First of all, your first quoted above statement isn't true since I answered your questions and if you don't understand something in the answers then you should ask about it rather than to repeat the questions. Then I might try to explain it to you in a simpler language that won't look to you like an "impressive word salad".

I don't know you since BAUT displays on my comp with a lot of errors and doesn't allow to see the profile of the person whom I'm responding to (neither allows to set a profile). I was able to figure out that you are not a physicists if you have to look to wikepedia for definition of Poynting vector. Had I have known this I wouldn't use Poynting vector as an example but I'd try to use some other vector that is also conserved and which you might understand better. Like e.g. (pseudo)vector of angular momentum (I hope you know this one). Since the principle works for either of them the same way in curved spacetime. This way you might start understanding what it is all about and why your ideas about conservation of energy in curved spacetime are ATM ideas.

Of course you need to understand what curved spacetime is, but if you want to discuss Einstein's universe coming to this thread you have to understand at least what we are talking about here.

This doesn't sound promissing since apparently you aren't aware of the fact that we all live in a curved spacetime (otherwise there wouldn't be any gravitation where we live) and so the physics to be accurate has to work in a curved spacetime without even mentioning it. That's why what you said above makes no sense to a physicists. Since you didn't know that, it was easy to guess that you are not a physicists. Which is of course OK since everybody should understand the world including non physicists.

Second, your questions aren't about "Einstein's universe" that I hoped to discuss in this thread but they are your private ATM questions on a different subject (and so your action is called here "highjacking the thread" and is a bannable offense).

Third, I'm not interested very much in discussing your ATM ideas on curved manifolds and Noether theorem, that you don't understand. What I answered is a plain mainstream response and if you don't accept the mainstream you should open your own ATM thread dedicated to those questions and put there your point of vew on conservation of energy. I might come there and explain to you why you should rather stick to the mainstream point of view.

I said in my first message that I hope to bring into the discussion "people who are supporting the mainstream view (others don't need to apply)" and I'd like to keep it this way. Your ATM ideas, though interesting, I can handle when you open a thread about them. I might come there and explain all your doubts in detail. Just make your own thread and don't highjack mine.

Fourth, wikipedia does not represent the mainstream view. By design it expresses the opinion of majority (decided by editors through concensus) in hope that it turns out to be the mainstream opinion. In most cases it is unless about things that people have strong opinions about. An example may be wikipedia's article on gravitation where the authors, almost a century after Einstein's gravitation theory has been discovered, are still talking about the "attractive force", since this is what the majority still believe in (they think that Einstein didn't explain gravitational force just made it more accurate -- whatever it means). Of course it is not the mainstream opinion. The mainstream uses Einsteins gravitation since always. If you want to follow wikipedia blindly then you are bound at some point to get into conflict with the mainstream (like those "gravitation" authors).

I may be a sculptor, but I have also MS in electronics, so I happen to know a lot of physics and math and since I'm involved in gravitation for over 20 years and I'm right now doing my PhD work in it I could also explain to you some interesting things if you are willing to learn. At least I can tell you what's ATM and what's the mainstream. I don't have any business in misleading you about anything and if wikipedia delivers partial knowledge don't blame me for not agreeing with wikipedia but rather learn what is the mainstream view on it from some mathematical physics or astronmy professor whom you trust.

Fifth, about your questions: let specify in sufficient detail what you didn't understand in my last response. When I know what you don't understand I may explain it to you better. Repeating the same thing twice without saying what part you don't understand makes no sense.

I propose to skip this question as irrelevant. E.g. all astronomers opposed Copernicus (one guy) because of lack of paralax and yet it turned out that they were wrong and paralax was simply too small to be observed. So it turns out (and you must know that) that the truth can't be decided by concensus (and that's why wikipedia isn't a reliable source). Let's rather limit our discussion to relevant issues for this thread which is only Einstein's universe.

Ah yes, the old "I'm not wrong, you just didn't understand what I said" ploy. No, there wasn't anything in your answer that I didn't understand. Your answers were just plain wrong.

Are you serious? Mainstream science holds that yes, we live in curved spacetime and that energy is conserved globally. Your accusation of conservation of energy in curved spacetime as an ATM idea is plain wrong.

That's precisely my point. Poynting's Theorem establishes conservation of energy for EM fields, and makes no mention of an exception in curved spacetime, which means the result is valid in curved spacetime. So your attempt to invoke the Poynting vector as proof that energy is not conserved in curved spacetime is plain wrong.

My questions are about the claims you have made in support of your ATM ideas, and as such, are indeed relevant.

No, it is you who have shown an incorrect or ATM understanding of Noether's theorem and such.

Yes, I'm aware of Wikipedia's various faults. However, I believe its articles on Noether's and Poynting's theorems are accurate representations of mainstream science. I'll get to this in a second.

I believe the third question is quite relevant, as you made your original claim as support for your ATM idea that conservation of energy is incompatible with an expanding universe. You made the claim that "many physicists happen to doubt it because of the consevation of energy". Now the burden of proof is on you to show your evidence for this claim, or withdraw it.

Before I get to the questions, I would like to point you to the rules of the board, which includes the following:

(bold mine)

Note that it does not say ATM proponents may pick and choose which questions to answer; all direct questions must be answered.

As I said earlier, it wasn't that I didn't understand your previous answers. They were simply wrong. So, once again, here are my direct questions for you:

1. Please show us, mathematically, why energy cannot be conserved in an expanding universe.

2. Please show us, mathematically, why conservation of energy necessarily implies a stationary universe.

3. Which physicists oppose Big Bang because of conservation of energy? So far you have only one who may or may not fit that description. Needless to say, "one" != "many".

To which I will also add:

4. If Wikipedia's description of Noether's theorem is incorrect, please cite relevant scientific sources (published papers, journal articles, textbooks, etc.) that refutes Wikipedia's description and/or confirms your description of Noether's theorem.

5. If Wikipedia's description of Poynting's theorem is incorrect, please cite relevant scientific sources (published papers, journal articles, textbooks, etc.) that refutes Wikipedia's description and/or confirms your description of Poynting's theorem.

