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

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.

Zanket

Professor_Fink wrote:

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

I don’t deny that R_ab != 0 for my metric. Yes, you proved that mathematically. I’m assuming that the form of your analysis is correct (i.e. that your set of equations into which you plugged the inputs is correct), but neither do I doubt it.

What I don’t trust is your application of the result R_ab != 0; namely, your claim that it shows that my metric is inconsistent with SR. (And I don’t doubt that other sources support you on that.) This application is independent of the math; it has nothing to do per se with the math.

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.

These are linked by the R_ab argument. More on that below.

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!

OK. #1 is a tautology. #2 and #3 apply here.

The Schwarzschild metric must be either consistent or inconsistent with SR (#2); it cannot be both (#3). You claim that R_ab shows whether or not a metric is consistent with SR: If R_ab = 0 when T_ab = 0, then consistent, otherwise inconsistent. You showed that R_ab = 0 when T_ab = 0 for the Schwarzschild metric. Hence you say it is consistent with SR. But my paper shows that the Schwarzschild metric is inconsistent with SR. By #2 and #3, only one argument, yours or mine, can be valid. Neither is known to be invalid. I say that mine is the valid one, for the reasonable reasons I gave above. Then #2 and #3 show that I must reject the R_ab argument as an indicator of a metric’s consistency with SR. Which I do.

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

In the experimental test I reference, here, which I claim to be the strongest-gravity test, it says: “a highly-relativistic double-neutron-star system, allowing unprecedented tests of fundamental gravitational physics”. I did an extensive search to reasonably conclude that this is the strongest-gravity test to date. Several recent magazine articles that summarized the tests to date included that one and showed no others involving stronger gravity. Nobody can prove that a particular test is the one with the strongest gravity. (Nobody can prove that an experimental confirmation section covers all relevant experiments.)

You claimed it diverged smoothly from the Schwarzschild metric!

OK, I rephrase: it diverges smoothly as r decreases, up to the Schwarzschild radius. I’m not paying much attention to this particular topic because no problem of my paper has been indicated by it. Can you show a problem?

Zanket

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.”

Son Goku

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.

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 I will spell this out for in very plain language.
The fact that the equations match when r/R is at least five thousand isn't enough. The metrics could still have vastly different orbits.

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?

Chaotic means sensitive to initial conditions (the physical definition, it is an entire area of physics), which gravitational systems are. This is why section 6 isn't enough. If gravitational systems were not chaotic then section 6 would be enough. However because gravitational systems are highly chaotic, even two very similar metrics can make vastly different predictions.
That is why I need to see the orbits.

Do you understand?

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:

Zanket you know what I mean. Please stop posting pointless statements like this.

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?

First of all, I don't buy your arguement that the Schwarzschild metric is inconsistent, so asking me that is a loaded question. Second, even if I did, it is possible for the Schwarzschild metric to give R_ab = 0, even though it is incorrect on other accounts.
Just because something is incorrect doesn't mean it is incorrect in every concievable way.

The Schwarzschild metric must be either consistent or inconsistent with SR (#2); it cannot be both (#3). You claim that R_ab shows whether or not a metric is consistent with SR: If R_ab = 0 when T_ab = 0, then consistent, otherwise inconsistent. You showed that R_ab = 0 when T_ab = 0 for the Schwarzschild metric. Hence you say it is consistent with SR. But my paper shows that the Schwarzschild metric is inconsistent with SR. By #2 and #3, only one argument, yours or mine, can be valid. Neither is known to be invalid. I say that mine is the valid one, for the reasonable reasons I gave above. Then #2 and #3 show that I must reject the R_ab argument as an indicator of a metric’s consistency with SR. Which I do.

Zanket, Schwarzschild could have R_ab = 0 correct and still be wrong. It doesn't refute R_ab = 0 as a way of testing a metric.
R_ab = 0 could be satisfied and the metric be incorrect in some other way.
It is simply one of the tests, which you can fail or pass.

Now, your universe has Ricci Curvature around when there is no Matter. That can't happen Zanket, stop talking about the Schwarzschild metric and actually address this.
For special relativity to work R_ab must equal 0 in a vacuum.

The reason for this is because otherwise it would be impossible to ever obtain Minkowski spacetime.

Son Goku

Zanket wrote:

“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.”

What book states this?

