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

Zanket

Professor_Fink wrote:

Yes, of course I can refute this. Those quantities are christoffel symbols (the capital gammas) and so already contain partial derivatives with respect to r, so of course the there is differences between the two sections, d/dr g_00 and d/dr g_33 are not the same for both metrics!

Before I reply to the rest of your posts, let’s focus on this. Look closely at what you quoted of mine. I agree that there should be differences between the two sections for the expressions I mentioned in that quote; that’s what I’m saying there.

Let’s focus just on the second lines in eqs. 23 and 55. You say that these expressions should be different between the sections, but clearly they are equivalent. Both of the second lines are equivalent to 4 / r. Why is that not a problem, when you agree they should differ?

Zanket

Son Goku wrote:

Hilarious Zanket, you know that's not what I'm saying.

Seriously, I don’t. Let’s focus on this:

Zanket wrote:

Eq. 55: The second line should be equivalent to the second line in eq. 23 except that r is replaced with r + R, but it’s not. Instead it is equivalent to the second line in eq. 23, for no apparent justifiable reason.

Look at the two Christoffel symbols being multiplied. If you work out the derivation you'll see they can't come out the same.

By “they”, you mean the second lines in eqs. 23 and 55, right? But they are the same. They are both equivalent to 4 / r. We both think that is a problem. So how is it that you are not contradicting yourself? I really don’t get it.

Zanket

Professor_Fink wrote:

Yes, of course I can refute this.

Son Goku wrote:

Hilarious Zanket, you know that's not what I'm saying.

There seems to be some miscommunication here. To be clear, when I say above that the second lines in eqs. 23 and 55 are the same, both equivalent to 4 / r, I’m not saying that I derived them and they are the same. I’m saying that they are the same right in the Professor’s derivation. In other words, it is the Professor who says that they are the same, not me.

Professor_Fink

Ok, here is the derivation using your substitution. As you see, R_00 is still non-zero. You are not making the correct coordinate substitutions.

Professor_Fink

Zanket wrote:

There seems to be some miscommunication here. To be clear, when I say above that the second lines in eqs. 23 and 55 are the same, both equivalent to 4 / r, I’m not saying that I derived them and they are the same.

Why should they be different? It doesn't matter that the metrics are different, this particular function of both metrics is the same for both.

The g_00 and g_33 terms cancel in both, only the g_11 and g_22 terms contribute here, and g_11 and g_22 are the same for both!

What is your problem with this?

Zanket

Professor_Fink wrote:

Ok, here is the derivation using your substitution. As you see, R_00 is still non-zero. You are not making the correct coordinate substitutions.

Thanks, I’ll come back to this if needed.

Why should they be different? It doesn't matter that the metrics are different, this particular function of both metrics is the same for both.

The g_00 and g_33 terms cancel in both, only the g_11 and g_22 terms contribute here, and g_11 and g_22 are the same for both!

Then why does Son Goku disagree with you?:

Son Goku wrote:

Look at the two Christoffel symbols being multiplied. If you work out the derivation [for the second lines in eqs. 23 and 55] you'll see they can't come out the same.

Please show your work here, for the second line in eq. 55. The g_00 term cannot cancel. You said that g_00 * g^00 = 1. Then the g_00 term in the second line must = R / (r * (r + R)), to be consistent with eqs. 43 to 45. I believe the 1 / r in eq. 56 should be 1 / (r + R).

Also please show your work between eqs. 50 and 51. There is a mistake there too; more on that below.

Eqs. 64 and 65 are invalid. Between eqs. 63 and 64 you have:

(∂ / ∂x^3) * g_00 = -(R / r^2)

But between eqs. 43 and 45 you have:

(-∂ / ∂x^3) * g_00 = (R / (r + R)^2)

Eq. 43 to 45 are consistent with eqs. 11 to 13, but eqs. 63 to 65 are inconsistent with eqs. 31 to 33. Eq. 65 should be = R^2 / (2 * (r + R)^4).

