Chinese Scholar Yang Jian liang Putting Wrongs to Rights in Astrophysics

[NotEinstein]

I look seriously through the chapter and find that your question is still the definition's question, indeed in some book, for example Carroll's book , the Ricci tensor is defined as R^uviuj, in other book defined as R^uviju, different contracted index, thus there exist the sign difference, inYang's article use the form R^uviju

As the Wikipedia article says in the very sentence under the equations: if you are contracting over the wrong indices, you'll indeed pick up a minus sign. In that case, you are no longer using the Ricci tensor, because that's not the Ricci tensor anymore; in other words, you also draw the conclusion that Yang is wrong. (S)he mistakenly contracts over the wrong indices, and is thus a minus sign off.

when use the form R^uviuj field equation read G^uv=8paiGT^uv, when use the form R^uviju field equation read G^uv= - 8paiGT^uv, both they are correct

This is trivially proven false. G^uv=8paiGT^uv and G^uv=-8paiGT^uv can only both be true is G^uv=0, which obviously is not the case in general. You are wrong.

 

[heyuhua]

As the Wikipedia article says in the very sentence under the equations: if you are contracting over the wrong indices, you'll indeed pick up a minus sign. In that case, you are no longer using the Ricci tensor, because that's not the Ricci tensor anymore; in other words, you also draw the conclusion that Yang is wrong. (S)he mistakenly contracts over the wrong indices, and is thus a minus sign off.


This is trivially proven false. G^uv=8paiGT^uv and G^uv=-8paiGT^uv can only both be true is G^uv=0, which obviously is not the case in general. You are wrong.

You are wrong, because the signs of the Ricci tensor defined in these two ways are the opposite, while the energy-stress tensor is defined in the same way, field equation must have two forms namely G^uv=8paiGT^uv and G^uv=-8paiGT^uv, which appear in different textbooks, obviously you read too few books

 

[heyuhua]

the definition of Ricci tensor used by Yang is being used in a lot of textbooks, it's completely correct. Obviously, Your knowledge is very incomplete, not systematic, not proficient, you know one and don't know the other.

 

[arfa brane]

You are wrong, because the signs of the Ricci tensor defined in these two ways are the opposite,

Unfortunately, because the Ricci tensor is the contracted Riemann tensor, the sign is defined by the latter.

The sign of the Ricci tensor does not change, because the two sign conventions concern the sign of the Riemann tensor.

--https://en.wikipedia.org/wiki/Sign_convention

As NotEinstein has been saying, Yang disagrees with Wikipedia. One version is wrong, and we're supposed to take your word for it it isn't Yang's?

Here on sciforums? Because we're all dumbasses?

 

[NotEinstein]

You are wrong, because the signs of the Ricci tensor defined in these two ways are the opposite, while the energy-stress tensor is defined in the same way, field equation must have two forms namely G^uv=8paiGT^uv and G^uv=-8paiGT^uv, which appear in different textbooks, obviously you read too few books

You can't define a term in two contradictory ways, and expect the results to make any sense.

But let's say that Yang indeed uses that different definition, causing a sign-change in the EFE. That means that the sign-change Yang gets in the EFE is just notational: it's not a real difference. All the discussion in Yang's article that follows about how this sign-change means this-or-that is thus wrong.

Let's try this trick elsewhere: say I define force to point in the opposite direction, so: $$F\rightarrow -F$$
Then I get: $$F=-ma$$
Look! Negative mass!
No, obviously not. The minus-sign is needed to correct for the fact that the force $$F$$ now points in the opposite direction. It's just a notational (or if you will, definitional) change. None of the physics have changed.

Whether Yang does this or not, Yang is wrong. Either about the sign, or about its interpretation.

the definition of Ricci tensor used by Yang is being used in a lot of textbooks, it's completely correct.

Please provide even a single one of these textbooks.

Obviously, Your knowledge is very incomplete, not systematic, not proficient, you know one and don't know the other.

Then explain it to me. You've written more than 50 posts now after my initial pointing-out of the minus-sign, and you still haven't managed to explain anything at all. Why do I have to drag all the answers out of you? Why are you so unwilling to share this supreme knowledge? Why are you here, if that's not your goal?

 

[NotEinstein]

Unfortunately, because the Ricci tensor is the contracted Riemann tensor, the sign is defined by the latter.

