201. Comment #204268 by Steve Zara on July 4, 2008 at 2:40 pm

Comment #204224 by Oystein Elgaroy

It sounds like the paper, but what I am reporting is only my vague impression of what I remember!

Stenger's more pragmatic view avoids huge metaphysical commitments like that, so I think it has a few things going for it.

It seems to me to be a bit like the "selfish gene" idea as first proposed by Dawkins - a different perspective on things that can give a simpler and clearer view of what is going on.

Of course, the selfish gene idea turned out to be more than that..

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202. Comment #204281 by mordacious1 on July 4, 2008 at 3:09 pm

Oh crap, how did I miss this discussion going on?

Some extremely interesting points made.

Let's not discuss them NOT finding the Higg's particle. That is just too depressing to think about, since all the evidence points to its existence.

Stenger: I agree with Steve about some of the things Stenger proposes. But I find myself being persuaded not just by his physics, but by his writing style and abilities to put forth his arguments. I love to read his books. I just have to be careful to go back and extract the facts and his ideas, then think about them without getting wrapped up in the totality of his writing.

Thanks all for having an enlightening discussion.

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203. Comment #204283 by Steve Zara on July 4, 2008 at 3:17 pm

Let's not discuss them NOT finding the Higg's particle. That is just too depressing to think about, since all the evidence points to its existence.

That is not depressing at all. It should be considered exciting. It means we have to consider new physics.

The wonderful thing about the LHC is that whatever the results, they will change our understanding of the universe.

I think it is wonderful to have forums like this to discuss such matters, and we now have a real expert - Oystein Elgaroy - who, I sincerely hope, will guide us through the results that come from the LHC.

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204. Comment #204287 by Donald on July 4, 2008 at 3:42 pm

If I understand him correctly he certainly thinks that there is an objective reality out there, but that all physicists do is to create models for how that reality behaves. If we want these models do be independent of viewpoint, they have to satisfy certain symmetries (invariance under translations in space and time, rotationas etc.), and these symmetries restrict the mathematical structure of these models.

This point of view is certainly very different from my intuition, which is that our models are approximations, hopefully steadily improving, to the true laws of nature. That there are laws of nature lying out there, waiting to be discovered is dangerously close to platonism. - Oystein

There is a lot in common here. We all agree there is an objective reality out there. We all agree that physicists create models for how that reality behaves. And we all acknowledge the usefulness of symmetries in guiding recent successful models. I would guess we are all in agreement up to this point? So I'm not sure where you feel your intuition is different from Stenger's. It seems to be something about the nature of the "real" laws that our models approximate, but I can't see the crucial difference.

For myself, if tempted into Stenger-style metaphysics, I would be tempted to speculate that symmetries themselves are emergent properties rather than fundamental generating principles. I would speculate that the key to the fact that the universe is understandable from within itself (and understandable by such a minute fraction of it (i.e. us)) is that it is constructed of vast numbers of repetitive elements, each following the same formula for action. Any such construct is potentially understandable from within (so I speculate anyway). So I would place repetition of elements, not symmetries, at the centre of my metaphysics.

Of course, I do not mean the repetitive elements are the current particles in the standard model zoo. There must be layers (perhaps several) below that before we get to model whatever the truly fundamental elements of the universe are.

Anyway, Decius is probably right that I should read both Stenger's books before commenting further. I'm not sure I will though - despite cheering on his atheism, I'm not a great fan of metaphysical speculations.

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205. Comment #204291 by Donald on July 4, 2008 at 3:51 pm

Steve, I thoroughly agree that the LHC will be exciting whatever is found, and that new physics of some kind will emerge.

Perhaps we should place our bets on the Higgs though?

I would bet it is not found, although I predict there will be false alarms before a conclusion is reached!

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206. Comment #204297 by Steve Zara on July 4, 2008 at 4:22 pm

Comment #204291 by Donald

I would bet that the Higgs is found, but I hope it isn't - it would be wonderful if we had to involve new physics.

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207. Comment #204332 by mordacious1 on July 4, 2008 at 7:50 pm

Steve

That's like saying "I wish Columbus hadn't discovered America, so he could keep sailing and discover Hawaii".

