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

Professor_Fink

Zanket wrote:

In the new cosmological model proposed in section 7, spacetime always existed; it never arose. There is no requirement that a cosmological model have a beginning of spacetime. There is no direct observational evidence that our universe had a beginning.

Zanket, a couple of points. 1) Stars form. 2) I can't see how this statement can agree with cosmic microwave background anisotropy measurements.

For the spacetime in question to be possible, it cannot be a fixed point of your theory, which it is. So even if it did predict exactly the same results as GR outside the schwarzchild radius (it doesn't), it would still not be able to fit experimental data since we know stars have a finite life.

Zanket wrote:

If the mass is zero, neither r nor R applies. These apply to only material objects.

Zanket, the mass is not zero when you produce a pair which later anihilate nor is the energy. These are not conserved in vacuum fluctuations.

Zanket wrote:

The only place that GR is incompatible with quantum mechanics is at a singularity.

Actually thats not strictly true. If the curvature of space is high compared to the wavelength of the particles involved you cannot do QFT on a curved background.

Zanket wrote:

Then my theory need not predict BECs or the observations that quantum mechanics predicts.

Your theory is not GR. I'm not saying that it should predict them, rather that you rule them out, which is counter to experiments. Well, at least if it is compatible with QM, as you have claimed. GR isn't completely compatible, but I thought you were claiming to have solved that problem.

Actually if no particle can be exchanged between two masses, then it would seem that you have ruled out at least 3 forces which rely on exchange particles 1. Electromagnetism 2. The weak interaction 3. The strong interaction.

So the very fact that you exist to propose the theory disproves your theory.

planck2

Zanket wrote:

I would like to acknowledge you in the paper. Is that okay with you?

No you may not

planck2

Nice to have confirmation on that, thanks.
I don’t deny that “doing so from the action is more powerful”, but I don’t see how the metric has a “very limited power”, given that T&W say:
Then nothing else is needed to make predictions of GR for Schwarzschild geometry. That is powerful indeed. Elsewhere they say:
It’s extra clear from this that my theory needs no more than a metric.

The metric is the fundamental requirement, but you need other things in order to get the equations of motion such as the Euler-Lagrange formalism or the Hamilton-Jacobi method. See any standard graduate text on classical mechanics

Now that I use dphi, the Schwarzschild metric in the image above and the new metric in the paper differ only by the difference between eqs. 8 and 9 in the paper (that is how the new metric is derived, by swapping eq. 8 for eq. 9), a difference shown by fig. 3, which shows that the curves converge as r increases.
More mathematically, the right-hand side of eq. 9 is equivalent to sqrt(1 - (R / (r + R))). Comparing that the right-hand side of eq. 8, sqrt(1 - (R / r)), it is easy to see that the effect of R in the denominator of eq. 9, the only difference between the two equations, diminishes as r increases. Then the curves given by the equations must converge as r increases.

but they don't converge and never will

That’s a non sequitur. The order of those events does not show a scientific requirement for field equations. I already have reader comments in the paper for this:

Reader: A metric must be derived from field equations.

Author: The scientific method lets any type of equation be presented without derivation. Then no particular method of derivation is required.

Reader: Without new field equations, your theory is worthless.

Author: Field equations are not required. A metric makes falsifiable predictions.

but then you are just guessing, the point is that Schwarzschild had a set of field equations (which related the curvature to the presence of matter) to work from, he used them to find a possible solution for the spacetime outside a star and this happened to agree with experiment.

Come up with new field equations and solutions to it such as your metric

Given that it answers “every possible question about trajectories of light and satellites around the black hole as well around more familiar centers of attraction such as Earth and Sun”, it sure seems to meet the definition of an equation of motion, given by Wikipedia as “equations that describe the behavior of a system (e.g., the motion of a particle under an influence of a force) as a function of time”. How do you explain that it doesn't meet that definition?

See my answer above.

Do you still think there is a problem, now that I changed the paper? If yes, then how can the Schwarzschild metric be asymptotically flat yet mine not, when the difference between the two metrics approaches nothing as r goes to infinity?

Yes I do, because they don't agree at infinity. Simple.

And Professor Fink is correct on the matter of QFT's on Curved Spacetime

planck2

and if you even dare credit me i'll sue your sorry ass all the way to seattle and back again

Son Goku

Zanket wrote:

Suppose beings on some other planet have a metric that approximates the Schwarzschild metric for the tests done so far on Earth, plus it accurately predicts phenomena that GR fails to predict (like stars that accelerate away), but it doesn’t have a “rule for the response of matter to curvature”. Is it useless?

Yes. Theories cannot have no equations of motion. I don't think you even understand what I'm saying.

How does stuff move in your metric? What is the rule for generating the equations of motion. It can't be Einstein's geodesic rule as you are rejecting GR, so how do the particles move in your theory?

i.e. Given the metric how do you obtain the trajectory of a particle within it, for some initial condition.

The fact that you don't understand this is dreadful.

Zanket

Professor_Fink wrote:

Zanket, a couple of points. 1) Stars form. 2) I can't see how this statement can agree with cosmic microwave background anisotropy measurements.

For the spacetime in question to be possible, it cannot be a fixed point of your theory, which it is. So even if it did predict exactly the same results as GR outside the schwarzchild radius (it doesn't), it would still not be able to fit experimental data since we know stars have a finite life.

What “spacetime in question”? A singularity? The new metric is experimentally confirmed by tests of the Schwarzschild metric; section 6 shows that, and you haven’t refuted it. And so what if stars have a finite life? My paper doesn’t suggest otherwise. Stars can be born and die in a universe that had no beginning. Even GR supports cosmological models in which the universe has no beginning. Is there a larger point of yours that I’m missing? Can you elaborate?

Zanket, the mass is not zero when you produce a pair which later anihilate nor is the energy. These are not conserved in vacuum fluctuations.

That’s outside the scope of my theory, just as it is for GR. It no more affects my theory than it affects GR. It invalidates neither theory.

Actually thats not strictly true. If the curvature of space is high compared to the wavelength of the particles involved you cannot do QFT on a curved background.

Offhand, I can’t refute that, and it makes some sense to me. You seem to be saying that GR is incompatible with QM not just at a singularity, but also in its immediate vicinity.

Your theory is not GR. I'm not saying that it should predict them, rather that you rule them out, which is counter to experiments. Well, at least if it is compatible with QM, as you have claimed. GR isn't completely compatible, but I thought you were claiming to have solved that problem.

I don’t rule them out. The new metric is compatible with QM because, unlike the Schwarzschild metric, it doesn’t demand a minimum radius for a body that is incompatible with QM.

Actually if no particle can be exchanged between two masses, then it would seem that you have ruled out at least 3 forces which rely on exchange particles 1. Electromagnetism 2. The weak interaction 3. The strong interaction.

So the very fact that you exist to propose the theory disproves your theory.

That my theory precludes singularities does not rule out any prediction of QM. You suggest that QM requires singularities. But that would be inconsistent, for it is singularities that create the incompatibility between GR and QM.

Professor_Fink

Zanket wrote:

What “spacetime in question”? A singularity? The new metric is experimentally confirmed by tests of the Schwarzschild metric; section 6 shows that, and you haven’t refuted it. And so what if stars have a finite life? My paper doesn’t suggest otherwise. Stars can be born and die in a universe that had no beginning. Even GR supports cosmological models in which the universe has no beginning. Is there a larger point of yours that I’m missing? Can you elaborate?

Yes, you are completely missing the point. The spacetime I am talking about is the manifold described by your metric.

The schwarzchild solution is not a cosmological model, so I'm not sure where all this talk of cosmology fits in (but for what it's worth the CMB is extremely compelling evidence in favour of a big bang).

I am talking about stars, blackholes, and anything else described by the schwarzchild solution. If you say that nothing can ever reach r=0 in any frame how can such objects form? Must they all be hollow?

Zanket wrote:

That’s outside the scope of my theory, just as it is for GR. It no more affects my theory than it affects GR. It invalidates neither theory.

My point is that your theory makes predictions which prevent anything in such a geometry from interacting with a central mass. If you apply this on a microscopic scale, you prevent particles from interacting. This messes up quantum field theory. But QFT is _extremely_ accurate (read >13 significant digits in some circumstances), so there most be a problem with one.