Also, a minor problem in eq. 32: the expression in parentheses should have a negative sign, to be consistent with eq. 64. This doesn’t affect your result.

Some background on the problem between eqs. 50 and 51:

Eq. 19 is equivalent to: (R * ((3 * R) - (2 * r))) / (2 * r^4)

Eq. 19 depends on only the inputs g_00 and g_33, so if I replace every r with r + R, I should get an equation that is equivalent to eq. 51. When I replace every r with r + R and simplify, I get:

(R * (R - (2 * r))) / (2 * (r + R)^4)

But eq. 51 is equivalent to:

(R * (R - (2 * r))) / (r + R)^4

There’s no justification for the difference in red. Eq. 51 is twice what it should be, if it was consistent with eq. 19. You must have made a mistake.

Son Goku

Zanket, this is a very simple derivation of a standard quantity in differential geometry. You're asking such confusing questions that I've probably made a slip up along the way.

To reset everything and lose the confusion, I ask that you list by number your current contentions with Professor_Fink's derivation.

i.e.:
1. Eq. 64 has........
2. Eq. 45 should be the same as.....
e.t.c.

Then the thread will continue from there. I ask for Professor_Fink and planck2 to wait until Zanket has done this and only respond based on Zanket's next post.

Professor_Fink

Ok, I'll wait.

Professor_Fink

Actually, Zanket does point out mistakes in my calculation. I'm just correcting it now. I'll post it in about 10 mins.

Professor_Fink

Zanket wrote:

Please show your work here, for the second line in eq. 55. The g_00 term cannot cancel. You said that g_00 * g^00 = 1. Then the g_00 term in the second line must = R / (r * (r + R)), to be consistent with eqs. 43 to 45. I believe the 1 / r in eq. 56 should be 1 / (r + R).

No, you're wrong. I have added the derivation as eq 69/70.

Zanket wrote:

Also please show your work between eqs. 50 and 51. There is a mistake there too; more on that below.

Eqs. 64 and 65 are invalid. Between eqs. 63 and 64 you have:

(∂ / ∂x^3) * g_00 = -(R / r^2)

But between eqs. 43 and 45 you have:

(-∂ / ∂x^3) * g_00 = (R / (r + R)^2)

Eq. 43 to 45 are consistent with eqs. 11 to 13, but eqs. 63 to 65 are inconsistent with eqs. 31 to 33. Eq. 65 should be = R^2 / (2 * (r + R)^4).

Also, a minor problem in eq. 32: the expression in parentheses should have a negative sign, to be consistent with eq. 64. This doesn’t affect your result.

Some background on the problem between eqs. 50 and 51:

Eq. 19 is equivalent to: (R * ((3 * R) - (2 * r))) / (2 * r^4)

Eq. 19 depends on only the inputs g_00 and g_33, so if I replace every r with r + R, I should get an equation that is equivalent to eq. 51. When I replace every r with r + R and simplify, I get:

(R * (R - (2 * r))) / (2 * (r + R)^4)

But eq. 51 is equivalent to:

(R * (R - (2 * r))) / (r + R)^4

There’s no justification for the difference in red. Eq. 51 is twice what it should be, if it was consistent with eq. 19. You must have made a mistake.

Yes, I made a few slips. All are fixed in the new version here. Note that this is a new link!

R_ab is still non-zero though. It is absolutely impossible to make R_ab = 0 for your metric.

Zanket

Son Goku wrote:

To reset everything and lose the confusion, I ask that you list by number your current contentions with Professor_Fink's derivation.

OK, I'll do that after I've evaluated the Professor's latest version of the PDF.

Zanket

Professor_Fink wrote:

Note that this is a new link!

Got it, thank you.

Can you show your work on g_11 and g_22 as well, for the second line in eq. 55? I'd like to see how these sum to 1 / r.

Professor_Fink

Zanket wrote:

Got it, thank you.

Can you show your work on g_11 and g_22 as well, for the second line in eq. 55? I'd like to see how these sum to 1 / r.

They sum to 4/r, not 1/r.