Physics is going to be exciting whether they discover the Higg's bosun or not. I think that they will, which will be good. But don't worry, there are so many other things yet to be discovered. Columbus discovered America (sort of), and someone else discovered Hawaii.

Every time we put a piece of the puzzle in, we get closer to completing the puzzle. But don't worry, this is a jumbo puzzle and it's nowhere near completed. Is that enough metaphors for everyone?

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208. Comment #204432 by Oystein Elgaroy on July 5, 2008 at 12:52 am

Comment #204287 by Donald

Stenger seems to think that his take on the "laws of nature" involves fewer metaphysical commitments than more traditional views. Whether he is right or not, the question of where the laws of physics come from frequently pops up in discussions with theists, so it is important to think about this.

Comment #204297 by Steve Zara

I think quite a few physicists agree with you. Personally I hope they find both the Higgs and supersymmetry. In fact, I think it is unlikely that they will find one without the other at the LHC, because the hypothesis of SUSY at LHC energies is closely tied to properties of the Higgs boson.

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209. Comment #204455 by Donald on July 5, 2008 at 2:59 am

Oystein, #204432: "the question of where the laws of physics come from frequently pops up in discussions with theists, so it is important to think about this."

I just say: "I don't know. But I do love to read and understand the discoveries that have been made. Do you know about those?"

But you made a remark "This point of view is certainly very different from my intuition, which is that our models are approximations, hopefully steadily improving, to the true laws of nature."

Your intuition there is the same as mine, and most physicists. So where exactly is the crucial difference of Stenger?

We all agree there is an objective reality out there. I think we all agree that physicists create models for how that reality behaves. And we all acknowledge the usefulness of symmetries in guiding recent successful models. So what exactly is the crucial difference between Stenger's view and your view?

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210. Comment #204457 by Oystein Elgaroy on July 5, 2008 at 3:04 am

Comment #204455 by Donald

Donald, I get the impression that Stenger denies, or at least is agnostic about, whether there are true laws of nature out there.

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211. Comment #204555 by Donald on July 5, 2008 at 7:37 am

Oystein, thanks for the information about Stenger.

Could I ask you a question more related to practical cosmology?

I have seen on this site a claim about the energy in the universe and gravitational potential energy. I am suspicious of this claim, which I think is spurious. It can be found in several places on the web - one article ascribes the original idea to a physicist "Edward Tyron" in 1973, and there is a layman's description given by Stephen Hawking in his book "A Brief History of Time".

The claim is: "the total energy in the universe is zero, because the total amount of negative gravitational potential energy is exactly equal to the positive mass in the universe". Here is the layman text from Stephen Hawking:

The matter in the universe is made out of positive energy. However, the matter is all attracting itself by gravity. Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart, because you have to expend energy to separate them against the gravitational force that is pulling them together. Thus in a sense, the gravitational field has negative energy. In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.

This seems to me to be just plain wrong. Known physics has established convincingly that all physics processes leave the total energy unchanged - it merely gets converted from one form into another (with temporary exceptions being allowed during quantum processes). So the consistent view of the conversion of gravitational potential energy into kinetic energy would be that the positive gravitational potential energy is converted into positive kinetic energy when apples fall. Conversely, when energy is injected to separate two masses against the mutual gravitational attraction, the positive energy injected is converted into positive gravitational potential energy. Am I missing anything?

Do you recognise the claim as being based on anything sound? Is this respectable, serious cosmology? Is there any reasonable justification for assigning a negative sign to gravitational potential energy, from cosmosology or anywhere else?

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212. Comment #204563 by Oystein Elgaroy on July 5, 2008 at 8:39 am

Donald,

in Newton's theory the potential energy for a system of two point masses is defined so that it is zero when they are infinitely far from each other. As a consequence it is negative for finite separations. All this means, of course, is that you have to do positive work on the system to bring the particles infinitely far apart. Since only differences in potential energy matters in Newtonian gravity there is no physical significance in the fact that potential energy is negative by convention. So one can just as well describe the situation in the way you do.

