A response to AlphaNumeric re closed thread

As the ill-fated thread http://www.sciforums.com/showthread...ke-vs-stress-as-a-source-of-gravitation-in-GR
was locked prior to my having any chance to defend against imo a diatribe in #15 there by AlphaNumeric, here I attempt to go public in response. Not in some backwater infrequently visited 'lounge' arena, but here in Physics & Math section, where I should have been allowed the decency of responding in that sadly derailed thread. So I reproduce posts #15 and #44, with my comments.

#15:

Huh? It is you assuming here. Where did I even so much as suggest that likes of yourself need such stimulation? Retract please - I will not tolerate being made to say what I have not.

So you and Tach asserted, and you continued to relentlessly assert below. What I would have considered a reasonable attitude would be to ask for clarification on any details of scenario that are genuinely not clear. Or more likely, give a reasoned, to-the-point argument setting out just precisely where and why any problems exist. That is being reasonable - and genuine. Instead, you simply maintain a relentless negative tone, choosing to tackle the man rather than the ball. Just keep accusing me of being 'incoherent', 'lacking any feel for subject' etc. etc. Accuse me of being 'hand-wavy', and in supreme irony, do exactly just that yourself in adopting a relentless critical tone. But never once so much as attempt to tackle the guts of what I maintain is a clearly enough presented gedanken experiment. And basically demanding, as you have below, that I present this as some full-blown academic treatise at expert general relativist level, replete with 'appropriate field equations for the metric'.

What?! Why on earth is there a need to do that? It is genuinely not clear to you that what is being treated in #1 is one simple property of one part of stress-energy tensor. Namely, if a principal stress component is a source of gravity, then it's also a source passive gravitational mass, and inertial mass. Then - here's a simple example of what that means. Which I have provided. And that example - 'disc brake' scenario, genuinely stumps your comprehension? Pull the other one!

See above comments. But on that score, all I need do to destroy that line of criticism is point to the 'famous' A-wal incoherent wall-of-text threads, and your enthusiastic, lengthy and detailed point-by-point replies, that went on page after page. Oh s**t - what do you know, try searching for them, and nowhere to be found! Looks like admin have been doing quite some housekeeping of late. Vacuuming up unwanted stuff. Maybe my turn next. Anyway, you obviously can and often are very specific and detailed in responding to even quite genuinely vague posts where it suits.

Again - I refer you to your manner of dealing with those amazingly wordy A-Wal threads, and similar, which gives the lie to above criticism.

Then explain your response to those A-Wal threads - and don't try and tell me you can't recall them.

Dealt with that unreasonableness earlier. We are asking about just one thing - consequences of the passive gravitating mass behavior of matter under uniaxial stress, given what the stress-energy tensor assigns to stress. All this crap about needing to figure out the fully detailed curvature side of things is imo nonsensical. Why is there such a need in this case? But I'll say more on that in finishing up.

Forgetting the unjustified polemic, you have gone back on that committment twofold. Firstly, by never waiting for me to come back with a chance to answer this tripe. And second, by locking the thread - killing it dead, rather than moving it to said backwater. Not true to your word.

#44:

No, it confirms, as stated above, you are not true to your word. And yes it does confirm my articulated fear at end of #1 - deja vu it is!

Will finish this with a question for AN. Place solid matter under uniaxial compressive stress (like energized disk pads do to a brake disk). Does or does not the passive gravitational mass of that matter so stressed increase, or not? And as clearly enunciated in #1, this is quite separate to any associated elastic energy induced. And one really and truly needs to solve the EFE's to answer that question? If so, Strange then the authors of that article at I linked to in #1:
http://arxiv.org/abs/gr-qc/0505040
didn't need to do so in very simply obtaining gravitational contributions from shell stresses. But what would they know. And if this post gets instantly locked or made to disappear, so be it. Taking a precautionary 'snapshot' just in case.

 

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The total ( invariant ) mass of that matter does not change. All that happens is that you are getting some additional factors in the stress-energy-momentum tensor which reflect the presence of stresses and energy fluxes, as well as their densities.

It depends on what exactly the question is. If you simply want to know if the presence of stresses affects the gravitational field in any way, then the answer is obviously yes without having to do any maths. If, on the other hand, you wish to know exactly how it affects the fields, i.e. in what way those stresses change the geometry of space-time, then you will need to do a full solution of the EFEs with the specific SEM tensor in question present, because the field equations are non-linear. And that is usually a highly non-trivial task. One may be able to simplify this task if symmetries are present in the system, or by using the linear approximation method instead of the full EFEs.

 

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Are you quite sure about my question? I agree that an internally stressed body has no net change - but that is a consequence of the overall cancellation between positive and negative stresses there. My question relates just to that portion of matter under a given sign of uniaxial stress. in disc brake scenario, that equates to just the disc area squeezed by pads. The whole assembly - disc + pads+caliper has no net contributed mass from stress sure. According to Ehlers et. al., uniform biaxial stress acting on a shell does make a net contribution to active mass (therefore passive mass). Cancellation as shown there comes from the counteracting pressure within enclosed volume. (I gave wrong link in #1 here. Proper one is: http://arxiv.org/abs/gr-qc/0505040)

My point exactly, and imo entirely sufficient in context of scenario.

But my point again is, we are looking at stress as contributor to passive mass, not active mass. Why would one be the least interested in a truly infinitesimal change in already infinitesimal curvature owing to something like a disc brake as source of field? We assume the primary source of active mass gravitational field is e.g. vastly greater mass of terra firma. Anyway thanks for making specific comments dealing with the issue.

 

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It depends on the specific scenario. For something like a disc brake obviously you wouldn't use GR. But the contribution does make a difference if one looks at, for example, stresses in the interior of a star or similar. This has a quite a substantial effect on the gravitational field.