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Maybe you should read first Is Energy Conserved in General Relativity? by Michael Weiss and John Baez (which is a mainstream opinion).

If you still insist that the mianstream supports global conservation of energy in expanding universe then we may move ''Einstein universe" from ATM section to the mainstream section since we may utilize conservation of energy as legitimate means of deriving results. Which so far the mainstream opposed since it maintanied (e.g. prof. John Baez) that energy is not globally conserved.

Read it. Here's my synopsis: in SR's flat spacetime, energy conservation can be formulated as either a differential equation or an integral equation, which are mathematically equivalent. When the two forms are generalized to GR's curved spacetime, the equivalence breaks down... until one introduces pseudo-tensors, which allows one to restore the equivalence.

You know what I don't see? Anything that actually supports your claim that energy is not conserved in curved spacetime. Your citation of this article to support your claim is... puzzling (I've already used "plain wrong" enough times in my previous post).

Your insistence throughout this thread that the universe is not expanding roots this thread firmly in ATM territory.

Maybe you should read Prof. Baez's article again.

Still waiting for you to answer my direction questions to you.

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Thanks for addressing JimJ's assertions, which, like you, I believe are built on misconceptions, but I'm not quite studied enough to differentiate whether there are any serious assertions within what looks like word salad.

I am a little puzzled, however, at the above quote, where you agree with JimJ that "we live in curved spacetime." Locally, of course, this is true due to the gravitation of the Sun and galaxy. But cosmologically, observations point to a flat spacetime, or very nearly so. So JimJ's attempt to apply local conditions to the universe as a whole rather goes nowhere, as far as I can tell.

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I believe you are right, that on a cosmological scale, our universe resembles a flat spacetime. My comment was intended only to point out to JimJast that even in curved spacetime, such as found in our local vicinity, mainstream science holds energy to be conserved. I did not to mean to imply that spacetime is curved on the cosmological scale. I am not a cosmologist, nor have I played one on TV Please feel free to point out any other errors I have made!

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I'm happy to hear you saying this since it is also my opinion. Actually my opinion is that its "total curvature" is exactly zero everywhere (unfortunately also an ATM opinion but I don't want to argue this point now, since there are more imporatant things to argue first, like e.g. the expansion of the universe, so far ATM as well).

You havan't made any (in my ATM opinion, but since I'm exactly of your opinion we don't need to argue about it) and it gives us an adventage that you don't have the prejudices about the conservation of energy that some mathematical physicists have (e.g. all in my university). They don't even want to discuss my PhD work unless I admit that energy is not conserved globally and so the principle of conservation of energy can't be used as an argumet for "Einstein's universe" as I believe it can.

This way without any other delay we may skip arguing an irrelevant (since I'm exectly of your opinion about conservation of energy) question whether the conservation of energy is an ATM or for the mainstream issue. We have also an expansion to discuss, which is for sure an ATM issue, and also it is related to astronomy.

Since the rules are that we may only discuss questions related to astronomy and what's ATM and what's not is not an astronomy question then fromally we can't even discuss it. In any case I propose to discuss formal things like "what's what" only when we have time left for it since we have only a month for everything (for discussing my whole PhD work about "Einstein's universe"). And questions related to astronomy are more interesting anyway. Since you both are representing (at least in your mind) mainstream opinion, and luckily both agree (like me) to the conservation of energy (which I consider ATM but you don't) than it may be easier job (than with cosmologists from my U) to show you why I think that the universe is "Einstein's".

Let's start with a question why mainstream physicists don't believe that the universe is (a non expanding) "Einstein's universe".

You can present your thoughts about it. My knowledge (since I discussed it already with mathematical physicists so it is a concrete konwledge) is that mathematical physicists don't believe in conservation of energy. But since you believe that energy is globally conserved, what are your reason for such mainstream thoughts like that the universe is expanding?

My role is to show you that you can't have both thing: the expansion and conservation of energy at the same time. That's why mathematical physicists has chosen the former against the latter. They think it is better assumption. But you apparently hadn't (the same as me) so if you are cosistent in your beliefs, you have to tell me what your belief that the universe is expanding is based on.

JimJast, apparently you don't understand how this works. As the proponent of an ATM idea, it is your responsibility to address questions asked about your idea and claims you make in support of your idea. We, on the other hand, are under no obligation to answer your attempts to challenge mainstream science. If there is a mainstream concept you wish to inquire about, feel free to create threads for your questions in the Q&A section (with the caveat that you do not attempt to advocate your ATM position in the Q&A threads).

Then show us! You can start by answering the questions I posed to you. For the third time, here are my direct questions on claims you have made in support of your ATM position:

1. Please show us, mathematically, why energy cannot be conserved in an expanding universe.

2. Please show us, mathematically, why conservation of energy necessarily implies a stationary universe.

3. Which physicists oppose Big Bang because of conservation of energy? So far you have only one who may or may not fit that description. Needless to say, "one" != "many".

4. If Wikipedia's description of Noether's theorem is incorrect, please cite relevant scientific sources (published papers, journal articles, textbooks, etc.) that refutes Wikipedia's description and/or confirms your description of Noether's theorem.

5. If Wikipedia's description of Poynting's theorem is incorrect, please cite relevant scientific sources (published papers, journal articles, textbooks, etc.) that refutes Wikipedia's description and/or confirms your description of Poynting's theorem.

Oh, and since you're throwing around remarks like this one:

I will also add:

6. Which mathematical physicists do not believe in conservation of energy?

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I subscribed to this thread in order to keep an eye on it. I got an email notification this morning that Chris Hillman had responded to this thread. But I don't see his post for some reason, so I'm reposting it below as it appeared in the notification I got.

---

Text deleted.

Codeslinger, Chris Hillman chose to delete his post. You should not post it here.

(If I erred and deleted your words, let me know and I can restore them.)

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My apologies, Jim (and Chris Hillman). I thought the forum hiccuped and ate his post. Did not realize he had deleted it on purpose.