I can't remember where the idea that the total energy of the universe can be zero came from, but Tryon certainly put the idea to dramatic use when he suggested that the universe could be a vacuum fluctuation. The idea was simple: take Heisenberg's uncertainty principle for energy and time, Delta E x Delta t > hhbar /2. If Delta E is the energy of the vacuum fluctuation, then the closer Delta E is to zero, the larger will Delta t be. A zero-energy vacuum fluctuation can exist indefinitely. So if the total energy of the universe is zero, it may possible have started as a vacuum fluctuation. As Tryon says in the closing paragraph of his paper: Our universe may be just one of those things that happen from time to time.

But is the energy of the universe zero? The quote from Hawking suggests that it has, but is, I think, misleading because it applies Newtonian concepts in a situation where they are not valid. In cosmology we have to use general relativity and there the concept of gravitational potential energy simply does not exist, at least not in a coordinate-independent way. In fact there is in general no law of global energy conservation, only local. For some special cases, like in the case of the Schwarzschild spacetime one can prove that there is global energy conservation and talk sensibly about thinks like, e.g., the energy carried by gravitational waves. But for the spacetimes of interest in cosmology the situation is unclear. Some people argue claim that energy is conserved, and that the total energy of the universe is zero, but these claims are again refuted in other papers.

In Hawkings field, quantum cosmology, much of the work is based on the so-called Wheeler-de Witt equation for the wavefunction of the universe. It turns out that in the case of a closed universe containing just a scalar field (or vacuum energy) the Wheeler-de Witt equation looks just like the time-independent Schrodinger equation with the energy eigenvalue equal to zero. This is the justification for saying that the total energy of the universe is zero in this approach.

Sorry if I was too technical, but you asked a difficult question with no simple answer. Simplifications, like the your quote from Hawking, easily end up being misleading. The short answer is that it is not at all clear that it makes sense to talk about "the total energy of the universe" at all, much less that it is equal to zero.

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213. Comment #204565 by Steve Zara on July 5, 2008 at 9:00 am

The idea that the energy of the universe could be zero is pretty old.

There is a story that George Gamow told in his autobiography of a conversation he had with Einstein in Princeton during the second world war.

Gamow pointed out to Einstein that a star could be created out of nothing at a point, as the negative gravitational energy cancels the positive mass-energy.

"Einstein stopped in his tracks," says Gamow, "and, since we were crossing a street, several cars had to stop to avoid running us down."

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214. Comment #205122 by Donald on July 6, 2008 at 3:57 pm

Very helpful reply indeed, thanks Oystein.

I now realise my error! All my life I have assumed that all energy is positive, and that all physical process convert positive energy into other forms of positive energy. But it's not so. And negative energy is involved right at hand, in the simple concept of gravitational potential energy!

I had always assumed that the convention of taking masses at infinite separation to have zero potential energy was merely a convenient "shift by a constant" to avoid the introduction of an awkward constant into the formulas for handling potential energy (most practical calculations are about potential energy differences, so the constant disappears anyway, as you say). (The "awkward" constant being the integral w.r.t. d from 'zero' to infinity of G*m1*m2/d*d. Incidentally, I don't know how to typeset formulas into these comment threads in a convenient way - anyone here who can tell me a convenient way?)

I had never realised that negative energy has a physical reality. Once one realises that gravitational fields are negative energy, then it is entirely natural to postulate that the negative gravitational field energy exactly cancels the positive energy in the masses, in a vaguely analogous way to the way that positive and negative electric charges, etc, are exactly balanced in the universe.

Hawking's layman quote is not misleading at all - I just didn't recognise it as true, because of the erroneous assumption embedded in my thinking. My question didn't really need addressing via the more complex spacetime models (although I'll think about how the issue looks in those later, perhaps).

This has set me thinking about all sorts of consequences.

