A Flaw of General Relativity, a New Metric and Cosmological Implications [Technical]

Son Goku wrote:

Can I refute that if your metric was identical to the Schwarschild metric, they would make identical predicitons? Of course I can't refute that because it's true, although I don't understand why you think I said that.

It’s an example to show that an argument is good enough on its own. Calculations aren’t necessarily required.

I'm saying that the two metrics being similar doesn't mean their predictions are similar.

OK, but that’s different from what I was addressing in what you quoted of mine. I was addressing this:

And since we are tackling this at a scientific level you have to show the calculations, not an argument. An argument is a good placeholder, but not good enough on its own.

All section 6 does is assert that they make similar predictions, it doesn't show they make similar predictions. I don't see any calculations, I don't even see an arguement.

It shows that with logic. It does not just assert that. Let’s take section 6 step by step:

Zanket&#8217 wrote: »

The new metric for Schwarzschild geometry (eqs. 10 and 11) is derived by replacing instances of eq. 8 incorporated into the Schwarzschild metric with eq. 9.

That’s a given. It agrees with section 5.

Zanket&#8217 wrote: »

When r / R is at least five thousand, results of eqs. 8 and 9 match to at least seven significant digits.

Let’s confirm this statement. When I plug R = 1 and r = 5000 (or R = 2 and r = 10000; the same ratio returns the same result, which makes sense because the units are arbitrary) into eq. 8, I get: 0.99989999. Rounding to seven significant digits, I get 0.9999000.

When I plug R = 1 and r = 5000 into eq. 9, I get: 0.99990001. Rounding to seven significant digits, I get 0.9999000.

Do the results match to seven significant digits? Let’s list them together:

0.9999000
0.9999000

Yep, they’re identical. And just by eyeballing the equations, it can be seen that the results of eqs. 8 and 9 converge as r alone increases. Then the metrics return identical results where r / R >= 5000 and there are no more than seven significant digits in the result.

Zanket&#8217 wrote: »

In the experimental test of the Schwarzschild metric having the strongest gravity (the smallest r / R) to date, r / R is always greater than five thousand.

I give a reference for that, here. I did an extensive search to reasonably conclude that this is the strongest-gravity test to date. While it does not explicitly state the smallest r / R, anyone proficient at astronomical calculations should be able to derive it from the data given therein. I found it by computing the orbit using published numerical integration software (verified by seeing that the software’s results agreed to all significant digits with the reference’s result for the relativistic orbital precession), and recording the smallest r / R. It was 104900, as noted next to the reference in my paper.

Note that, even if I listed individual experiments and the calculations for those, there’d still be a question as to whether I had included every experiment, including the strongest-gravity experiment. Logically there’s no way I can prove that I cover every experiment or even the strongest-gravity experiment. Every paper is in the same boat on that.

Zanket&#8217 wrote: »

The result of every experimental test of the Schwarzschild metric to date has at most six significant digits since that is the current best precision of the gravitational constant G factored into R.

It is easy to google for G and confirm that it is known to no more than six significant digits. In geometric units, G is factored into M, hence it is factored into R, because R = 2M in my paper. Then Math 101 says that a result of either metric can have no more than six significant digits.

Zanket&#8217 wrote: »

Then all those tests confirm the Schwarzschild metric and the new metric equally.

This follows from the statements above. Do you disagree? If this statement is false, then one of the statements above it must also be false. Do you disagree with any of them?

Son Goku wrote:

What? That doesn't even make any sense. Why, if it was chaotic would it disagree with experiment? To agree with experiment it should be chaotic, beause that is what we observe around spherically symmetric objects.

My dictionary says that “chaotic” means “inherently unpredictable”. But the predictions either metric makes agree with observations; then those observations are predictable, not chaotic. What do you think “chaotic” means? And if you weren’t posing a problem with my metric, then what was your point?

It doesn't matter what you think of the Schwarzschild metric, your metric still gives R_ab != 0. The fact that it is inconsistent isn't based on the Schwarzschild metric, it is based on SR.

It does matter what I show about the Schwarzschild metric, as I noted above to the Professor (please see). What I show about it rejects the R_ab argument before it can be applied against my metric.

A Vacuum has to have R_ab = 0 in the real world, because this is what we observe, if it wasn't true SR wouldn't be true.

Then explain to me why R_ab = 0 when T_ab = 0 for the Schwarzschild metric even though it’s inconsistent with SR, as my paper shows. Why should I trust the R_ab argument as an indicator of consistency with SR when it doesn’t work as an indicator of that for the Schwarzschild metric?

Thisis an independant criteria.
You have an extremely unusual way of refuting arguements.

Above I showed the Professor that my way is logical.

We don't assume it! R_ab = 0 for T_ab = 0 in the real world. I haven't seen how you managed to refute it.

Nature knows squat about R_ab or T_ab. The R_ab argument is a purely mathematical argument. I added this reader comment to the paper:

Reader: Nonzero Ricci curvature in a vacuum is not observed. Therefore your metric must be invalid.

Author: Section 6 shows that the new metric is fully experimentally confirmed to all significant digits.

My dictionary says that “refute” means “to prove something to be false ... either through logical argument or by providing evidence to the contrary”. I gave a logical argument that shows that the R_ab argument doesn’t prove whether or not a metric is consistent with SR. In my basis for that I make a necessary choice between two incompatible and unrefuted arguments, using the laws of thought the Professor listed.