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It's a very fortunte thing since Chris is a guy who knows what he's talking about. I'm on the other hand a sculptor who got himself into cosmology through an accident. This accident was a result of my calculaton of the density of "Einstein's universe" (static, more properly called "stationary") that turned out to be in the middle of estimets that were 1 to 10 while my result came as 3 (in units of 10^{-27}kg/m/^3). Since my calculations were based on Hubble redshift (50 km/s/Mpc then and I just wanted to know how much of it is due to density of the universe because of gravitational friction of photons) after I got this result I started to suspect that the whole Hubble redshift is (kind of) due to dynamical friction of photons. After some discussions with mathematicians (like Chris Hillman), physicists, astronmers, and cosmologists and reading some of their books this suspicion of our universes being Einstein's deepened (to make a long, over 22 years old story, short).

---

Hi Chris, I'm impressed by your memory if you still remember me. I hope you don't pretend any more that you are just a computer program (Jonh Baez gave you out).

Yes, however my understanding of Einstein's gravitation prevents me from thinking that there is such a thing in nature as "gravitational attraction". Actually, I'm puzzled why you even mentioned it since you must know that Einstein's gravitation does not allow gravitational forces acting at the distance. Gravitational forces exist only as tidal forces when particles press against each other because of their inetia (that's why they are called pseudo forces) or e.g. your butt presses the Earth when you happen to sit on the Earth.

It can be easily shown with differentiating E=mc^2 along distance (taking dE/dx and showing in about 5 minutes that it is equal -mg, just try it substituting -g/(2c) for dc/dx as it follows from Einstein's accelerating rocket or elevator, and from his equivalence principle).

It prevents it observationally: if energy is consered the universe is not observed to be expanding since there is no Hubble redshift left for the expansion. The whole 70km/s/Mpc is used for the dynamical friction of photons that generations of cosmologists thought it is "negligible" without ever calculating it exactly. Try to calculate it then you'll see for yourself. It should take a smart mathematician less than an hour. I did it in about eight, once I gave up all the unwarranted approximations. Now I demonstrate it to professors in a few minutes, so they rescue themselves by claiming that energy is not conserved in GR. As John Baez did in the same situation, dispite that you don't believe it. And he even tried to convince me that the kinetic enery of a falling brick comes from nowhere (when I asked him directly about it). And that's why I had to figure it out myself and now I know where it comes form. Though only one professor in my university agrees that it my explanation is strictly what Einstein's must have meant.

As I said, if you try to ignore dynamical friction of photons you need to supply energy to keep Hubble redshift to be the result of expansion. Is there any error in such a reasoning?

Of course it is not true since it would require just a one good kick, but if you want the same ball moving through the universe it is subject to dynamical friction and then it needs constant injection of energy to counter the dynamical friction. With photons it is even worse since it is not a Newtonian effect but purely relativistic. And so it is not some mysterious "tired light effect" but the effect of time runing slower at their origin similarly as reqired also by the regular gravitatinal redshift. Only that in the Hubble type redshift it turns out not quadratic with distance but exponential. And that's why it carries with itself the illusion of accelerating expansion with acceleration that is actually observd since it's theoretical value is H_o^2/2 (second term of Taylor series, first is H_o) while observed value is 0.45 H_o^2 (at least it was like that last time I looked at the data).

I might and that's why I'd like smart people in this forum to tell me what it might have been.

I appreciate this, however also I like Feynman's approach when he says: "Let me also say something that people who worry about mathematical proofs and inconsistencies seem not to know. There is no way of showing mathematically that a physical conclusion is wrong or inconsistent. All that can be shown is that the mathematical assumptions are wrong. If we find that certain mathematical assumptions lead to a logically inconsistent description of Nature, we change the assumptions, not nature."

I think that conservation of energy is true in any frame and a total energy of the particle is its Mc^2 (M being total mass, including its kinetic energy) which does not change with its position, and its so called "gravitational energy" is mc^2 (m being rest mass), that may be radated out on occasions, most likely just in photons. It isn't relevant here since it does not change anythng in the mechanism of Hubble redshift. The mechanism is the slowing of time exponentially with the distance to the source of light to compensate for the curvature of space which produces an easily derived relation that d^2T/dt/dx + 1/R = 0, where T is proper time, t coordinate time, x is distance, and R "radius of curvature of space" (all derivations are in my paper quoted at the first message).

Of course it produces Hubble constant H_o=c/R. Which happens to be observed if R=4.3 Gpc. What is not observed is about 57% of the mass of the universe required to produce average density needed for conservation of energy to work. One reason why my professors maintain that energy "is not concerved in gravitation". What do you think?

Might be. I think I mean "Ricci flat" but I'm not sure if it is what I mean since I never heard the term. I mean that the contraction or Ricci tensor gives zero. If you mean the same than it is "Ricci flat". I support it by hypothetizing the existence of a 3-D tensor (which I called "general time dilation tensor") that with 3-D Ricci tensor adds to zero. But not being a mathematician I might do here something silly. However it comes out from the above d^2T/dt/dx + 1/R = 0 generalized over all 3 spatial directions after multiplying it by R. I think that as for a sculptor I did anough work to make it interesting for a mathematical physicist to take it over and fix all mistakes, since I think that physics is right here. Yet Phys. Rev. Lett. editors maintain that lack of any new physics in it makes it uniteresting to their readers. So it can't be even published. And BAUT forum is the only available place where it can be kept for one month. Except of course my web page which nobody reads. So I can't even learn what are the objections against the "Einstein's universe" dispite that it sems to be physically viable proposition.

But notion of gravitational energy in gtr might be wrong and according to what I said above it is since if (d/dx)(mc^2)=-gm then mc^2 is the only "gravitational energy", and it is localized. And it can be also radiated out because it changes by quanta of energy (photons in this case). So I don't see problems with localizing it. Why do you say it can't be localzed?