I can now see a rationale, and a numerical solution, to avoid the 'zero' I put in scare quotes in the integral above. (It can't actually be zero, because we would introduce an unrealistic infinity.) If we consider a unit mass in a classical gravitational field in relation to a mass m, we can find a critical finite radius for the mass m to make the negative-energy field integral equal to the mass. We need a conversion factor for mass into energy, but we can get that from special relativity, we don't need general relativity. So something like a planck distance emerges from elementary gravitation. If we assume two unit masses at infinite distance and require that their two gravitational fields should equal their combined mass, we get something like 2*m"c*c = 2*(Integral From L to Infinity G*m*m/d*d) where L is the putative planck-like distance, and is determined by something like this equation. (I know this requires significant amendment to become accurate, but I'm trying to focus in the basic idea.)

So, if done properly, a critical distance should emerge. The m's don't cancel, so the critical distance depends on m, so to get a minimum critical distance, there has to be a mimimum mass, so quanta are needed from somewhere else for that. Nevertheless, this method gives a certain kind of critical radius for any mass. One might call it the "equality of positive and negative energies" radius. Is this standard physics, but just rather unimportant? This is all within a purely Newtonian spacetime. I wonder if this "EPNE"critical radius has any relationship to the Schwarzchild radius. (I know the Schwarzchild radius is about avoiding collapse to a singularity within a general relativity spacetime, but I wonder if this "EPNE" radius has any relationship to it.) The EPNE radius idea is so simple I suppose it might be covered in elementary physics texts. Is it? Or have I just wandered off into nonsense with some more misconceptions?

Ah, and the whole question of negative energy raises more questions. Standard gravitation only considers the positive energy component and how that reacts with other positive energy components. Does the negative energy play any direct role? Does matter move in response only to the positive component, or is it a combination of reacting to the positive component and also reacting to the negative component?

Is there a proof that any formula based on interaction with the positive and negative fields separately will turn out to be equivalent to a simpler formula describing the interaction in terms of the positive components only, for all kinds of irregular mass distributions?

You make the very good point that this whole issue disappears into the geometry of spacetime in general relativity.

However, continuing as far as possible within Newtonian spacetime, and exploring the notion that the negative energy field might require explicit consideration, does negative energy repel matter as a contribution to the total effects of gravity? If so, the behaviour of matter would depend not only on distance to nearby masses, but also on the intensity and size of nearby negative energy fields. The galactic voids would be the places with the most negative energy, so is there any possibility that that could be an appropriate foundation for Milgrom's MOND theory?

And if negative energy repelled itself, would that merely turn out to be equivalent to Einstein's cosmological constant, or would lumpy distributions with big voids behave any differently as regards their overall expansion?

I am sure all my questions have already been considered by physicists or cosmologists, so are there web resources that discuss these particular questions in terms I might be able to understand?

Also this whole issue of negative energy and Steve Zara's story about Gamow, Einstein and the star popping out of nowhere has made the questions raised about the safety of the LHC seem much more vivid. I remain confident that the scientists who really understand particle physics (and cosmology) are right when they say it isn't going to unleash black holes or hyper-inflating mini-universes, but the safety issue seems much more of a real concern than it did before!

Hmmm... This became an absurdly long and rambly post. But if you are a patient man Oystein, perhaps you could correct any more misconceptions of mine that you notice in the above.

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215. Comment #205128 by Steve Zara on July 6, 2008 at 4:15 pm

Also this whole issue of negative energy and Steve Zara's story about Gamow, Einstein and the star popping out of nowhere has made the questions raised about the safety of the LHC seem much more vivid.

There is nothing to worry about. Just because the mass energy and gravitational energy of a star cancel out does not mean that stars are popping into existence out of empty space. You have to have a mechanism for this to happen, and there isn't one. There are various conservation laws for particles, which is why you can't create an electron by itself - you get a positron too.

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216. Comment #205205 by Donald on July 6, 2008 at 7:19 pm

There is nothing to worry about. Just because the mass energy and gravitational energy of a star cancel out does not mean that stars are popping into existence out of empty space. You have to have a mechanism for this to happen, and there isn't one. There are various conservation laws for particles, which is why you can't create an electron by itself - you get a positron too. - Steve Zara

Obviously there aren't whole stars popping into existence in the observable universe today (at least not anywhere easily observable).

