is not GR as a whole, but one specific simple solution that is maximally Newtonian (e.g. can be modeled with an effective potential depending only on position). Over and over you seem to draw an equality between this one solution, and comments Einstein may have made in respect to this one solution, as if they were the full content of the theory.

As to the specifics of interpreting this solution via the river model, this solution is exactly the one it was first designed for (then extended, with some difficulty, to the rotating perfect BH case). I don't understand how you can read the paper and not see the exact mathematical equivalence. All you do is transform between GP coordinates and SC coordinates.

Do you really believe using different coordinates to compute observables (which are all defined as invariants) can produce a different result?

 

[zonde]

This is nonsense. The river is not a material fluid following fluid flow laws. It is a flow of imaginary (figurative sense, not √ -1) space, and its laws are as derived in the paper. In this regard, your first calculation is correct, and is consistent with equation (2) of the paper. Your second is something you made up that is wrong. You have refuted a nonsensical straw man.

I am inclined to wait for harrylin's thought experiment before any further discussion.

 

[harrylin]

OK, I figured it out now. I was thinking of a falling clock from a tower, and at first sight it looked to me as if that could reveal a difference in prediction.

However, the "river flow" model is in a certain sense the equivalence principle put on its head. As a result, it may be expected to give the same predictions at least in a number of basic cases - and I now also see why this will be so for a falling clock: I had overlooked that the ECI frame synchronisation is "right" according to convention but "wrong" according to the river model. [EDIT, precision: in a river model, the downward speed of light differs from the upward speed of light relative to the Earth]. That leads, as I now understand it, also according to Hamilton's model to an apparent clock retardation of the falling clock according to an Earth observer. Thus I still find phenomenologically no difference with GR. Note that I didn't bother to plug in numbers, because I now see that it should work based on the equivalence principle.

It's a bit similar to Lorentz's stationary ether which gives the same predictions as SR, and which is in that sense compatible with SR. If we similarly stick to GR without Einstein's metaphysics (Einstein's GR is strictly speaking a field theory which corresponds to a very different ether model)*, then we can also say that Hamilton's flowing ether model is compatible with GR for a number of situations.

Thus it appears that two conflicting "ether" models are largely compatible with GR (I notice that nobody claims perfect correspondence). They correspond to the same testable phenomena but characterise very different opinions about physical reality. No wonder that there are such disagreeing opinions in the literature about black holes.

Thanks for the discussion!

* As to the part which the new ether is to play in the physics of the future we are not yet clear. We know that it determines the metrical relations in the space-time continuum, e.g. the configurative possibilities of solid bodies as well as the gravitational fields; but we do not know whether it has an essential share in the structure of the electrical elementary particles constituting matter. Nor do we know whether it is only in the proximity of ponderable masses that its structure differs essentially from that of the Lorentzian ether; whether the geometry of spaces of cosmic extent is approximately Euclidean.
- http://en.wikisource.org/wiki/Ether_and_the_Theory_of_Relativity

 

[zonde]

This is nonsense. The river is not a material fluid following fluid flow laws. It is a flow of imaginary (figurative sense, not √ -1) space, and its laws are as derived in the paper. In this regard, your first calculation is correct, and is consistent with equation (2) of the paper. Your second is something you made up that is wrong. You have refuted a nonsensical straw man.

Hmm, river model uses analogy with material fluid. Oh well, whatever.

Ok then, concerning my first calculation - it makes no difference between v and -v i.e. river flowing inwards or outwards.
Do you consider them as different alternatives?

 

[harrylin]

I have been thinking a little more about the conceptual differences. Space in Einstein's GR is devoid of kinematic qualities (not including cosmology); in stark contrast, Hamilton fancies a space that at places flows like a water fall - the antithesis of what Einstein had in mind.

Hamilton vs. Einstein is a bit like Newton vs. Huygens but with a twist. Where according to Einstein's model from a distant perspective the speed of a light ray heading towards the Sun decreases, according to Hamilton's river model it instead increases. Newton's theory of light propagation could be experimentally disproved and it is obvious why: the physics of increased light speed inside a lens is very different from the physics of decreased light speed inside a lens. So why is that, presumably, not the case with the river model? The answer is of course that it uses a "cheap trick": if I understand it correctly then it has a discontinuity in the speed of light, right in the middle of a heavy body. And I'm not talking "black hole" here: I'm talking about the Earth or even a heavy piece of glass.