You are not mean. You just say what you think that is right and I'm telling you why I think my way. I'm not concerned with my PhD at all. I'm just using it as a vehicle to find the truth about the universe. I've seen so many stupid things in literature, contradicting not only Einstein's theory (like e.g. existence of "gravitational attraction") but also contradicting the common sens (like lack of conservation of energy in gravitation) and revealing that the authors don't know physical facts, that I stopped beliving text books (and I have over 20 kg of them, since I trusted them once, starting with MTW that I bought first). And it is difficult to learn if you don't trust your teacher. So I can learn only through a dialog, and if you convince me that truth is different than I thought, that the universe expands, it would be great. I like to learn things that I didn't expect being true. It is the gratest thing in science. Untrue science is like a kitsch. I just suspect cosmology being a kitsch not science. And only since cosmologists (at least in my U and on the internet) say "we won't talk to you unless you give up that nonsense that energy can be conserved in gravitation". But if it is conserved then "Einstein universe" can handle quite nicely the illusion of accelerating expansion, CMBR, and presumably other things that I don't know about, so I'd like to learn which things it can't handle.

The Codeslinger's questions (not necessarily "pertinent") with my answers are:

I don't think it can be done in a rigorius way if this is what you mean by "mathematically" and if you mean by this something else, please explain what it is. Consequently my best answer to this question would be like it was the first time when I answered it and you called it "word salad" not specifying what you considered "salad".

The answer is the same as answer to question 1.

[QUOTE]
3. Which physicists oppose Big Bang because of conservation of energy? So far you have only one who may or may not fit that description. Needless to say, "one" != "many".
[\QUOTE]
I have to ask them if they want to have their name published on BAUT forum and if they agree I come back and let you know which.

JimJast, the answers you just gave are word salad.

You said "It cannot be done mathematically."
Nonsense.
You may as well have answered "because it's magic."

My definition of word salad: a superficially impressive but meaningless jumble of buzzwords (which may or may not have been used correctly).

Let me remind you what you said in comment #24 of this thread:

(bold mine)

Your claim was that "energy can't be conserved in the expanding universe" is an easy-to-show mathematical result. But you seem unwilling or unable to show this math. I do not consider this question answered.

By that, I assume you mean your best answer to the question is the one you gave last time. You previous answer to this question was "Noether's theorem". As has been pointed out to you, Noether's theorem does not say what you think it says. That was what prompted me to ask you question 4, asking you to provide evidence for your ATM interpretation of Noether's theorem. As you have not answered that question, I do not consider this question answered.

Yes, you do that. In the meantime, kindly cease from making comments about what "other physicists" believe or say. Without providing means for us to verify your claims, such comments are unsupported allegations at best (at worst, complete fabrications).

I remind you again that the rules require you to answer all direct questions. You do not get to pick and choose. Once again, here are my direct questions that you have not answered:

1. Please show us, mathematically, why energy cannot be conserved in an expanding universe.

2. Please show us, mathematically, why conservation of energy necessarily implies a stationary universe.

4. If Wikipedia's description of Noether's theorem is incorrect, please cite relevant scientific sources (published papers, journal articles, textbooks, etc.) that refutes Wikipedia's description and/or confirms your description of Noether's theorem.

5. If Wikipedia's description of Poynting's theorem is incorrect, please cite relevant scientific sources (published papers, journal articles, textbooks, etc.) that refutes Wikipedia's description and/or confirms your description of Poynting's theorem.

6. Which mathematical physicists do not believe in conservation of energy? (This is a different question than question 3, because they are asking about opposite beliefs. Question 3 asks which physicists oppose Big Bang because of their belief in conservation of energy. This questions asks which physicists do not believe in conservation of energy.)

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Hi speedfreek, thanks for the links. The wiki link shows the shape of the angular size redshift relation that it has to be necessarily the same in Einstein's universe. In particular it has to start with zero, have maximum at some distance and then drop to nearly zero for (pi)x(radius of curvature). This is required by the curvature of space of Einstein's universe. The place were this line may differ from the line for Einstein's universe are the scales on both axes. So now I'm going to do the calculations necesary to decide whether the observed line complies with Einstein's universe.

Unfortnately it requires to repeat my calculations of redshift for curved space to make them more accurate as required by your question. It might requre solving some nonlinear equations. For the time being I just demonstrated in a nearly flat space that contrary to the mainsteam assertion there is a non negligible Hubble type redshift in Einstein's universe, which also simulates an accelerating expansion of space, hoping that astronomers take over from there. Becaue of lack of interest in such issues (as editors of Phs. Rev. Lett. assured me) there was no reason to work on the details.

Since you are the first guy who asked about "increase in the apparent angular diameter of galaxies with redshifts" I'm going to try to derive what this curve should show exactly for Einstein's universe. I hope at least that except working out the scales on both axes I'm going to get the density of the unverse more accurately. So this work will have more advantages than one. It may also have an advantage of eliminating Einstein's universe as a possibility, which, to the best of my knowledge, nobody worked on it yet.

But before I can do this I have to respond to a few questions related to sociology of science, which I don't even understand yet exactly. So please be patient, since it might take time.

OK.

My problem is that I don't know whether you understand mathematical result the same way as I do. One guy's mathematical result may be another's "a superficially impressive but meaningless jumble of buzzwords". I hope we'll know when I respond to you question and then you tell me if it satisfies your idea of mathematical result.

OK.

OK.

One point is that according to the Noether theorem (after wikipedia, I just make more important things bold) "the conservation of energy is a consequence of the fact that all laws of physics (including the values of the physical constants) are invariant under translation through time; they do not change as time passes."

In expanding universe we don't have the universe (and whatever is there) the same as time passes. So at least if we insist that energy can be conserved in an expanding universe we should deliver a separate theorem for such case when all things do change as time passes. We need something better then the Noehter theorm for the conservation of energy to be proved, not to be just our assumption. E.g. we might want it at least to be shown by observations.

So let's look for observations to see if energy can be conserved in a non expanding universe. It can (since Noehter theorem works there: the universe does not change as time passes). And also we see only as much redshift as delivered by this conservation of energy (see my paper). If it were any greater then we would have imbalance of energy. Luckily we don't so we just showed that we don't have automatic conservation of energy in expanding universe, but we have in stationary.

... to be coninued (for lack of time) ...

And then we are going to address the rest of this question and other questions as ...
...within next week.