(I have been extremely sloppy, and have been calling it the contracted Ricci tensor throughout this thread (I figured out my mess-up some posts ago; now I'm sticking with it to avoid confusing heyuhua). Really should brush up on my GR.)​

 

[heyuhua]

the Ricci tensor has indeed two ways to define, but they have no essential difference and do not bring new physics, for example in the book " introduction to general relativity" 俞允强， the definition is the same as Yang's article. see:
http://www.doc88.com/p-0592619797194.html PP-50

 

[NotEinstein]

the Ricci tensor has indeed two ways to define, but they have no essential difference and do not bring new physics, for example in the book " introduction to general relativity" 俞允强， the definition is the same as Yang's article. see:
http://www.doc88.com/p-0592619797194.html PP-50

I can't read Chinese (I think that's Chinese?) so I can't really comment in detail. I assume this is an (illegal?) copy of Yu Yun Qiang's 1997 work, correct? But, it seems you're right: there's a swapping of the terms in the Ricci tensor, on page 50, equation 3.6.8. This results in the EFE on page 52, first unnumbered equation in section 3.7. And based on that, I (re-?)discovered this:
https://en.wikipedia.org/wiki/Einstein_field_equations#Sign_convention
"Authors including Einstein have used a different sign in their definition for the Ricci tensor..."

Which is discussed in a bit more detail here: https://www.physicsforums.com/threads/einstein-equation-quick-sign-question.794916/

So there we have it. Yang is using this convention, which straightforwardly results in a minus-sign in the EFE. Then Yang incorrectly compares this result to the EFE that's using the other convention. This comparison is, of course, fundamentally invalid. In other words, Yang is misinterpreting his/her results based on his/her mix-up of minus-sign conventions. And thus, with yet another source considered (this time kindly provided by you, heyuhua), we have to once again draw the conclusion that Yang is wrong.

Notice also how all sources in this thread (including the one just provided by you) state in no unclear terms that Yang is definitely wrong with his factor 2 difference in the EFE. In other words, even if this minus sign difference could be justified, Yang's result would still be wrong. And that's without considering all the other questions I brought up earlier, that you, wangchaoqing, and Yang have failed to address so far.

 

[heyuhua]

you can't read Chinese, but the maths is common and you can see. In a lot of textbooks Ricci tensor is so defined like Yang's articles , not only the textbook I recommend to you above, it is impossible that all authors are wrong, in fact, the two definitions are completely equivalent and the two ways of definitions have the same effect

 

[heyuhua]

I don't think it's necessary for us to continue to waste our time on this issue. If you can't calculate it yourself, your doubts will not really be eliminated, only through calculus can you really understand the beauty of this.

 

[heyuhua]

The two ways to define Ricci tensors have the same effect and respectively correspond to the two methods to write the field equations, namely G^uv=8paiGT^uv and G^uv=-8paiGT^uv, corresponding to each of them. The two methods of field equations distribute in a large number of teaching books, you can find them yourself

 

[arfa brane]

This thread is based on a load of rubbish. The two forms of the Ricci tensor are an artefact of the sign convention (the metric signature). Obviously it's important to make sure you stay with the convention you use, and not compare your equations with those where a different signature is used.

Otherwise you might as well say 1 = -1. Further, Yang's claim about cosmic expansion and the creation of matter just isn't supported by any evidence. This is definitely crank material and it's very likely I and everyone else is wasting their time here.

Note the denials, the lack of evidence that heyuhua has any intention of engaging in any kind of discussion, the presentation hinting at "new and revolutionary" results . . .

What a joke, it seems to be based on a mathematical error that the author isn't prepared to admit. It's the kind of error undergraduates make in GR courses and indicates a lack of understanding of the metric (distances are always positive, for instance; if you get a result based on negative distances you probably made a mistake somewhere).

 

[heyuhua]

The two sets of schemes to definn Ricci tensor are independent of each other, and if you use one, you can't use the other, there is no problem like 1=-1 at all. Besides, such the two sets of schemes are don't start from me, before, a lot of textbooks do so, if you feel incomprehensible, you can go to blame those experts

 

[heyuhua]

Random attacks are irrational. There have been a lot of facts about the continuous generation of matter, as described in Yang's article.
You're ignoran

 

[arfa brane]

The two sets of schemes to definn Ricci tensor are independent of each other, and if you use one, you can't use the other

It's interesting then, that Yang compares his version with another, "independent" version, as NotEinstein mentions.

There have been a lot of facts about the continuous generation of matter, as described in Yang's article.
You're ignoran

A lot of facts, huh? So where are the experiments confirming these "facts"? And why can't you spell the word "ignorant"?
Never mind that last question, I know the answer.

 

[NotEinstein]

you can't read Chinese, but the maths is common and you can see.

Yes, and if you read my post again more carefully, you'll notice I did just that.

In a lot of textbooks Ricci tensor is so defined like Yang's articles , not only the textbook I recommend to you above,

You keep claiming things about "a lot of textbooks" this, but the first textbook you brought up didn't. The second one you (eventually, after 50+ posts) brought up did, but that's hardly "a lot".

it is impossible that all authors are wrong,

True, just as Carroll isn't wrong, and that Wikipedia-author isn't wrong either. Additionally, all authors of textbooks (and Wikipedia) mentioned in this thread so far agree about the $$8$$ in the EFE. Everybody, except Yang. But, as you said, "it is impossible that all authors are wrong", so Yang must be by your own argument ad populum.

in fact, the two definitions are completely equivalent and the two ways of definitions have the same effect

Exactly. So when Yang compares the two directly, that's fundamentally nonsense, and a wrong thing to do. It appears you agree with me: Yang is wrong in claiming that this minus-sign has any physical meaning; it's just a minus-sign due to conventions, nothing more.