I can see how as a calculation tool this can produce correct predictions about observations. However as a physical model such a discontinuity is extremely ugly and it looks very unreasonable; there is to my knowledge no precedent for it in physics (except perhaps some abandoned theories that I don't know of). This appears to me as a strong argument against using such a toy model for the purpose of trying to understand what "really happens".

 

[harrylin]

Hmm, river model uses analogy with material fluid. Oh well, whatever.

Ok then, concerning my first calculation - it makes no difference between v and -v i.e. river flowing inwards or outwards.
Do you consider them as different alternatives?

That is an interesting observation! Can an outward flowing decelerating space perhaps equally well emulate the phenomena? I guess not, but at first sight it's not clear to me where it goes wrong. Nice puzzle.

PS perhaps light bending goes the wrong way? My mind boggles!

 

[PAllen]

Hmm, river model uses analogy with material fluid. Oh well, whatever.

Ok then, concerning my first calculation - it makes no difference between v and -v i.e. river flowing inwards or outwards.
Do you consider them as different alternatives?

Did you make any attempt to read the paper? One case is the white hole model, the other the black hole model. This is fully discussed in the paper.

 

[harrylin]

Did you make any attempt to read the paper? One case is the white hole model, the other the black hole model. This is fully discussed in the paper.

I had skipped the "white hole" part, but yes indeed, that's an outflow model. Good one!

 

[zonde]

Did you make any attempt to read the paper? One case is the white hole model, the other the black hole model. This is fully discussed in the paper.

And ... ? Can you now answer my question? Is black hole and white hole the same thing or two different things?

I would think that you mean they are two different things. But on the other hand you said this (in response to harrylin):

I don't understand how you can read the paper and not see the exact mathematical equivalence. All you do is transform between GP coordinates and SC coordinates.

Do you really believe using different coordinates to compute observables (which are all defined as invariants) can produce a different result?

And as I understand that would imply that black hole and white hole is the same thing because you can transform SC to either - BH GP coordinates or WH GP coordinates.

So please clear up my confusion or admit that your statements are not consistent.

 

[harrylin]

And ... ? [..] Is black hole and white hole the same thing or two different things?

I would think that you mean they are two different things. [..]

Yes, just as the name suggests - and as I intuitively thought - according to Hamilton inverting the direction makes everything fall away from the center ("an object is compelled to fall [..] outward, in the case of a white hole").

His inflow model does not lead to the same description by a far away observer as in standard GR (Einstein-Schwartzschild), but it does seem to reproduce the same phenomena so that it may be useful for computer simulations.

as I understand [PAllen's comment] would imply that black hole and white hole is the same thing because you can transform SC to either - BH GP coordinates or WH GP coordinates. So please clear up my confusion or admit that your statements are not consistent.

That will be also be instructive for me, as I am not familiar with those!

 

[PAllen]

And ... ? Can you now answer my question? Is black hole and white hole the same thing or two different things?

They are physically different. The maximally completed, eternal BH geometry includes a white hole followed by a black hole. For many other coordinates that only cover half the maximal geometry, you can get either one you want (depending on e.g. sign choices).

You can say a white hole is the time reversal of a black hole; and the equations of GR are such that for any solution, its time reversal is also a solution.

I would think that you mean they are two different things. But on the other hand you said this (in response to harrylin):

And as I understand that would imply that black hole and white hole is the same thing because you can transform SC to either - BH GP coordinates or WH GP coordinates.

So please clear up my confusion or admit that your statements are not consistent.

A metric does not completely determine a manifold. For example, a flat, cylindrical manifold has the Minkowski metric everywhere, but is topologically distinguishable from a flat 'planar' manifold.

In the case of SC metric, where the interior is not static, while the exterior is, you can get either global interpretation by choice of time direction for the interior. Remembering that r is a timelike coordinate inside the BH, you can say time flows from r=0 to r=2m, or vice versa. Either interior interpretation will join smoothly with the exterior metric. The former give a white hole, the latter a black hole.

All of this is hidden in SC coordinates, which are two non-overlapping coordinate patches with some open topological choices. When you transform to coordinates that cover both interior and exterior, you are forced to make a choice (or include both options in a single, maximally extended, manifold - where you smoothly join a copy of each interpretation to make one maximal manifold).

This is a confusing area. I don't know if I've cleared up any of your confusion here. Perhaps someone else can also chime in.

Of course, since 'almost nobody' believes white holes exist in our universe (except for the ability to treat the big bang itself as somewhat like a white hole), these issues are often glossed over.