Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.

If I'm reading right, and my background is in experimental solid state physics, you are merely stating that the Schwarzchild metric is an approximation at low gravitational strength.

What you propose may get good agreement with experiment (as does Schwarzchild) but until large gravititional fields can be found and observed, you still lack evidence, right? There is research being conducted by astonomers on the rather large gravitational field at the galaxy center that may help shed new light.

BTW, Exploring Black Holes by Taylor and Wheeler is fantastic. I love their writing style.

After thinking about this a little, I'm confused.

The Schwarzchild metric is for a spherically symmetric, non-rotating mass and as such is a good approximation to, say, our solar system. Nobody argues that it is merely an approximation and breaks down when massive objects rotate rapidly. But this metric is not General Relativity.

You have "derived" a new metric from a "fixed" version of GR that contains the same predictions as Schwarzchild, but apparently doesn't break down for larger gravitational fields. The problem is, it seems from what you wrote, you are still assuming spherically symmetric, non-rotating mass to derive your metric. So even if your "fix" is right, the Zanket metric would still break down for rotating mass, especially at higher gravitational fields. So your cosmological conslusions are unjustified.

The Kerr metric assumes rotating symmetric bodies. Experiment has shown that very massive, fast rotating binary pulsars can be modeled using the Kerr metric to within experimental error. And no "fix" of GR is needed. Try deriving the Kerr metric with your fix of GR and see how it compares. I do not envy you in this task.

Zanket, where are the field equations for your "fix"?

The following is Einstein's field equations:



where the term on the left represents the curvature of spacetime and the expression on the right represents the matter/energy content of spacetime.

A metric is a solution of the field equations. Solutions are generally approximations based on assumptions since the equations are non-linear. The Schwarzchild metric is an approximation as discussed above.

(There are exact solutions, the problem being there are many. Though, the only valid solution would be the one that models the actual universe. The department chair at my alma matter is the father of the so called "Gowdy Universe." He simply found one exact solution for GR, it just doesn't jive with reality.)

If you want to define a new metric based on a fix of GR, you need to show your fix produces a new field equation. You then need to solve that field equation assuming non-rotating, spherical symmetry. Then you can compare it to the Schwarzchild metric. You do this, and I guarantee that it will at least be publishable in a math journal.

You cannot simply say that you have found a better gravitational distortion factor and then plug it into a metric that relied on the original distortion factor for its derivation.

BTW, Section 9 of your paper contains some algebra mistakes. The rest of your paper relies on this section.

Here is your derivation:

(1)

(2)

combining (1) and (2) yields:

(3)

or

(4)

Everything is OK up to this point. Next you say:

(5)

and therefore substituting (5) into (4) yields:

(6)

Here is the problem. This suggests the following: combining (5) and (2) yields:

(7a)

or, using (3)

(7b)

That is to suggest the following:

(8)

Of course, this is only possible when v = 0.

I fixed it.

Your eq. 7b is okay for v <> 0. Let v = 0.5. Then, by your eq. 5, γ = ~1.1547. Then the left-hand side of the equation = ~1.1547, and the right-hand side = ~1.1547.

I'm seeing empty space where it looks like equations go. All the equations disappear when I refresh.

I think I know what equations you put there, though. The derivation in section 9.1 is just a rearrangement of the equations in section 8. I equated a new symbol, veff, to v / sqrt(1 – v^2). That's not circular reasoning; that’s just algebraic substitution. Wherever you see veff in the paper, you can replace it with v / sqrt(1 – v^2).

Last edited by Zanket (2005-08-05 20:34:14)

It's okay to "define veff such that it must be equal to at", since that's just a rearrangement of the equations in section 8. veff is not claimed in the paper to be an actual velocity. "Effective velocity" is just a name given to the symbol veff. I don't substitute veff in Galilean or Newtonian equations. I just show that veff = a * t is a valid (relativistic) equation. Therefore a * t does not yield v, as Galileo and Newton thought, but rather veff.