Are you trying to equivocate on the definition of "mathematical result"? Mathematical result: a result expressed mathematically. As opposed to, say, hand-waiving by throwing out jumbles of incorrectly used buzzwords, which is what you have given us thus far.

... and the mis-representation of Noether's theorem continues. Look again at the sentence you quoted: "the conservation of energy is a consequence of the fact that all laws of physics (including the values of the physical constants) are invariant under translation through time; they do not change as time passes." So what Noether's actually says is that energy is conserved as long as the laws of physics do not change over time; it is not required that the universe and everything within it remain unchanged. In Big Bang cosmology, while the universe is expanding, the laws of physics do not change over time. So Noether's applies (and establishes conservation of energy) in Big Bang's expanding universe just fine.

Oh, and I note that you are now quoting directly from Wikipedia's description of Noether's theorem; does this mean you concede that Wikipedia's description is correct?

I wait with bated breath.

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Thanks to Jim (the moderator) for trying to fix it. Codeslinger, you are forgiven.

I deleted my post because on reflection I began to recall why I stopped talking to JimJast 15 years ago and decided that despite his mangling a theory I have come to know and love (general relativity), nothing would be gained by my weighing in. Unfortunately, JimJast replied with quotes of my self-deleted critique after Jim (the moderator) appeared to have fixed things, which places me in an awkward position.

I myself bear some responsibility for creating this mess but beg indulgence for a newbie (to BAUT) if I push any boundaries. I don't wish to appear to bully JimJast but at this point it's difficult to avoid stating that it seems to me that despite 22 years of study, he just doesn't get it.

Yet you don't listen to me, you don't listen to John Baez, and you don't listen to your own professors. We are all saying you as wrong as wrong can be.

[sic]

Well, there you go again. Your butt pressing against the Earth does -not- represent a tidal acceleration, it represents your world line bending away from the geodesic path it would otherwise follow due to your butt encountering the surface of the Earth.

Near an isolated massive ball, tidal acceleration scales like m/r^3 while the acceleration required to sit on the surface r=R of the ball scales like m/R^2 (approximately), in both Newtonian gravitation and in gtr.

Mathematically speaking, tidal acceleration is represented in gtr by part of the Riemann tensor while the acceleration of a small body (test particle) sitting on the surface of the Earth is represented by the magnitude of the curvature vector of that test particle's world line. The latter vector is the covariant derivative of the tangent vector to the world line taken along itself.

In geometric units, tidal acceleration has the units of reciprocal area, i.e. the units of sectional curvature, or the units of energy density. The magnitude of the acceleration vector of a test particle has units of reciprocal length, i.e. the units of path curvature.

These are three ways in which it is clear that you are confusing two completely different things.

And again. A spacetime is called "stationary" if it possesses a timelike Killing vector field. It is called "static" if this Killing vector field is also vorticity-free or equivalently, hypersurface-orthogonal. Thus, "static" is a stronger property than "stationary". See for example section 14.1-2 of D'Inverno, Understanding Einstein's Relativity.

The particular FRW dust (with nonzero Lambda) which you are calling "Einstein's static universe" (see for example eq. (5.7) of Hawking and Ellis) is -static- because its timelike Killing vector field is vorticity-free. The Kerr vacuum (for example) is only -stationary- because its timelike Killing vector field has nonvanishing vorticity.

You can obviously generate misstatements faster than I (or anyone else) can try to correct them. The two I just noted are minor in comparision with several whoppers which I tried to correct in my self-deleted post. To recapitulate:

That's completely incorrect. There are legions of excellent textbooks where one can read about Noether's theorem; my favorite is Olver, Applications of Lie Theory to Differential Equations. In the study of one or more (partial or ordinary) differential equations, it turns out that the "variational symmetry group" of an equation (or system of equations) which is given in terms of a Lagrangian reveals the existence of certain invariants, if they exist. In Riemannian or Lorentzian geometry we can apply this general theory to the geodesic equations, which govern (for example) the motion of test particles in a given spacetime. (If anyone wants to know more, ask in the Questions forum and I'll see what I can do, at least if I can figure out how to get some mathematical typography here.)

It is true that in gtr, a timelike Killing vector field is associated with a quantity which remains invariant during the motion of a test particle and which can often be interpreted as the "energy" of the test particle. It is also true that expanding or contracting FRW models lack timelike Killing vector fields.

The existence (or not) of invariants has to do with whether or not we can integrate the geodesic equations in closed form, in other words, in how easy it is to mathematically describe test particle motion. But this is a purely mathematical issue and largely irrelevant to "conservation of energy" in the sense you are trying to discuss.

In any Lorentzian (or Riemannian) manifold, if you parallel transport any vector around a small -loop-, and compare with its original position, in general it will indeed have rotated. This is one of the geometrical interpretations of the Riemann curvature tensor. But is has nothing to do with "conservation of energy" in the sense you are apparently trying to discuss. And contrary to what you appear to believe, the energy-momentum tensor of the EM field is actually very well behaved in general relativity.

You appear to claim that "conservation of energy" is only possible in locally flat (not "globally flat") spacetimes, i.e. ones in which the Riemann tensor vanishes. Depending upon precisely what you mean by the phrase "conservation of energy", that is either misleading or wrong. It is true that many purely mathematical issues arise in curved spacetimes which "break" some useful facts which hold only in locally flat spacetimes. It is also true that the local versus global distinction is crucially important in the theory of manifolds. But I hesitate to even attempt to discuss this because this is pretty subtle stuff, not easy to discuss even when the other party has already acquired the requisite mathematical background and is paying close attention.

To repeat what I said in my self-deleted post: I know John and I know he doesn't claim any such thing. You must have misunderstood something he told you.

A tiny anecdote about John Baez, which I heard from Nathan Urban: a student came up to him after the first day of class and said "I didn't understand a word you said. I think I need to get into the calculus for poets class". John replied "This -is- the calculus for poets class!"