It's easy. g^22 d/(dx^3) g_22 = r^-2 d/(dr) r^2 = 2/r.

g^33 d/(dx^3) g_33 = r^-2 1/(sin theta) d/(dr) r^2 sin (theta) = 2/r.

Adding these you get 4/r.

Zanket

Professor_Fink wrote:

They sum to 4/r, not 1/r.

Oops; agreed.

Adding these you get 4/r.

OK, thanks.

Professor_Fink

Am I to take it that you now accept R_ab !=0 for your metric?

Zanket

Professor_Fink wrote:

Am I to take it that you now accept R_ab !=0 for your metric?

I'll have an answer for you today.

Zanket

Professor_Fink wrote:

Am I to take it that you now accept R_ab !=0 for your metric?

I can’t refute your analysis that shows that.

In your latest version I see no inconsistencies. I verified eqs. 23, 69 and 70, including the derivatives, and otherwise I see no mathematical mistakes. (And kudos for the excellent presentation.)

In my proof that R_00 = 0 for my metric above, I said that g_11 and g_22 drop out. But I had misread your paper on that.

The question becomes, have you refuted my paper? Above I said that there are only two ways to refute a theory of physics: show that it is internally inconsistent, or show that it disagrees with observations of natural phenomena (beyond the margin of error).

Your R_ab !=0 argument does not show that my metric disagrees with observations of natural phenomena. Your analysis shows that all the inputs needed to calculate R_00 are all the components of the metric. Then an experimental test of R_00 is an experimental test of the metric, and vice versa. Section 6 in my paper shows that the Schwarzschild metric and my metric make identical predictions given the parameters of every experimental test of Schwarzschild geometry to date. And that section has not been refuted.

In section 3 of your analysis, when you say “Zanket’s metric does not satisfy Rab = 0 when Tab = 0, and hence is not conformal to Minkowski space”, you seem to imply that this proves that my metric is internally inconsistent. Is that what you imply there? I would disagree that this shows an internal inconsistency, because it would be backwards logic. In GR, the equivalence principle assumes that spacetime is flat (Minkowskian) at a mathematical point. If it was provable whether or not spacetime is flat at some mathematical point given a metric, then GR would not need the assumption. So I would not be convinced that your argument shows that my metric is internally inconsistent.

Also, section 2 of my paper shows that the Schwarzschild metric is internally inconsistent, and that has not been refuted here or anywhere. So if you are correct that R_ab !=0 for my metric, then it seems that R_ab !=0 in nature.

Professor_Fink

Zanket wrote:

Your R_ab !=0 argument does not show that my metric disagrees with observations of natural phenomena. Your analysis shows that all the inputs needed to calculate R_00 are all the components of the metric. Then an experimental test of R_00 is an experimental test of the metric, and vice versa. Section 6 in my paper shows that the Schwarzschild metric and my metric make identical predictions given the parameters of every experimental test of Schwarzschild geometry to date. And that section has not been refuted.

The system is non-linear. Just because the metrics are very close does not mean that they should give wildly different predictions (which is essentially the definition of a chaotic system).

Zanket wrote:

In section 3 of your analysis, when you say “Zanket’s metric does not satisfy Rab = 0 when Tab = 0, and hence is not conformal to Minkowski space”, you seem to imply that this proves that my metric is internally inconsistent. Is that what you imply there? I would disagree that this shows an internal inconsistency, because it would be backwards logic. In GR, the equivalence principle assumes that spacetime is flat (Minkowskian) at a mathematical point. If it was provable whether or not spacetime is flat at some mathematical point given a metric, then GR would not need the assumption. So I would not be convinced that your argument shows that my metric is internally inconsistent.

You use special relativity to deive your metric. R_ab!=0 means that your metric does not give a space time conformal to special relativity, and so any arguements assuming special relativity to hold in any reference frame (i.e. all your relatiistic rocket stuff) cannot be applied. Since the metric is based on an assumption of special relativity, but the metric is inconsistent with it, it is impossible for your arguement to be self consistent. It is hence wrong.

