Yes, I know that anyone who challenges GR is by definition a crackpot. I also know that a paper showing a flaw of GR is uninteresting even if valid, and that I need to fix the Kerr metric and predict gravitational waves too or else it's junk. (Just trying to forestall some typical comments.)

A Flaw of General Relativity, a Fix, and Cosmological Implications

Abstract: A flaw of general relativity is exposed and is shown to source from a misapplication of the equivalence principle, the theory’s core postulate. A replacement for the Schwarzschild metric is simply derived. (The vast majority of experimental tests of general relativity have been tests of the Schwarzschild metric.) The new metric is shown to be confirmed by experiments of the four classical tests of general relativity. The predictions of the new metric are shown to diverge from those of the Schwarzschild metric as gravity strengthens. The cosmological implications explain some observations simpler than do alternative explanations.

For those interested, it seems new member Zanket (Welcome to Universe Today, Zanket!) also posted the same thing in the BadAstronomy forum.

Some discussion has ensued.

No comment here? Oh well. Since the original post, the paper has been significantly revised based on reader input. The math is equivalent (one less derivation) and the conclusions are the same though.

Zanket,

Actually there is a problem...not necessarily with your math but your presentation.
It can be quite misleading since it leaves out too much that you may have taken for granted..Most folks on this and many forums do not have a background in tensor calculus and you might be taking your background for granted.

John Archibald Wheeler's "A Journey into Gravity and Spacetime" was an effort to build a communication bridge toward such understandings..I was given the impression that since Einstein insisted that forces result from spacetime geometry, then all the laws of physics would have to be shown to be derived from the spacetime geometry of worldlines..He did not assume Kepler's or Newton's Laws to be valid..

He used simple thought experiments like the boomerang shaft experiment where test masses in free falls would change shape in their fall differently on the outside of a planet than on the inside...where areas of responsibility are associated with changes in the rate of changes in the space separating free falling objects in very nearly parallel journeys...where turning moments relate to that ratio...where conservation of momentum energy can be explained with scissors cutting paper or an arc weldor welding a box ( that last one I cooked up..)...He showed how spacetime gripped mass with those turning moments and binding energies and showed how mass gripped back with the tidal forces..

He further showed how 63 ants all crawling up the inside of a pottery vase while dropping red markers in their journey at discreet intervals would display a series of circles, each with a different circumference than the proceeding and following one and where the first coordinate of each marker expressed a radius while the second expressed a radian distance..

He dropped pottery on the floor, shattering it into shards and reassembling it with matchsticks for guides along the rafter and swing with the points of the sticks from the rafter all touching the axis of rotation..

With your background you could probably come up with a better explanation and draw someone like me into a better listening mode and maybe you could take some of the mystery out of your journey..

The misapplication of the equivalence principle you see should be made with an elementary understanding that may not necessarily need all that math..Or, does it?

Blueshift, thanks for your comments. I think the paper does need the math, to derive an equation that makes predictions that are confirmed by experiment. But the math is very simple; only elementary algebra is used.

If your issue is with GR, why so much Newton? GR showed that Newton was only applicable to non-relativistic situations, where speeds were less than a small fraction of c and gravity was low (non-Schwartzchild).

And I agree that you need to fill out your paper with more of a narrative explaining what you looking at, why you are looking at it, and what you see as the implications of your work. The list of equations and graphs doesn't help those of us that are less versed in mathematics.

__________________
...and we'll be saying a big hello to all intelligent life forms everywhere; and to everyone else out there, the secret is to bang the rocks together, guys...

GR shares Newton's escape velocity equation, which is proven in the paper to be non-relativistic. That's the flaw of GR.

Thanks for the suggestion. I'll likely be adding introduction and conclusion sections.

Zanks-

while I love crackpot theories (as Anton will attest to), I think that using elementary algebra really is not enough to cast evidence against something which has involved a far higher, more complicated mathematics.

There's no scientific reason why elementary algebra is not enough.

What I meant was, for example the escape velocity equations, it might help to narrate a seudo-thought experiment of starting with the rocket on the launch pad. A list of equations, whether they are correct or not, will not draw and hold the attention of even the most interested reader.