Of course GR predicts some very weird stuff when you reach the Planck scale, but you are claiming that your theory is completely consistant with quantum mechanics. I am saying that it is not.

Zanket wrote:

Offhand, I can’t refute that, and it makes some sense to me. You seem to be saying that GR is incompatible with QM not just at a singularity, but also in its immediate vicinity.

Yes I am, but I am also saying it is incompatible (or at least the curved background approach is incompatible) in isolated areas of high curvature, even if they are no accompanied by a black hole. Hence all the interest in quantum gravity.

Zanket wrote:

I don’t rule them out. The new metric is compatible with QM because, unlike the Schwarzschild metric, it doesn’t demand a minimum radius for a body that is incompatible with QM.

No, it's not. It doesn't work on a small scale as the curvature becomes large compared to the wavelength of the particles. Yours is infact worse, since it completely prevents them from interacting.

That my theory precludes singularities does not rule out any prediction of QM. You suggest that QM requires singularities. But that would be inconsistent, for it is singularities that create the incompatibility between GR and QM.

I'm not saying that the singularities are necessary for QM. I'm not talking about singularities at all. I'm saying that in your theory a particle at r=0 cannot interact with any other particle. If we apply this to subatomic particles, this causes a major problem. NOTHING INTERACTS WITH ANYTHING ELSE!!!

Of course if you back off on claiming that your theory is compatable with QM and QFT then the problem goes away, but you can no longer claim that your theory has any advantage over GR in terms of how nicely it can play with quantum mechanics (as I have already mentioned, your proposal is actually less compatible).

Zanket

planck2 wrote:

No you may not

As you wish.

The metric is the fundamental requirement, but you need other things in order to get the equations of motion such as the Euler-Lagrange formalism or the Hamilton-Jacobi method. See any standard graduate text on classical mechanics

Then how do you explain T&W’s ultra-clear comment that only the metric is needed to predict motion? How do you explain that their book Exploring Black Holes is full of predictions of motion, all using the metric exclusively?

but they don't converge and never will

So what? The difference between them becomes arbitrarily small as r goes to infinity. They converge as r increases.

but then you are just guessing, the point is that Schwarzschild had a set of field equations (which related the curvature to the presence of matter) to work from, he used them to find a possible solution for the spacetime outside a star and this happened to agree with experiment.

You’re just describing the history of the metric, that’s all. You’re not showing that field equations are a scientific requirement. You don’t think Einstein was “just guessing” when he formulated his field equations using trial and error?

Come up with new field equations and solutions to it such as your metric

Nah, it’s not required.

See my answer above.

See my question to your answer above.

Yes I do, because they don't agree at infinity. Simple.

So if the metrics differ only beyond the trillionth significant digit beyond some r, you think my metric is not asymptotically flat whereas the Schwarzschild metric is? Or do you think there’s some other problem with that?

and if you even dare credit me i'll sue your sorry ass all the way to seattle and back again

Take a deep breath. Now, why do you suppose I asked if it was okay?

Son Goku

Zanket wrote:

Then how do you explain T&W’s ultra-clear comment that only the metric is needed to predict motion? How do you explain that their book Exploring Black Holes is full of predictions of motion, all using the metric exclusively?

That's because the fact that you need a law of motion is blatantly obvious and they've already given it.
What is your law of motion?

Look at the potential V(x) = (kx^2)/2, on its own it can't tell you anything about motion, you need F=ma, or a Euler-Langrange equations in that formalism or the Hamilton Equations in Hamiltonian Dynamics.

What are your equations of motion?

breadmonkey

Please forgive my spamminess. I was just thinking it would be hilarious if Zanket's theory turned out to revolutionary but gets dismissed only to be taken seriously in 20 years time (this has happened quite a lot, right?). Then, in the future, someone will write about how his theory was originally rubbished by a bunch of guys on an internet message board!

Professor_Fink

breadmonkey wrote:

Please forgive my spamminess. I was just thinking it would be hilarious if Zanket's theory turned out to revolutionary but gets dismissed only to be taken seriously in 20 years time (this has happened quite a lot, right?). Then, in the future, someone will write about how his theory was originally rubbished by a bunch of guys on an internet message board!

No, it hasn't happened often at all.

But we're not just saying its unphysical or something vague like that, there are specific errors in Zankets paper where he has made incorrect assumptions (such as where he concludes that curvature along geodesics has no effect). General relativity doesn't make these additional assumptions, and so is more rigorous. I have yet to hear of a theory being rplaced by another theory which makes more assumptions. Thats just not the way science works.

And for what it's worth, all three of us (me, Planck2 and Son Goku) are theoretical physicists. I know this because I met Son Goku while doing my PhD and Planck2 was in my undergraduate class (theoretical physics).

planck2

Zanket wrote:

Then how do you explain T&W’s ultra-clear comment that only the metric is needed to predict motion? How do you explain that their book Exploring Black Holes is full of predictions of motion, all using the metric exclusively?

Of course they say the metric is all you need because that is were you start from. And then you you use the fact that you are dealing with spacelike/timelike/lightlike(null) geodesics.
but you still need a methodology in order to get the geodesics. And how do you explain the fact that the Schwarzschild metric approximates to Newtonian gravity and hence classical mechanics in the weak field limit where as your's doesn't.

Zanket wrote:

Nah, it’s not required.

Einstein said field strength=curvature, so what are you saying?
you just say Einstein is wrong, Schwarzschild metric is not unique and give a metric as a replacement which is not spherically symmetric. I'm sure I can get the geodesics but your not telling me anything with these. The metric describes a curved manifold and I can obtain how the particles move on it if one postulates that particles move along geodesics, but how do you relate curvature to gravity? This is what the field equations do.

Zanket wrote:

So what? The difference between them becomes arbitrarily small as r goes to infinity. They converge as r increases

So if the metrics differ only beyond the trillionth significant digit beyond some r, you think my metric is not asymptotically flat whereas the Schwarzschild metric is? Or do you think there’s some other problem with that?

but they actually don't converge and it is not by some mere trillionith significant figure difference. your metric diverges from flat spacetime whereas the Schwarzschild one converges to flat spacetime in the limit as r goes to infinity. So your metric is not asymptotically flat and never will be.

Zanket

Son Goku wrote:

Yes. Theories cannot have no equations of motion. I don't think you even understand what I'm saying.

I do understand you. I agree that a theory of gravity should have an equation of motion. I say that the metric is an equation of motion. By itself it predicts motion, so it must be an equation of motion. The new metric in my paper is the only expression that is needed to predict any motion for Schwarzschild geometry, the scope of my paper.

How does stuff move in your metric? What is the rule for generating the equations of motion. It can't be Einstein's geodesic rule as you are rejecting GR, so how do the particles move in your theory?

i.e. Given the metric how do you obtain the trajectory of a particle within it, for some initial condition.

I suggest you get the book Exploring Black Holes by T&W. For example, in chapter 4 (which is not online) they use the principle of extremal aging and the Schwarzschild metric, and only those as a basis, to compute an orbit. Throughout the book they prove their claim that “this one expression [the metric] tells it all!” (boldface mine).

Look at the potential V(x) = (kx^2)/2, on its own it can't tell you anything about motion, you need F=ma, or a Euler-Langrange equations in that formalism or the Hamilton Equations in Hamiltonian Dynamics.

Then how do you explain that T&W use no equation other than the metric to compute an orbit?

planck2

Zanket wrote:

Then how do you explain that T&W use no equation other than the metric to compute an orbit?

they assume like Einstein that particles move along geodesics and use the metric to obtain the geodesics. Since you are rejecting Einstein's geodesic assumption how do you use the metric to obtain the equations of motion?

Zanket

Professor_Fink wrote:

If you say that nothing can ever reach r=0 in any frame how can such objects form? Must they all be hollow?

All right, now I think I see what you’re getting at. That r=0 is invalid does not mean that an object is hollow. It means that the surface of the object cannot be at r=0; i.e. the object cannot be contained in zero volume. For the Earth, r is > 0 and matter can be at r=0 within the Earth. My paper handles only Schwarzschild geometry, which is defined in the paper as "The geometry of empty spacetime around a Schwarzschild object". So r refers to an r-coordinate at or above the surface of an object.

