Hello Richard:

You referenced the Shapiro time delay. I'll have to look into it (try and read through Will's book which is tough sledding), but I believe the only part that does depend on strong fields to 2.5 PPN is the loss of energy from gravity waves. That not only depends on the 2.5 PPN coefficients, but the masses and distances one puts into the system. Since GEM is all of 12% different at that order, I bet one could make a slightly different binary model that was consistent with the data.

doug

Hello:

I am going to work through a calculation involving gravity waves. I will be paraphrasing the paper "Relativistic Scalar Gravity: A Laboratory for Numerical Relativity" by Watt and Misner, gr-qc/9910032v1. For those who do not read papers that are this technical, I hope to give you a sense of what is going on. The big picture conclusion is that the GEM calculation is darn similar to the one for GR. Being the skeptic, I will tell you my objection to the exercise at the end.

The power of a gravity wave is tiny because there is a factor of G⁴/c⁵. One needs to look for places where there might be a great deal of gravitational energy changing hands. A candidate is mass that dives into a black hole. What we will do is to find the smallest, stable circular orbit for a black hole. Here goes!

Write out the exponential metric:

dτ² = exp(-2 GM/c²R) dt² - 1/c² exp(2 GM/c²R) dR² - R²/c² exp(2 GM/c²R) dθ²

Divide through by the interval:

1 = exp(-2 GM/c²R) (dt/dτ)² - 1/c² exp(2 GM/c²R) (dR/dτ)² - R²/c² exp(2 GM/c²R) (dθ/dτ)²

Look at what we have: a term with a dt, dR, and dθ, but only R appears in their coefficients. This means that there will be two conserved quantities, energy E and angular momentum L. The normalized to the test particle energy and angular momentum (normalized so that E and L are dimensionless) are:

E = exp(-2 GM/c²R) (dt/dτ)
L = R²/c² exp(2 GM/c²R) (dθ/dτ)

Plug these definitions of constants back into the interval expression:

1 = exp(2 GM/c²R) E² - 1/c² exp(2 GM/c²R) (dR/dτ)² - exp(-2 GM/c²R) (L/R)²

Now there is only one partial derivative, so solve for it:

(dR/cdτ)² = E² - exp(-2 GM/c²R)(1 + exp(-2 GM/c²R) (L/R)²)

The effective potential is the square root of the last term of the above expression. One can plot the potential for different values of L/R. Toss in a value of 4, and you can see a small pit in the potential:



Time to go extremum hunting. Take the derivative with respect to R, and solve for L. To be honest, Mathematica found this to be a trivial thing to do (Solve[D[veff, R] == 0, L]), but I could not work through those details myself.

L = R exp(GM/c²R) (GM/c²/(R - GM/c²))

Now we look for the minimal value of R for this minimal L. The setup is just like before, take a derivative, set it equal to zero, solve for R, and again the details are beyond me, but the answer is:

R = 3 + sqrt(5) = 5.236

If one were to do this same calculation for GR, R = 6, a difference of 12.7%.


Now my critique of this class of exercises. You notice in the graph that things are pretty darn flat, and then the graph crashes. Those who read deep into the literature of black holes know the Schwarzschild radius is a mirage based on the choice of coordinates, and can be whisked away by those highly skilled in the mathematical arts. An esteemed pair of physicists in England was able to show that the singularity cannot be avoided: the land of infinite tidal forces would greet the unfortunate surfer going past the Schwarzschild radius.

For me, the math that says the tides become infinite also tells me that that the math must change. We must go from a relativistic gravity metric (indicated by the constants c and G respectively), to a relativistic quantum gravity metric, which if we had one, would have c, G, and h. This is the transition that must be done, seamlessly. We don't have it yet, that is certain. Until we do, it is my opinion that all this work with black holes is wrong. That cannot be a popular position, but I hope the gentle reader will see it has to do with the logic of physics, and nothing here is personal.

doug

I agree with this, at least in as far as that of a body of mass collapsing to a singularity. As I have stated before, my simple thinking is that the total energy within the body is specific and will remain constant. The energy per volume, then, is the internal pressure. Apply this to the area of a particle on the surface, and we have the force directed outward. The gravitational force on the particle on the surface is the force directed inward. But since the internal pressure is inversely proportional to the cube of the radius while the gravity is only proportional to the square, the force directed outward climbs much more rapidly than that of the force directed inward upon collapse, and will prevent the body of mass from reaching a singularity at some point. Any thoughts on that?

__________________
Let's put together the pieces of The Grand Puzzle . (website)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."

...see, all it takes is one statement like this, and...

I'll let you answer grav's (and numerous others) querry of degeneration past Neutron stage to 'real' black hole status first, and then I will querry another possibility

__________________
RussT
________________________________
Everything is, as it should be, otherwise, it wouldn't be!

According to energy conservation a star can not collapse till the kinetic energy is radiated out. A Black Hole Like Object is a closed system (more energy absorbed than emitted).
There is a balance between potential gravitationally energy and kinetic energy inside the Black Hole Like Object.
The energy conservation prevents to collapse into a singularity, I suppose.