I don't think it's necessary for us to continue to waste our time on this issue.

Indeed. You have thoroughly helped prove that Yang is wrong.

If you can't calculate it yourself,

We now have four sources that do the calculations; I don't need to do it myself anymore.

your doubts will not really be eliminated,

Why should I have doubts? We have four authors agreeing with each other, and as you said, "it is impossible that all authors are wrong". So I believe their derivations, which means Yang is wrong.

only through calculus can you really understand the beauty of this.

I don't disagree there, but I don't see how that's relevant to the discussion at hand? Or are you saying that Yang can't understand the beauty of this, because (s)he can't go through the calculus properly?

The two ways to define Ricci tensors have the same effect and respectively correspond to the two methods to write the field equations, namely G^uv=8paiGT^uv and G^uv=-8paiGT^uv, corresponding to each of them.

True, and I don't think I've claimed otherwise?

The two methods of field equations distribute in a large number of teaching books, you can find them yourself

Yes, and we've visited several of those in this thread. Well, eventually, after 50+ posts when you finally managed to find one source using the alternative definition. And from that source (you provided) we learned conclusively that Yang is wrong, even if we take this alternative convention into account.

 

[NotEinstein]

The two forms of the Ricci tensor are an artefact of the sign convention (the metric signature).

Actually, I don't think that's the case. (I initially thought this as well.) There are two ways of defining the Ricci tensor; basically, you can contract the Riemann tensor over either the third or fourth index. It results in an overall minus-sign difference in the form of the Ricci tensor. This minus-sign difference then has to be 'compensated' in the EFE. This is unrelated (as far as I can tell) to the metric minus-sign convention.

But of course, just as the metric minus-sign convention, it has no effect on the physical predictions made by the EFE.

Note the denials, the lack of evidence that heyuhua has any intention of engaging in any kind of discussion, the presentation hinting at "new and revolutionary" results . . .

And the insults. Don't forget the insults!

What a joke, it seems to be based on a mathematical error that the author isn't prepared to admit.

Funny thing is, heyuhua has already admitted Yang is wrong multiple times in this thread, just not explicitly. There's some massive cognitive dissonance at play here.

It's the kind of error undergraduates make in GR courses and indicates a lack of understanding of the metric (distances are always positive, for instance; if you get a result based on negative distances you probably made a mistake somewhere).

I think the concept of minus-sign conventions is even explainable to and understandable by high school students...

 

[NotEinstein]

The two sets of schemes to definn Ricci tensor are independent of each other, and if you use one, you can't use the other, there is no problem like 1=-1 at all.

Exactly, and since Yang does switch between the two when (s)he compares his/her EFE to the usual EFE, Yang is guilty of doing exactly that. So you once again agree with us that Yang is wrong.

Besides, such the two sets of schemes are don't start from me, before, a lot of textbooks do so, if you feel incomprehensible, you can go to blame those experts

Can you rephrase that? I don't understand the point you're trying to make?

Are you saying that you didn't come up with the two Ricci tensor definitions, so if they are confusing, we have to blame the experts for that? Nobody here is confused (anymore?) about this; only Yang is. If (s)he wants, Yang can go blame the experts for making him/her make simple mistakes; I have no need for it. (Although I will admit it would be nice if all these conventions were centrally documented somewhere, so it's much easier to find out about them, but I fully understand why this isn't the case, and that you can't blame the experts for this.)

Random attacks are irrational.

Are you referring to the insults you've been throwing at me in this thread?

There have been a lot of facts about the continuous generation of matter, as described in Yang's article.

We didn't even get to that part of Yang's work, because we found a fundamental flaw much, much earlier on. I would suggest Yang fixes that first; most likely it changes the "facts" about the continuous generation of matter Yang describes in his article.

You're ignoran

Perhaps, but we're no longer ignorant about Yang being wrong.

 

[heyuhua]

the earth is growing up, the sun is bright and bright, the moon is going away from the earth, the earth is going away from the sun, the earth's spin is slowing and slowing, and so on, such a series of phenomena an facts can uniformly and systematically explained based on continuous creation of matter

 

[NotEinstein]

the earth is growing up, the sun is bright and bright, the moon is going away from the earth, the earth is going away from the sun, the earth's spin is slowing and slowing, and so on, such a series of phenomena an facts can uniformly and systematically explained based on continuous creation of matter

Perhaps, but what we do know is that Yang is wrong with his/her analysis of the EFE. Care to address that first?