Gravitational Time Dilation

Yes 3 space coordinates.

The point was that in your argument from authority.., you invoke a 1908 quote of Minkowski, that predates GR and was specifically about SR. Very often when you quote authority, it does not seem that you fully understand the limitations of the lay oriented quotes! Hamilton's waterfall analogy presumes an acceptance of specific conceptual interpretation of GR. It also speaks to aspects of spacetime that remain in the domain of theory. It speculates about the physical characteristics of spacetime, inside of an event horizon, where aside from the predictions of mathematical solutions, that eventually end in a singularity he does not believe exisits, everything anyone imagines about the character of spacetime is speculation.., and not all authorities agree on the details. Theoreticians don't even agree exactly what happens at the event horizon, let alone inside...

You latch on to lay oriented comment and analogy, and beat it to death, without acknowledging the speculative limitations, of those lay descriptions... You don't discuss and often even kill the chance of discussion by others. In some cases much like this thread, where the thread itself should have been closed or moved long ago, your contributions keep it moving down a track you are complaining about.

Science is not about one mainstream interpretation. And theoretical science would be nowhere, if no one questioned the mainstream and tossed around alternate ideas and speculation.

Very often your insistence on deriding anything that does not fit your understanding of mainstream, actually winds up turning the discussion into personal argument.

So all of this to say yes, the waterfall analogy has some merit introducing speculation about the classical dynamics of spacetime and photons as they cross an event horizon.., and in limited lay oriented explainations... But no one who really understands GR, including Hamilton believes it is a definitive description of the character and nature of space.., or spacetime. No one it seem other than you.

Ask Hamilton yourself if he believes that analogy is the exact description, you seem to believe it is.., or maybe just an imperfect analogy intended as an introduction to something far more complex.

It is common knowledge that Bruce and I have some conceptual differences about GR, but it seems that in this case we both understand that the waterfall analogy is just that, an imperfect lay analogy.., which was never intended as an absolute description....

 

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@ - OnlyMe

Grok'd!

 

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Gee OnlyMe, most times your posts seem to at least reflect accurately what others have said or are saying. In this case though, you have appeared to fail miserably.

It is also common knowledge and in black and white that I have also disagreed with brucep at times, and on this issue also. Not sure what that proves though.
Your use of the phrase "imperfect lay analogy" is very interesting.
Let's look at it...imperfect, well yes, all analogies are imperfect or have limitations. Lay, in reference to me?..what can I say? Except to say that so far in this little berating exersise of yours, you have already accused me unjustly of not knowing it is an analogy and not knowing that analogies do have limitations. But yes, I'm humble enough to admit I'm only a lay person.

As yet though, I have yet to see you refute any of Professor Hamilton's mathematics with regards to the "mathematically sound" river model analogy
Perhaps you have yet to read the paper. Here it is again.
http://arxiv.org/pdf/gr-qc/0411060.pdf
Part of the summary is as follows.
We have presented the details that place the river model on a sound mathematical basis. We have shown that the river model works for any stationary black hole, rotating as well as non-rotating, charged as well as uncharged. The Doran35 coordinate system provides the coordinates of the flat background through which the river of space flows into the black hole.

 

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That's also false. All I ask from those that propose the invalidity of SR/GR the BB etc, is some observational evidence to support their stance.
That will most certainly continue. I don't believe in letting crazy claims as put by Rajesh, go unchallenged. While you may find the challenge too hard, I'll do my best in making sure what he claims about invalidating BHs and GR, does not go without challenge.
As far as developing into "personal arguments" a couple of points.....
Isn't it true that you yourself have also been rather short and less then complimentary [in fact insulting] in relation to the person in question?
And isn't it obvious that you yourself are now promoting another "personal argument" simply because [to use your own words] you don't like my style of debating our alternative hypothesis pushers?

 

Once again, and despite your inference to the contrary, the real reasons why discussions with Rajesh do turn into personal arguments [which include yourself] is of course he completely ignores all expert authoritive replies that in all cases I am aware of, refute his picture of BH cosmology.
eg: my answer from post 2 in answer to the OP:
For some reason, you have a knack of complicating scenarios that could be expressed far simpler.
Anyone falling into a BH with a watch for example, will fall in as though nothing has happened. [Ignoring tidal gravitational effects] He crosses the EH, and his clock ticks as per normal.
Anyone from a remote or distant FoR, will see that person gradually fade from view as they are red shifted further and further along the spectrum, never actually crossing the EH.
This is a fact of SR, just as it is a fact that each and every FoR, is as valid as each other.
This is explained with the other example I have given you many times...regarding photons emitted just on the EH but this side directly radially away. From the photons FoR and point of view, it hovers forever, never secumbing, never getting away. All other photons of course will arc back and secumb to the BHs EH.
But from a remote FoR the photons are red shifted until faded from view and are never seen to cross.
For time for anyone foolhardy enough to cross the EH, he only has one choice and reaches the singularity/mass in a small but finite amount of time, but certainly in a broken down form of fundamental structure, as he is at first stretched and then literally torn apart and disassembled.

