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

Professor_Fink

Ok, if you think I don't quote the paper to back up my claims, here is a direct quote.

Zanket's Paper wrote:

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

This statement is completely false.

It's like saying that because a ball appears flat on a small enough scale, it must be flat everywhere and is hence actually a plane.

planck2

this may be out of line, but you know joe and son goku, i wouldn't even bother replying to the thread any more, i haven't even read it [zanket's paper] and i'm not going to

Professor_Fink

planck2 wrote:

this may be out of line, but you know joe and son goku, i wouldn't even bother replying to the thread any more, i haven't even read it [zanket's paper] and i'm not going to

Yeah, I know I should stop, but it's sucking me in.

Like watching a car crash.

Zanket

Professor_Fink wrote:

Ok, if you think I don't quote the paper to back up my claims, here is a direct quote.

Great. Was that so hard?

This statement is completely false.

It's like saying that because a ball appears flat on a small enough scale, it must be flat everywhere and is hence actually a plane.

No, it's not like that. The quote does not suggest that g is constant globally, as your ball example suggests. You read that into it. It’s like saying that because the surface of a ball appears flat on a small enough scale, a tiny bug moving on the ball always moves in a region that can be deemed flat.

Let’s examine the quote. First, the basis:

since a gravitational field is everywhere uniform locally

You didn’t contest that. Next, the conclusion:

The particle always falls in a uniform gravitational field

This must be valid when the basis is valid. Nothing here suggests that the “uniform gravitational field” is global. The basis says “locally”, and the definition of “uniform gravitational field” specifies “local”.

Zanket

planck2 wrote:

this may be out of line, but you know joe and son goku, i wouldn't even bother replying to the thread any more, i haven't even read it [zanket's paper] and i'm not going to

By all means depend on hearsay, for it's doubtful you could refute the paper scientifically.

Professor_Fink

Zanket wrote:

This must be valid when the basis is valid. Nothing here suggests that the “uniform gravitational field” is global. The basis says “locally”, and the definition of “uniform gravitational field” specifies “local”.

Since you only talk about how the spacetime appears locally, then you are stuck in a comoving frame. In a comoving frame the particle doesn't fall, it's stationary.

Now I realise that you won't believe me, and don't seem to have the mathematical ability to deal with GR to see why your wrong without having to ask us, and even if some kind of zombie Einstein rose from the grave to challenge you, you'd just take so quote from a pop science book and say he doesn't understand GR. So at this point, I'll take Planck's advice and try to ignore further comments.

But it is like a car wreck, so I might occasionally give in to temptation.

P.S. I haven't read many of the books on intelligent design, but I am familiar with much of the evidence for evolution. I hear what creationists say, but I can dismiss their claims.

There are currently 381,469 preprints on the LANL archive, none of us have read them all. Nor have you. So we are forced to ignore the vast majority papers even some of those that are in our field. Because of this, we rely (at least somewhat) on the judgement of others to some extent in highlighting what is important.

If Planck2 has decided not to read your paper, it should not be taken as an insult. Physicists simply do not have enough time to read every paper, and I for one am certainly not offended when people chose not to read mine. I certainly do not insult them (i.e. "it's doubtful you could refute the paper scientifically"). So attack me all you want, and Son Goku too (sorry S.G.!), but leave Planck alone. He hasn't said anything against you.

planck2

So tell me what do the Penrose -Catrer diagrams for this new metric look like. Is the space time globally hyperbolic.

Zanket

Professor_Fink wrote:

Since you only talk about how the spacetime appears locally, then you are stuck in a comoving frame. In a comoving frame the particle doesn't fall, it's stationary.

There’s no problem here. Section 2 says: “Let a test particle fall radially from rest at infinity toward a large point mass while measuring the velocity v of objects fixed at each altitude as they pass directly by”. The “comoving frame” to which you refer can only be the particle’s inertial frame or one comoving with it, so that the particle is stationary relative to it, as you say. But that’s a moot point, because the particle is measuring its velocity relative not to itself, but rather to the objects passing directly by.

You say I am “stuck in a comoving frame”. That’s vague. The particle’s inertial frame applies for the duration of the particle’s fall. It applies globally.

Now I realise that you won't believe me, ...

It’s not a matter of belief. It’s a matter of being able to refute you scientifically. Make a relevant argument I cannot refute and then I’ll believe you.

... even if some kind of zombie Einstein rose from the grave to challenge you, you'd just take so quote from a pop science book and say he doesn't understand GR.

Good one. But I haven’t said you or anyone else here doesn’t understand GR. And the only quotes I’ve used from books were said by Hawking, Taylor, Thorne, and Wheeler, i.e. from the top echelon of relativity physicists. And the quotes were specific. You have suggested that in books they sometimes all say the exact opposite of what is valid, even all of them about the same thing, which is not convincing.