Zanket wrote:

Also, section 2 of my paper shows that the Schwarzschild metric is internally inconsistent, and that has not been refuted here or anywhere. So if you are correct that R_ab !=0 for my metric, then it seems that R_ab !=0 in nature.

As I have said time and time again, your refutation of the Schwarzchild metric is wrong, because you assume that the escape velocity is always defined.

Zanket

Professor_Fink wrote:

Just because the metrics are very close does not mean that they should give wildly different predictions (which is essentially the definition of a chaotic system).

Both metrics are experimentally confirmed. Their predictions diverge as gravity strengthens, but the divergence is smooth.

You use special relativity to deive your metric. R_ab!=0 means that your metric does not give a space time conformal to special relativity, and so any arguements assuming special relativity to hold in any reference frame (i.e. all your relatiistic rocket stuff) cannot be applied. Since the metric is based on an assumption of special relativity, but the metric is inconsistent with it, it is impossible for your arguement to be self consistent. It is hence wrong.

I’d rather not take your word that R_ab != 0 proves that a metric is inconsistent with SR. Can you offer any decent source to that effect, hopefully one that uses plain English?

As I have said time and time again, your refutation of the Schwarzchild metric is wrong, because you assume that the escape velocity is always defined.

I have said that this argument puts the cart before the horse, and you haven’t refuted that. Escape velocity is defined in GR as long as v (as defined in section 2) is less than c. Section 2 shows that v is always less than c, and this is inferred by means GR allows. Then escape velocity is always defined, and GR cannot demand otherwise without being inconsistent. In other words, GR says:

- Escape velocity is always defined.
- Escape velocity is not always defined.

which is inconsistent. You can’t just ignore the first statement, since it is shown to be inferable by means GR allows. Instead you'd have to refute the basis given for it.

Son Goku

Zanket wrote:

Both metrics are experimentally confirmed. Their predictions diverge as gravity strengthens, but the divergence is smooth.

You haven't shown this. I've read your paper. The metrics are indeed similar but I see no calculations to support this claim. 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.

Calculate the perihelion of mercury for example.
(Remember how similar your g_ab's are, but how different your R_ab's are.)

Section 6 is not enough to support this claim. I want to see them predict the same thing.

Your R_ab !=0 argument does not show that my metric disagrees with observations of natural phenomena.

It does. You have constant curvature in a vacuum.
This isn't observed.
You can't argue that away, because otherwise Special Relativity would be wrong. SR needs R_ab = 0 in a vacuum, otherwise you wouldn't be able to get Minkowski space ever.

Then an experimental test of R_00 is an experimental test of the metric, and vice versa. Section 6 in my paper shows that the Schwarzschild metric and my metric make identical predictions given the parameters of every experimental test of Schwarzschild geometry to date. And that section has not been refuted.

No, Zanket, would you please stop making arguements like this.
Professor_Fink went to alot of trouble and now you're back to your old lazy arguements.
Section 6 doesn't support its own claims. Sure when we reach large (r/R) they are similar, but that doesn't show they give the same orbits or anything.
This is a choatic system, claims like that don't work.

In GR, the equivalence principle assumes that spacetime is flat (Minkowskian) at a mathematical point. If it was provable whether or not spacetime is flat at some mathematical point given a metric, then GR would not need the assumption.

Lazy Zanket, you know exactly why this isn't applicable.
GR doesn't assume this, it comes from the manifold picture. Einstein used this as an argument for adopting the manifold picture.

Zanket please make an actual effort when responding. And you're going to have to start showing calculations. Your hand-wavy arguements aren't enough.

Professor_Fink

Zanket wrote:

I’d rather not take your word that R_ab != 0 proves that a metric is inconsistent with SR. Can you offer any decent source to that effect, hopefully one that uses plain English?

That's why I derive R_ab for Minkowski space after I do it for your metric and the schwarzschild metric. It's on the last page.

Professor_Fink

Zanket wrote:

Both metrics are experimentally confirmed. Their predictions diverge as gravity strengthens, but the divergence is smooth.