I write audit reports all the time and if I just listed the issues I found and the solutions, no one would read the report. I have to throw in paragraphs of descriptive explanations of the operating unit I'm reviewing, its history and structure, and a more descriptive explanation of what the issue is, why anyone reading about it should care, what the outcome would be if nothing was done about it, what I think should be done about it, and what the people who manage the operating unit intend to do about it. The sandwich isn't just the meat in the middle. Its the bread and the way its cut, the fix'ns (I'm from Texas and here that's a real word meant to encompass all of the various veggies and such that can be added to a sandwhich), the condiments, side dishes, the drinks, garnishments, etc. All of this in the culinary world is called the presentation, which in my opinion is what your paper is still lacking.

__________________
...and we'll be saying a big hello to all intelligent life forms everywhere; and to everyone else out there, the secret is to bang the rocks together, guys...

I hear you. I think some people like a presentation like that, whereas others dislike such. In my job I'm on the receiving end of something like your audit reports. I read detailed design specs about things needing change, where I'm the one doing the change. I'd say out of any given ten pages of a spec, it turns out I really needed to know only one page. I've necessarily become skilled at quickly identifying that one crucial page and then ignoring the rest. Granted I'm just one type of reader of the spec.

I removed a section from the paper that had what I thought was a nice explanation of something, but it raised so many bogus issues that I removed it. People were arguing against basic algebraic substitution because the text (that the math supported) didn't match their worldview. Generally I've found that, in physics, the more you can stick to the math, the better. Still, I'll likely add a short introduction and conclusion section.

One factor here is that the paper is almost certainly going to die on the vine even supposing it is valid and has a nice presentation. So I won't spend time on it beyond the minimum. My goal is to get the paper vetted so that I'm confident that it's valid. Then I'll forget about it.

About the relativistic rocket equations in section 7, since those come from another website (a link to it is in the paper), I let that website do the talking about them.

BTW, I think "fix'n" and "y'all" are great words.

Now THAT is a good place to start. You might start out with such a statement as an opening when you write..

Now THAT is a good place to start. You might start out with such a statement as an opening when you write.. [/b][/quote]
Agreed! Thanks for the suggestion.

Further, since omega basically deals with escape speed of the universe, this points out why you see this as a major flaw...Right so far?

Regarding how the paper affects cosmology, I put it this way: if the paper is valid, then cosmology is significantly upset, including omega. The concepts in section 7 are new; they are not featured in generally accepted cosmology today. This section—using gravity alone—resolves the flatness and horizon problems, and explains the observed accelerating expansion of the universe. It would probably take several papers by cosmologists (not me) to revise cosmology to include the concepts in section 7.

Since you seem open to some suggestions, I do have one more that I feel would be quite helpful. In section 7 of your paper you could add the calculations used by Newton's formula to arrive at 7 miles/sec for the escape speed of Earth and use your metric to arrive at another precise answer..Is it higher or lower and by how much?
Likewise, you could throw in some calculations concerning the sun's escape speed and make some predictions of what spacecraft will have their pathways altered due to the failure to realize your metric..Do you see Pioneer and Voyager sending back some unpredicted results that are due to this?

Is the Columbia disaster or some other possible future wreck that you might see tied to such a failed understanding ?

I think that such predictions would give strong attention to what you are proposing.

Personally, I am still pursuing the investigation of your paper and am quite interested. Even if you are proven false, you are helping me to understand GR and the universe more than if you didn't bring the matter up..It has me probing..

For the Sun or Earth, the escape velocity at the surface is the same for both Newton and the new equation in the paper. The results of the two equations match on all significant digits. I did have this calculation for the Sun in the paper, but removed it as extraneous, since the calculation is pretty simple and the equations can be eyeballed to see that the results would be very close to each other. Fig. 1 shows that the two escape velocities are very close at r / R = 10, and no experiment has been conducted at r / R <= 10,000.

I think it's a kind of balancing act; if I include too many figures and example calculations then it can make the paper seem daunting at first glance. I might add some of those things as links, since the paper is a web page.

The experimental confirmation section shows that their pathways would be negligibly altered. The difference does not show until the result has at least eight significant digits.

If you mean the Pioneer anomaly, no, that is not predicted by the paper.

No, the difference is too slight for that. My understanding is that NASA still uses Newton, not relativity, because Newton is precise enough in the Solar system. The paper does not change that.

That’s good to hear, thanks. I think general relativity (GR) is often explained in an overly complicated way. For example, no source that I know of explicitly explains that curved spacetime is the same thing as a nonuniform gravitational field, as defined in the paper. (The book Black Holes and Time Warps by Kip Thorne covers this, but doesn’t explicitly equate them.)