If Planck2 has decided not to read your paper, it should not be taken as an insult.

His comment is obviously meant to be rude to me, and not just to inform us that he had decided to not read the paper.

Zanket

planck2 wrote:

So tell me what do the Penrose -Catrer diagrams for this new metric look like. Is the space time globally hyperbolic.

Papers aren't refuted by posing problems to the author. Mine speaks for itself. Can you refute it directly?

Son Goku

Zanket, would you agree that it is possible that you cannot understand GR without understanding the language it is written in?

Would you also agree that it is possible that GR cannot be expressed using the mathematics that you are employing?

Zanket

Son Goku wrote:

Zanket, would you agree that it is possible that you cannot understand GR without understanding the language it is written in?

No, I disagree. GR can be understood in the mind, with visualizations, the way Einstein understood it before he expressed it mathematically and with thought experiments. The language GR was originally written in, math, is just one way to express what’s in the mind. It works in reverse too: the math can be used to create visualizations (plots, say, or even stories) that help one to understand GR. That is what laymen’s books and introductions to GR do, and when they do it correctly, what those visualizations convey is no less valid than the math. They are simply written in a different language than GR was originally written in.

Would you also agree that it is possible that GR cannot be expressed using the mathematics that you are employing?

For the whole theory, yes, I agree. But my paper does not express the whole of GR. The only equation of it that it derives is eq. 8, for gravitational time dilation / length contraction. And it handles only Schwarzschild geometry (the simplest curved spacetime geometry) and not, say, Kerr geometry.

Had you asked whether it is possible that a theory of gravity for Schwarzschild geometry cannot be expressed using the mathematics that I employ, I would disagree, if only because my paper contradicts that. It shows that a metric for Schwarzschild geometry can be derived by only analyzing a free-falling test particle, and takes valid shortcuts to reduce the complexity of the math to that of simple algebra. For example, it shows that the new metric is experimentally confirmed by showing that the results it returns differ from those of the Schwarzschild metric only beyond the number of significant digits in the tests. While a mathematical purist would balk at that technique, there is nothing scientifically wrong with it.

planck2

i haven't tried to refute it. I am just wondering if you have worked them out.

Zanket

planck2 wrote:

i haven't tried to refute it. I am just wondering if you have worked them out.

No, I haven't.

planck2

ok then

Son Goku

If General Relativity is flawed, how do you obtain the dynamics of your theory?

If you throw out the Einstein-Hilbert action, what is the new action and what difference does it make to the dynamics of your theory?

planck2

Son Goku wrote:

If General Relativity is flawed, how do you obtain the dynamics of your theory?

If you throw out the Einstein-Hilbert action, what is the new action and what difference does it make to the dynamics of your theory?

Yes, I am wondering about this too. How do you get the energy-momentum-stress tensor for the theory? Is it divergence free?

And I also don't understand how you can have two metrics. Only one is allowed. Are the geodesics timelike or spacelike? Is casaulity preserved?

planck2

and another thing, neither of your metrics are asymptotically flat. you also use different sign conventions in both metrics, which is inconsistent and you also argue that your knowledge of general relativity is irrelevant in regard to some point of the arguement. Funny because I would think that someone who was trying to dismiss GR would know it inside out.

Professor_Fink

I'm also unclear how Zanket's theory is supposed to prevent a physical singularity at r=0. While he has no longer got an event horizon, he seems to be left with a naked singularity.

The reason I ask is because one of his main criticisms of GR is that it 'breaks down' at the physical singularity.

Zanket

Son Goku wrote:

If you throw out the Einstein-Hilbert action, what is the new action

The Einstein-Hilbert action is used to derive Einstein’s field equations. Then I have nothing to say about that, because the new metric for Schwarzschild geometry that is derived in the paper is not derived from field equations.

Einstein did not derive his field equations from the Einstein-Hilbert action; only Hilbert did. Einstein’s “derivation” (actually a trial-and-error method) is scientifically valid, so the Einstein-Hilbert action is superfluous.

If General Relativity is flawed, how do you obtain the dynamics of your theory?

The dynamics of my theory are completely given by the new metric. Taylor and Wheeler say:

By T&W; google for it:

Every (nonquantum) feature of spacetime around this kind of black hole [a Schwarzschild object] is described or implied by the Schwarzschild metric. This one expression tells it all! [italics theirs]

Likewise, the new metric should also describe or imply every nonquantum feature of spacetime around a Schwarzschild object. (Section 6 shows that the new metric is experimentally confirmed to all significant digits. So the Schwarzschild metric approximates the new metric in weak gravity. And those tests cover the vast majority of experimental tests of general relativity.) Keep in mind that my paper handles only Schwarzschild geometry.