See Kroger and Dunning, "Unskilled and Unaware of It: How Difficulties in Recognizing One's Own Incompetence Lead to Inflated Self-Assessments", J. Pers. and Soc. Psych. 71 (1989):1121-1134 http://www.apa.org/journals/features/psp7761121.pdf

So you say. Given how badly you have misunderstood those texbooks you say you read, my corrections, and John Baez's corrections, I am disposed to doubt you understood this unnamed professor's remarks correctly.

For anyone who is not already familar with these terms, a short glossary off the top of my head, where A < B denotes "condition A is weaker than condition B":

(vanishing Ricci scalar) < "Ricci flat" (vanishing Ricci tensor; equivalently, vanishing Einstein tensor, or in gtr, vacuum solution) < "locally flat" (vanishing Riemann tensor, locally isometric to Minkowski spacetime).

"conformally flat" (vanishing Weyl tensor; no light bending) < "locally flat"

The FRW dusts are conformally flat but not Ricci flat (and thus, not Riemann flat). The Schwarzschild vacuum is Ricci flat but not conformally flat (it exhibits light bending). The Reissner-Nordstrom solution has vanishing Ricci scalar but is neither conformally flat nor Ricci flat. Any solution with nonzero Lambda term (these days this is normally considered just another term in the energy-momentum tensor) will have a nonzero contribution to the Ricci scalar coming from this term.

You don't listen to me, you don't listen to John Baez, you don't listen to your professors, you don't listen to the Phys. Rev. Lett. referees...

I explained it. The trouble is that you didn't (can't?) understand what I wrote.

Anyone interested can see Misner, Thorne, & Wheeler, Gravitation, section 20.4.

One of the best books ever published, in any genre. Too bad you misunderstood what you read there, because this is wonderful, wonderful stuff, and I wish many more understood it!

You're asking me to teach you, but you say you don't trust me and on the evidence of your own writings, you don't understand anything I try to tell you. For this reason, I'll bow out of this thread here.

Most certainly? I saw Codeslinger's quote of Chris Hillman's letter to all, I quoted the letter, and I started to put my replies and comments between Chris texts which were written to me (since I already know that I'm supposed to answer all direct and perinent questons), and then I submitted the reply a few hours later (most likely much more than two hours). During the whole time I was not aware that there was some screwup. I noticed it only after I submitted the reply. And then what I was supposed to do?

No. It was an open letter to me, wasn't it?

What does "probably contains mathematics" mean exactly? It has to contain e.g. numbers, mathematical symbols, equations? Just words don't suffice? Codeslinger didn't specify what he means by "mathematically" so I'm just trying to apply a trial and error method to figure it out. I hope we are able to defind what he means before the month is over. I don't see many people interestd in the subject of the thread anyway so we stll have almost a month to clear these matters up.

Shouldn't I answer your questions first? Should I treat them only as rhetorical questions? I'm rather new guy here so I don't know the culture here yet.

Jim asked me not to place anything in this forum before answering direct Codeslinger's questions. To honor Jim's wish I can't write to Chris and ask him why he avoids answering direct questions (e.g. how the gravitational attractive force is acting through vacuum in his opinion) and I'd like to turn his attention to a more important problem the best expressed by Feynman: "Let me also say something that people who worry about mathematical proofs and inconsistencies seem not to know. There is no way of showing mathematically that a physical conclusion is wrong or inconsistent. All that can be shown is that the mathematical assumptions are wrong. If we find that certain mathematical assumptions lead to a logically inconsistent description of Nature, we change the assumptions, not nature.

The possible existence of Hubble redshift in "Einstein's universe" in observed amounts leads to a logically inconsistent description of Nature. This inconsistence is in a form of expanding universe hypothesis and all the briliant math of many briliant people behind it. So briliant that it would be real pitty if it were not true. That's the only thing that I wanted to show in this thread.

I might very well be an uneducated moron who just noticed this one inconsistence. So I'll leave this briliant math to the billiant people who created it, for them to fix it. Since Jim asked me to switch back to responding to Codeslinger questions, the best as I can, this is what I'm intending to do.

Hi Codeslingr, I'm back!

You may hand-wave mathmatically too (isn't the Big Bang hypothesis just that?) I bet you are going to call this way also the math presented in my article about Einstein's universe. So I'd rather wanted you to define all your statements formally like <this and this>::=<something>|<another something>&<something else> (of course after defining presecence of all operators) so at least the same time next year or maybe even earlier we would define tha algebra that we are using for this exchange of deep thoughts. Why do you think algebra course takes so many semesters? Before this we necessarily have to use some informal hand-waving and from time to time lose ourself completely. But since none of us is a mathematician it is bound to happen. Would be different with Chris Hillman, but I think he's gone for good by now.

A weak point in your resoning: how do you know that in expanding universe the laws of physics don't change? It is just your assumption. Unfortunately Noether is dead so we can't even ask her how she would interpret what you just have written. But even if she said it is fine with her a rigorous mathematician wouldn buy it. Conservation of energy is only an observational fact nothing proved yet.

Supprised ? Did I ever told you that Wikipedia's description of Noether theorem isn't correct? I told you that wikipedia description of gravitation isn't correct since the editors believe that Newtonian gravitation is right. In their minds gravitational forces "attract masses" through vaccum. Even Chris Hillman subscribes to this ancient point of view on gravitation and didn't responded to my direct question about it despite that he thinks that in all other place Einstein's gravitation is fine. At leaast he kew that tidal forces result from deviations of wordlines from geodesics. Yet he though that "gravitational attraction" is a different kind of force than tidal since tidal force has a cubic relation to the distance from the center of gravity. And the "attractive" one has quadratic though it is not existing at all (how non existing force can have the Newtonian quadratic relation with distance? Must be one of the mysteries of the expanding universe, just kidding). But we are drifting into physics instead to continue answering your direct questions.

Let's recall the question:
We are done with Noether part, which we can't apply to the expanding universe (while you might still think that we can apply it, but then just prove it in the next message) and so we are ready to show that it is not conserved at least in general (I allow, just not to argue unnecessarily) that in some special cases it may be conserved, but generally it can't.