 

Sure, and I have no problem with that pressure there does, at least according to stress-energy tensor formalism, make a substantial contribution as you say. But to quote from your #2:

In disk brake scenario, even if one were out to compute the field curvature owing to stresses, we surely are very much into the linear approximation regime. Anyway, the matter of interest is effect of stress on passive and/or inertial mass, and for that case, demanding need for solving full EFE's is imo just such a red herring.

We treat patch of compressively stressed disc as a 'test mass' immersed in constant g field, and reasonably note such 'test mass' negligibly perturbs the ambient field. Further, if gravity is still made to be problematic despite this observation, note I gave an alternate scenario. Mount 'disk brake' on a spinning carousel. Gravity replaced with 'artificial g'. Now gravity can be entirely absent and all we need concern ourselves with is inertial mass change as spinning disc material moves in and out of stress field owing to notionally frictionless caliper pads. I say that IF stress is a real source of active/passive/inertial mass, an 'overbalancing wheel' situation exists. And I say that put's into question role (or lack thereof) of stress as bona fide source term(s).

 

G * (2.2590 × 10^4 kg / m^3) = (G/c^2) * (2.0303 × 10^21 N/m^2) = (G/c) * ( 6.7723 × 10^12 kg m/s /m^3 )

For comparison, 2.2590 × 10^4 kg / m^3 is the density of osmium while 0.000057 × 10^21 N/m^2 is the pressure inside a uranium nucleus and greater than the pressure at the core of the sun. http://en.wikipedia.org/wiki/Orders_of_magnitude_(pressure)
0.0000000003 × 10^21 N/m^2 is the order of maximum pressure from a diamond anvil cell and represents the highest mechanical pressure that one could expect to achieve with brake calipers.

It's disingenuous (at best!) to claim that the gravity of osmium density is "equal" to the gravity of this super-nuclear pressure in the same way that a year is not equal to a light-year.

But this is not the reason that the thread is wrong headed. The first is the mention of the overbalanced wheel, which requires a study of asymmetry which requires a study of the symmetry of GR. The second is that the break pressure stress is magical, in that the breaking apparatus is nowhere described. That's because if the rotor is moving relative to the brakepad there is transfer of momentum from brakepad-apparatus to disc. This requires orders of magnitude more calculation than the typical textbook exercise and much more description of the system than provided. In addition, GR forces you to study the whole apparatus because of the symmetry of GR -- GR is very unkind to magic masses and forces and momentum appearing out of nowhere. Thirdly, since there is contact, there must be friction, and since the magnitude of the GR effect of realizable pressure is negligible, braking dominates over any possible GR dynamics. Finally, the whole apparatus-breakpad-rotor system ultimately only shuffles mass and momentum and forces among itself -- it's expected to move as pressure is applied and released in the absence of gravity, so concentrating on just the wheel is not justified in Newtonian gravity-free physics, let alone GR.

The reason the scenario is kaput is that the requested calculation is neither of utility nor illustrates the principle that the OP seeks to illuminate. The OP impermissibly mixes magic and physics to try and demonstrate that physics is nonsense but the only thing illuminated is the unwisdom of mixing magic and physics. This causes unkind opinions to be formed about the OP, among the least of which are that the OP has no grasp of GR and has not well-thought-out how to model a brake rotor in even Newtonian mechanics.

 

Oh wow! And I was accused of presenting an incoherent posting!!! Above is truly incoherent. First, a line of math with no intro and a piecemeal reference to just some of the terms in following lines. And with a choice phrase like "the gravity of osmium density" thrown in?!! Please, if you get the chance, go back and severely edit before too many amuse themselves with this bit, and rest of above.

So you simply assert. And I say rubbish. If stress is a source term for gravitating mass, by equivalence principle it must equally be a source term for passive and inertial mass. The rest follows inexorably. You want link to that article again? Here:
http://arxiv.org/abs/gr-qc/0505040
See section 5. Simple, straight correspondence between stress terms and assumed active field ensuing. No BS of 'full EFE's' requirement.

Total BS. Evidently you have no knowledge of how a disc brake is constructed and works. No magic to it. And my 'disk brake' (yes I consistently used inverted commas) does no breaking - savvy? It applies pressure frictionlessly - savvy? And that's a fully justifiable idealization.

Do you expect to get away with such bald nonsense? Go back and actually read what I stated in #1 of that defunct thread. That we make the perfectly reasonable idealization to frictionless pads. That kind of thing is done routinely in modelling of physical scenarios - as you must well know. I am not trying to sell working 'free energy devices', or you think so? Even though I argue against there being any actual effect?

You are the type that could make the simplest problem into something infinitely complex. The advantage to that being not just zero but hugely negative.

No doubt most physics is unkind to magical anything. What I have been showing, despite a barrage of ornery polemic from likes of yourself, is that stress as source term does indeed suggest 'magical' energy conservation violation is possible in principle - IF it genuinely is a source term. And I say it is not.

And this disingenuous piece has been answered above. We choose to simplify via a perfectly legitimate idealization. You amaze me. Can doubtless get all excited by articles dealing with typically fantastically minute Hawking radiation - despite it being totally swamped by e.g. ambient CMBR. Yet dare to claim that because effect of brake pressure stress will be tiny - something I fully acknowledged btw, it somehow 'shouldn't count'. Utter hogwash - principle is what counts here, not practicality. And you know this full-well. Calculations for where it would count like deep inside a neutron star, can very much depend on determining consistency of principle in this scenario.

That piece disjoint and not worth any further comment. Try very much harder to undermine me next time, or better still, just keep out of this. None of your #6 attempted to address my earlier posts in any meaningful way, especially #5. You've hit me with the force of a feather. And it's no secret you and AlphaNumeric are real close buddies here.

 

Yes. But as I said on the previous thread, I don't like your scenario. Imagine a simpler scenario - a coil spring. It has an active gravitational mass, an inertial mass, a passive gravitational mass, and so on. Now compress the spring. You did work on it. You added energy. You stressed it. As a result it now has a greater active gravitational mass, inertial mass, passive gravitational mass, and so on. Whilst the extra mass is so slight as to be practically undetectable, if you had sufficient accurrate equipment, you would find that the spring was harder to move. You can do the same sort of thing with "a photon in a box".