I'm afraid I don't believe this. You have no calculations, and you make a claim that the best test of the metric so far done only test it at a huge distance. This is patently obsurd. Measurements of gravitational redshift measure effects from the photosphere outwards.

There is no way they will agree for both metrics, and these have been measured!

I'm afraid that without proof of your claim, I'm lead to believe you don't know what constitutes a valid test of the metric.

Professor_Fink

Zanket wrote:

Both metrics are experimentally confirmed. Their predictions diverge as gravity strengthens, but the divergence is smooth.

That is clearly false! The Schwarzschild metric has a curvature singularity at r=R while yours remains analytic.

How can you have a smoth transition from an analytic function to one with a pole? It's completely impossible!

Zanket

To save time, I’ll address both your points (Son Goku’s and the Professor’s) in one post. But I’ll endeavor to cover all your points.

On section 6, the experimental confirmation: If two metrics are identical, they give the same results, right? Then if my metric was identical to the Schwarzschild metric, I’d need not show any calculations for Mercury (say), right? What if, after rounding to the number of significant digits in the experiment having the strongest gravity to date, my metric gives results identical to those given by the Schwarzschild metric? Then I’d need not show any calculations for any experiment to date, right? How could an experiment in weaker gravity return a different result between the metrics? It could not.

Son Goku wrote:

An argument is a good placeholder, but not good enough on its own.

This is unscientific thinking. An argument is good enough on its own; you haven’t proven otherwise. For example, if my metric was identical to the Schwarzschild metric, then it would be a mathematical certainty that my metric would return the same result for any experimental test of the latter. Can you refute that, without just ignoring the issue by saying that logic alone is not good enough? Likewise, Einstein’s “relativity of simultaneity” argument was good enough on its own to advance physics. Logic underlies mathematical arguments. (Indeed, math is a form of logic.) Then logic alone must be sufficient to prove a point. You’re just showing a bias for calculations. You're being hypocritical too, by using logic to try to refute me here. Show me a calculation that proves that an argument is not good enough on its own! Since we are tackling this at a scientific level you have to show the calculations, not an argument.

The reason I use the logic in section 6 is because it’s the simplest way to show that my metric gives the same results as the Schwarzschild metric for every experimental test of the latter to date. It also shows for what ratio of r to R the metrics will agree in future experiments. I’m saving my readers gobs of time with that logic, unless they are unscientific, in which case I can’t help them.

Son Goku wrote:

This is a choatic system, claims like that don't work.

If my metric was chaotic, then I’d expect it to not agree with every experimental test to date. But section 6 shows otherwise.

On the R_ab argument: It supposedly shows that my metric is inconsistent with SR, and shows that the Schwarzschild metric is consistent with SR. But the argument in section 2 shows that the Schwarzschild metric is inconsistent with SR. Only one argument can be right. When Einstein was faced with the same situation, for a paper that showed that SR is invalid, he rejected it with simply (paraphrasing) “it disagrees with SR, so it must be invalid”. That’s okay; he basically put the onus on the author to disprove SR directly. I will do the same. I don’t know what the problem is with the R_ab argument except that it disagrees with section 2, but that’s good enough to reject it. In section 5 I added the following reader comment:

Reader: Ricci curvature is not zero for your metric. Only metrics with zero Ricci curvature (like the Schwarzschild metric) are conformal to the metric for flat spacetime. Therefore your metric is not.

Author: Section 2 shows that the Schwarzschild metric is inconsistent with special relativity. Then an analysis that shows that the Schwarzschild metric is consistent with special relativity cannot be trusted as an indicator of that.

To improve my case I added, as an introduction to the paper, the simplest-yet example of an inconsistency of GR (implicitly the Schwarzschild metric). It is a simplification of the inconsistency shown in section 7. Please check it out (see fig. 1). You may reject my paper due to the R_ab argument. You may even lock the thread. That’s fine with me because I’m not here to convince you. I’m here to see if anyone can refute my paper. You will not be able to convince me with the R_ab argument that my metric is flawed unless someone can refute the inconsistencies of the Schwarzschild metric that the paper shows.