The proof is this: Let establish signature + - - - (as it is done in physics) and let's forget signature - + + + used more often by mathematicians (I just mention this since I don't want to argue unnecessarily about the signature of our spacetime when you might have different prefference than I have). Take a Poynting pseudo vector s0^i (where i is 0 for time coordinate, and 1,2,3 for spatial coordinates) (with which you are already familiar and you know that it represents the energy of an electromagnetic wave) and locate it at coordinates x0^i. Now parallel transport s0^i to a new event in our spacetime by randomly chosen worline A to an event x1^i and call the Pointing vector sa^i. Then do the same thing to the same event x1^i by another path B and call the resulting coordinates of the Poynting vector sb^i. Note that there is a non vanishing difference sd^i=sa^i-sb^i which is another pointing vector representing energy of a some electromagnetic wave. Then try to respond to a question where the hell this energy came from? Of course in flat spacetime this enegy represented by sd^i=0 since paralled transport by any wordline results in the same vector.
To be continued...

Chris, a hearty welcome to BAUT. It's really nice to have someone with your knowledge of GR here. When I first began studying GR on my own, yours and John's posts in the physicsforums were very helpful in working through some questions I didn't understand on my own.

I and others here fully understand this feeling. You should have seen some of the threads here before the thirty day rule was instituted. Again, welcome.

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No, it is not just "my assumption", it's what the theory says. I have never come across a formulation of Big Bang cosmology that involves the laws of physics changing over time. What makes you think Big Bang cosmology has the laws of physics changing over time? (This is a direct question)

You launched into your rant about how Wikipedia does not represent the mainstream view right after I pointed you to Wiki's description of Noether's and Poynting's theorems. The obvious implication, then, is that you did not agree with those Wiki articles. It's great that you acknowledge Wiki's description of Noether's as correct; now, if only you would display some understanding of it...

If you have something to say to Chris Hillman, I suggest that you address it to him in a separate comment instead of burying it in comments addressed to me.

No, we're not done with it, as you have failed to show why it does not apply to an expanding universe.

You then say you are going to answer my first question. But all you did was repeat the same argument about transport of Poynting vectors from before. As Chris Hillman has already told you, the argument does not work:

Repeating a flawed argument is not an answer. I do not consider my question answered. Where is the mathematical result you said was so easy to show? A mathematical result would involve math. For example, show us how conservation of energy in an expanding universe would lead to a mathematical contradiction.

For your convenience (and as Nereid might say, avoidance of doubt), here are my direct questions that you have yet to answer:

1. Please show us, mathematically, why energy cannot be conserved in an expanding universe.

2. Please show us, mathematically, why conservation of energy necessarily implies a stationary universe.

3. Which physicists oppose Big Bang because of conservation of energy?

4. If Wikipedia's description of Poynting's theorem is incorrect, please cite relevant scientific sources (published papers, journal articles, textbooks, etc.) that refutes Wikipedia's description and/or confirms your description of Poynting's theorem.

5. Which mathematical physicists do not believe in conservation of energy?

6. Why do you think that Big Bang cosmology involves the laws of physics changing over time?

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Delete your response or PM/leave a post for a Mod to delete it.

It was an open response to one of your posts, which Chris Hillman chose to delete. The implication is clear (was to me anyway) - he did not wish for it to remain public or to solicit a response.

That's the general understanding of "contains mathematics."

Don't. Ask.

No, you do what the Mod suggests you do. If you wish to respond to my post, PM me or post after you do what was suggested.

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Nothing makes me think that "Big Bang cosmology has the laws of physics changing over time". Consequently, I don't think so. But it is not forbidden to make such an assumption in the Big Bang cosmology as it would be if the Big Bang have been a scientific theory (at least according to Popper). So when the observations won't fit the Big Bang cosmology next time (as it already happened with decelerating expansion only 10 years ago) then the Big Bang cosmology is free to use an argument of the laws of physics changing over time to rescue itself from collapsing. Which makes us responsible for considering all possibilities even the most exotic.

And that's why it is easier with scientific theories. In a scientific theory after one false prediction the theory is out. Like e.g. Einstein's universe would be out if it predicted something wrongly. So far it exists in my mind as a possibility since, as far as I know, all its predictions agree with observations. The first suspected observation that I learned about, thanks to this thread, is the relation between angular diameter of galaxies and the reshift distance to them. On which I don't have time to work being busy with responding to your direct questions without which the thread can't continue.

My results from my paper can't be used since they are derived only for small redshifts in approximately flat space, so they cover only linear part of the curve. The interesting question is how the angular size redshift relation would look for distances of order of Gpc, where space curvature decides about the shape of the relation. Qualitatively it looks the same as observations indicate and it is interesting if the scales on both axes come up the same as what is observed. If they do then it will be the sixth independent piece of evidence in favor of Einstein's uiverse. If not than it would be its first fatal flaw. And then it could go down as a serious piece of evidence supporting the Big Bang cosmology. So basically also the Big Bang supporters have a stake in testing the shape of the angular size redshift relation for Einstein's universe.

Since you considered my first response to your questions insufficient, I'm now trying to find out what is your point of view on laws of physics. Since you don't agree with me that we should rather agree that energy is conserved, I'm trying to find out why you think so. Had you specified your point of view I could just say "agreed" or "not agreed, because of this or that" and then it were much faster discussion and we even might get to some conclusions before our time for chatting runs out.

I want to continue the thread to find out either whether there is somethng wrong with Einstein's universe as an explanation of observed phenomena or why people don't understand that "Einstein's universe" might be all that we need to explain the observed phenomena. Perhaps members of this forum know something that I don't know and so when they reveal this knowledge I'll be satisfied. But before the thread can continue I have to answer all your "direct" questions, which I'm trying to do right now trying to figure out what you don't know.

...but if my opinion doesn't agree with yours we switch to discussion of Noether's theorem instead of discussing Einstein's universe, wasting even more time. While I like chatting with you on various subjects, I'd like the most just to hear in your own words why are you against application of Einstein's universe as a model of our universe. After we are thru with this we may discuss also Noether's theorem, Poyntig vector, and whatever else you want to chat about, if we still have enough time left i this thread. Or you may open separate threads on Noether's theorem an Poynting vector and discuss them with any one who has enough time to do this.