No, it's not. It doesn't work on a small scale as the curvature becomes large compared to the wavelength of the particles. Yours is infact worse, since it completely prevents them from interacting.

I assume that you think it “doesn't work on a small scale...” because of the hollow argument above. Now that I have refuted that, do you still think this? If so, why? The new metric doesn’t require a minimum r for a body. So there’s no reason to believe that the curvature must become too large compared to the wavelength of the particles.

I'm not saying that the singularities are necessary for QM. I'm not talking about singularities at all. I'm saying that in your theory a particle at r=0 cannot interact with any other particle. If we apply this to subatomic particles, this causes a major problem. NOTHING INTERACTS WITH ANYTHING ELSE!!!

When r is > 0 for an object, a particle at r=0 within the object can interact with other particles. This should resolve all of your objections regarding QM.

But we're not just saying its unphysical or something vague like that, there are specific errors in Zankets paper where he has made incorrect assumptions (such as where he concludes that curvature along geodesics has no effect).

You’re twisting my words again. Please stop. Nowhere did I conclude that. My theory is one of curved spacetime. I said that spacetime curvature has no effect on the conclusion in section 2. As in, the degree of spacetime curvature does not change the conclusion.

General relativity doesn't make these additional assumptions, and so is more rigorous. I have yet to hear of a theory being rplaced by another theory which makes more assumptions. Thats just not the way science works.

My paper makes no new assumptions; you haven't shown otherwise. The paper shows that GR is not rigorous. It is shown to be inconsistent (in sections 2 and 7), and that has not been refuted in this thread or elsewhere.

Zanket

planck2 wrote:

Of course they say the metric is all you need because that is were you start from. And then you you use the fact that you are dealing with spacelike/timelike/lightlike(null) geodesics.
but you still need a methodology in order to get the geodesics.

Ah, so the metric is an equation of motion after all. No other equation is needed to predict motion. We’ve made progress.

Geodesics are implied by the metric itself. An object simply goes straight, and the curved spacetime that is completely described by the metric curves its path. So one doesn’t “need a methodology in order to get the geodesics”. As T&W emphasize, the metric is a complete description of spacetime around a Schwarzschild object. More on that below.

And how do you explain the fact that the Schwarzschild metric approximates to Newtonian gravity and hence classical mechanics in the weak field limit where as your's doesn't.

Newtonian gravity approximates my metric, because, as the paper shows, the Schwarzschild metric approximates my metric. You haven’t refuted that. You’ve made only empty claims.

Einstein said field strength=curvature, so what are you saying?

I don’t need to say anything to that effect. I give a metric that makes falsifiable predictions of observations. That’s enough.

you just say Einstein is wrong, Schwarzschild metric is not unique ...

I don’t say that the Schwarzschild metric is not unique, which implies that I think there is more than one solution to Einstein’s field equations for Schwarzschild geometry, which I don’t. Rather I say that the Schwarzschild metric is invalid, for it is inconsistent with the finding in section 1, which was inferred by means GR allows. Then Einstein’s field equations, because they are proven to yield only the Schwarzschild metric for Schwarzschild geometry, must be invalid.

... and give a metric as a replacement which is not spherically symmetric.

What is your evidence?

I'm sure I can get the geodesics but your not telling me anything with these. The metric describes a curved manifold and I can obtain how the particles move on it if one postulates that particles move along geodesics, ...

There’s nothing magical about geodesics; it doesn't need to be a postulate. An object goes straight in curved spacetime that curves its path, that’s all. Does my paper need to explain that? No. Geodesics are implied by the metric.

... but how do you relate curvature to gravity? This is what the field equations do.

In GR, spacetime curvature is the sole indicator of gravity. They are inseparable. That is how the Schwarzschild metric (and my metric) can be a complete description of Schwarzschild geometry.

but they actually don't converge and it is not by some mere trillionith significant figure difference. your metric diverges from flat spacetime whereas the Schwarzschild one converges to flat spacetime in the limit as r goes to infinity. So your metric is not asymptotically flat and never will be.

The Schwarzschild metric and the new metric do converge as r increases. That does not mean that they eventually meet; it means that they approach each other ever more closely. They are asymptotic to each other. You haven’t shown otherwise. You just make an empty claim. I gave the only difference between the two metrics, which are simple equations, the curves of which can be easily seen to converge as r increases. How do you expect to be a scientist when you make unsupported claims that are so easily seen to be wrong?

they assume like Einstein that particles move along geodesics and use the metric to obtain the geodesics. Since you are rejecting Einstein's geodesic assumption how do you use the metric to obtain the equations of motion?

They assume that a particle would go straight were it not for the curved spacetime that curves its path. That’s not something that needs to be explained, for if the spacetime were not curved, it would be flat, and then the particle would surely go straight. There are lots of things they can assume without the need for explanation. For example, they can assume that the particle continues to exist.

I do not reject the notion of geodesics. You’re reading that into the paper; it’s not there. My theory is built on parts of GR, like SR and the equivalence principle. Unless I say or imply that something is invalid, the reader can assume that I hold it to be valid. The paper shows a specific flaw of GR. It does not reject GR in its entirety. For example, do I think field equations are worthless? No. Someone can take my paper as a starting point, figure out where the flaw is in Einstein’s field equations, and rebuild GR in all its glory. (The new metric for Schwarzschild geometry that the new field equations yield should be consistent with section 1 in my paper. It need not match my metric, but I doubt there’s a simpler metric that is consistent with section 1, and nature seems to prefer simplicity.)

Son Goku

I suggest you get the book Exploring Black Holes by T&W. For example, in chapter 4 (which is not online) they use the principle of extremal aging and the Schwarzschild metric, and only those as a basis, to compute an orbit. Throughout the book they prove their claim that “this one expression [the metric] tells it all!” (boldface mine).

I suggest you read Wald or at least Schutz.

Ah, so the metric is an equation of motion after all. No other equation is needed to predict motion. We’ve made progress.

Geodesics are implied by the metric itself. An object simply goes straight, and the curved spacetime that is completely described by the metric curves its path. So one doesn’t “need a methodology in order to get the geodesics”. As T&W emphasize, the metric is a complete description of spacetime around a Schwarzschild object. More on that below.

Geodesics are implied in General Relativity, all we wanted all along was what your rule was for particle dynamics. Your rule is the geodesics as you just stated above although it took along time to get that out of you.

Zanket did you understand what our question meant?
The part in bold is totally incorrect and I think at this point you're being triumphant on purpose.

I do not reject the notion of geodesics. You’re reading that into the paper; it’s not there.

You reject GR though, so it's difficult to understand how you accept the generator of its dynamics.

The Schwarzschild metric and the new metric do converge as r increases. That does not mean that they eventually meet; it means that they approach each other ever more closely. They are asymptotic to each other.

Zanket, do you not think it's possible that you simply haven't read enough physics and are biting off more than you can chew?
You must admit that your inability to understand basic dynamical questions indicates a alck of familiarity with a lot of the sunject.

Tell me, what did you read before you read Taylor's book.

planck2

look it's pointless arguing with this guy. He clearly doesn't understand what is going on. We are wasting our time

planck2

Zanket wrote:

What is your evidence?

That's easy to prove. The proof of this is given by Werner Israel[1967], who I know.

and besides I am not emotionally attached to GR, you are just saying things that you cant back up.

You have derived stuff which you say GR allows which disagree with the Schwarzschild solution and Einstein's field equations.

It is most likely that there is a serious flaw in your arguement

planck2

Zanket wrote:

They assume that a particle would go straight were it not for the curved spacetime that curves its path. That’s not something that needs to be explained, for if the spacetime were not curved, it would be flat, and then the particle would surely go straight. There are lots of things they can assume without the need for explanation. For example, they can assume that the particle continues to exist.

They assume that particles do not move along a straight line in flat spacetime, but along a geodesic in any spacetime manifold, curved or flat?

