decraig

ok, ok. My oversight. I couldn't figure out your use of the prime. Not a change of coordinates but a schematic derivative.

In any case, It makes mathematical sense, of course. But can you describe the physical frequency?

I don't know what F( R ) theories are.

As you might have suspected, I heard of this on your web site

Thanks for your help. I only object to the designation "source", in presuming charge causes fields. This is not well-thought physics, but I know everyone thinks this way. They might invoke Biot-Savart. Given some effort, I think we could come up with something that says, with equal weight, that fields cause charge.

by the way, I found the electromagnetic lagrangian for a line integral for discrete charges in Jackson's classical electrodynamics text (chapter 12). It's a start. I want the lagrangian density for charge/current fields. I might have a program to follow. I take Jackson's relativistic Lorentz force equations for discrete charges and raise them to covariant densities.

I'm not a mathematician. Could you define your terms and operators,please?

Add enough dimensions and you explain anything.

Look at string theory. What a mess of mathemagic.

I like the discussions of infinite vs. finite universes. I see that there is a barrier between the infinity of mathematics (the theoretical) and the extant universe, or universes (the real). This calls into question is there even an infinity in mathematics? If there is a limit to the rate of any calculation set up by the underlying logic of the universe, than only an "approaching infinteness" can be achieved even in the theoretical realm of mathematics...so the real universe(s) seem less likely to posess any infinities in them, if the underlying mathematical information is limited to non-infinities. However, I see the realm of math as have a defacto infinite possibility within it. Not true infinity, but as infinite as the underlying sub-structure of mathematical constructions, or logic itself, allows and that this heading towards infinity in a theoretical realm, translates into the real universe's plank scale basic increment of time that keeps everthing from happening at once on this side of the theoretical / real divide.....edd

You have a lot of ideas churning; most my own as well. Are you aware of nonstandard analysis?

endercreeper dude:

In all you escapdes you have not defined once what you mean by :"angular motion" . Would you care to share?

G00d grief!!!!!!!!!!!!!!!!!!!!!

 

I should never have started this frikin thread.

 

Those who have an piss ant's education in relativity beyond the special theory, raise your hands.

 

Those who don't, but are in love with black holes, can count themselves among the faithful, unthinking followers of authority.

 

 

 

 

Do you really want to understand the mathematical underpinnings of general relatvity?

No one will care.

Is this the naked singularity requiring infinite energy density, or have you got something meaninful?

 

This is a very good point Airbrush. I've wondered also.

 

If you could instruct me how black holes could produce jets, and not incipients produce jets, I would appreciate it

 

 

A

Sorry Airbush,and...i think someone else. too. I can be a horrible person. I have not excuse.

If you read this, please forgive; there is nothing wrong with you, only me.

In explanation, (no excuse),I become over impassioned. It is my failing

consider for a moment, Bruce. There are no source terms. This is bullshit.

No insult to your person implied. There is no one on this forum that respects you more than I.

I don't mean to imply the the mathematics is nonsciencical, but the physics in meaningless.The implication in such language is that charge causes fields. There is no causality in this: charge does not generate fields an more than fields generate charge. This is 20th century thinking.

Sorry. I got carried away.

"My theory challenges the long-held paradigm, that the asteroids did not have a planetary origin."

I didn't know this was the common belief. Can you be more specific about your idea?

There seem to be some major hurtles yet outstanding in the formation of our solar system. Perhaps you have a good idea.

But I will tell you one thing Bignose. If you cant do the math, get out of the fire, or lose your dignity. It won't be the first time I've seen this. The calculus is intrinsic to modern physical science (Blame Newton, Leibniz and one hundred others for daring to divide by zero). Your ideas may be exactly right. But if you cannot express them in mathematical terms, no one will take your rhetoric seriously. And if someone else also thinks of your idea, but who does know the math, you will get all huffy-puffy claiming your theory was stolen. I'm just telling you how it is.

No one will care if you cant do the math. And you better darn well keep your logic straight, or people like me will have you for lunch.

What is Ostrogradski instability?

In formulating a Lagrangian of gravity, I have many terms to choose from.

In a highly schematic notation the usual form of a Lagrangian might be,

[math]{D_{*}}^{2} X\times D^2 X + \frac{1}{2}( X \times D^3 X)[/math].

D respresents derivatives of spacetime displacements, and the X are spacetime coordinates. Alpha is a scalar constant to be determined.

But there are an infinitude of higher order derivatives to choose from. There are products of these terms that are perfectly happy to sit within a Lagrangian with consistent dimension.

It would be nice to know if Ostrogradski instability precludes these terms.