To try and compare the time in a FoR for anything or anyone that is inside the EH to someone outside of the BH does not make any sense for obvious reasons.
One being that time comes to a standstill at the EH [although we never see time coming to a stop] and evidenced in the fact that an outside observer will never really see anything fall inside a BH. Strange as it may seem, this even includes the surface of the star that collapses to form a BH.

I hope that this is a genuine question Rajesh, and not another beat up dishonest round about way of pushing another of your ideas.

After the usual stone-walling and false fabricating by Rajesh, tashja posted the following reply......
Hi Tashja,

I believe paddoboy has answered the question as thoroughly
as anyone can. As he says, the question has no answer,
because there is no link between an interval of coordinate
time inside the horizon and an interval of coordinate time
outside the horizon; the internal and external coordinate
systems are not related to each other.

Cheers!

Eric
_________________________________
Eric Poisson
Professor of Physics
University of Guelph

In any normal society that would have been the end of the debate.

 

That would be easy. If some vector field is named a "flow" or connected with an image like a river, then it should be connected with some conservation law of the thing which flows. The BH is a static spacetime, ok, in the Kerr case one could use a cyclical flow once it is rotation. But the flow is incoming, from all sides, and goes nowhere - but does not lead even metaphorically to any "increase of space" in the BH region too.

To construct a reasonable flow picture for GR is not only possible, it is even simple and straightforward, and can be done not only for particular solutions in some particular coordinates, but with a general coordinate condition which is at least locally possible on every solution.

This coordinate condition is the so-called harmonic condition. Harmonic coordinates are the natural candidat for preferred coordinates, because they essentially simplify the Einstein equations. The condition consists of four equations \(\square x^m = 0\), that means, the preferred coordinates have to be harmonic functions on the spacetime metric. More important here is that they can be rewritten as

\(\partial_m (g^{mn}\sqrt{-g}) = 0.\)

But these are classical conservation laws, of the same symmetric type as the energy-momentum laws of condensed matter theory:

\( \partial_t \rho + \partial_i (\rho v^i) = 0 \\ \partial_t (\rho v^i) + \partial_j (\rho v^i v^j - \sigma^{ij}) = 0. \)

All one has to care about is that one correctly identifies one of the harmonic coordinates as time-like, the other three as space-like. Then you can make the following identifications: \(v^i = g^{0i}/g^{00} \) is the velocity of the flow or river or how you name it (I name it ether), \(\rho = g^{00}\sqrt{-g} \) is the density, which is conserved by the flow, and then there is a more complex expression for the stress tensor of this flow, \(\sigma^{ij} = (g^{0i}g^{0j}/g^{00} - g^{ij})\sqrt{-g}\). This 3-metric \(\sigma^{ij}\) is, by the way, also a well-known object of GR mathematics, it appears in the ADM decomposition.

So, in comparison with the natural velocity \(v^i = g^{0i}/g^{00} \) in harmonic coordinates, which nicely corresponds to a whole set of energy and momentum conservation laws completely analogical to those of a flow of a river, the "flow" in the paper has nothing of this, cannot be extended in such a way because the "space" is flowing inside but the solution is static, and is, moreover, only a construction for a single particular solution, unextendable to general solutions.

 

That is brilliant !! That sums up the de-contribution of one man in this forum. I could not have put it so nicely without adding lot of sarcasm and disdain....

 

Don't expect to impress someone who simply worships before 'authorities' - even if such worship is highly selective. A case in point - his continued pushing of the 'zero-energy universe' position. Shouting it out via irresponsibly and seemingly endlessly re-posting the same full webpages but 'enhanced' with enlarged bolded text. Rather than responsibly saving server capacity by simply linking to the relevant webpage (and this same shouting/server-clogging tactic is applied to the river model endless re-postings - e.g. #448 here). I have given up pointing him to the fact many other authorities simply reject the idea and instead hold to that conservation of energy-momentum is not a general feature of GR, hence 'zero-energy universe' is on that basis without logical foundation.