What is your understanding of a geodesic?

planck2

Zanket wrote:

Ah, so the metric is an equation of motion after all. No other equation is needed to predict motion. We’ve made progress.
Geodesics are implied by the metric itself. An object simply goes straight, and the curved spacetime that is completely described by the metric curves its path. So one doesn’t “need a methodology in order to get the geodesics”. As T&W emphasize, the metric is a complete description of spacetime around a Schwarzschild object. More on that below.

i am afraid one does. they [T&W] use the principle of extremal aging which is
the same as calculating the geodesics using the Euler-Lagrange method.

Zanket wrote:

Newtonian gravity approximates my metric, because, as the paper shows, the Schwarzschild metric approximates my metric. You haven’t refuted that. You’ve made only empty claims.

I really haven't too be honest.

Zanket wrote:

I don’t say that the Schwarzschild metric is not unique, which implies that I think there is more than one solution to Einstein’s field equations for Schwarzschild geometry, which I don’t. Rather I say that the Schwarzschild metric is invalid, for it is inconsistent with the finding in section 1, which was inferred by means GR allows. Then Einstein’s field equations, because they are proven to yield only the Schwarzschild metric for Schwarzschild geometry, must be invalid.

yes you do say that is not unique by simply saying that your metric is spherically symmetric, because you say this in the abstract

Zanket wrote:

The Schwarzschild metric and the new metric do converge as r increases. That does not mean that they eventually meet; it means that they approach each other ever more closely. They are asymptotic to each other. You haven’t shown otherwise. You just make an empty claim. I gave the only difference between the two metrics, which are simple equations, the curves of which can be easily seen to converge as r increases. How do you expect to be a scientist when you make unsupported claims that are so easily seen to be wrong?

well i am afraid that if you don't understand mathematics then i can't convince you that they don't converge.
they don't converge as i showed earlier, read my previous posts.

Zanket wrote:

There are lots of things they can assume without the need for explanation. For example, they can assume that the particle continues to exist.

the less assumptions a theory makes the better it is, the more predictions it can make the better.

Zanket wrote:

(The new metric for Schwarzschild geometry that the new field equations yield should be consistent with section 1 in my paper. It need not match my metric, but I doubt there’s a simpler metric that is consistent with section 1, and nature seems to prefer simplicity.)

if your metric were simple then it would be asymptotically flat which you have agreed that it is not. It scalar curvature would be zero and the Ricci tensor would be zero. It has none of the above mentioned traits.

Zanket

Son Goku wrote:

I suggest you read Wald or at least Schutz.

Why? Do you think they’ll disagree with T&W, who show that the metric is the only equation needed to predict motion? Is this how you try to refute me, by suggesting I read some book with no explanation? If you still disagree that the metric is an equation of motion, then know that you disagree with planck2, who now agrees that the metric is the only equation needed to predict motion.

Geodesics are implied in General Relativity, all we wanted all along was what your rule was for particle dynamics. Your rule is the geodesics as you just stated above although it took along time to get that out of you.

If you knew all along that the metric fully implies a geodesic, then you needn’t have touched on the subject at all. The paper need not explicitly state everything. It need not rebuild all the concepts in GR, especially superfluous paradigms like geodesics.

“Geodesic” is just a label given to the path of a particle, a path that is fully described by the metric. A paradigm is just a way of looking at something, no better than another equivalent way. For example, one who talks about spacetime curvature—another paradigm—automatically talks about the tidal force, which is synonymous. One who talks about the path of a free particle computed using a metric automatically talks about a geodesic.

Zanket did you understand what our question meant?
The part in bold is totally incorrect and I think at this point you're being triumphant on purpose.

To get a geodesic for a particle, all one does is assume that the particle would go straight were it not for the curved spacetime (fully described by the metric) that curves its path, and then apply the metric. Then one does not need a methodology beyond that. That is what I mean by the part in bold, and that is why T&W can compute an orbit with only one equation, the metric.

So when you asked for the dynamics, I told you that the dynamics are given by the metric, the only equation needed to predict the motion. That is a correct answer, and nobody here has refuted it.

You reject GR though, so it's difficult to understand how you accept the generator of its dynamics.

Just because I show a flaw of GR does not mean that I reject all of its concepts. As I said above:

Zanket wrote:

My theory is built on parts of GR, like SR and the equivalence principle. Unless I say or imply that something is invalid, the reader can assume that I hold it to be valid.

By your logic, you could just as well argue that I disagree with SR, because I show a flaw of GR, which incorporates SR. So why did you harp on geodesics instead of SR?

Son Goku wrote:

Zanket, do you not think it's possible that you simply haven't read enough physics and are biting off more than you can chew?

I might think that, if someone could refute the paper. Do I know the entire subject of GR? No. But I know what I need to know to meet the objectives of the paper.

You must admit that your inability to understand basic dynamical questions indicates a alck of familiarity with a lot of the sunject.

I answered your question correctly, as noted above. As it is, you apparently still believe that the metric is not an equation of motion, which is incorrect.

Tell me, what did you read before you read Taylor's book.

It’s irrelevant. I decline to answer.

Professor_Fink

Son Goku wrote:

I suggest you read Wald or at least Schutz.

Well if we're suggesting books, then why not my favourite physics text of all time: General Relativity by Dirac!

Professor_Fink

Zanket wrote:

Why? Do you think they’ll disagree with T&W, who show that the metric is the only equation needed to predict motion? Is this how you try to refute me, by suggesting I read some book with no explanation? If you still disagree that the metric is an equation of motion, then know that you disagree with planck2, who now agrees that the metric is the only equation needed to predict motion.

That is complete rubbish Zanket. Planck2 is insisting that both the metric and an assumption about the dynamics (i.e. that the particle follows a geodesic) are necessary. These are two seperate requirements. He knows what he said, I know what he said, Songoku knows what he said, and more importantly YOU KNOW WHAT HE SAID! Stop trying to play games, this is getting ridiculously childish.

Also I think the suggestion is that you are severly misinterpreting the methods applied in T&W and that some more reading may help clarify the required mathematics for you.

Professor_Fink

Zanket wrote:

If you knew all along that the metric fully implies a geodesic, then you needn’t have touched on the subject at all. The paper need not explicitly state everything. It need not rebuild all the concepts in GR, especially superfluous paradigms like geodesics.

You're joking right? You're saying space is curved, but how that actually effects stuff is superfluous.

You need to assume something about the dynamics, and it seems that you have eventually settled on particles following geodesics. This was not a given, and you seem to have taken a suspiciously long time to even work out what the question meant. This really does not bode well for future conversations.

Zanket wrote:

“Geodesic” is just a label given to the path of a particle, a path that is fully described by the metric. A paradigm is just a way of looking at something, no better than another equivalent way. For example, one who talks about spacetime curvature—another paradigm—automatically talks about the tidal force, which is synonymous. One who talks about the path of a free particle computed using a metric automatically talks about a geodesic.

No Zanket. You're wrong. A geodesic is essentially a path of shortest distance. It is not a given that particles follow such paths. For example in quantum mechanics the path integral used to calculate the position of a particle is a sum over all paths (not just the shortest). If you expand the unitary evolution of a particle, you find that the shorter paths are more likely (in for example the tight binding model or XXZ spinchains), but all paths do in fact effect the results.

It's pretty clear from this that you need to reexamine the basis for GR, before your next attempt to disprove it.

Zanket wrote:

I might think that, if someone could refute the paper. Do I know the entire subject of GR? No. But I know what I need to know to meet the objectives of the paper.

But we have been refuting it, time and time again. You just refuse to accept our refutations, (it's called denial, and I believe there are people you can talk to about it).

Zanket

planck2 wrote:

look it's pointless arguing with this guy. He clearly doesn't understand what is going on. We are wasting our time

That’s funny, considering you backed down from your claim that the metric is not an equation of motion, after I showed otherwise. And convenient too, since I am pressing you to support your empty claims.

That's easy to prove. The proof of this is given by Werner Israel[1967], who I know.

Alluding to some proof without explanation is not proof. Your claim remains empty. I’ll assume you can’t support it.

and besides I am not emotionally attached to GR, you are just saying things that you cant back up.