You don't show any logic though. In section 6 you just say that your metric and the Schwarschild metric give similar predictions. You don't argue how. How do we know the orbits are the same?
This is getting stupid, every time we raise an objection you say it doesn't matter without any good reason.

Above I show that the logic was in section 6 all along. Can you refute it?

R_ab = 0 for T_ab = 0 in nature, no way around that no matter what you think of GR.

You haven’t proven this. You haven’t shown any experimental test of natural phenomena that disagrees with my metric even though R_ab != 0 when T_ab = 0 for it. You need to support this claim with at least one experiment.

It's true independant of GR. You don't need to assume GR or even talk about GR for this to be a condition for a proposed theory of gravity.

Its independence of GR is immaterial. There’s no reason I should trust the R_ab argument when:

1. No experimental test of natural phenomena disagrees with my metric.
2. R_ab = 0 when T_ab = 0 supposedly indicates consistency with SR, but that doesn’t work for the Schwarzschild metric (it’s inconsistent with SR).
3. The argument in the paper that shows that the Schwarzschild metric is inconsistent with SR is simple, yet remains unrefuted.
4. My metric resolves several major problems of physics while removing assumptions (including some giant ones, like inflation and dark energy) and adding no new assumptions.

Physics has been at this point many times before, where neither of two competing theories is directly refuted. Occam’s razor typically prevails, and it clearly favors my paper over GR. There’s a quote in one of my books about Einstein’s unsuccessful attempt to unify gravity and electromagnetism. It seems to be relevant here:

“In developing the general theory of relativity from 1905 to 1915, Einstein had been guided by an existing mathematical formulism, the Riemann theory of curved space, and perhaps he had acquired too great a respect for the power of pure mathematics to inspire physical theory.”

Professor_Fink wrote:

Zanket, we keep telling you where there are problems in the derivation of your metric (like in your use of local results to build the manifold, and a misapplication of escape velocity), and you keep denying they exist.

I didn’t just deny your reasoning; I refuted it with a basis. For example, about my “use of local results to build the manifold” I gave a simple example that showed that it is deducible, from the given that an object falls in a uniform gravitational field, that an object falls in a nonuniform gravitational field as well, because a nonuniform gravitational field is everywhere uniform locally. Thereby I showed with basis that local results can be used to deduce global results, which refutes your point, and you didn’t refute my refutation. Why should I be convinced by your argument when I poked a hole in it and you didn’t patch the hole?

Both your proof of a “misapplication of escape velocity”, and your argument that there is an event horizon at the Schwarzschild radius, featured nothing more than an assumption that GR is correct. Reasonably, I should be unconvinced by arguments that boil down to “GR is right, therefore you’re wrong”.

So we know that your metric is not conformal to SR, from my derivation. This proves your metric is wrong.

That would presumably be the case if I did not find a hole in your argument. But I found one. More on that below.

You can't argue that you metric disproves my result, because your metric makes physical assumptions and mine does not.

I don’t argue that my metric disproves your result about R_ab. I argue that the Schwarzschild metric’s inconsistency with SR (that section 2 shows) disproves your conclusion about R_ab. Your claim that my metric makes physical assumptions is based on your R_ab argument. But you can’t use that argument because I have shown that it doesn’t work for its stated purpose, as an indicator of consistency with SR. You need to (scientifically) refute section 2 of my paper before you can use the R_ab argument. (Actually my new introduction should make it even easier for you. It is the simplest example in my paper of an inconsistency of GR.)

Physics cannot disprove maths. It just doesn't work like that Zanket. So the must be an error in your derivation. And as I have already said, we already pointed out where it is.

As I said above, I don’t doubt your math. I doubt your application of it; namely, your conclusion that it shows that my metric is inconsistent with SR. A correct mathematical proof can reach an incorrect conclusion. It doesn’t matter how widely accepted the conclusion is. My paper refutes the conclusion using a basis that you have not refuted.

Two minutes searching and I came up with this:
http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v512n1/38173/38173.html

Measurement of gravitational redshift can be used to measure the mass of neutron stars, and it is. However you can also calculate their mass when they are in binary systems, and some are. Lastly we have a theoretical mass range given by the chandrasekar limit. And guess what! They basically all agree!

Now, r/R for the photosphere of a neutron star is roughly 3. Which is way beyond the limit you claim accuracy to in your paper! These measurements confirm redshift predictions in a regime where your metric is wildly different from the Schwarzschild metric.

I see nothing in that paper that disagrees with section 6 in my paper. Look at the introduction to section 2 in your reference, which says “... no lines have been identified in radio pulsar spectra, and other gravitational effects on the observed emission from pulsars are sufficiently complex and theory dependent that no useful limits on the neutron star properties have yet been possible. In the following we thus limit ourselves to the determination of stellar masses in binary systems”. In other words, gravitational redshift experiments for neutron stars are not feasible, so instead they use only the properties of binary systems to deduce the masses. Then any r in that paper that could apply to my metric is not the surface of a star, but rather the far greater orbital radius of a star around its companion star, as is the case as well for the experimental test that is referenced in section 6 of my paper. Your reference is dated 1999; mine is 2004 and says “a highly-relativistic double-neutron-star system, allowing unprecedented tests of fundamental gravitational physics” (italics mine). Then I doubt that anything in your reference involves an experimental test of GR in gravity stronger than that in my reference. But if you still disagree, please point it out.

Well it's time to get a better dictionary. Chaotic means that for two inputs a, and a+e the answer diverges exponentially.

OK. The metrics still return identical results when r / R >= 5000 though, as I showed Son Goku above.