But getting back to 'river' model. It can be attacked as dubious in more heuristic ways:

1: Given the 'space inflow' is everywhere, including exterior to the EH, it should follow an observer outside of and static wrt EH will sensibly 'feel' the 'inflow' as manifesting as an anisotropy in proper light speed c. The only logical deduction compatible with a 'hovering' photon at EH 'swimming' at c against inflowing space at speed c.
Yet we know proper c is an invariant that in no way depends on being in any particular frame - inertial or otherwise. If space can be likened to a physical fluid as waterfall picture implies, it should be easy to determine the frame in which such fluid is static. Ever since MM experiments, we know that is just false. Hamilton et al may argue the flow concept only applies to gravitational systems, but that simply 'doesn't hold water' (pun intended). Fact is, the true proper speed of c is an invariant regardless of acceleration - BUT - over extended distances anisotropy enters as a higher order effect. See e.g.
http://physics.stackexchange.com/questions/33816/does-the-speed-of-light-vary-in-noninertial-frames
http://arxiv.org/abs/gr-qc/9909081v7 (first two expressions p9)

Which standard GR results are imo quite incompatible with the 'river' notion. Wherein, irrespective of distance over which measurements are made, the proper speed c* should be c* = c ± c', where c' is the 'river' speed at static observer's locale, and measurement is directly with or against 'river flow' respectively. Seems obvious to me there is a clear conflict.

2: On the usual reading of accelerating universe, there is a non-zero CC/Dark energy content to 'empty' space, the consensus position having it represented by a small positive energy density ρ plus numerically equal and opposite pressure p. The net and negative gravitational content is ρ+3p -> 2p = -2ρ. Well golly gosh, if the river model holds water, the clear implication is a net negative gravitational mass inflow that should dwarf anything owing to purported Hawaking radiation for instance. Well at least on a 'proper' basis where everything is flowing inward at c over the entire EH area. Most reject any physical significance to seeing it from a coordinate basis (from which the flow rate is zero), preferring to say such is just 'optical illusion'. Consequently, this predicted, proper basis 'BH shrinkage' owing to 'inflowing negative pressure space' surely should be big news by now - well and truly trumping the nauseatingly over studied and argued 'Hawking-radiation evaporation'. Maybe tashja might like to contact Prof. Hamilton and get an opinion on this.

 

Dummy energy, momentum, and angular momentum are conserved over the natural geodesic path in SR and GR. whether you realize it or not is irrelevant. I showed you the derivation and you were disinclined to reveal you didn't know this. LOL.

 

Who is dummy? Learn to read, then read http://www.sciforums.com/threads/gravitational-time-dilation.145889/page-21#post-3301220 again. You would have understood that I know that special solutions with special symmetries have special conservation laws - related with the corresponding Killing fields (no, not those in Cambodia, but http://en.wikipedia.org/wiki/Killing_vector_field ) - for geodesics. To quote Wiki: "Each Killing vector corresponds to a quantity which is conserved along geodesics. This conserved quantity is the metric product between the Killing vector and the geodesic tangent vector."

And, by the way, this does not give you any momentum conservation law, and for the Kerr metric there is only one direction where one gets angular momentum conservation.

 

That's rather funny coming from the forum clown.
I mean one minute I'm the flavour of the month, and the next minute when someone, anyone "rebukes me, even though he has been shown to be wrong, you simply jump on the band wagon.

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I suppose I do have a lot to answer for in your eyes, being the prime poster who has shown you up as a fraud and a hoaxter in near every thread you have started, including the ones banished from science to the fringe sections.
Really Rajesh, the contents of your post remind me of a young school boy.
Do better.

 

Is that right? You don't need to read them you know.
In the mean time, I'll keep on keeping on.

The article itself admits to being speculative, so your false bravado, gnashing of teeth etc, is rather pointless.
See qureeus, what you fail is to distinguish the wheat from the chaff, as per example in your old thread was was moved from science into the fringe sections.....You know, the one you hold me responsible for.

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Getting back to the river/waterfall model, if you had anything at all to invalidate the analogy and the mathematics supporting it as a valid analogy, then take it up with Professor Hamiliton.
I'll wait for the result with patience.
But all I see is a lot of hot air.