I didn’t suggest such attachment. What have I not backed up? It is you who do not back up your claims, like the one above and the specious one about the new metric diverging from the Schwarzschild metric as r increases.

You have derived stuff which you say GR allows which disagree with the Schwarzschild solution and Einstein's field equations.

Well, I wouldn’t say I derive it so much as point out what’s in plain sight. Otherwise, yes, and thereby I show a flaw of GR.

It is most likely that there is a serious flaw in your arguement

The Professor says you are a theoretical physicist. If so, then it should be a simple matter for you to refute two paragraphs of simple logic showing a flaw of GR. But you have been unable to do so. And the Professor and Son Goku have been unable to do so, and they are supposedly also theoretical physicists. That should be a clue to you that my argument is valid.

They assume that particles do not move along a straight line in flat spacetime, but along a geodesic in any spacetime manifold, curved or flat?

They assume the particle moves straight unless directed otherwise, in which case it moves in a straight line in flat spacetime, and moves on a path whose curve is given by the metric in curved spacetime. And the path of the particle is a geodesic in either case.

i am afraid one does. they [T&W] use the principle of extremal aging which is
the same as calculating the geodesics using the Euler-Lagrange method.

Yes, I grant that one could say the principle is part of a methodology to predict motion. But using the principle is nothing more than assuming that the particle goes straight unless directed otherwise by the curved spacetime described by the metric. “"Go straight!" implies extremal aging”, T&W say. The principle is not an equation. Then it remains that the only equation needed to predict motion is the metric. And then it remains that the metric is an equation of motion. My paper does not reject the principle. Then my paper gives all that is needed to make falsifiable predictions of observations.

I really haven't too be honest.

You have. I’ve asked you repeatedly to support your claim that the new metric diverges from the Schwarzschild metric (or is not asymptotically flat, take your pick). But you don’t. I’ve shown you that the opposite is so, because the only difference between the metrics is the difference between eqs. 8 and 9, the curves of which can be easily seen to converge as r increases, approaching each other ever more closely. But you just keep making your claim to the contrary without supporting it.

yes you do say that is not unique by simply saying that your metric is spherically symmetric, because you say this in the abstract

The abstract says “General relativity is shown in two ways to be inconsistent. A new metric for Schwarzschild geometry is derived ...” If I were to suggest that the Schwarzschild metric is not unique, I would be suggesting that, after deriving the new metric, there are two valid metrics for Schwarzschild geometry, neither unique. But that is not so, for the paper shows that the Schwarzschild metric is invalid. Before the paper derives the new metric, the Schwarzschild metric has been refuted, hence no valid metric exists.

well i am afraid that if you don't understand mathematics then i can't convince you that they don't converge.
they don't converge as i showed earlier, read my previous posts.

Nice try. Anyone who can enter the equations into a spreadsheet can see that they converge as r increases. You can’t point to a post of yours where you have supported this claim.

the less assumptions a theory makes the better it is, the more predictions it can make the better.

That’s beside the point.

if your metric were simple then it would be asymptotically flat which you have agreed that it is not.

I have not agreed to that; quote me. I have specifically and repeatedly denied that and have repeatedly asked you to support this claim, a few more times in this post. I challenge you to identify the post in which you supported it. You can't do it, and I predict that you will ignore this challenge.

Zanket

Professor_Fink wrote:

That is complete rubbish Zanket. Planck2 is insisting that both the metric and an assumption about the dynamics (i.e. that the particle follows a geodesic) are necessary.

Not rubbish. What planck2 insisted is that the metric is not an equation of motion. That is incorrect. The assumption that the particle follows a geodesic is nothing more than an assumption that the particle goes straight unless otherwise directed by the curved spacetime described by the metric. That does not need to be mentioned in my paper. Nowhere in my paper do I reject this concept.

He knows what he said, I know what he said, Songoku knows what he said, and more importantly YOU KNOW WHAT HE SAID! Stop trying to play games, this is getting ridiculously childish.

The beauty of a thread is that everything’s on the record. So we don’t have to rely on our memories. Here is what he originally said:

planck2 wrote:

The metric is the fundamental requirement, but you need other things in order to get the equations of motion such as the Euler-Lagrange formalism or the Hamilton-Jacobi method.

Here is where he watered down that claim:

planck2 wrote:

they assume like Einstein that particles move along geodesics and use the metric to obtain the geodesics.

And here is where his claim died:

planck2 wrote:

i am afraid one does. they [T&W] use the principle of extremal aging which is the same as calculating the geodesics using the Euler-Lagrange method.

To which I pointed out, backed up by a quote by T&W, that using the principle is nothing more than assuming that the particle goes straight unless directed otherwise by the curved spacetime described by the metric.

So it turned out that neither the Euler-Lagrange formalism nor the Hamilton-Jacobi method was needed to get the equations of motion. It turned out that the metric is an equation of motion, and the only equation needed to predict motion for Schwarzschild geometry, just like I said all along. Then my paper, which does not reject the concept of the particle going straight unless otherwise directed, need have no more than a metric to make falsifiable predictions of observations, in contradiction to what has been vehemently claimed in this thread.

And now I have shown that what you called “complete rubbish” is not that at all, but rather a scientific refutation of incorrect statements.

Professor_Fink wrote:

Also I think the suggestion is that you are severly misinterpreting the methods applied in T&W and that some more reading may help clarify the required mathematics for you.

Another baseless comment that anyone could make.

You're joking right? You're saying space is curved, but how that actually effects stuff is superfluous.

How did you translate “superfluous paradigms like geodesics” into “how that actually effects stuff is superfluous”? Man, you should be a politician.

You need to assume something about the dynamics, and it seems that you have eventually settled on particles following geodesics.

I didn’t “eventually settle” for anything. The paper does not reject the concept of geodesics.

No Zanket. You're wrong. A geodesic is essentially a path of shortest distance. It is not a given that particles follow such paths. ...

You twist my words again. I did not say that it is a given that particles follow such paths.

It's pretty clear from this that you need to reexamine the basis for GR, before your next attempt to disprove it.

Notice that the paper still stands unrefuted and complete.

But we have been refuting it, time and time again. You just refuse to accept our refutations, (it's called denial, and I believe there are people you can talk to about it).

Denial is when I clearly refute your refutations with logic and reason, and you don’t respond to that, but then say this. No, I don’t “refuse to accept” them. I refute them, time and time again. I didn’t see you respond to my answer to your “hollow” argument, for example. You haven’t even refuted section 2, showing a flaw of GR with just two paragraphs of simple logic. Your attempt to refute it was based on reading something into the paper that isn’t there, as I pointed out. I challenge you to find one “refutation” of my paper above to which I did not subsequently refute with reasoning, excepting the problem found by planck2 regarding dphi. You can’t do it, and I predict that you’ll ignore the challenge.

(This is typically where the mod closes the thread, even though it’s clearly unwarranted, for not only have I been the only one consistently backing up my claims here, but also my words have been repeatedly and apparently intentionally twisted to make specious points against me. Oh well, as I said, in that case I lose nothing.)

Son Goku

Zanket, you do realise that planck2 says the exact same thing in each of those quotes.

He actually just gets less specific.

The metric is the fundamental requirement, but you need other things in order to get the equations of motion such as the Euler-Lagrange formalism or the Hamilton-Jacobi method.

This would be the most general statement.

I don't see how this:

i am afraid one does. they [T&W] use the principle of extremal aging which is the same as calculating the geodesics using the Euler-Lagrange method.

Is is his claim "dying".

I refute them, time and time again.

Zanket, the problem is you don't understand our refutations.
Aside from our claim that you don't fully understand GR, you more drastically don't understand the basics of how dynamics is generated in physics.

How did you translate “superfluous paradigms like geodesics” into “how that actually effects stuff is superfluous”?

Zanket read what you read again. Geodesics are how curved spacetime effects matter.

I was going to demonstrate that you're metric is asymptotically flat, but then when I scrolled down, you had two metrics labelled "spacelike" and "timelike".
Why?

That is what makes attacking your paper so difficult, it's far to vague and ill formed, but not only that you lack the prerequesties to understand basic physics questions.

That is why it is important to know how much of a background you have.
You must admit that if you haven't a solid background in other areas of physics, trying to learn GR was too big a leap.