Son Goku wrote:

Zanket wrote:

In GR, the equivalence principle assumes that spacetime is flat (Minkowskian) at a mathematical point. If it was provable whether or not spacetime is flat at some mathematical point given a metric, then GR would not need the assumption.

Lazy Zanket, you know exactly why this isn't applicable.

I agree that my logic is invalid there.

Professor_Fink wrote:

Measurements of gravitational redshift measure effects from the photosphere outwards.

Section 6 covers any experimental test where r / R is always >= 5,000. The r / R is always > 100,000 for any experimental test of the Schwarzschild metric to date. The mean r for the Sun 6.9598 X 10^8 meters. The R for the Sun is 2.954 X 10^3 meters. Then the mean r / R for the photosphere of the Sun is 235,606. And then section 6 covers every experimental test of Schwarzschild geometry for our solar system (even future ones).

Plus, you don’t even need the metrics to calculate the gravitational redshift. Just plug the appropriate values into eqs. 8 and 9 and compare. (Eq. 8 is Einstein’s equation for the gravitational redshift. Eq. 9 is mine.) Round to at most six significant digits, the current best precision of the gravitational constant G incorporated into R. You’ll see that the results are identical for any experimental test of gravitational redshift to date. They must be, because (as section 6 notes) eqs. 8 and 9 return results that agree to at least seven significant digits when r / R is >= 5,000. And to test that, just plug r = 5,000 and R = 1 into eqs. 8 and 9 and compare. (Only the ratio between r and R matters in those equations, which you can also quickly confirm.)

On “smooth divergence”: Fig. 4 (used to be fig. 3) shows that they smoothly diverge. The divergence becomes inapplicable at the Schwarzschild radius, only because Einstein’s equation (eq. 8) doesn’t apply below there.

Professor_Fink

Zanket wrote:

To improve my case I added, as an introduction to the paper, the simplest-yet example of an inconsistency of GR (implicitly the Schwarzschild metric). It is a simplification of the inconsistency shown in section 7. Please check it out (see fig. 1). You may reject my paper due to the R_ab argument. You may even lock the thread. That’s fine with me because I’m not here to convince you. I’m here to see if anyone can refute my paper. You will not be able to convince me with the R_ab argument that my metric is flawed unless someone can refute the inconsistencies of the Schwarzschild metric that the paper shows.

I never used the Schwarzschild metric to calculate R_ab for your metric. I calculated it completely independantly. R_ab!=0 for your metric has nothing to do with GR. It is pure maths.

You metric is not conformal to Minkowski space and hence disagrees with special relativity, completely independantly of what GR may or may not say. This is a matheatical fact, and you an't get around it.

Your arguement is not self consistent since you use A->B (where A is special relativity, and B is your metric), yet from R_ab we can see that B->¬A.

Therefore there is a flaw in the logic of your arguement since you have A->¬A. Which violates essentially the first axiom of logic.

Zanket wrote:

Section 6 covers any experimental test where r / R is always >= 5,000. The r / R is always > 100,000 for any experimental test of the Schwarzschild metric to date. The mean r for the Sun 6.9598 X 10^8 meters. The R for the Sun is 2.954 X 10^3 meters. Then the mean r / R for the photosphere of the Sun is 235,606. And then section 6 covers every experimental test of Schwarzschild geometry for our solar system (even future ones).

And I said the sun where?

Zanket wrote:

On “smooth divergence”: Fig. 4 (used to be fig. 3) shows that they smoothly diverge. The divergence becomes inapplicable at the Schwarzschild radius, only because Einstein’s equation (eq. 8) doesn’t apply below there.

Yes they do! The field equations describe the whole space time, as does the Schwarzschild metric.

Professor_Fink

Zanket wrote:

This is unscientific thinking....

...I’m saving my readers gobs of time with that logic, unless they are unscientific, in which case I can’t help them.

Aside from the fact you seem to have completely missed the point of both posts, I take offence at all your claims that we are somehow 'unscientific'.