Last edited by Zanket (2005-08-05 20:49:19)

The whole of (2) is relativistic, because this equation is just a rearrangement of the relativistic rocket equations. The variables a and t in (2) are from those equations. These variables as defined in the paper are compatible among Galilean physics, Newtonian physics, and relativity. (See footnote 8 referenced at the end of the first paragraph in section 7.)

Consider a relativistic problem involving a rocket accelerating at 1 Earth gravity as the crew feels, for 1 year in the gantry’s frame. Then, given the definitions for a and t in the paper, a = 1.03 ly / yr^2 (equivalent to 9.8 m / s^2) and t = 1 year. Consider the same problem in Galilean physics. In that theory, a = 1.03 ly / yr^2, and t = 1 year.

Even assuming it’s valid, the section in the paper on effective velocity fails because it raises red flags. You are not the only one to raise these issues. To forestall them from coming up again, today I removed that section from the paper and reworked another section. As you saw, veff is now k. The paper had previously claimed that effective velocity is synonymous with Newtonian velocity, so now k is defined as Newtonian velocity, and now there is no mention of “effective velocity”. The math is equivalent, save one less derivation, and the conclusions are the same. Hopefully I’ve made the paper more convincing; time will tell. Here is the paper. Please take a look. I’ve greatly appreciated your input so far.

Last edited by Zanket (2005-08-08 23:41:43)

”Chris” wrote:

You were claiming Galileon at is the same as relativistic at. It is not.

I claim that they are equivalent in the paper. How do you think the Galilean at differs from the relativistic at? The time t is the same in both theories; the gantry’s time is the same as Galileo’s universal time. The acceleration a can be measured in more ways in Galilean physics than in relativity, but the way it is measured by definition in the paper (the way it must be measured in relativity) is one of those ways. In the example I gave above, a and t respectively have the same values in both theories for the same story problem. I'm not seeing a pertinent difference that prevents an at in a Galilean (or Newtonian) equation from being equated to an at in a relativistic equation, as I do to derive eq. 3 in the paper.

I've looked at the new version, and it is much clearer now.

That’s good to hear, thanks. Your input helped on that.

Basically you are saying Einstein used a non-relativistic escape velocity to arrive at the gravitational distortion factor.

Yes.

I'm still a little concerned with how you just plug this new value into the old Scharzchild metric. It was my understanding that a proper metric was a solution to the field equations. and you have presented no field equations.

If Einstein had skipped creation of his field equations and instead just come up with the Schwarzschild metric, showing that it predicted Mercury’s anomalous orbital precession, which theretofore had not been predicted so closely with so simple an equation, would that have been an insignificant advance of physics? Physics is, above all, about predictions matching observations. To that end, field equations are just a nice-to-have. Einstein’s field equations are ad hoc, hence anything derived from them is ad hoc. That they do not necessarily make better predictions than other types of equations, then, should show that they are not a scientific requirement. People who work with GR are just used to seeing them. Field equations are just one type of an equation. Any type of equation that makes a prediction is acceptable in a theory.

There are texts that say essentially that a proper metric is a solution to the field equations, but that’s only in the context of GR. In other words, a proper metric in GR is a solution to its field equations. The paper shows a flaw of GR, invalidating it, and then builds a new theory of gravity in the form of a standalone metric. The paper is not beholden to the way metrics are derived in GR.

Anyway, I'd still prefer to pass final judgement on your theory when it has been peer-reviewed by Gravity Physicists.

I’d like to get it peer-reviewed too, but there’s not much chance of that. From what I’ve learned, while journals officially review papers from uncredentialed people like myself, unofficially they automatically reject them for that reason. Even the odds of getting the paper onto arXiv, a non-peer-reviewed repository, are slim. Science is unofficially a credentialed-members-only club. By positing that, I’m officially a crackpot, so it’s a perfect system.

I've had to re-learn a lot about general relativity duirng this conversation, so thank you for that.

You’re welcome. I got gypped, ‘cause I still know nothing about solid state physics.

When I have some time, I will try to read it.

I think this thread should be studied by most of the other "theory promoters" out there. I don't necessarily have a closed mind when you can at least show some understanding of fundamental physics and mathematics.

You're still a crack-pot of course :p

No, it isn't based on that at all.