The point was that the LHC is (claimedly) recreating conditions that only existed in the first fraction of a second after the big bang. Hopefully the "only" is hype.

There is only one way to be reassured about the safety of the LHC. And that is to establish that the events it produces are events occuring today routinely in other places in the observable universe, and that we are merely bringing those events into the lab, as it were, to examine them at closer quarters.

If we were genuinely recreating conditions that have not existed for the lifetime of the universe, I think the concerns would be major indeed.

As I said, I am confident that the real experts have examined the issues, and will have looked at any issues we might raise here.

You said a mechanism is required. Quite right. But there was. At the start of the big bang, while matter was still being created, during inflation, all of matter DID just pop into existence. Allegedly.

Until we have more information about the conditions that were associated with inflation (assuming that theory is correct) we would be unwise to try to recreate similar conditions.

However, I assume (hopefully correctly) that the LHC is aiming at conditions that, although they were early in the history of the universe, were nevertheless long after the inflation period. Hopefully.

I remain fascinated by the this kind of science. And I really don't want to argue with you - you make very valuable contributions to this site. I make this response in the spirit of mutual fascination rather than argument.

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217. Comment #206199 by latsot on July 8, 2008 at 7:01 am

> quantum lore

*ROAR*.

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218. Comment #206210 by Diacanu on July 8, 2008 at 7:10 am

Are your new theories not only explosive, but painful, runny, oily, or perhaps even bloody?

Try Shmegalamonga!!

http://dickynoo.blogspot.com/

Not only will your orifices thank you, but so will your spouse/life-partner/maid/whomever cleans up after you.

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219. Comment #213013 by Oystein Elgaroy on July 18, 2008 at 2:23 am

Donald,

a brief (and late) response to your questions:

I would maintain that the sign of the gravitational potential energy in Newtonian theory has no special significance. The important point is that the potential energy of two point masses is lower at a finite separation than when they are infinitely far from each other. In other words, you have to do positive work on the system to break it up.

The reasoning behind your EPNE radius is similar to the reasoning leading to the so-called classical electron radius, which is the radius of a sphere of constant charge density with electrostatic potential energy equal to the rest mass energy of an electron. Your EPNE radius is of the order of the Scwharzschild radius, and its physical significance is to signal the breakdown of Newtonian gravity.

In Newtonian gravity only mass (or mass density) contributes to gravitation fields, so negative energies are of no importance when it comes to gravitational forces. In GR, both mass, energy and pressure contribute to spacetime curvature. Vacuum energy can be positive or negative. If it is negative, it has positive pressure, and the pressure contribution makes sure that gravity is still attractive. The opposite holds for positive vacuum energy.

Milgrom's idea of MOND is more like a modification of Newton's second law than a modification of gravity. A theory that contains MOND will therefore in some sense have to violate the equivalence principle. Bekenstein has built such a theory, but it doesn't seem to pass all the observational tests.

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220. Comment #214922 by Donald on July 21, 2008 at 4:07 am

Another helpful reply Oystein.

Yes, I agree that, for typical calculations, the gravitational potential energy in Newtonian theory, is not treated with any special significance. But it was a new insight to me to realise that the potential energy seems to have a physical reality as a negative energy, and I'm still trying to get my head around various implications.

The "EPNE" radius that I considered in the previous post, I calculated to have an aproximate numerical value of 0.74 x 10^-27 m/kg, using the accepted values for G and c. So, the EPNE radius for a mass the size of the Sun would be 0.74 x 10^-27 x 2 x 10³⁰ = 1.5 x 10³ m. The Schwarzchild radius is 3 x 10³ m, almost precisely twice as large. It seems to be clearly related, as you say, but I can't see why the relationship should be exactly a factor of two. Is there any reason you can see? You said you thought it would be of the same order. Was that a result of algebra or intuition?

Perhaps I've lost a factor of two somewhere. I'm suspicious of my "separation of two unit massses" reasoning. I wonder if I'm not taking proper account of the fact that if the masses were separating themselves in a self-contained universe, the masses would steadily reduce. However, that makes the integral horrid, and I tried to avoid that by considering the behaviour of fixed masses (with implicit external energy input, but I thought that would still be valid reasoning).