Professor_Fink

Zanket wrote:

The Schwarzschild metric must be either consistent or inconsistent with SR (#2); it cannot be both (#3). You claim that R_ab shows whether or not a metric is consistent with SR: If R_ab = 0 when T_ab = 0, then consistent, otherwise inconsistent. You showed that R_ab = 0 when T_ab = 0 for the Schwarzschild metric. Hence you say it is consistent with SR. But my paper shows that the Schwarzschild metric is inconsistent with SR. By #2 and #3, only one argument, yours or mine, can be valid. Neither is known to be invalid. I say that mine is the valid one, for the reasonable reasons I gave above. Then #2 and #3 show that I must reject the R_ab argument as an indicator of a metric’s consistency with SR. Which I do.

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.

What I did was to derive a result, rigorously, which proves your derivation cannot be correct. There are no physical assumptions in my derivation. It is purely maths. As long as I didn't make a numerical slip (and at this stage we all seem to be in agreement that the calculations are correct), then it is right. You can't challenge the assumptions, because there aren't any.

So we know that your metric is not conformal to SR, from my derivation. This proves your metric is wrong. You can't argue that you metric disproves my result, because your metric makes physical assumptions and mine does not.

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.

Zanket wrote:

In the experimental test I reference, here, which I claim to be the strongest-gravity test, it says: “a highly-relativistic double-neutron-star system, allowing unprecedented tests of fundamental gravitational physics”. I did an extensive search to reasonably conclude that this is the strongest-gravity test to date. Several recent magazine articles that summarized the tests to date included that one and showed no others involving stronger gravity. Nobody can prove that a particular test is the one with the strongest gravity. (Nobody can prove that an experimental confirmation section covers all relevant experiments.)

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.

Professor_Fink

Zanket wrote:

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?

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

Zanket

Son Goku wrote:

Chaotic means sensitive to initial conditions (the physical definition, it is an entire area of physics), which gravitational systems are. This is why section 6 isn't enough. If gravitational systems were not chaotic then section 6 would be enough. However because gravitational systems are highly chaotic, even two very similar metrics can make vastly different predictions.
That is why I need to see the orbits.

Do you understand?

OK, I see your meaning on “chaotic”.

Section 6 is still enough though. Consider this: In the limit, numerical integration, just like calculus, gives answers accurate to a number of significant digits that is limited only by the number of significant digits in the data. Numerical integration of a metric involves inputting into it values for its variables at each and every step along, say, an orbit. Section 6 shows that at each and every step where r / R >= 5000, the results of the metrics are identical after rounding for the number of significant digits. Then the final results (for the whole orbit, say) for the metrics must also be identical.

It follows that any calculation that shows a difference between the metrics when r / R is always >= 5000, are different only because of a rounding error. This does not mean that the metrics predict the exact same trajectories—they do predict differently. It means that the detectable difference in the predictions is limited by the number of significant digits in the data. Given the current best precision of G, no difference between the metrics is detectable when r / R is always >= 5000.

Zanket you know what I mean. Please stop posting pointless statements like this.

I’ll stop making statements like that when you stop saying things like “R_ab = 0 for T_ab = 0 in nature” without showing that nature agrees. Show me an experiment that disagrees with my metric; otherwise I’ll justifiably continue to call it a purely mathematical argument. In science, empty claims are presumed false. And you know that.

Zanket, Schwarzschild could have R_ab = 0 correct and still be wrong. It doesn't refute R_ab = 0 as a way of testing a metric.

It does refute R_ab = 0 as a way of testing a metric for consistency with SR, which is the only way the argument is being used here.

R_ab = 0 could be satisfied and the metric be incorrect in some other way.

Sure, but that’s beside the point. The point is, R_ab = 0 is given here specifically as an indicator of consistency with SR, and I have refuted it as an indicator of that, by showing that it gives a false positive for the Schwarzschild metric (it shows that the Schwarzschild metric is consistent when it’s not). Then it has no value against my paper. You need to refute section 2 (or my new introduction) before you can restore its value.

Now, your universe has Ricci Curvature around when there is no Matter. That can't happen Zanket, stop talking about the Schwarzschild metric and actually address this.
For special relativity to work R_ab must equal 0 in a vacuum.