 

You're the dummy since you don't understand the concept of local conservation of energy, momentum, and angular momentum over the objects geodesic path. It's first revealed to the student when he derives the relativistic energy equation. In the fucking beginning. Guess what Schmelzers? You should quit referring to your gravitational theory as an analogue of GR. This is what Visser has to say about your theoretical models. His reference numbers 545, 546, 547,and 548 on page 48. "non-standard viewpoints on quantum mechanics and general relativity". Basically nothing interesting. Tonite I finally read some of the bu.llshit you've been spewing like what you like to call the ether vector flow. Bullshit Schmelzer. Like the bullshit where you claim your theory will come to prominence once string fades into oblivion. LOL. You're a bigger nut case than I thought. Your theory of gravity was dead before you wrote it down. Your gravistar is unsubstantiated bullshit. You're trying to survive using data found in experimental error bar. You didn't do any analysis that would suggests all the pulse train light would fall back on the surface of your bogus gravistar. What you should hope for is a sign that the dying pulse train hits the surface of your Gravastar so we can record it. The thing about GLET and string theory is a good reason to laugh. LOLOL. BTW this paper on analogue gravity was recommended by one of the good professors Tashja introduced to us. I can't remember or find out which one so I apologize. The main interest with the analogue gravity at this time is to build experiments to test for Hawking radiation. Can't do that with Schmelzer's analogue ether theory.
http://relativity.livingreviews.org/Articles/lrr-2011-3/download/lrr-2011-3Color.pdf#page114

 

Whatever you think of the river/waterfall model is really of no consequence.
Like your rather hysterically warped view of "freedom"and "politics" and the ranting and raving you do with regards to them, you are making no difference whatsoever.
As I just told another rather mixed up poster, if you have anything of substance, then take it to Professor Hamilton. I'm sure he can defend it quite admirably...or is that actually the problem?

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More hot air, sheesh!

 

That is the reason he is infesting this forum with his crap. From all reports, his thread was closed over at Cosmoquest, but they do not suffer fools gladly at all over there.
Delusions of grandeur reign supreme with this one.

 

False bravado? How so exactly? Gnashing of teeth? My - evidently you have psychic abilities - 'seeing' things about me I never have! How would a militant atheist explain that?!

So cheap and nasty - again. Yet any reciprocal name calling doubtless would be decried. Hypocrite. Resting safe in the knowledge such behavior is condoned by upstairs.

Endlessly dredging up an issue where there was never any fault on my part in any sense. How stupid. All you do is again allow me to call you - truthfully - a coward. Being no doubt unwilling once again to go back there and make good your vacuous claims.

Decoded - paddoboy cannot mount any technically proficient and relevant counterargument, having zero mathematical competence or genuine physical insight. Yet persists in arrogantly claimimng to be able to 'sort the wheat from the chaff'. BS.

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All evidenced by your posts in general and your attitude.

No name calling intended. I do have a weird habit of placing a "u"after my "q"

Coward? What, for exposing you for what you are? an anti GR crank?

Like I said, take it up with Professor Hamilton, I'm sure he'll defend it successfully...or is that what worries you?

 

Militant Atheist?

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Not in the least. I am though a militant realist, with an abhorrence towards religious zealots that come to a science forum to deride science, and trollish alternative cranks that vainly seek to invalidate or deride established science and cosmology on a science forum.
Making absolutely no difference to the established academia, they waste their time here thinking that they are achieving anything.
And by the way, I have nothing against any religious person, other than those that come here with an agenda to try and disrupt science...In fact my Mrs is a Christian in the true sense of the word, and that coupled with a few other qualities has seen us now married for 40 years next year and going strong still.
I also regularly allow her to entertain her church choir once a month at our home.

 

As usual - personal attacks, without substantiation. And, as usual, the arguments I have provided - in particular, the connection between local conservation laws for geodesics and Killing fields related with special symmetries of the solutions - is completely ignored, the consequence that your claim about momentum conservation for geodesics on Kerr and Schwarzschild solutions is wrong is ignored too. As usual.

Thanks. I have not known that I have four citation by living reviews. And I do not refer to my theory of gravity as an "analog of GR". Analogue gravity is, indeed, a completely different thing, even if there are quite interesting mathematical connections.

As usual (and, therefore, already expected) we can find another exercise in unjustified name-calling, and the only real attempt for justification is simply a lie:

Reread http://www.sciforums.com/threads/black-holes-a-opposed-to-the-big-bang.145854/page-7#post-3298535 where I have simply quotet literature. Its a trivial known fact, no necessity for a big analysis.

It is of course a good source, I have seen earlier variants. And, of course, my ether theory is an ether theory, not an "analogue ether theory" (whatever the meaning of this phrase) and does not even pretend to have anything to do with experiments with Hawking radiation. (Hawking radiation is, BTW, pseudscience, because it has a "trans-Planckian problem" which is essentially ignored).

 

Indeed, my threads have been closed - after 30 days, following their stupid rule which requires that every non-mainstream-thread is closed after 30 days. Many years ago, BTW, so this has nothing to do with this forum.