In any case, the EPNE assumption seems to be quite different from the GR assumptions of equivalence of inertial and gravitational mass, plus a fixed speed limit for light. Why should the two critical radii be related at all? Is it merely a numerical coincidence?

Yes, my EPNE radius calculation does sound similar to your description of the classical electron radius calculation. However, the electron radius calculation seems to mix two concepts, mass and electric charge. I'm not sure the calculations are really the same. Perhaps the assumption is that the rest mass of the electron comes exclusively from its charge. I've no idea whether that's true or not. Even if it is, there is not going to be any simple analogy with gravitation, because mass is unipolar and charge is bipolar. I'm not only out of calculation depth there, I'm even out of my depth as regards speculation and intuition.

Getting back to my small clutch of questions about whether negative energy plays any direct role in the way matter moves in gravitational fields. My thinking was that if negative energy is physically real, it is natural to consider where it is located and how it is distributed throughout space. It is natural to expect the positive energy to concentrate in a small volume (up to some limiting density - we don't think singularities are going to be real) because it is self-attracting. But what about the negative energy? Perhaps it is mutually repulsive? That would result in it being space-filling, which seems to match what we observe. Then there is a question about whether positive and negative energy have any direct effect on one another. Another natural intuition is that if they do interact directly, the interaction must be repulsive, because if it were attractive, the central positive sphere and the surrounding negative field would be continuously in contact, and the positive and negative energies could progressively (perhaps rapidly) cancel each other, leading to an energyless vacuum, instead of retaining a stable particle of matter surrounded by a negative-energy gravitational field.

The mutual repulsion of negative energy, and the repulsion of positive and negative need not be large effects. They might only be slight adjustments to the main effect of the mutual attraction of positive energy. They would of course have to obey the conservation of energy law, which might be tricky to arrange.

But this was the reasoning that led me to thinking there might be scope here for a refinement of the theory of gravity based on these adjustments. My intuition is that this would not be equivalent to the cosmological constant in GR when applied to irregular mass distributions, but I'm open to being corrected here.

You seem to be right that Milgrom's MOND theory is a proposal to modify Newton's second law, not the theory of gravity, although the page http://www.astro.umd.edu/~ssm/mond/faq.html refers to it being interpretable either way. In either case, Milgrom's theory is based on assuming that the modification occurs at a fixed magnitude, rather than on what is in neighbouring parts of the universe. Perhaps what I should have said was "perhaps repulsion of negative energy and positive energy could be a foundation for explaining the observations that Milgrom's theory attempts to explain".

Thank you for mentioning Beckenstein. I looked at some Wikipedia pages, especially the pages on the Bullet Cluster and dark matter. It seems there is probably no need after all to refine the theory of gravity to explain the galactic motions observed.

But I still wonder about the negative energy effects. Are we sure that gravity only requires consideration of the positive energy components?

There are other cosmological implications. If negative energy is mutually repulsive, then it will behave rather like a gas, and the pressure will increase if the volume is smaller. This means the expansion of the universe will have proceeded faster in the past, in fact dramatically so. It would also change all the calculations about the timing of galaxy formation - that would happen earlier too.

I feel sure these speculations have already been considered by some cosmologists. Is there any refutation of these ideas?

Any more thoughts from you would be welcome, of course.

Other Comments by Donald

221. Comment #215130 by Oystein Elgaroy on July 21, 2008 at 10:58 am

Donald,

if you construct a length scale from a mass, the speed of light and the gravitational constant, you are bound to end up with the Schwarzschild radius, modulo a numerical constant. It's just dimensional analysis. Your EPNE radius is exactly half the Schwarzschild radius.

Regarding negative energies, as I've said before there is in general no way of defining gravitational potential energy in general relativity. In Newtonian theory the gravitational field is determined by mass density alone, so negative energies play no role. Note that even in the Newtonian case the question of localization of the energy of the gravitational field is a tricky one. If you want to think about cosmology, then you have to do your thinking in terms of GR where there is no such thing as gravitational potential energy.