See the wikipedia Mass in General Relativity and note this:

In special relativity, the invariant mass of a single particle is always Lorentz invariant. Can the same thing be said for the mass of a system of particles in general relativity?

Surprisingly, the answer is no.

In general relativity, which "subsumes" special relativity, mass is not invariant. The mass of a brick on the ground is less than the selfsame brick above the ground. You do work on the brick to raise it. You give it potential energy. You increase its mass.

NB: I think you should cut rpenner some slack, his response could perhaps be more succinct, but I agree with the sense of what he's saying - your scenario was not a good one. And I'd say your complaint re the previous thread should be that the moderator permitted a host of "derail" irrelevant posts then closed the thread when I posted a physics response.

 

Farsight - first off let me say I respect you (as I do Markus Hanke) for this much - you tackle the ball and not the man, which is a healthy, genuine attitude. The same cannot be said for AN or his good buddy rpenner, or a number of others. Unfortunately your example of coil spring I in turn will say is lacking, in several respects.

Firstly, mass increase via doing work comes under the banner of the T00 energy term in stress-tensor. I made it very clear early on in #1 of defunct thread and this one, the terms we are dealing with here are strictly the 'pure stress' ones - the lower three diagonals - Tii principal stresses - in that tensor. Their character as purported sources of gravity are strikingly different to stress as contributor to elastic energy - T00 term. For latter there is essentially a parametric dependence; W ~ T00 ~ σ^2/E (E is Young's modulus), which is always of the positive sign, and dependent on material stiffness. The Tii terms however not only are linear wrt σ, and thus can take on equally positive or negative values, but additionally have no sensible relation to energy input. And that key feature imo makes them 'magical' and suspect. Which is what my example attempts to highlight. Elsewhere I gave other examples, but such has been the combative and hostile climate, no point in bringing any of those up here.

But secondly, you picked a bad example in coil spring, even if principle stress Terms Tii were meant. That's because a coil spring works not by way of tension or compression in the spring material, but torsion, which means shear stresses, thus the off-diagonal shear stress terms Tij. I figured out quickly quite some time back that even if the principle stresses genuinely contribute as source, this could not be true of shear terms for a solid anyway. See if you can figure out why - I'll test your knowledge of strength of materials. Hint - shear stress can be resolved into.....

It's true if one traces a given element of disc in it's circular path, it moves up and down in such a potential, and indeed on that basis, with a purported input of mass owing to stress patch, we have a net energy change per cycle. To say mass depends on potential is true on a coordinate but not local basis, but is irrelevant wrt that power is being generated here owing to stress patch - IF stress is a genuine source term (how many times now have I emphasized that IF? Too many.). What's more, have you forgotten what last para. in #5 is saying? We can ditch gravity as source of 'field'. Key element is stress in that disk.

That thread was shamefully derailed by two reckless individuals in particular, and I agree you had made every effort there to be constructive.
Disappointed you actually agree with rpenner's attack in #6 as imo I have torn everyone of his arguments to shreds. You think otherwise? Where exactly did I fail to knock out all his futile critique? Regardless of that, rpenner deserves no slack as he set out here with the entirely hostile intent of undermining my credibility. And that was the case on our very first encounter btw:
http://www.sciforums.com/showthread...ts-debunked-when-talked-as-a-source-of-energy
Check out posts #24, #27, #28, #29, 2nd para. in #104, and you will appreciate just why I hold that individual to be disingenuous, and I suspect the bizarre antics there hint at acting as a proxy for some disaffected who's ego balloon I pricked elsewhere. Just supposition on my part, but I have no respect for those who out-of-the-box choose to attack the man and not tackle the ball. This place in general has too much of a nasty combative spirit to it unfortunately. Enough said on that. Do you accept my analysis above re spring etc.?

 

It isn't all that different to having an elastic disk on a fixed spindle, grabbing the rim steering-wheel style, and twisting it. Which isn't all that different to your brake-pad.

See wiki. Do you mean the "normal" stress components T11 T22 T33 which are labelled as pressure in the green diagonal strip in the picture at the top of the page? I'll presume yes and say I'm sorry Curious, I just don't see how field equations relate to the pressure on a brake pad.

I'd say the "material" we're dealing with here is space. Or field if you prefer. Pressure is energy x volume, and it's in the \ diagonal along with energy density.

Fair enough. But we could have used a gas piston, then we limit ourselves to pressure. Just think of a piston that you push down, without knowing whether you're compressing a gas or a spring.

The "normal" force, the tensile plane, and the angle between them. You can simplify the coil spring to a piece of wire like this \ fixed at the bottom. Push down on the top and it bends because you've got a tension along the wire. Let go and it springs back. In physics the strong force is effectively a tension, think of the bag model of quark confinement.

Hang on, let's have a look:

"We treat patch of compressively stressed disc as a 'test mass' immersed in constant g field, and reasonably note such 'test mass' negligibly perturbs the ambient field. Further, if gravity is still made to be problematic despite this observation, note I gave an alternate scenario. Mount 'disk brake' on a spinning carousel. Gravity replaced with 'artificial g'. Now gravity can be entirely absent and all we need concern ourselves with is inertial mass change as spinning disc material moves in and out of stress field owing to notionally frictionless caliper pads. I say that IF stress is a real source of active/passive/inertial mass, an 'overbalancing wheel' situation exists. And I say that put's into question role (or lack thereof) of stress as bona fide source term(s)."

There's a couple of things I'm not keen on.