I already did in one of comments to his letter and he igonred it. Before he had a custom of answering to different question than asked. Now he does not answer at all just tells me that I'm wrong leaving for me to figure out why. Which is BTW not that bad since then one might analyze one's stuff and find out the answer oneslef as it happened when I asked John Baez "where the kinetic energy of a falling brick is coming from" and he didn't know. Though it turned out to be easy to figure out. If you don't know I can explain it to you too, after we finish with your direct questions.

I'm trying to. Apparently I failed so I still have a job to do.

Chris Hillman didnt' tell me WHY my argument didn't work. Anybody can say that "the argument does not work" but without showing why such a statement has no practical value for the author of the argument. I know that Chris Hillman makes his own errors and I even tell him where. Consequently I don't consider him knowing much about gravitation. He is a mathematician so he doesn't need to know anything about gravitation, just is supposed to think clearly.

If you showed me where the argument has a flaw then it would be easier for me to see the flaw. As it is now I have to guess what you consider a flaw.

In my last message I thought that I showed you that depending on the path of transport the results are different in curved spacetime (contrary to the results in flat spacetime). Since both transports are legitimate, one can't choose one over another. So both transpors give legitimate results. But the law of conservation says that the result for x1^0>x0^0 is supposed to be unique. Since it is not unique (which is verifiable) it does not expresses the principle of conservation (in this case of energy). Q.E.D.

Now is your turn to point to a flaw (rather than write "it is flawed" and make me guess what you mean).

In a case you accept that curved spacetime does not produce unique results while parallely transporting vectors (since the results of such transport depend on the path) I should add that expanding universe corresponds to a curved spacetime of non zero global curvature (one that is proportional to the angle of rotation of parallely transported vector) and therefore the above reasoning is directly applicalble to the expanding uiverse. Which would concluded the respnse to question 1.

It's done if you accept the above demonstration. If you don't than please specify the flaws that you see in the demonstation.

As shown by John Baez in a paper that you know the time translation has no meaning in expanding uinverse and so neither has Noether's theorem and no other way of testing the principle of conservation of energy mathematically is known then we have to rely on observations. Since the Hubble type redshift in a stationary cloud of dust in which energy is conserved (derived in my paper which you should have read by now) depends on energy desity of this cloud of dust and its size which for the whole universe translates into
Hubble constant H_o=sqrt(4pi G rho),
where G is gravitational gonstant and rho is energy density of the universe (in units of mass), then we may observe both (H_o) and (rho) and verify with sufficient accuracy that it is so. Then any other result would violate the principle of conservation of energy. From which we conclude that a stationry universe is the only universe possible where energy is conserved. The expanding universe would have an additional Hubble type redshift resulting from Doppler effect and it had to be subtracted from the already determined Hubble type redshift violating the conservation of energy. Q.E.D.

No one except me (without PhD though) agreed yet for his name be placed in this forum. But I'm working on it.

As far as I know it is correct.

...in "general relativity":
(1) Prof. Chris Meissner (you may buy his book on the Theory of Fields if it is still available). Prof. Meissner assured me personally in front of several witnesses that energy is not conserved globally (which makes my derivation of the Hubble redshift invalid) and he attributes to it a possibility of existence of supernatural being(s). He oranized a conference (which I witnesed) about relation between physics and faith, at Warsaw University with cooperation of a Catholic priest a Catholic thelogian and another mathematical physicist, prof. Kijowski, where all of them anylized in front of an audience of about one thousand arguments for and against the possibility of existence of a supreme being (for which the law of conservation of energy might have been a serious obstacle when treated seriously).
(2) Prof. John Baez (who assured me personally through the internet that energy is not conserved "in general relativity", and there is a proof of his assertion, available through google).

If you need more names for some reason I might be able to get a few more since most (if not all) mathematical physicists in my university as well as most (if not all) PhD candidates agrees with this proposition.

I don't.

Good, then we are agreed that Big Bang cosmology does not involve laws of physics changing over time. Which brings us back to the original context for that question: why do you insist Noether's does not apply to Big Bang's expanding universe? For the nth time, Noether's says that if the laws of physics remain unchanged over time, then energy is conserved. Having acknowledged that laws of physics do not change over time in Big Bang's expanding universe (the requisite conditions for conservation of energy in Noether's theorem), please show why Noether's does not establish conservation of energy in Big Bang's expanding universe.

Chris Hillman ALREADY explained to you why your argument does not work, in the comment from him I quoted. But since you appear not to have understood his response, I will break it down as best as I can. Yes, if you parallel transport a vector around a small loop in a curved manifold, there will be a difference from the original position. But this difference is one of rotation, which is unrelated to conservation of energy. So your attempt to argue that energy cannot be conserved in curved spacetime by comparing the results of parallel transporting a vector is simply non-sense.

Do you have an actual, valid, mathematical argument for why energy cannot be conserved in an expanding universe? If so, please show it.

In which paper did Prof. Baez say that time translation has no meaning in an expanding universe? I would like to read it for myself, since you have demonstrated a tendency to mis-understand and mis-represent others' writing. The rest of your argument is a non-starter since you have not shown how time translation and Noether's theorem has no meaning in an expanding universe.

Come back to this one when you actually have some names and citations (papers, articles, books) where those people actually said that they oppose Big Bang because of conservation of energy.

Good. Then please explain why you do not think Poynting's theorem, which establishes conservation of energy for EM fields (using the Poynting vectors you seem to be so fond of), does not apply to an expanding universe, since you are claiming that energy cannot be conserved in an expanding universe. I see nothing in Wiki's descrption that says Poynting's result does not apply in an expanding universe.

I'm disinclined to take your word for what people have said. Where in Theory of Fields did Meissner say he does not believe in conservation of energy? Where, in anything he has published, does John Baez say that he does not believe in conservation of energy?

Addressed above.

Please answer all questions/requests I have bolded. Take as long as you need to in order to address them. But I will not put up with any more non-answers.

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