For instance why did it take you so long to understand the dynamics question?
Don't mention anything about who said what or why they said it, just answer the question in bold.
Do you understand now?

planck2

Quote:
if your metric were simple then it would be asymptotically flat which you have agreed that it is not.

Zanket wrote:

I have not agreed to that; quote me. I have specifically and repeatedly denied that and have repeatedly asked you to support this claim, a few more times in this post. I challenge you to identify the post in which you supported it. You can't do it, and I predict that you will ignore this challenge.

Zanket wrote:

You have. I’ve asked you repeatedly to support your claim that the new metric diverges from the Schwarzschild metric (or is not asymptotically flat, take your pick). But you don’t. I’ve shown you that the opposite is so, because the only difference between the metrics is the difference between eqs. 8 and 9, the curves of which can be easily seen to converge as r increases, approaching each other ever more closely. But you just keep making your claim to the contrary without supporting it.

from post 113

planck2 wrote:

but they actually don't converge and it is not by some mere trillionith significant figure difference. your metric diverges from flat spacetime whereas the Schwarzschild one converges to flat spacetime in the limit as r goes to infinity. So your metric is not asymptotically flat and never will be.

to put it more plainly

r/(r+R) diverges as r goes to infinity and does not converge to 1 as it must for flat spacetime.

(r+R)/r also diverges as r goes to infinity and doesn't converge to 1 as it must for flat spacetime.
one gets infinity/infinity
where as the Schwarzschild spacetime does.

By the way the metric only describes how the manifold is curved . One can obtain the geodesics from it using the Euler-Lagrange formalism, but to say that the metric is an equation of motion is fundamentally not true.

If one postulates that particles move along geodesics, which is the analogue of hamilton's principle of least action in Classical mechanics, then one can call the geodesics the equations of motion.

I would not bother to prove something to you which has already been proved some 40 years ago by a gentleman far smarter than I.

so just go look up the paper.

You just don't get it do you?

Zanket

Son Goku wrote:

Is is his claim "dying".

Yes. It’s because there he admits that to “get the equations of motion”, in addition to the metric, one needs not the “Euler-Lagrange formalism or the Hamilton-Jacobi method”, but rather only the principle of extremal aging, which comprises all of one sentence and is implied from the particle simply going straight. The metric is the only equation needed to predict motion after all, just like I said all along.

I think it is arguable whether the metric qualifies as an equation of motion, since to predict motion one also needs at least the principle of extremal aging. From my perspective, since the metric is the only equation needed to predict motion, it must be an equation of motion.

Zanket, the problem is you don't understand our refutations.
Aside from our claim that you don't fully understand GR, you more drastically don't understand the basics of how dynamics is generated in physics.

Actually the above shows that I understand it fine.

Geodesics are how curved spacetime effects matter.

I don’t deny that. One thing I backtrack on, I should not say that geodesics are a paradigm. They are a term within the paradigm of curved (or flat) spacetime. They are a label for the path a free particle takes within curved (or flat) spacetime.

When I say “superfluous paradigm”, I don’t mean that it’s useless. I mean that it’s more than necessary. For example, the tidal force is synonymous with spacetime curvature. Then one can have a theory of gravity that mentions only the tidal force, and it can be wholly compatible with a theory of curved spacetime. Personally, I think that the paradigm of curved spacetime is a great way to visualize motion.

I was going to demonstrate that you're metric is asymptotically flat, but then when I scrolled down, you had two metrics labelled "spacelike" and "timelike".
Why?

Because the new metric in the paper is derived from the metric in my main reference, Exploring Black Holes by T&W. Their Schwarzschild metric is the same as mine, except that eq. 9 incorporated into my metric is replaced by eq. 8 in their metric. T&W say that the timelike version is useful when a clock can be carried between two events at less than c. Otherwise they use the spacelike version.

That is what makes attacking your paper so difficult, it's far to vague and ill formed, but not only that you lack the prerequesties to understand basic physics questions.

Actually the above shows that the paper is well-defined. It is also well-referenced. For example, had you looked up my reference for the metric, reference #10, for which not only an online link is given but also I posted an image of the relevant page above, your question about the spacelike and timelike versions would have been answered.

What has become clear to me, based on misconceptions I’ve seen in this thread, is that y’all have apparently learned relativity physics in a more difficult and more mathematical, less intuitive way. Apparently T&W (and other fine authors) make it much simpler, but y’all aren’t familiar with it. I decline to use superfluous methods just to appease others. I’m not going to fill the paper with loads of unnecessary math.

That is why it is important to know how much of a background you have.
You must admit that if you haven't a solid background in other areas of physics, trying to learn GR was too big a leap.

I think that’s irrelevant. Your example basis for it has been refuted. Where you thought I am vague (re spacelike and timelike versions of my metric), I showed that I actually match my reference. The bottom line is that papers are not refuted by delving into the author’s background. Why not stay scientific and try to refute the paper directly?

For instance why did it take you so long to understand the dynamics question?
Don't mention anything about who said what or why they said it, just answer the question in bold.

I understood the question the first time. The question asked, what are the dynamics for my theory? I said the metric gives the dynamics, because it is the only equation needed to predict motion. Y’all disputed that. But I am right. Yes, you also need the principle of extremal aging, but that is part of SR, a theory held as valid in my paper. Any confusion on my part came from me not grasping why y’all think I need to rebuild the concept of geodesics, when my paper does not reject them. It took me a while to figure out that y’all mistakenly think that by showing a flaw of GR, I must reject it in its entirety.

Do you understand now?

Yes, I understand the contention now. It didn’t show a problem with the paper. I have fully addressed it in there, with the following changes:

[In the conventions at top]: Parts of general relativity not rejected in this paper (either explicitly or implicitly) are held as valid. For example, special relativity is held as valid.

Reader: A metric must be derived from field equations.

Author: The scientific method lets any type of equation be presented without derivation. Then no particular method of derivation is required. (That said, the new metric is derived.)

Reader: Without new field equations, your theory is worthless.

Author: Field equations are not required. Using only the new metric and the principle of extremal aging, a principle of special relativity (a theory held as valid in this paper), one can make falsifiable predictions. (11)

planck2

so apparently the metric is asymptotically flat, my mistake. I apologise.

planck2

we know that the Schwarzschild solution is the unique spherically symmetric solution to Einstein's vacuum field equations

planck2

there are other theories of gravity which are not symmetric and don't predict singularities at r=0, or r=2M, i.e. the manifolds are completely smooth. Just google the topic. However yours does give a singularity at r=0, but there is no event horizon. This is a naked singularity.

planck2

so i don't think that you are saying that field strength=curvature anymore, at least in the way Einstein says it. I think you are saying something else. plus i don't think that metric is spherically symmetric either

So one does essentially need the field equations in order to figure out what you are saying, i.e. I need an action principle and there are restrictions on the possible form of the action. I may point you to the excellent book by Lovelock and Rund.

Zanket

planck2 wrote:

By the way the metric only describes how the manifold is curved . One can obtain the geodesics from it using the Euler-Lagrange formalism, but to say that the metric is an equation of motion is fundamentally not true.

I back away from my claim that the metric is an equation of motion, for two reasons. First, although it is the only equation needed to predict motion, it is true that it is at least one step removed from predicting motion, so whether it is an equation of motion becomes arguable. Second, it’s a moot point that doesn’t affect my paper, so there’s no reason for me to care. What I care about is that my paper is complete, by having all that is needed to predict motion for Schwarzschild geometry.

we know that the Schwarzschild solution is the unique spherically symmetric solution to Einstein's vacuum field equations

Your point being? I agree. I get this comment so often that I added a reader comment for it to section 5:

Reader: Birkhoff’s theorem proves that the Schwarzschild metric is the only solution to Einstein’s field equations for Schwarzschild geometry.

Author: Because the Schwarzschild metric is shown herein to be inconsistent with section 1, hence flawed, the theorem indirectly proves that Einstein’s field equations as well are flawed.

there are other theories of gravity which are not symmetric and don't predict singularities at r=0, or r=2M, i.e. the manifolds are completely smooth. Just google the topic. However yours does give a singularity at r=0, but there is no event horizon. This is a naked singularity.

