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Are flowing space models compatible with GR? 
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#73
Nov712, 09:53 AM

PF Gold
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#74
Nov712, 10:28 AM

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PF Gold
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#75
Nov712, 10:34 AM

PF Gold
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Anyhow, thanks for the clarification of 'observable'. 


#76
Nov712, 10:44 AM

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PF Gold
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#77
Nov712, 10:58 AM

PF Gold
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But different observers instruments may disgree. 


#78
Nov712, 11:08 AM

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PF Gold
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That is, I may say: your instrument measures a B field because it is moving relative to the E field; you say: there is a B field that my instrument (at rest) measures. Mathemetically, the measurement in either frame is characterized by contraction of a tensor field and vectors derived from the instrument. 


#79
Nov712, 11:24 AM

PF Gold
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#80
Nov712, 04:07 PM

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Here are a few things that may need more elaboration. PAllen, sorry if I did not make the subject matter clear enough for you:
"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. "  Hamilton We are here not discussing a precise transformation equation (which is necessarily only valid for a particular case) but a physical model, which pervect presumed to be a serious one. Equations fail with a little change of situation, while a physical model accommodates itself to the changed situation. Zonde understood this subtle point of the topic, see my post #29 where I explained this, and his post #38. A correct, functional physical model does not require tinkering with mapping, although one can make of course maps from it. Which brings me to the next point: First, let's recall GR's equivalence principle; certainly the free fall case is valid and standard use of GR. And no Einstein free fall reference system will break either the law of inertia nor the law of local constancy of the velocity of light. My illustration of yesterday does not sufficiently "catch" what is going on in Hamilton's model. It comes closer if we take a second Mercator projection, put that one its head, and stick it to the first one, with the North poles against each other. Now the description looks like something much more fancy, as the traveller from the equator to the North pole and on to the equator on the other side does not need to make bends anymore. Of course the resulting patchwork is still not a globe and neither is it really a Mercator projection anymore. And it still has a velocity discontinuity at the North pole, but some people might not notice. A true Mercator projection is centred around the area of interest, and admits that it provides a distorted perspective except very close to the centre. It is similar with the equivalence principle, which knows no flowing space. I gave the example of a hole in the Earth, or in any heavy piece of matter: Hamilton's model is in several ways a fake Einstein free fall frame, and it breaks GR's laws of inertia and local speed of light. This is why I concluded that not only in spirit but also in action, the model does not explain GR; it is its antithesis. It is not compatible with GR in that sense, even though it gives for a number of cases the right answers. 


#81
Nov712, 04:48 PM

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"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. applies only to two special geometries. If you want to be pejorative, the whole river model is a trick for understanding perfectly ideal black holes (or regions of spacetime that match a portion of such  e.g. outside the earth, but not on or in the earth)  and for nothing else in GR. This is why few authors on relativity besides Hamilton (maybe Visser, on occasion?) bother with it. 


#82
Nov712, 05:01 PM

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The river model does not have any violation of local speed of light or inertia that I can see. Light moves through the river at all times with local speed of c relative to the comoving observer at that point. The river itself, which is a nonobservable abstraction, moves at speed > c relative to infinity; but > c coordinate speeds are actually quite common in GR. I definitely don't see where inertia is violated since SR applies in comoving frame; and each comoving frame is a 'free fall from infinity' frame. The real break down of the river model is that it wants to describe the motion of the river against a flat background, governed by Newtonian laws (then apply SR at a local frame at each point in the river, and boosts based on the difference in river velocity between points). This conceit can only be made to match GR for the very special geometries described in the paper. [As admitted and proven in Hamilton's paper.] 


#83
Nov712, 10:59 PM

PF Gold
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When we speak about gravity of gravitating body we always view it in the rest frame of gravitating body. Do you agree? 


#84
Nov712, 11:09 PM

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PF Gold
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It seems you cannot let go of the idea that there really are preferred frames and preferred coordinates. That is the antitheses of relativity. 


#85
Nov712, 11:33 PM

PF Gold
P: 1,376

In SR they are frames where speed of light is isotropic (and has particular value). "... the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate ..." "Let us take a system of coordinates in which the equations of Newtonian mechanics hold good." I think you are a bit confused. 


#86
Nov812, 12:22 AM

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Further, in GR, SC coordinates are as far as you can imagine from being an 'inertial frame'. As I mentioned, lines of constant r have proper acceleration approaching infinity near the EH. It is actually GP coordinates that are built around a family of inertial frames. One sign of this is that 3spaces of constant GP time are flat, Euclidean space; 3spaces of constant SC time are nonEuclidean. 


#87
Nov812, 05:45 AM

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#88
Nov812, 06:04 AM

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While I think that we have covered the topic well enough by now, there are a few loose ends:



#89
Nov812, 08:37 AM

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PF Gold
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For SC or KerrNewman geometry (and no others), you can use this model to make exact predictions and visualize behavior. It is then equally silly to respond: well, for other spacetimes you can't. You can argue (and this is my general opinion), that its limited applicability make it not a particularly useful method. Hamilton may argue (correctly) that most situations in astronomy are characterized by large regions where the river model applies to a good approximation, and it is easy to know when to not apply it. It's not a right/wrong decision. 


#90
Nov812, 10:43 PM

PF Gold
P: 1,376

SR certainly is not defective. It has limited applicability. And GR is meant to overcome this limit. But that means one important thing  GR should reduce to SR at appropriate limits. And that in turn means that if two different coordinate systems when reduced (under appropriate limits) to SR give coordinate systems that are not related by Lorentz transform then they describe two different physical situations. So we can try to compare coordinate systems in that sense to find out if they are equal. Would you still say that this somehow goes against Einstein's view? 


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