Other Comments by Oystein Elgaroy

222. Comment #215335 by Donald on July 21, 2008 at 4:43 pm

if you construct a length scale from a mass, the speed of light and the gravitational constant, you are bound to end up with the Schwarzschild radius, modulo a numerical constant. It's just dimensional analysis. Your EPNE radius is exactly half the Schwarzschild radius.

This seems to be mainly a put-down, rather than an attempt to consider and explain.

First, the only reason for the speed of light entering into my calculation was to convert between mass and energy (from SR, not GR).

I do not see why integrating gravitational potential energy as if it were a real physical field of negative energy in Newtonian space, and setting it equal to the positive energy in the mass, should have anything to do with the GR calculation, let alone give an answer that appears to be strongly related (or identical, if I go back and find a pesky missing factor of two).

Why should a purely Newtonian calculation about summing putative negative energy fields, have anything to do with a GR calculation about a boundary characterised by the ability of a mass to prevent the escape of light?

"It's just dimensional analysis" seems to be a useless put-down argument. By that reasoning any number I might obtain from any nonsense calculation using mass, energy and G and preserving dimensionality would be "the Schwarzschild radius, modulo a numerical constant". How about assuming there is no negative energy field and deducing a radius of zero? Would that still be "the Schwarzschild radius, modulo a numerical constant"?

Regarding negative energies, as I've said before there is in general no way of defining gravitational potential energy in general relativity.

And as I said before I acknowledge that gravity, including gravitational potential energy, disappears into the geometry of GR spacetime.

In Newtonian theory the gravitational field is determined by mass density alone, so negative energies play no role.

Yes, I know that's the case for conventional Newtonian theory. But Newtonian mechanics was formulated without any concept of negative energy (at least not physically real negative energy), and before the discovery of the equivalence of mass and energy. Newtonian mechanics can incorporate the idea of negative energy in the gravitational field in a trivial way, by simply assuming it is distributed throughout space and plays no part in the gravitational dance. But it struck me that if one treats the negative energy as physically real, there is the possibility of tweaking Newtonian mechanics by considering the possibility of interactions involving the negative energy directly. It's fine with me if that's of no interest to you, or if it seems elementary, misguided or foolish, but obviously you could have made a more tactful (and helpful) response had you wished.

If you want to think about cosmology, then you have to do your thinking in terms of GR where there is no such thing as gravitational potential energy.

Perhaps so, except I would prefer to say that the gravitational potential energy is implicit in the geometric equations rather than there is no such thing. But I'm not familiar with the GR equations, and it's rather a steep learning curve. I don't know how to modify GR to incorporate curvature equivalent to repulsive interactions involving negative energy.

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223. Comment #215467 by Oystein Elgaroy on July 22, 2008 at 1:23 am

Comment #215335 by Donald,

no putdown intended, I was just trying to explain (rather badly I can see) why heuristic arguments can give insight in the behavior of physical systems prior to solving, e.g., the equations of GR in gory detail. Your argument seems to me to show that (in Newtonian terms) the gravitational potential energy of a black hole is equal in magnitude to its rest-mass energy. I haven't thought about this point before, and it is certainly interesting.

I don't want to discourage you from exploring your ideas further. All I am saying is that one has to be careful (because in Newtonian theory and in SR you can always shift the zero point for energy, so the sign of the energy has no obvious meaning in itself), and one has to think carefully about where to start, since Newtonian theory is linear and the gravitational field is sourced by mass only, not energy. Maybe you can get some ideas by starting from linearized GR. There one works with gravitational fields in flat spacetime, and can build up systematically better approximation to GR using mostly Newtonian concepts. In this approach the gravitational field is also a source of gravity, so maybe one can then better understand the consequences of negative energies for gravity. There is a good description of this approach in a textbook by Hobson, Efstathiou and Lasenby: "General relativity: an introduction for physicists".

Again, sorry that I came across as an asshole.

Other Comments by Oystein Elgaroy