I'm a physicist. That is, a scientist. I am paid as such. You however, are clearly not. You seem to completely understand the scientific method, the basics of logic, and virtually all the maths necesary to deal with curved spacetime.

Calling myself, Planck2 or Son Goku unscientific is both offensive and obsurd. Also it makes you look like a complete crackpot.

Since you mention John Baez's website quite a bit, have you measured your paper on the crackpot index?

I did when you first posted it, and by my reconing you got 146. Considering you start off at -4, that does not bode well for your paper. That was before the rest of this thread, which can only serve to up that rating!

Zanket wrote:

If my metric was chaotic, then I’d expect it to not agree with every experimental test to date. But section 6 shows otherwise.

Eh, the metric is smooth, it's functions of the metric that are chaotic. Like all the three body problems you get when you take Jupiter in to account.

Zanket

Professor_Fink wrote:

I never used the Schwarzschild metric to calculate R_ab for your metric. I calculated it completely independantly. R_ab!=0 for your metric has nothing to do with GR. It is pure maths.

You used R_ab != 0 to show inconsistency between my metric and SR. Then by implication, R_ab = 0 indicates consistency. R_ab = 0 for the Schwarzschild metric, but my paper shows that the Schwarzschild metric is inconsistent with SR. Then I cannot trust the R_ab argument as an indicator of consistency/inconsistency. Then I cannot trust that it validly shows that my metric is inconsistent with SR.

You metric is not conformal to Minkowski space and hence disagrees with special relativity, completely independantly of what GR may or may not say. This is a matheatical fact, and you an't get around it.

Sections 2 and 7 and my new introduction refute it as an indicator of consistency/inconsistency. That is a logical fact. Only one argument, R_ab != 0 or those in my paper, can be right. I trust mine because the logic is so simple, it leads to clean solutions to many major problems of physics (not only are no new assumptions added, but also some are removed), and after one year it has not been refuted.

Your arguement is not self consistent since you use A->B (where A is special relativity, and B is your metric), yet from R_ab we can see that B->¬A.

Therefore there is a flaw in the logic of your arguement since you have A->¬A. Which violates essentially the first axiom of logic.

The flaw in your logic is that you assume that R_ab != 0 proves that my metric is inconsistent with SR. You treat it as fact rather than refute simple logic that shows a problem with that. You make the same mistake in your argument against section 2, when you assume that there’s an event horizon at the Schwarzschild radius, rather than refute simple logic that shows that GR contradicts itself about that.

And I said the sun where?

It’s an example. Any experimental test of Schwarzschild geometry that you can find will have r / R > 100,000.

Yes they do! The field equations describe the whole space time, as does the Schwarzschild metric.

This is true; good point. But my metric can’t be blamed for not smoothly diverging from the Schwarzschild metric below the Schwarzschild radius. My metric features no concept of a black hole. That’s a point in its favor, not a strike against it.

Aside from the fact you seem to have completely missed the point of both posts, I take offence at all your claims that we are somehow 'unscientific'.

I state that scientifically, and mean no offense. It is indeed unscientific to reject logic alone simply because it contains no calculations. I’m still waiting for the mathematical proof that shows that logic alone must lead to invalid conclusions.

Eh, the metric is smooth, it's functions of the metric that are chaotic. Like all the three body problems you get when you take Jupiter in to account.

Section 6 shows—in probably the simplest possible way—that both metrics return identical results for all experimental tests of Schwarzschild geometry to date, and will for any test of that within our solar system. Then there’s no chaos indicated. You need to be more specific. Show that a different result is possible. You don’t need to compute an entire orbit. Only the ratio of r to R matters (since g_11 and g_22 are shared by the metrics), so just plug in the values for R and r for the smallest r / R ratio (the strongest gravity) for some experimental test. If that’s identical between the metrics after rounding for significant digits, then the predictions for the whole orbit will be identical between the metrics (because the predictions will likewise be identical for any larger r / R).