Zanket

planck2 wrote:

How do you get the energy-momentum-stress tensor for the theory? Is it divergence free?

I have nothing to say about that, because the new metric for Schwarzschild geometry that is derived in the paper is not derived from field equations. See also my reply to Son Goku immediately above.

And I also don't understand how you can have two metrics. Only one is allowed.

Only one metric is derived in the paper. It is given in timelike and spacelike forms, just like the Schwarzschild metric is (see reference 10 in the paper for an online reference).

Are the geodesics timelike or spacelike? Is casaulity preserved?

I could take a stab at these, but I decline.

and another thing, neither of your metrics are asymptotically flat.

The spacetime predicted by the new metric is asymptotically flat at a great distance from the center of gravitational attraction, just like it is for the Schwarzschild metric, as shown by fig. 3. The Schwarzschild metric approximates the new metric in weak gravity; see section 6 for experimental confirmation of that.

you also use different sign conventions in both metrics, which is inconsistent ...

Then how do you explain that the Schwarzschild metric uses the same signage for its own timelike and spacelike forms? (see reference 10 in the paper)

and you also argue that your knowledge of general relativity is irrelevant in regard to some point of the arguement. Funny because I would think that someone who was trying to dismiss GR would know it inside out.

It isn’t necessary for someone to fully know a theory in order to “dismiss” it. Not only am I proof of that, but also there is nothing in the realm of science to suggest otherwise. A theory can be felled by knowing only its Achilles heel.

Zanket

Professor_Fink wrote:

I'm also unclear how Zanket's theory is supposed to prevent a physical singularity at r=0. While he has no longer got an event horizon, he seems to be left with a naked singularity.

Section 6 says, “Unlike the Schwarzschild metric, the new metric is compatible with quantum mechanics since it precludes singularities (r = 0 is invalid) and nothing need fall to r = 0 when the escape velocity is always less than c”. Singularities are not a requirement in a theory of gravity. They are required by the Schwarzschild metric because its interpretation demands that objects below the Schwarzschild radius must fall all the way to r=0. In a theory of gravity in which the escape velocity is always less than c (in which case escape is always possible) and there is otherwise good reason to believe that r=0 is invalid, like mine, there need not be singularities.

The reason I ask is because one of his main criticisms of GR is that it 'breaks down' at the physical singularity.

To be clear, I wouldn’t call it a main criticism since I mention it only tangentially in a reader comment. It isn’t a basis for the inconsistencies of GR that the paper shows.

Professor_Fink

Zanket wrote:

Section 6 says, “Unlike the Schwarzschild metric, the new metric is compatible with quantum mechanics since it precludes singularities (r = 0 is invalid) and nothing need fall to r = 0 when the escape velocity is always less than c”. Singularities are not a requirement in a theory of gravity. They are required by the Schwarzschild metric because its interpretation demands that objects below the Schwarzschild radius must fall all the way to r=0. In a theory of gravity in which the escape velocity is always less than c (in which case escape is always possible) and there is otherwise good reason to believe that r=0 is invalid, like mine, there need not be singularities.

Below are the metrics from you're paper:

dT^2 = ((r / (r + R)) * dt^2) - (dr^2 / (r / (r + R))) - (r^2 * do^2)
ds^2 = (-(r / (r + R)) * dt^2) + (dr^2 / (r / (r + R))) + (r^2 * do^2)

Taking r =0 I get dT^2 = -infinity*dr^2 and ds^2 = infinity*dr^2
This is a singularity Zanket!

Professor_Fink

Or are you saying that nothing can ever reach r=0?

If that is the case you have a major problem. How can the spacetime even arise. How does the central mass reach that position? What about if the mass is zero? This gives R=0 and you're back to flat space. This is fine. But what happens if you have vacuum fluctuations? Well, you'll get spontaneous productions of electron/positron pairs, etc. Consider what happens to one of these. They occupy different positions in space and each will have your proposed space time in its immediate vicinity. As such they can never anihilate, as they should do, and the vacuum starts pumping out particles from nothing.

This is interesting because it violates conservation of energy, but also because it means that matter would be produced all around us all the time, at a constant rate. It isn't!

Last but not least, it would prevent the formation of BECs, since no two particles could be made occupy the same space. Unfortunately for your theory, BECs can and do exist. So your theory does not agree with all known experiments, let alone full blown quantum field theory.

Zanket

Professor_Fink wrote:

Or are you saying that nothing can ever reach r=0?

Yes.

If that is the case you have a major problem. How can the spacetime even arise. How does the central mass reach that position?