1) See Einstein's Leyden address where he said "'empty space' in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν)..". A constant g field is where the inhomogeneity is constant. Focus on just the energy-pressure diagonal \ in the stress tensor and focus on space. The gravitational field is like an energy-density / pressure-gradient in space. Which can take a shear stress as per gravitomagnetism. So it's got a tension property. Stress is directional pressure and negative tension. Increasing the pressure is the same as decreasing that tension. Again, the strong force is effectively a tension, think of the bag model of quark confinement. Look at the coupling constants, the fine structure constant, and this.

2) If we replace the brake pad with a pair of rollers you can say that they compress the portion of the elastic disk passing through, and that this is like compressing a spring. But there's no work being done, and no energy input to give the apparent increase in inertial mass. The rollers are part of the system, the stress they impart is balanced by a tension in the spring that connects them. I think your scenario omits this.

Honestly I think you're being too hostile to rpenner. He at least gave you a physics response. In fact, I think you owe him an apology. And after following your link*, I think he owes you one too. My advice is to try to stick to the physics and keep emotion out of it.

* I like to think that I know a thing or two about electromagnetism.

 

Far from true. Maybe you still have some completely different idea of what's involved.

Yes of course I meant those components. And the field equations relate to pressure similarly as they do for the energy term in that tensor - scalar-like in both cases. in other words, GR says pressure acts as though it's a source of gravitating matter, except with pressure, the sign can be negative. And you are forgetting all my earlier commentary in e.g. 4th from top, last and 4th from bottom para's in #1, or last para. in #3, or especially 2nd para. in #7. We are not the least interested in any utterly minute contribution to field curvature, we only want to know the passive and inertial mass contribution. Good grief - how many times must I repeat this!!

Try squeezing down on empty space. Not much happens. Surprised?

You have again forgotten everything I said last post on this. Get it through your head - energy and stress contributions are similar in the scalar aspect, but totally different otherwise. There is NO general connection between energy input and stress-only contribution - to active or passive or inertial mass.

Evidently you did not understand my hint at all. Just forget this bit.

No - you have this all wrong. See my comments in para. 1 in #3.

I note your position, and disagree in certain respects. Leave it at that.

 

So rather than starting a new thread where you properly formalise the scenario you are interested in, showing the problem you claim exists through clear and precise logic, as I suggested you do, you start up a new thread to continue with more derailing?

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If you wanted to get down to the details you should have started a thread talking about them. Instead this is just going to be more arm waving and complaining.

You said " presented as a stimulating challenge, especially to certain resident physics 'heavyweights'". It clearly frames your post as "Hey 'physics heavy weights', fancy a stimulating challenge?" and then when more of your post is read it is clearly a "I demand you jump through a bunch of hoops and provide a level of detail and specificity I'm not willing to do myself" type of post. This makes it clear the effort which is going to be needed to have a precise and detailed discussion is considerably higher than would be needed if you'd been competent/non-lazy enough to put in some formalisation. So what really is the draw for us 'heavy hitters' that would make us want to jump through all these hoops for you? Oh, it's a 'stimulating challenge' you say? Well that's different, we all need stimulating challenges and that's enough to make your unwillingness or inability to formalise your own challenge properly acceptable

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I did. I said that given the thread derailment and the lack of detail the thread was to be closed but you were welcome to start a new one in which you provide a formalised derivation of the problem you claim exists. I told you what was necessary and rather than doing that you start a thread with more complaining.

What a wonderful choice of words you have used. I asked you to give a clear, precise and methodical formalised derivation of the problems you claim exist within relativity and you haven't met that request. But not only that you complain I should have given a reasoned, to the point argument setting out precisely where I see the problems in your post. See the hypocrisy here? I asked you for details of problems, you ignored me only to them ask me to provide details of problems.

I attacked both, the former because you failed to justify the latter and in failing to justify the latter you show you're unwilling to put in the effort you demand of others.

How was it supreme irony? I didn't attempt to provide a physics argument, you did. You assert something about relativity but you fail to give any quantitative formalisation to justify your assertion about relativity. You arm waved. I didn't try to make an argument about anything in relativity, so at no point did I make an arm wavy statement which I could have done with quantitative formalism. If I'd tried to respond to your claims about relativity but all I'd done was just arm wave and assert then you might have a valid complaint but I didn't respond to it. Instead I criticised your failure to present your claim properly and how you didn't deduce your conclusion using rigorous methodology but rather a sequence of flimsy wordy assertions.

If you'd started this thread with a quantitative construct of your claim and a precise and methodological derivation then we could be discussing the details right now. But we're not, as you carried on with the arm waving.

More laughable hypocrisy. You failed to 'clearly enough present' your case. You were asked to do so, including by me, and you still haven't. Instead you've whined. I didn't run from you, I asked you to put in some effort you hadn't done. It's not exactly unreasonable, seeing as you were demanding the time and effort of 'heavy hitters' here.

If you're unable to properly formalise your thought experiment then you should say so. You should also then present your 'challenge' as a query, in the manner of "I don't know how to do the details of this scenario but could someone explain to me how to ....". Instead you concluded a fundamental flaw in GR exists, a flaw you couldn't actually show but just assert, and demanded time and effort from people who have opened a relativity book at some point in their lives.

Where did I say that? I like how you complain when you think I misquote/misrepresent you and then do it to me.

If you think doing the relevant equations is 'a full blown academic treatist at expert general relativist level' when you're just showing how little relativity you've actually experienced. I didn't ask you for anything which an undergraduate would find unreasonable. Metrics, field equations, conservation of energy and/or momentum, all arise at undergraduate level and are covered in introductory GR books. Spinning disks are a common example and talking point in relativity literature too.

If you're unable to formalise the scenario then admit it and hold your 'conclusions' in a bit more of a questioning mind set.

So you view it as 'simple' and yet you didn't go through the details? The best way to counter my complaints would have been to show you can do the details but instead you made this thread.