Professor_Fink

Zanket wrote:

You used R_ab != 0 to show inconsistency between my metric and SR. Then by implication, R_ab = 0 indicates consistency. R_ab = 0 for the Schwarzschild metric, but my paper shows that the Schwarzschild metric is inconsistent with SR. Then I cannot trust the R_ab argument as an indicator of consistency/inconsistency. Then I cannot trust that it validly shows that my metric is inconsistent with SR.

There is no trust involved. I proved it mathematically. I'm not asking you to trust me. I derived the whole thing for you.

Zanket wrote:

Sections 2 and 7 and my new introduction refute it as an indicator of consistency/inconsistency. That is a logical fact. Only one argument, R_ab != 0 or those in my paper, can be right. I trust mine because the logic is so simple, it leads to clean solutions to many major problems of physics (not only are no new assumptions added, but also some are removed), and after one year it has not been refuted.

I know you think you're being logical, but you're not! What you are doing is hand waving.

I gave the three axiom earlier, but here they are again:

1: The law of identity: A if and only if A
2: The law of the excluded middle: Either A or not-A
3: The law of non-contradiction: Not A and not-A

If you can prove your point using these then you are making a logical argument, if you cannot, then you are not. What you have put forward so far is not logic, its just some hand waving. But by all means, go ahead, have a go with these!

Zanket wrote:

The flaw in your logic is that you assume that R_ab != 0 proves that my metric is inconsistent with SR. You treat it as fact rather than refute simple logic that shows a problem with that. You make the same mistake in your argument against section 2, when you assume that there's an event horizon at the Schwarzschild radius, rather than refute simple logic that shows that GR contradicts itself about that.

You are confusing two separate arguments here. 1 is that your metric is in consistent with SR and the other that the Schwarzschild metric is consistent with SR.

Zanket wrote:

It's an example. Any experimental test of Schwarzschild geometry that you can find will have r / R > 100,000.

That's a very strong claim. What proof of this do you have?

Zanket wrote:

This is true; good point. But my metric can't be blamed for not smoothly diverging from the Schwarzschild metric below the Schwarzschild radius. My metric features no concept of a black hole. That's a point in its favor, not a strike against it.

You claimed it diverged smoothly from the Schwarzschild metric!

Zanket wrote:

I state that scientifically, and mean no offense. It is indeed unscientific to reject logic alone simply because it contains no calculations. I’m still waiting for the mathematical proof that shows that logic alone must lead to invalid conclusions.

You aren't using logic properly! how many times do I have to say this!!!

Son Goku

Zanket wrote:

Show me a calculation that proves that an argument is not good enough on its own! Since we are tackling this at a scientific level you have to show the calculations, not an argument.

Zanket, come on, please act seriously.

Zanket wrote:

This is unscientific thinking. An argument is good enough on its own; you haven’t proven otherwise. For example, if my metric was identical to the Schwarzschild metric, then it would be a mathematical certainty that my metric would return the same result for any experimental test of the latter. Can you refute that, without just ignoring the issue by saying that logic alone is not good enough?

Again Zanket, you didn't address what I said.
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.
I'm saying that the two metrics being similar doesn't mean their predictions are similar.
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.

Son Goku

If my metric was chaotic, then I’d expect it to not agree with every experimental test to date.

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.

Zanket wrote:

You used R_ab != 0 to show inconsistency between my metric and SR. Then by implication, R_ab = 0 indicates consistency. R_ab = 0 for the Schwarzschild metric, but my paper shows that the Schwarzschild metric is inconsistent with SR. Then I cannot trust the R_ab argument as an indicator of consistency/inconsistency. Then I cannot trust that it validly shows that my metric is inconsistent with SR.

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.

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

The flaw in your logic is that you assume that R_ab != 0 proves that my metric is inconsistent with SR. You treat it as fact rather than refute simple logic that shows a problem with that.

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.

I state that scientifically, and mean no offense. It is indeed unscientific to reject logic alone simply because it contains no calculations. I’m still waiting for the mathematical proof that shows that logic alone must lead to invalid conclusions.

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.

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