Fracturing crude oil is not exact art. An assay would find heptane and octane already present in diesel fuels. And probable in quantities greater than one part per thousand.

In following quoted article, Penrose examines the collapse of matter toward an r=2m event horizon.

Rodger Penrose,

Gravitational Collapse and Space-Time Singularities

Physical Review Letters, Volume 14, #3

“Before examining the asymmetrical case, consider a spherically symmetrical matter
distribution of finite radius in C³ which collapses symmetrically. […] Note that an exterior observer will always see matter outside r =2m, the collapse through r =2m to the singularity at r =0 being invisible to him.

After the matter has contracted within r =2m, a spacelike sphere S² can be found in the empty region surrounding the matter.[…]”

In the first paragraph Penrose recognizes that matter will not collapse to the event horizon in finite time in the coordinate system of an exterior observer. In the second paragraph he goes on to examine this collapse, anyway, in a coordinate system where the metric is well behaved, then continues onward to examine the interior solution.

In this article my objections to transfinite time of collapse are unaddressed. It sees to be either glossed-over or not recognized in going from one paragraph to the next. No references to previous work were made to fill this void.

A similar examination of a 1970s Hawking-Penrose article was equally disappointing.

The elements of the 4-velocity have dimension [D/T].

The vector itself with bases included has dimension [1/T] in the usual representation.

But if we use a metric tau^2, then the vector has units [D/T^2].

I hope you see something I don't see.

F^*F the is the electromagnetic energy density term.

J^A is potential energy of field acting on charge, so we already appear to have an interaction term. ??

Maybe I shouldn't have used the term "dynamical." I tend to use arcane language. It's kind-of a fuzzy term.

In any case, it implies forces. Maxwell's equations don't give us any forces. The Lorentz force does.

But the background is not Newtonian physics but relativity, so we probably won't see dp/dt without some effort, but a Hamiltonian formulation. Just guessing.

dS/dA=0

David Hilbert solved the vacuum solution of general relativity.

I haven't bothered to solve for spatial curvature due to electromagnetism. However Hilbert points the way.

Over all possible 4-volumes of spacetime [math]\int F^*F[/math] is minimal in vacuum with respect to the electromagnetic vector potential.

F is the Faraday tensor with lower indices. *F is the Hodge dual of the Faraday tensor. (^), is the wedge product operator--reference Grassmann algebra and the exterior calculus.

The result is an untested conclusion of general relativity.

I don't know what "carrier of gravitational field" means.

As we are aware Richard Feynman proposed that a particle can take any path in a double slit experiment (albeit hypothetically) but ultimately probabilities resolve to a deterministic pattern (interference pattern).

 

Actually, he doesn't. Feynman's QED is about fields, not particles.

Now, it is also true that he admits to thinking in terms of particles and talks about particles, then tells us that he has made a slip and that he is prone to do this noticing his mistake.

You implicitly suppose, in spherical symmetry, that a particle (or worse, two particles; not a "single quantum" here) is described by one single wave. This is not the case, for instance with entangled photons, who can be of linear or circular polarization; a single wave does not explain the correlation both in linear and in circular detectors.

 

If you properly describe the spherical symmetry as a spherical distribution of possible waves, then these individual waves have the proper spin, polarization and so on.

Not spherical symmetry, but radial symmetry.

A particle is described by a single non-particulate field, so I'm not sure why you seem to be arguing differently. Again, I get the argument about detectors or measurements.

Detection breaks symmetry. You are changing the scenario. Once measured, or detected the mass/energy of a quanta has no issue. The issue I present is before measurement.

I'm perplexed. It seems to be a standard way of thinking among amatures that fundamental particles act like little bee-bees. But no theory beyond bohmian mechanics supports propagation of particle-like matter. And bohemian mechanics has it's own issues requiring field propagation as well as particulate matter, and has other problems.

I think the confusion in particle physics stems from the naming. It shouldn't be called 'particle physics' at all. 'Wave mechanics' would be closer.

I suggest watching the Feynman lectures he gave in New Zeeland. http://www.youtube.com/playlist?list=PL5DB4C82BDD7375E4

Reference http://en.wikipedia.org/wiki/Lagrangian

Toward the end of the article is are sections titled,

"Electromagnetism in general relativity" and

Electromagnetism using differential forms".

I happen to use forms. Though the argument is just as valid in the standard notation up to a difference in parity. Both are generally covariant.

Through the usual method, we can derive maxwell's equation, and define electric charge assuming charge/current density is invariant with respect to the vector potential.