As for 'stumping my comprehension' once again I didn't say that but thanks for once again putting words in my mouth, despite you saying you 'won't put up with that' when you think I did it to you. You're hardly taking the moral high ground here. I'm familiar with spinning disk scenarios in relativity, along with plenty of other things in relativity but I don't think you are. I asked you to show you are, that your complaint wasn't just a disguised "I don't understand anything about relativity, including the mathematics, and this particular example seems odd to me so I claim relativity is wrong!". You want a quantitative response? Show you are capable of grasping it. Show you're willing to put in effort you demand of others.

Of course I don't always request someone shows a quantitative grasp before I show mine but given the general tone of your post, including the "heretic" bit, I suspected that any quantitative response would be incomprehensible to you, just like responding to Farsight or Motor Daddy with algebra is a waste of time. As such asking you to formalise your complaint and show methodically how you reached your conclusion provides you with an opportunity to show such a response wouldn't fall on deaf ears. Given you didn't start this thread with said quantitative formalisation but instead more whining I continue to hold my suspicion that you haven't got a clue how to do it.

Awal was banned at some point, so his threads and posts vanish. I don't know who did it or when, as I was away from the forum for several weeks in a row, during which time it occurred.

You want to know why? It's your attitude, typified by comments like those in the previous quote, the 'what do you know, nowhere to be found', 'maybe my turn next' and the 'heretic' comments from the previous thread. You come across as someone who thinks they've got some deep insight and that the responses you get, ie shutting of threads, are somehow an act of desperation or fear from people when faced with your claims. You come across as someone with a deluded vision of their own capability/importance and last night I wasn't really in the mood to bother with you, the thread was awash with irrelevant posts and despite you being asked you'd failed to formalise anything. Yes, perhaps if I'd had more energy or the right mindset I'd have spent the time to do all the formalism for you but I couldn't be bothered. But I didn't prevent you from starting a new thread, I even suggested it. But the tone of your post suggested that doing the formalism for you would only serve to enable you, giving you the excuse to tell yourself you've done something insightful or that you're really worth the response or that you're really doing physics because you're in a discussion where there's lot of technical detail, even if the detail is due to someone else.

As such I thought "Fine, if he wants to talk about the specifics then he can show he can grasp them". If you cannot do the specifics then you shouldn't have the attitude about your 'conclusion' that you have, it is misplaced. If you cannot formalise what you said, which you have now called 'simple', then why should anyone else bother?

I didn't say anything about curvature. Chalk up another case of you misrepresenting me. Jesus, do you have daily injections of hypocrisy or something?

You brought up the stress energy tensor, which links to the space-time stuff via the field equations. The conservation of momentum you also brings up is a specific property of the space-time metric (though I don't suppose you know that). Asking you to do that stuff, to show your workings, is not unreasonable. The conservation of momentum is linked to a specific property of the metric. You talk about the stress-energy tensor and it links to the metric by the field equations. As such what you're talking about is directly about what I asked you to give details of, though the fact you don't realise this suggests you are unaware of this.

You hadn't returned in more than a page and that page was utterly off topic. Rather than restructure the thread I suggested you start a new one. You could have addressed all my criticism of your presentation if you'd just given the details in this thread. But you didn't. And now you're whining.

What's your definition of 'passive gravitational mass'. Algebraically.

You mean other than in Section 1 and Section 2 where they consider the field equations, the components of the metric, the relevant stress-energy terms and then manipulate them to reach their conclusions, which is precisely the sort of thing I was asking you to do? You mean other than that?

You had a bloody crib sheet, a paper which has all the formalism for you, laid out in pretty simple terms. You could have provided details without having to do any work and rather than doing so you complain and whine and imply there's possible action to scrub the threads from the forum.

Besides, do you know how to check whether or not energy and momentum are conserved? It's pretty direct and utterly avoids all the guff in your attempt to describe the scenario. But since I suspect you can't do any general relativity I suspect you don't.

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I think that says everything about you. Why would I delete this thread? Do you think I would do that because that's what your response would be if shown to be ignorant or incorrect? You'd do it to others so you expect it done to you? This thread and the previous one show you've got a chip on your shoulder about something, though I don't care what it is. You don't invoke fear in people, in the 'heavy hitters', just exasperation and a sense of weariness about yet another person who cannot formalise their claims but believe they've got a critical flaw in some area of science.

 

Obviously I cannot assist you in any way, Curious. Good luck with your conversations with others.

 

Are you utterly shameless in continually distorting my true position like that? I demanded such? Where? No don't bother answering - there would only be personal embarrassment in doing that honestly.

So your idea of asking for genuine clarification is that? Why continue this pretense. You imo simply don't like the uncomfortable implications of my little thought experiment - which I'm quite sure you well enough understand. Can't think of an answer to it that fits your worldview. So the best way out is, as you have done in #15, #44 of that ill-fated thread, to just continue a personal attack by droning on about how hopeless I am - as you paint it anyway. And that is a reasonable conclusion given that never once was there an attempt to address the straightforward core argument of the scenario itself. Not once. Deftly skirting the core physical issue - go for the man every time. This says it all as far as I'm concerned. No point in answering the rest of the #12 clone of those earlier posts of yours. Same old tackle the man, never play the ball. OK you have successfully torpedoed my effort to inject something novel and interesting into this sad little site. Not an attitude to be proud of though. End of story. Feel free to now lock this thread also. As I expect you will be itching to do.

[Actually, on further thought, that last suggestion is too much an easy out invite. Best to finish this post by again posing that straight question at bottom part of #1:
Q-reeus: "Will finish this with a question for AN. Place solid matter under uniaxial compressive stress (like energized disk pads do to a brake disk). Does or does not the passive gravitational mass of that matter so stressed increase, or not?"
(And will supplement that here for sake of completeness: will any such passive mass change be dependent on relative orientation of said uniaxial stress wrt ambient gravitational field?
And of course, original question above assumes, as repeatedly stated elsewhere many times, said disk pads are notionally frictionless, thus not complicating things with frictional torque and related stresses, heat etc. KISS!)

Your response in #12: "What's your definition of 'passive gravitational mass'. Algebraically."