You have no basis for this. It does not have a singularity at r=0. The paper clearly shows why singularities are precluded ...

so i don't think that you are saying that field strength=curvature anymore, at least in the way Einstein says it. I think you are saying something else.

... hence you have no basis for this either.

plus i don't think that metric is spherically symmetric either

Or this. You’re just spouting empty claims, again.

So one does essentially need the field equations in order to figure out what you are saying, i.e. I need an action principle and there are restrictions on the possible form of the action.

By using only the new metric and SR, falsifiable predictions can be made. Then the paper is a complete theory of gravity. Then field equations are not required. You can’t prove otherwise without rejecting the scientific method. More than what is required to make falsifiable predictions—while not necessarily a bad thing—is superfluous according to the method.

Zanket

[size=+1]Checkpoint[/size]

At this point I contend that no problem of the paper has been claimed in this thread that I did not subsequently refute, save that re "dphi" noted by planck2 (thanks again).

If you disagree, then please briefly restate your claim, and I will show you the post number in which I refuted it, beyond which you did not respond.

I appreciate everyone’s comments so far.

Professor_Fink

I wrote a long post on this last night, but it seems to have vanished. Basically the proposed metric does satisfy spherical symmetry, but it does not satisfy R_ab=0 and hence does not satisfy T_ab=0, which means that it can't be regarded as a valid vaccum solution.

The interesting thing is that I can't spot anywhere in Zankets paper where he considers the distribution of mass, or lack there of, outside the central mass. I think has happened is that his assumption that all the shell objects observed by the particle must pass at less than c, and that it must be possible for such objects to be there etc., takes the place of an assumption about mass distribution. (i.e. there may well be a mass distribution which yields Zankets metric).

The problem is that this would invalidate his claims that the schwarzchild metric is not unique, since his proposed spacetime would correspond to a different distribution of mass.

Since R_ab!=0 in Zanket's paper, this must imply that either there is other mass present (assuming mass warps space in some, not necessarily Einsteinian way, since R_ab=0 for vacuum solutions if in the case of no mass the space would be flat), or space is inherently curved, and that SR is not valid in weak gravitational fields (since you do not obtain the Minkowski metric by working backwards from Zanket's).

Neither of these seem like strong arguements against GR as both are arbitrary to some extent.

Professor_Fink

Sorry Zanket, I was typing the previous post as you were posting. But it points out one specific problem with your paper.

And yes, I disagree (see my previous post).

Son Goku

What has become clear to me, based on misconceptions I’ve seen in this thread, is that y’all have apparently learned relativity physics in a more difficult and more mathematical, less intuitive way.

First of all, humans have no "intuition" regarding curved spacetime. To bring up a statement like that is completely trite.
Relativity can only be competently expressed either using Differential Geometry or, if you're good at algebra, Clifford Algebra.
You can't play the "I understand it in a more physical way" card.

Apparently T&W (and other fine authors) make it much simpler, but y’all aren’t familiar with it. I decline to use superfluous methods just to appease others. I’m not going to fill the paper with loads of unnecessary math.

Let's look at this claim.
Me, Professor_Fink and planck2 don't understand GR.
Everybody on the physics forum (most of whom are physicists) didn't understand GR, including ZapperZ who works on testing QFT and is one of the world's foremost condensed matter physicists.
A few people on other forums, who had obviously studied GR, didn't understand it.
You are also "anti-maths" to a ridiculous degree.
(There are people who dislike advanced mathematics, but claiming you don't need Differential Geometry to understand a theory of curved spacetime is ludicrous)

Do you not think this points suspiciously towards you not understanding it and being difficult to reason with?

Zanket

Professor_Fink wrote:

Basically the proposed metric does satisfy spherical symmetry, but it does not satisfy R_ab=0 and hence does not satisfy T_ab=0, which means that it can't be regarded as a valid vaccum solution.

For one, this is an empty claim.

For another, this puts the cart before the horse. My paper shows that Einstein’s field equations are invalid (search for “Birkhoff’s theorem”). You can’t logically use invalid field equations to refute me. To restore possible validity of the field equations, you have to refute sections 2 and 7, both of which show that GR is inconsistent.

The interesting thing is that I can't spot anywhere in Zankets paper where he considers the distribution of mass, or lack there of, outside the central mass.

That’s because Schwarzschild geometry, the only geometry my paper handles, is the geometry of empty spacetime around a Schwarzschild object. There is no mass “outside the central mass”.

A distribution of a lack of mass is nonsensical.

My comments above seem to cover your whole post.

Zanket

Son Goku wrote:

First of all, humans have no "intuition" regarding curved spacetime. To bring up a statement like that is completely trite.

What you quoted of mine doesn’t mention curved spacetime. And your next statement amply demonstrates my point as I actually stated it:

Relativity can only be competently expressed either using Differential Geometry or, if you're good at algebra, Clifford Algebra.

You suggest here that T&W, who use neither of those in their book Exploring Black Holes, do not competently express relativity. Which is a joke, since they faithfully represent relativity while predicting all manner of motion. They start from metrics rather than, say, field equations, but there is no scientific requirement for field equations.

Let's look at this claim.
Me, Professor_Fink and planck2 don't understand GR.
Everybody on the physics forum (most of whom are physicists) didn't understand GR, including ZapperZ who works on testing QFT and is one of the world's foremost condensed matter physicists.

I did not say that y’all do not understand GR. An understanding of relativity physics in a “more difficult and more mathematical, less intuitive way” (my quote) does not suggest that one does not understand GR. It can, however, blind one to simpler, yet valid methods and viewpoints.

ZapperZ proved that he misunderstands the equivalence principle. I didn’t see your support of his position, for which I twice asked you. Walk your talk please.

After ZapperZ censored the thread, discussion with one participant continued for weeks in the form of PMs until he contradicted himself (which is expected, because GR is inconsistent—it contradicts itself).

A few people on other forums, who had obviously studied GR, didn't understand it.

Who? Instead of making an empty claim, let’s take it on a case-by-case basis.

You are also "anti-maths" to a ridiculous degree.

No, I’m anti-superfluous-maths, which makes sense. (And again, “superfluous” does not necessarily mean bad. It means “more than necessary”, as in more than needed to make a point.)

(There are people who dislike advanced mathematics, but claiming you don't need Differential Geometry to understand a theory of curved spacetime is ludicrous)

My paper handles only Schwarzschild geometry, which T&W and many other fine authors show can be well understood without the use of differential geometry.

Do you not think this points suspiciously towards you not understanding it and being difficult to reason with?

Is refusing to bow to ZapperZ’s clear misunderstanding of the equivalence principle, for example, being “difficult to reason with”? I think not.

In section 2 my paper purports to show a flaw of GR, in only two paragraphs of fairly simple logic. You haven’t refuted it. (Your claim that something can be so flawed as to be irrefutable does not qualify as a refutation.) Section 2 is either valid or invalid. If it’s valid, then my skill is proven. Or if it’s invalid, then you apparently don’t have the skill to show that, in which case you are the pot calling the kettle black.

Professor_Fink

Zanket wrote:

For one, this is an empty claim.

For another, this puts the cart before the horse. My paper shows that Einstein’s field equations are invalid (search for “Birkhoff’s theorem”). You can’t logically use invalid field equations to refute me. To restore possible validity of the field equations, you have to refute sections 2 and 7, both of which show that GR is inconsistent.

How exactly is it an empty claim? g_11 and g_44 (the dr^2 and dt^2 coefficients) are explicitly derived from the R_ab, even if you do not accept GR. If the field equations don't hold, then R_ab may be related to T_ab in some different manner, but the relationship musyt exist if mass curves space in _any_ way. You cannot avoid this. The fact that you're paper does not have R_ab=0 for T_ab=0 implies some kind of additional curvature for space. Actually the fact that g_11 and g_44 are a function of the schwarzchild radius implies that space curves in a very odd way due to the presence of mass (it's a far from trivial function of mass).

The fact that R_ab is non-zero for T_ab=0 would seem to imply that special relativity is not correct in the absence of a gravitational field.