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.

What about if the mass is zero? This gives R=0 and you're back to flat space. This is fine. But what happens if you have vacuum fluctuations?

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

Unfortunately for your theory, BECs can and do exist. So your theory does not agree with all known experiments, let alone full blown quantum field theory.

The only place that GR is incompatible with quantum mechanics is at a singularity. Then my theory need not predict BECs or the observations that quantum mechanics predicts.

planck2

now you are digging an even bigger hole, saying that what quantum mech predicts cannot effect your theory.

your spacetime is not asymptotically flat because the line element blows up at r=infinity.
Also it can't be because you have the spherical solid angle in the line element and not the surface metric of a 2-sphere

The action principle is important because this can tell you the dynamics of the theory , i.e. how particles move in the spacetime providing you with predictions you can match with experiment.

the sign usage is not the same, if the line element is +--- , LL convention, then you have spacelike for <0 and timelike for >0.this is how the different signs occur.

I disagree with you absolutely 100%. Why dont you write down the geodesics, and show me that causality is preserved.

planck2

If your metric is as I presume contains r^2*(dtheta^2 +sin^2(theta)*dphi^2). All I do to get it is replace -2M (-R in your language) in the Schwarzschild metric with 2M or R and swap g00 and g11.

Zanket

planck2 wrote:

now you are digging an even bigger hole, saying that what quantum mech predicts cannot effect your theory.

How so? Quantum mechanics doesn’t contradict the Schwarzschild metric, except at a singularity. Then it does not at all contradict the new metric, which precludes singularities.

your spacetime is not asymptotically flat because the line element blows up at r=infinity.
Also it can't be because you have the spherical solid angle in the line element and not the surface metric of a 2-sphere

I gave you a reference for the Schwarzschild metric. Did you look at it? The placement of do (the increment of a spherical solid angle) in the new metric is unchanged from that of the Schwarzschild metric. There is no difference between the new metric and the Schwarzschild metric that supports your “not asymptotically flat” argument. Fig. 3 shows that they converge as r increases.

The action principle is important because this can tell you the dynamics of the theory , i.e. how particles move in the spacetime providing you with predictions you can match with experiment.

As I noted above yesterday, the new metric alone tells one everything about the (nonquantum) dynamics for Schwarzschild geometry, just as the Schwarzschild metric does in GR. The vast majority of experimental tests of general relativity are tests of the Schwarzschild metric, not tests directly of the Einstein field equations or the Einstein-Hilbert action principle.

the sign usage is not the same, if the line element is +--- , LL convention, then you have spacelike for <0 and timelike for >0.

The reference I gave you for the Schwarzschild metric shows that the sign usage is the same.

I disagree with you absolutely 100%.

You also disagree with Taylor and Wheeler, so I don’t find your argument convincing.

Why dont you write down the geodesics, and show me that causality is preserved.

Nah, I still decline. The objectives that the paper meets are enough.

If your metric is as I presume contains r^2*(dtheta^2 +sin^2(theta)*dphi^2). All I do to get it is replace -2M (-R in your language) in the Schwarzschild metric with 2M or R and swap g00 and g11.

What is your point? Section 5 clearly gives the difference between the Schwarzschild metric and the new metric.

Son Goku

Zanket wrote:

As I noted above yesterday, the new metric alone tells one everything about the (nonquantum) dynamics for Schwarzschild geometry, just as the Schwarzschild metric does in GR. The vast majority of experimental tests of general relativity are tests of the Schwarzschild metric, not tests directly of the Einstein field equations or the Einstein-Hilbert action principle.

You're missing the point, a set of field equations are useless without an action.

For instance solve Maxwell's Equations in a given scenerio. This will give you the E and B fields.
However without the action of a nonrelativistic particle, this tells you nothing about the motion of things in response to those fields.

To put it in plain english, in your theory matter tells spacetime how to curve, but curved spacetime doesn't tell matter how to move.

What are your new dynamics?

planck2

no i don't disagree with Taylor and Wheeler, the sign convention is +---, Landau and Lif****z. I have it right here in front of me, along with Gravitation by MTW and General Relativity by Wald.

the point is i know how to get your new metric and it doesn't predict anything.

clearly they don't converge as r goes to infinity.



you are missing the fundamental point which is that the EH action allows one to predict the equations of motion for the particle which can be tested against experiment. Therefore I need an action to determine the theoretical equations of motion so as to test them against experiment. You don't provide one. So how am I to believe you?

the increment of solid angle is not used any where in the Schwarzschild metric, the metric for the surface of 2-sphere of radius r is though.

planck2

your theory doesn't need to predict BEC's or any of QM's predictions because neither does Einstein's.