An evasive answer by way of another question. But I will play your game on this one to this point. Wikipedia defines all three masses - active, passive, inertial, to my satisfaction here:
http://en.wikipedia.org/wiki/Equivalence_principle#Active.2C_passive.2C_and_inertial_masses
Or try this site for perhaps a better vector presentation:
http://www.mth.uct.ac.za/omei/gr/chap5/node4.html

A simpler way of putting it re passive mass Mp might be in terms of Newtonian force F exerted on such a mass:
F = Mpg, where g = -GMar/r^3 is Newtonian gravitational acceleration experienced by test mass Mp in free fall, given as source of g field, a 'point' active gravitational mass Ma, (and better add; assuming 'weak gravity' applies, where weak implies gravitational binding energies are negligible relative to mass rest energies). Phew.

Between all those, that algebraic enough for you? I will suppose so. Are you now in turn prepared to provide a straight answer to my reproduced (and slightly modified) question above? Your chance to show the moral high ground and graciously educate this GR dumbo, and other similarly challenged readers, on such a small but perhaps important matter. Oh and I disagree re your repeated assertions I never gave any formalization to the problem. Given my assessment this is decidedly a very weak gravity regime scenario, the simple bit of math in 2nd para. here:
http://www.sciforums.com/showthread...tation-in-GR&p=3061964&viewfull=1#post3061964
was imo sufficiently clear as starter, since I adopted imo the perfectly reasonable view that similar findings re stress as source of active mass in that Ehlers paper carry directly across to passive mass - i.e. Ma = Mp. And why would it not?
But let's see how your straight answer I have asked for, if given, does or does not impact on that.]

 

Sad to say Farsight that we have too great a difference in conceptual outlook re this topic for any likely convergence of viewpoint. But thanks for the sentiment.

 

Oh please. You threw down a challenge to the 'heavy hitters' and made comments about how you've been treated as a 'heretic' elsewhere. You wanted answers and you were clearly trying to goad people into a response. It was clearly an attempt to be provocative, a style of behaviour your posts have not only continued to involve but you've ramped it up.

Yes, I get it, you have a chip on your shoulder about something and you don't like how you're just ignored or dismissed off hand by people who bothered to learn some science. Too bad for you. Case in point...

You clearly want to convince yourself (since you aren't convincing any of us) you're onto something, that we're scared of you in some way due to 'uncomfortable implications'.

You want to know why you get so little attention? Your attitude. Your original post was immediately confrontational, presenting yourself as someone being shut down by 'heavy hitters', as someone who is bringing 'uncomfortable implications' to the table and people are worried. Obviously you don't like it when you don't get the attention you want.

Remember how you just complained I misrepresent you. Funny how you have no problem being it to me. I closed the thread not with a "Shut up" but with a "There's too much off topic stuff here. Post again if you wish but be more detailed". I could have immediately closed and deleted the thread and this one. Instead I left it visible and this thread open. Of course your persecution complex and the chip on your shoulder was made clear when you assumed I'd do that, going so far as to save a copy of the thread. An insight into your mentality more than anything else, something you might do if the roles were to be reversed and so you assume others would do it to you.

Firstly not everyone is like that. Secondly I have no problem admitting when I'm mistaken, I've done it many times here. Thirdly you haven't even made a case for your position. Fourthly you figure so low on my mental radar I didn't read this thread after my last post for the better part of a week. I know you want to convince yourself otherwise but the reason you get so little attention is not from inciting anxiety in people so they run away but because you make it abundantly clear rational discourse is not possible and you're not worth much time or effort. No doubt you'll tell yourself otherwise but I really don't care.

Congratulations on being such a blatant liar. You were given plenty of opportunity in the other thread to elaborate, you didn't. You were given the opportunity to start a new thread, where you could start afresh and lay out your position in more detail, as had been requested by more than just myself, but instead you made this whining thread.

You want to inject 'something novel and interesting into this sad little site'? So why did you start this thread and not the one you were asked? At the very least you could have done that in addition to this thread so you could both complain and discuss. No, instead you just complained.

What a sad existence you must have if that is how you view the world. You distorted my reasoning to closing the last one, ignoring how I specifically said you could start a new thread without the off topic noise, and you assume I'm 'itching' to close this one. Nope. I'd be entirely justified given this forum isn't for moderator complaints and how it is nothing but a slew of your misrepresentations and complaints, real and imaginary. Hell, I'd be entirely justified in giving you an infraction warning for this sort of thing but I don't have any desire to. Clearly from your comments you'd not do likewise if our roles were reversed.

Since you didn't answer my question about conserved quantities in general relativity, which doesn't surprise me in the slightest, I'll elaborate. The simple way of determining whether a system in GR conserves energy or momentum is to apply Noether's theorem. Given the metric associated to the system all you have to do is see whether it has explicit t dependence. If it doesn't then energy is conserved. For momentum it needs a translation invariance, an invariance under \(x^{\mu} \to x^{\mu} + X^{\mu}\) for some constant \(X^{\mu}\). Since energy and momentum are wrapped up in the same object, 4-momentum, you can do them together. This amounts to showing there's time and space-like Killing vectors solving \(\mathcal{L}_{X}g = 0\) where \(\mathcal{L}\) is the Lie derivative.

The beauty of using Noether's theorem and things like Lagrangians, Hamiltonians and Killing vectors is that you don't have to solve specific dynamics. By this I mean that since the quantum electrodynamics Lagrangian is explicitly time independent, ie no t term appears in it directly, that there is no combination of electrons, positrons and photons with any physically valid initial configuration whose dynamics lead to a violation of energy conservation. Likewise with momentum. In GR once you have the metric you can immediately determine whether conservations are satisfied, you don't have to go any further and start computing geodesics and the motion of test particles. It's powerful tools like that which explain why the scientific literature isn't awash with people trying to construct elaborate examples where energy conservation doesn't work for models like QED. In the case of the metric in GR we have to still solve the Einstein field equations, which amount to the Hamiltonian equations of motion for the Einstein-Hilbert action.