Note: This arguement DOES NOT rely on the specific form of the field equations. Rather it is a more general arguement about what will happen if spacetime curvature is ANY function of mass.

Professor_Fink

Zanket wrote:

You suggest here that T&W, who use neither of those in their book Exploring Black Holes, do not competently express relativity. Which is a joke, since they faithfully represent relativity while predicting all manner of motion. They start from metrics rather than, say, field equations, but there is no scientific requirement for field equations.

I believe what he is saying is that a full discription of the physics involved is not possible without differential geometry or Clifford algebra. As such the book by T&W is not a full discription of the situation, but rather a gentle introduction to some of the ideas involved.

Zanket wrote:

I did not say that y’all do not understand GR. An understanding of relativity physics in a “more difficult and more mathematical, less intuitive way” (my quote) does not suggest that one does not understand GR. It can, however, blind one to simpler, yet valid methods and viewpoints.

Setting aside your paper, what evidence do you have for this claim? If anything it opens our eyes to the possible flawed assumptions that can be made.

Zanket wrote:

My paper handles only Schwarzschild geometry, which T&W and many other fine authors show can be well understood without the use of differential geometry.

So what happens if the central starts spinning? You should easily be able to predict this if you fully understand the theory. It's also experimentally verifiable since it describes the space around pulsars.

Zanket wrote:

In section 2 my paper purports to show a flaw of GR, in only two paragraphs of fairly simple logic. You haven’t refuted it. (Your claim that something can be so flawed as to be irrefutable does not qualify as a refutation.) Section 2 is either valid or invalid. If it’s valid, then my skill is proven. Or if it’s invalid, then you apparently don’t have the skill to show that, in which case you are the pot calling the kettle black.

Ok, here is an analogy (since you seem fond of analogies). It's a proof that the universe doesn't really exist:

asfdsefqwfasdfcasdcasdcacascasc
asdcasdascasxcasxcasxcasc3423qsx
awsf432tvb 4yt 4bvaswer2t5 q3gfva
34 rewgv ewrg etrhrf wr5y zd5ytbv543

hence the universe doesn't exist!

Prove it's wrong! Show me the exact spot!

The problem is that there isn't any one spot where it goes wrong, merely the whole arguement is nonsensical. This is the problem (all be it a slightly more extreme version) we are encountering when we try to point out the flaws in your arguement.

Son Goku

Zanket wrote:

What you quoted of mine doesn’t mention curved spacetime.

Zanket, you said we learned Relativity in a less intuitive way.
I'm saying that this is ridiculous, because GR deals with curved spacetimes, which humans have no intuition of.

You suggest here that T&W, who use neither of those in their book Exploring Black Holes, do not competently express relativity.

They present a toned down version of the Theory for interested students (secondary school to lower undergraduate) willing to take what they know of calculus and see it applied to GR. None of it is incorrect, however it cannot be used to attack GR itself, as some of its concepts don't generalise correctly.

Personally Zanket, what you are doing runs against what I consider intellectual honest.
For example, I couldn't imagine learning QFT and then suddenly stopping when I see a "contradiction" in the implications of the Klein-Gordon Field and using this to proclaim QFT was flawed. Then on top of that I'm looking at the Klein-Gordon Field presented in an easy manner that doesn't get into anything fully and only calculates the simplest quantities.

I wouldn't mind if you had actually found a contradiciton in GR-lite (in Wheeler and Taylor).


Here is what I think of your claim:
The escape velocity as observed by an infalling observer doesn't even asymptote to c, as it actually hits c at a certain r.
The simple fact of the matter is that the escape velocity doesn't asymptote to c in General Reltivity, it reaches c at a certain surface.
This you cannot contend with.

Next is the claim that because the observer never observes the escape velocity to be greater than c it therefore never is greater than c.
Now in a General Relativistic context what might escape velocity be defined as?
It could be defined as some number associated with the (timelike)geodesic which maintians a constant r.
So the escape velocity (or speed, which is all we need in this case, because of the spherical symmetry) at r = 3M, would be some number generated by the (timelike)geodesic which maintains constant r = 3M.
However past the surface at which this number is c there is no (timelike)geodesic which maintians a constant r.
(Which can be seen from computing geodesics using the Geodesic equation)
Therefore past the horizon this number is undefined and is not a sensible quantity to attempt to measure.

planck2

First of all I would like to say that you agree with special relaitvity don't you. Then you agree with that energy and momentum are conserved. That is T_ab,a = 0. this says that enrgy and momentum are conserved, i.e. the energy momentum tensor is divergence free.

You also say that matter causes the spacetime to curve.
Thus G_ab = f T_ab, where f is a constant, i.e. the metric is related to the matter and energy distribution. G_ab must be symmetric because T_ab is and so is the metric.
So we must write the conservation of energy and momentum in terms of when we are talking about curved manifolds. Thus we have T_ab;a = 0

The only tensor in a 4 dimensional spacetime which satisfies these conditions is
G_ab = R_ab - ( (1/2) g_ab R). It only contains derivatives of the metric up to 2nd order. Higher derivatives would lead to violations of energy conservation and the existence of ghost states.

In your paper you write

Zanket's paper wrote:

The particle falls in a uniform gravitational field since a gravitational field is everywhere uniform locally.

Gravitational fields are not globally uniform which is what you are saying. If a gravitational field where uniform even in the Newtonian sense then we would have a potential which is linear in the radial co-ordinate, i.e. U(r) = k*r hence F = - k.

Even you know that the Earth's gravitational field is not uniform.

You are contending that because observers in a uniformly accelerating reference frames feel a "force" that is locally equivalent to a uniform gravitational feel that they must be
in a uniform gravitational field. This is incorrect because you don't take into account the global behaviour of the gravitational field.

In Minkowski spacetime one can deal with uniformly accelerated observers, as you are aware. In this case v does asymptote to c, but to do so one would need infinite energy.

Professor_Fink

planck2 wrote:

First of all I would like to say that you agree with special relaitvity don't you. Then you agree with that energy and momentum are conserved. That is T_ab,a = 0. this says that enrgy and momentum are conserved, i.e. the energy momentum tensor is divergence free.

You also say that matter causes the spacetime to curve.
Thus G_ab = f T_ab, where f is a constant, i.e. the metric is related to the matter and energy distribution. G_ab must be symmetric because T_ab is and so is the metric.
So we must write the conservation of energy and momentum in terms of when we are talking about curved manifolds. Thus we have T_ab;a = 0

That's exactly what I have been trying to express (although perhaps less concisely). Of course, Zanket's metric doesn't satisfy R_ab = 0...

planck2

In your paper you wrote

Zanket's paper, Section 2 wrote:

Reader: Special relativity does not apply to curved spacetime.
Author: It is only used in flat spacetime.

I don't know why you put this in because you're saying exactly what the reader says.

And technically speaking this is not true, SR can be applied to any region big or small where the tidal forces are small enough to be neglected.

You also write

Zanket's paper, section 2 wrote:

The particle always falls in a uniform gravitational field since a gravitational field is uniform locally. Then v always asymptotes to c; i.e. as long as the particle falls. According to general relativity, when v is less than c it equals the escape velocity there. Then v always asymptotes to c, so does the escape velocity, in which case the escape velocity is always less than c and then there are no black holes.

Zanket wrote:

According to general relativity, when v is less than c it equals the escape velocity there.

Where is there?, here, there and everywhere.

Just because a particle has a velocity v at some point in a uniform gravitational field doesn't mean that it has the escape velocity or that the escape velocity is v. It needs to have a velocity >= to that given by the field.

planck2

In the case of a globally uniform gravitational field - providing you still contend that curvature =field stength - the components of the Riemann tensor are all equivalent and constants and R_abcd*R^(abcd) = h, h is a constant. So there is no infinite curvature, which is what a black hole is.

planck2

Don't think I'm contradicting myself because I'm not.

planck2

Professor_Fink wrote:

That's exactly what I have been trying to express (although perhaps less concisely). Of course, Zanket's metric doesn't satisfy R_ab = 0...

Yes you are correct, R_ab of Zanket's paper is not zero.

I think the case is closed at this point.

Back to calculating the geodesics of the 6 dimensional spherically symmetric spacetime.