How is the EFE not related to the EFE?
Yes, that's my point. They are incompatible.
No, I've been saying all this time they aren't compatible. Is your English really that bad?
Because I'm taking your advice, and am ignoring the minus sign? But I guess your own advice is too confusing for you. I'll try and include the minus signs.
Yes, and as one finds out when one learns mathematics: $$4\neq-8$$.
If my foundation is too poor, then so is Einstein's, Adler's, Weinberg's, Carroll's, your Chinese author's...
Like?
Which, seeing as the EFE is at the heart of GR, means you are no longer doing GR at all. The theory of gravity you are working on doesn't apply to our universe. In fact, with the changed 'strength' and the flipped sign, I don't think it's reasonable to call it gravity at all!
All six sources now provided (three by you) agree: the absolute value of the coefficient is $$8$$, not $$4$$. So even if you are able to resolve the minus-sign business by messing about with conventions and definitions, Yang is still wrong.
Yes, let's. That equation proves that Yang is wrong, because: $$-8\neq4$$.
Yes, and this modification is wrong. Weinberg's derivation of the EFE clearly shows this. If you disagree, please point out the mistake that Weinberg made.
No, it doesn't. There have been mentioned six sources in this thread that give derivations of the EFE, all resulting in the same EFE (when you take into account the differing conventions); three of these sources were provided by you. Yang is in direct conflict with all six sources; including the three sources you provided. Please point out the flaw in the derivations that these six sources have done.
So it doesn't matter that Yang is wrong in his derivation? If you don't care about correctness, then what the heck are you doing on a science discussion forum?!
about the modification from 4 to -8 we've calculated it countless times, and it's perfectly reasonable. For a person who can ' t complete the calculation , it ' s not eligible to deny.
It's perfectly reasonable to change the heart of GR by changing the 'strength' of curvature by a factor 2, and throwing in a minus sign? It's perfectly reasonable to get a different answer to a calculation that tens of thousands of experts on the topic over a 100+ year period?
Who said I can't complete the calculation? I'm merely relying on Einstein, Weinberg, Adler, Misner, Carroll, your Chinese author, etc. because I trust their textbooks have received more attention than whatever I could scribe onto a piece of paper in private.
But you are allowed to deny the validity of the works of Einstein, Weinberg, Adler, Misner, Carroll, your Chinese author, and those ten of thousands of experts on the topic over a 100+ year period, without providing even the slightest hint as to where they made a mistake? Sounds "perfectly reasonable" to me...
According to you, Yang's EFE and everyone else's should thus match at low velocities, because under that limit both should result in Newtonian gravity. Please demonstrate that when $$v\ll c$$ this indeed happens. I highly doubt it, because $$4\neq-8$$, not even when $$v\ll c$$.
(Please learn how to use the tex-tag on this forum. Or at the very least use "_" for subscripts.)
You are claiming that SR is not recoverable from GR (when using the usual EFE); in other words, that the Einstein Equivalence Principle doesn't hold for this EFE. Well, please explain that to, for example, these people:
GR should be indeed recoverable to SR, but the usual EFE indeed cann't make GR connect with SR in extreme case of weak field, namely not recoverable. It is Yang's work that achieved the recover . And the principle holds in any case, the equivalent principle is showed as geodesic equation without mass term, that is to say, that geodesic equations hold means the principle holds
What? I don't understand what you're trying to say.
Except that it does, as my links suggest. In fact, Carroll does this explicitly in his book on pages 50-53.
But this isn't unique to Yang's work; the usual EFE has this property too. That was my point earlier; a point you’ve apparently not fully understood.
Yang's EFE doesn't have a cosmological constant, because he apparently doesn't need it: heyuhua claims Yang's modification explains things like that without needing dark energy, etc.
indeed there is no cosmological constant in Yang's modification, but the Pressure term takes zero no longer, now it takes negarive, P=-rou, namely the negative value of cosmic density. So-called dark energy may be thought to absorb into pressure P , namely p is the comprehensive effect of ordinary stress and dark energy, and as for the dark matter needn't be considered again. So, the cosmological calculation becomes very concise
Sure, but you just admitted that Carroll thus does recover Newtonian mechanics in this limit, so the claim that only Yang does this correctly, is false. And while Carroll may not explicitly derive this for high speed cases, the two links I previously provided do claim to recover SR.
Please stop purposefully misrepresenting: there is a factor 2 difference in the absolute value of the coefficient of the EFE.
It isn't zero in standard GR in general either, so I don't know why you'd say that?
Does Yang derive the $$C_l$$ of the CMB somewhere (see: https://en.wikipedia.org/wiki/Cosmic_microwave_background#/media/File:PowerSpectrumExt.svg )? That would be quite convincing that his EFE doesn't need dark energy.