Sorry, am I going a bit fast for you? I can type slower if you want to keep up.

Anyway.... the nice thing is that we don't have to solve the Einstein field equations to see they lead to energy conservation. Instead we can manipulate them, use some Riemannian geometry, various curvature definitions and identities and conclude that the energy-momentum tensor is covariantly constant, \(G^{ab}_{\quad;b} = 0\) implies \(T^{ab}_{\quad;b} = 0\). The first expression, \(G^{ab}_{\quad;b} = 0\), follows from the definition \(G^{ab} = R^{ab} - \frac{1}{2}Rg^{ab}\) and the definitions \(R = R^{ab}g_{ab}\), \(R_{ab} = R^{c}_{acb}\), \(R^{d}_{abc}\xi_{d} = [\nabla_{a},\nabla_{b}]\xi_{c}\) and the Bianchi/Jacobi identity involving the covariant derivative's cyclic permutation combinations. Then the Einstein field equations saying \(G^{ab} \propto T^{ab}\) gives the second expression. Haven't even had to compute the metric for the given set up you describe.

Now I don't think you're sufficiently familiar with mathematical physics to have come across Hamiltonians, Lagrangians, Hamilton's equations of motion, the Euler-Lagrange equations of motion, Noether's theorem and Riemannian geometry, so I imagine this is all news to you, news you probably don't even understand since I've used a smattering of algebraic expressions.

I asked you to present your case including solving the EFEs because your position is such that you're going against some of their basic properties so it is necessary to see precisely how you construct your conclusion.

Again, I'm sure you're unaware of it but within general relativity there are numerous concepts of mass and therefore asking for clarification is hardly evasion.

Yet another case of "Do as I say, not as I do". Funny how you stamp your feet and complain when someone doesn't satisfy your requests but you have no problem ignoring requests of you when it suits you.

Funny how you'll do it when you can just quote Wikipedia but not when you're asked to do it yourself.

My answer is much like Rpenner's. If the disk is incompressible, a perfect material, I'd say the mass is unchanged. If the disk is compressible to some degree and the pressure comes from somewhere as if by magic then I'd expect a change. As Rpenner says, where the effects are coming from, the way in which they are generated and precisely how we separate such a construct into bits are important things to consider. If the conservation of a quantity is in question then we're considering the time evolution of some system which is not experiencing flux with some external environment so we need to be careful about how we build it and what we're considering. That's why it is important to properly formalise these things. Yes, in a Newtonian snap shot it is easy to say "That is passive mass" but the scenario you're interested in involves more than that, it's comparing some system effectively 'before and after' and how the system undergoes this reconfiguration is important.

As I've said, I don't expect you to be familiar with these sorts of requirements, I don't think you know much relativity. You have a chip on your shoulder about 'heavy hitters', as illustrated by comments like "Now if certain experts here can summon up enough courage and overcome fear of peer censure etc" and your repeated expectation you'll have your thread deleted. You clearly want to convince yourself you've got something insightful, with comments like "What I have shown is that stress as source of inertial/gravitational mass has consequences that amazingly have not it seems before been recognized. Hard to believe, but there it is" and you obviously cannot bear to be dismissed without a second thought. I've not given you a second thought since my last reply and while you obviously want to believe you incite fear in people you don't. Rather your posts incite a rolling of the eyes, a sigh and a "Oh, another one....". I've 'met' too many internet hacks to remember all of their names and I expect you'll be lost in the fog of time too. And if this "sad little site" is not to your liking don't feel you need to stay. I can give you the name of a reputable GR journal or two if you wish, so you can by-pass all of us and just jump to immediately rewriting a major pillar of physics. Hell, if you write up your work I'll even LaTeX format it for you to a journal's specifications so that your work can be judged on its *cough* "merits" *cough* and not its presentation. How's that for an offer! I'm so not in fear of you I'll help you to get your work submitted to a reputable journal.

I once gave this offer to Farsight too, after he made all his "This is worth 4 Nobel Prizes!" claims a few years ago. He didn't take me up on it and he's yet to get anywhere either. Maybe you could ask him for advice on how to self publish your work, when all the journals and publishers turn you down?

 

I never thought about this, this is actually brilliant. I always did that via the vanishing covariant derivative of the Einstein tensor, which can be extremely tedious to do given specific metrics. This seems a lot more straightforward !

 

From #1:

From #14:

So you knew precisely what was asked. And I gave you the superfluous definition of inertial mass as requested. Your brief and 'ify' response in #16:

Pressure comes as if by magic?!! You knew exactly how it comes in the scenario - apply by way of the notionally frictionless brake pads!! Let's for now forget about 'frictionless pads' or even relative motion between disk and pads. Just take the case of a stationary element of solid elastic matter under some uniform principal stress - compressive or tensile. Your answer above is saying in effect, but with a sense of guardedness I find annoying, that passive gravitational (or inertial) mass of an element of elastic solid matter so stressed is only changed if appreciable elastic deformation occurs. Now any real solid must deform under stress, but here you are saying, in the limit as stiffness tends to infinite, passive gravitational (hence also inertial) mass change owing to applied pressure tends to zero. Sounds awfully like elastic energy only counts to me. In fact it is saying that, but please just confirm or deny that obvious restatement by me of your position above. I care not for now to go into some point-by-point exchange with the rest of your #16, as was the case for your #13. Just unambiguously confirm your above position applies to the slightly more general case of any uniaxially stressed element of solid matter. For simplicity assumed stationary in a given frame of reference. (And just for pedantic overkill, system is assumed gravitationally very small - i.e. gravitational binding energy of system, specifically here including the considered solid element, are/is totally insignificant wrt rest energy(s).) Easy enough question to provide a clear answer, free of any 'I'd say' type subtle qualifiers? Sure hope so.