This is somewhat disappointing. Rather than obtaining the dynamical laws of electromagnetism, all we seem to get are maxwell's equations. However, the implicit assumption of the independence of charge/current with respect to the vector potential seems to be, itself, a dynamical constraint,

[math]\partial J / \partial A = 0[/math].

These are 16 constraints.

J is the charge/current density 4 vector, or charge/current density three-form

A is the vector potential, or covariant one-form.

I'm having a difficult time seeing if this leads to the lorentz force.

In the common representation, the mathematical structure of general relativity builds upon vectors. Specifically, Riemann geometry incorporates the notion of tangent vectors. (See "vector space".)

The four-velocity generalizes three dimensional velocity, v to include time:

[math]V = (\gamma c, \gamma v)[/math]

To be useful in curved spacetime, we need basis vectors. Velocity is represented as a contravariant vector with the basis normalized to distance.

It has dimensions of frequency[1/T]

D: distance

T: time

The covariant velocity has dimensions of [D^2/T].

(I'd put it all in LaTex, but the parser on this forum seems to be broken.)

Is anyone else uncomfortable with the units? Or perhaps thinks it could be done better?

As time slows in the trajectory of an object falling into a black hole to an outside observer, the redshift makes the object disappear, but if somehow you were able to still see it, the object continues to fall in a slowing finite manner....not stopping completely, [bold added] and would continue to fall in it's trajectory for the duration of the universe's existence... and that the object would "see" itself, fall right in...in an increasingly rapid finite manner.....isn't this the ultimate example of time dilation?

No, not stopping completely. See my post #29.

Maybe you're getting the idea. We are comparing things of transfinite ratio. This is, after all, why these things are called singularities. In one inertial frame an event has a single spatial and temporal coordinate. In another, there are an infinitude of coordinates. If we were mathematicians we would say that the coordinate systems are not one-to-one.

Yes. This is exactly the problem.

What does an infalling observer perceive vs. the exteranal observers perception. In the common perception an event that occurs to one observer is an event that occurs to any other observer. Usually this is the case. But this not universally true. but coordinates in which the black hole disappears from existence (Rindlard horizon) are beyond the kin of you'll, and plays no part in this argument.

You must consider the transfinite ratios of things.

I don't see how all three are related.

 

The expansion of the Universe is a global thing, local gravitational fields can overcome this and so we can have black why

no problem. Give it a day or a week or more, and get back to me. This is not an easy thing to consider.

You piss me off ajb, but I respect you all the more because you want to know if my crazy rantings, in your understanding, are really crazy after all. I don't think you are the pedantic thinker expected of you in the context of this forum. Send me a private email if this is so.

btw, I'm too poor to subscribe to the professional journals.

By the way, I love your icon/pic. We take so often take ourselves too seriously. I do. Will you send me a private message? I don't know how.

Penrose, R. (1965). "Gravitational Collapse and Space-Time Singularities". Physical Review Letters 14 (3): 57.

 

Hawking, S. W.; Penrose, R. The singularities of gravitational collapse and cosmology.

Proc. Roy. Soc. London Ser. A 314 1970 529–548.

I don't have access. Please post the relevant information. It is legal to do so if properly attributed.

I have supplemented my post #35. Read the last line. How do you address it?

The scientific consensus don't agree with you, the standard black hole model is a well established part of mainstream physics.

 

So you claim. Reference me an article addressing

black hole formation.

You are the one making extraordinary claims. Not I.

The discrepancy in observations could be more dramatic than that. The person entering the back hole observes himself just falling in uneventfully, but the observer watching him from outside the event horizon observes him being incinerated near the event horizon by Hawking radiation. Such is the assertion made by Brian Greene in his book "The Hidden Reality".

And there is more. According to current theory of dark energy, the very atoms of an infalling observer, and even his nuclei will be torn apart by dark energy infinitely sooner than he will enter the black hole.

Now, I'm not real big on dark energy, and consider it might be a failure of general relativity, but if you are a standard thinker then you could be comforted to know that the consensus of physicists must concede that nothing will ever cross the event horizon but thru spacelike displacements according to the point of view of an external stationary observer such as us on Earth.

I'm try to be concise, but "spacelike displacement" in this context means information travels faster than light. This is no small thing, and our consensus of experts would say this in not a element of established physics.

This is difficult to explain. (I've been trying to get it across for over 34! posts back.) The accepted foundations of physics preclude existence of black holes. These three accepted beliefs are incompatible.

In other words you cannot claim that all three of the following are true because claiming two of them will preclude the remainder: 1) The universe expands at an accelerated rate (dark energy), 2) Information propagates at less than the speed of light, and 3) Black holes exist.