You haven’t shown that nature agrees with you. Until you show an experiment that disagrees with my metric, the R_ab argument remains purely mathematical. Your claim that nature agrees with the R_ab argument remains empty.

The reason for this is because otherwise it would be impossible to ever obtain Minkowski spacetime.

I refuted this above. The R_ab argument fails as a test of consistency with SR. You don’t have to buy my basis for that, which is my argument that the Schwarzschild metric is inconsistent with SR, but until you refute that basis, you cannot say that I have not refuted the R_ab argument. Telling me to “stop talking about the Schwarzschild metric and actually address this” is tantamount to saying “stop giving a basis for your refutation of this”.

To recap, I’ve refuted the R_ab argument in two ways, by showing that:

- it doesn’t work for its only stated purpose here, to show consistency/inconsistency with SR
- no experiment disagrees with my metric

Those cover the only two ways that a theory of physics can be refuted (internal inconsistency or disagreement with observations).

Zanket

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.

planck2

ok, i don't know why you are still arguing with this guy? And I don't even understand how you both have physically the time to do so. I am so busy with other stuff.

Professor_Fink

planck2 wrote:

ok, i don't know why you are still arguing with this guy? And I don't even understand how you both have physically the time to do so. I am so busy with other stuff.

Look at the time stamp on most of my posts. They come way after midnight. I'm having a bout of insomnia at the moment.

Professor_Fink

Zanket wrote:

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?

What hole? It's air tight.

The refutation you give is complete rubbish. We have already argued over your claim that "an object falls in a uniform gravitational field, that an object falls in a nonuniform gravitational field as well", which is complete crap.

I've addressed this already, and I'm not going to waste time reheashing it.

Zanket wrote:

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”.

Differential geometry is not the same thing as general relativity. It is a field of mathematics. I have used it to disprove your claims, and unless you can show an error in one of the equations in my derivation, then there is no way to disprove it by claiming a counter example. There aren't any.

Zanket wrote:

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

No you didn't. This is getting ridiculous. What you did was point out that several sections of your paper have dodgy conclusions because they contradict a resut which is provably true. Hence they are wrong.

Zanket wrote:

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.)

Your arguement about the Schwarzschild metric is deeply flawed. As I have PROVED RIGOROUSLY MATHEMATICALLY the Schwarzschild metric is conformal to the Minkowski metric and yours is not. Hence it can agree with SR and yours cannot!

The claims you make to the contrary only serve to show more sections in your paper where you have fluffy reasoning.

Zanket wrote:

As I said above, I don’t doubt your math.

Game over! Thank you for playing.

Zanket wrote:

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.

Have you any idea how ridiculous that sounds? You are claiming that a field of mathematics must be wrong because it disproves your widely disputed theory.

That's essentially the definition of a crackpot Zanket. Someone who refuses to let go of their pet theory even when it is proved to be wrong, and simply claims that everyone else is wrong, maths, physics and logic are all flawed, etc.

Zanket wrote:

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.

That means they can't make accurate predictions of the mass. My point is that there are redshift experiments, and there are redshift experiments on white dwarfs two, all of which constitute tests of the metric in a regime where the two metrics vary wildly.

Zanket wrote:

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.

Zanket, just because the authors put that in the abstract does not mean there aren't better tests of your claim. What it means is that the way they used was novel, and allowed very accurate tests, not that it tested it closer to the central mass (oh, and that they were aiming for Nature or PRL I would think)!

Zanket wrote:

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

No they don't. Your claim based on numerical intergration is naive and childish. For chaotic systems, numerical methods are only accurate for short evolution of the system. As I said, different inputs diverge wildly. So no, you cannot use numerical integration to solve chaotic systems accurately. Hence the problem predicting the weather.

Do you mind me asking what level of maths you can actually deal with? It seems to me that its about leaving cert pass level here. I'm guessing you're not Irish though, so I suppose that corresponds to high school maths in the US.

Son Goku

planck2 wrote:

ok, i don't know why you are still arguing with this guy? And I don't even understand how you both have physically the time to do so. I am so busy with other stuff.

Sociological interest, not physics, would be my main reason for continuing. Also one post every day or two doesn't consume that much time.

Son Goku

Right Zanket, we gave you more time than the physics forum. You are not achieving the technical standard required to warrant a technical thread.
You still haven't refuted the R_ab = 0 argument.

Thread Closed.