Well I have made it especially simple now. To reiterate - passive gravitational (or inertial) mass for a stationary, uniformly and uniaxially stressed element of an elastic solid. So above 'concerns' should not be an issue. To rephrase it slightly differently, in a nutshell, what is the contribution of any relevant principal stress term(s) in stress-energy tensor, to this simple situation? No tricks.

 

AlphaNumeric; I know you're there - shown logged in as I post this #19. And I checked your activity record - making posts for several days following my #18 post (date stamp:04-27-13, 08:27 AM). So you must have been aware of it and available to answer back then. What seems to be the problem? Don't try that 'below my radar BS again please - it won't wash now any more than first time you tried it. You were specifically asked in #18 to confirm your one-line, amazingly hand-wavy answer in #16 to my query was in fact as I have stated it in #18. There can be about zero room for doubt my restatement was correct in essence, but there is a certain wriggle room flavor to your 'I'd say' and 'I would expect' that comes across as weasely. Something wrong with confirming or clarifying as asked? I even simplified the situation to rock bottom - static element of stressed matter, just to make it ever so simple and clear. Why have you not shown the minimal courtesy of answering, and much sooner to boot? How about doing so now!

 

To be honest I didn't even bother reading your reply, despite seeing you'd made one. I didn't even open the thread, you're pretty low on my priorities list even when considering the forum, never mind demands on my time in real life.

You want to give others lessons in courtesy? After all your whining, making a thread to complain, the immediate confrontational behaviour, the insinuation I'm itching to close and delete this thread, that awal was banned had something to do with covering up things? After all that?

To be honest I don't think you deserve 'courtesy'. Nothing to do with 'below my radar' nonsense, which is yet another example of how you have this delusion of people being afraid of you or there being some kind of cover up. You illustrate the sort of person you are by assuming others, such as myself, would close threads or delete them or ban people if we're shown to be wrong about something. This mentality you have has already shown having a rational discussion with you is difficult, given how you chose to start a whining thread rather than give quantitative details, as I asked you do when I closed the previous thread for being flooded with more than a page of off topic posts (which you interpreted as an attempt to close down discussion on the subject

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).

I also notice you ignored the chunk of my post where I gave a quantitative explanation of how, regardless of the scenario, any system obeying the Einstein field equations will have local energy and momentum conservation by virtue of curvature identities giving \(G^{ab}_{;b} = 0\) for \(G_{ab} = R_{ab} + \frac{1}{2}Rg_{ab} + \Lambda g_{ab}\) and how this then implies energy & momentum conservation \(T^{ab}_{;b}=0\) by the field equations \(G_{ab} \propto T_{ab}\). We don't even need to go into the specifics of your scenario, that covers ALL scenarios. Want another way of showing it which is more scenario specific but still general? Construct the relevant field equations component by component, solver them to give you \(g_{ab}\) and then show that there is a Killing vector associated to time translation. Or we could do it another way (though its just a reformulation of these) by starting with the Killing vector \(X^{a}\), which satisfies \(X_{\{a;b\}} = \frac{1}{2}(X_{a;b} + X_{b;a}) = 0\), and constructing a conserved current \(J_{a} = T_{ab}X^{b}\). We now do the usual thing of constructing the flow condition by computing \(\partial_{t}J_{0}\), which is the time variation of \(J_{0} = T_{0a}X^{a}\). This is standard stuff, \(\nabla^{a}J_{a} = \nabla^{a}(T_{ab}X^{b}) = (\nabla^{a}T_{ab})X^{b} + T_{ab}\nabla^{a}X^{b}\). The first term vanishes by the Einstein field equations and so \(\nabla^{a}J_{a} = T_{ab}\nabla^{a}X^{b}\). Since \(T_{ab} = T_{ba}\) this can be written as \(\frac{1}{2}(T_{ab}+T_{ba})\nabla^{a}X^{b} = \frac{1}{2}T_{ab}(\nabla^{a}X^{b} + \nabla^{b}X^{a})\) and since X is Killing \(\nabla^{a}X^{b} + \nabla^{b}X^{a} = 0\) and so \(\nabla^{a}J_{a} = 0\). We pick some coordinates, \(x^{\mu} = (t,\mathbf{x})\) and get \(\partial_{t}J_{0} = \nabla_{\mathbf{x}}\cdot \mathbf{J}\), so the time variation of \(J_{0} = T_{0a}X^{a}\) is a divergence and so by Stokes theorem \(J_{0}\) is constant, ie conserved. That's your energy and momentum conservation for the respective Killing vectors.

You can do these for your specific example if you wish. Construct the field equations and check \(T^{ab}_{;b}=0\). Solve them to get your \(g_{ab}\). Then use the metric to compute the space of vectors satisfying \(X_{\{a;b\}}=0\). Then show that they all solve \(\mathcal{L}_{X}g = 0\). Then use them to compute the various \(J_{a} = T_{ab}X^{b}\) currents and then show \(\nabla^{a}J_{a}=0\). You'll then have addressed energy/momentum conservation several times.

/edit

Oh and if you come back with "You're just trying to hide behind walls of algebra!" I'll point out this is all stuff covered in introductory courses on GR and anyone with a working familiarity of GR should have no problem understanding what I just said. The details also prevent issues with poor wordy descriptions and arm waving, which is a criticism I've levelled at you. If you cannot understand what I just said you illustrate you have insufficient familiarity with GR to justify the attitude you have about your claims, how confident you are in your conclusion and how you supposedly incite anxiety in the 'heavy hitters'. So I'll assume from your self assuredness you do understand it. Right?

Given the fact Lorentz transforms mix together the time and space parts of a system (or rather show there isn't a clear distinction between them) everything in GR should be expressible in a way which doesn't show this splitting, it is artificial. All the covariance stuff pertains to this. It also makes things a lot more streamlined. Another way of seeing it is the fact energy is conjugate to time and momentum conjugate to position and so if relativity blurs together space and time then it must blur together energy and momentum in a similar manner.