Hello Grav:

Energy, 3-momentum, angular momentum and electric charge density are all conserved for all objects in the Universe, even very dense small ones. I am not willing to go along with this speculation:

My post was based on dimensional analysis, the units needed by the equations that come into play. When there is a relativistic quantum gravity metric - one with c, h, and G - then the way it behaves will determine the dependence of the forces involved. There is certainly a chance that some or all of your speculation is true. Without the relevant equation, I am not willing to guess. I am willing to play Megabucks once in a while to support the state, but don't gamble on physics algebra. I need Mathematica's stamp of approval to get over my own self-skepticism.

As I understand the singularity theorems of Hawking and Penrose, the singularities of frozen stars (as they were known in the early days), cannot be avoided. I am not the first one to suggest that perhaps quantum gravity comes into play at that time, but I am not familiar with people who point out the implication of that switch in the metric: it means smallest stable orbit calculations are highly suspect because all the algebra changes due to a different metric. Everything in calculation #62 flowed out of the metric in play. Change the metric, and all the algebra changes.

doug

Nifty job with the graph, thanks.

correct so far. Next step would be?

__________________
I once put instant coffee in a microwave and nearly went back in time - Steven Wright

Hello:

In this post, the math should be both easier and more profound than the stuff on gravity waves, a dual winner!

In his book, "Not Even Wrong...", Peter Woit argues that any new proposal for how to deal with gravity must have some new guiding symmetry principle. That is what I hope to show you today.

There is another unspoken reason why professionals may not bother with a proposal to unify gravity and EM: there is also the weak and the strong forces, and without them, there is no meaningful unification. I'll bring them on board too.

My central thesis is that to account for 4D events on the 4D differential manifold of spacetime requires the use of quaternions (basically like 3 complex numbers that share the same real, and an i, j ,k. Wikipedia for more, or scan my site, quaternions.com, or youtube for quaternion animations). It is the properties of quaternions, many of them unfamiliar, that dictate the kinds of mathematics seen in theoretical physics, from special relativity, to gravity, and out to the standard model.

For a complete description of patterns of events in spacetime, you must define two things:

1. Those things that change in a way we understand (jargon: covariant quantities)
2. Those things that do not change in any way (jargon: invariant quantities)

Take for example Michelson and Morley's experiements. The invariant quantity is the speed of light c. What is covariant are the wavelength and the frequency of the light bouncing between the mirrors. In the direction of the spinning Earth, the wavelength has decreased, and the frequency has increased. It turns out that the amount of those changes - which can be measured - exactly cancel each other out so the velocity c is the same. Once I found that out, I was much more at peace with the experiment (something should change, and, well it does!).

What are the invariant and covariant quantities for folks in a gravitational field? In GR, and in GEM, the interval tau changes for people located at different places in a gravitational field, so it is a covariant quantity. Finding the invariant requires more investigation.

Measure an interval, (dt, dx/c, dy/c, dz/c). Square it using the rules of quaternion algebra:

(dt, dx/c, dy/c, dz/c)² =

(t² - x²/c² - y²/c² - z²/c²,
2 dt dx/c, 2 dt dy/c, 2 dt dz/c)

The first part is the interval. The second 3 terms don't have a name. Cool! Makes it feel like this is a discovery! I'll call it a 3-rope to make fun of people who work with strings.

If you are an inertial observer, and you change your inertial reference frame as happens in special relativity, then the interval is invariant and the 3-rope is covariant (we know exactly how it changes). In my GEM proposal, it is the interval that is covariant, and the 3-rope that is an invariant when the non-inertial reference frame is changed due to gravity.

t² - x²/c² - y²/c² - z²/c²,
Invariant for inertial observers
Covariant for non-inertial observers

2 dt dx/c, 2 dt dy/c, 2 dt dz/c
Covariant for inertial observers
Invariant for non-inertial observers

Neat!

If we write a current J as a quaternion, what kinds of symmetry does it have? Quaternions form a group under addition. They also form a group under multiplication if zero is omitted. If we concentrate on the standard model, it would be noted that the group SU(2) is also known as the unit quaternions. Algebraically, it is formed like so:

element of SU(2) = exp(J - J*)

That exponential always has a norm of 1. This depends on 3 of the 4 numbers in a quaternion because the subtraction disposes of one of the terms. Technically, one would say there are three generators for the Lie algebra su(2) [there is a difference between the continuous group SU(2) is capitals, and its corresponding finite Lie algebra su(2), lowercase].

A quaternion J has more than just the group SU(2). A second element in the standard model is the group U(1). It usually goes by the name of complex numbers with a norm of 1. This group is Abelian, a fancy way to say ab = ba because members of the group commute.

Choose two quaternions at random, and they do not commute because there is a cross product as part of the product. If two quaternions happen to point in exactly the same direction, then the cross product will be zero, and those two quaternions will commute. A quaternion will always commute with itself.

element of U(1)xSU(2) = J/|J| exp(J - J*) = exp(J - J*) J/|J|

Writing out the current as a normalized quaternion generates the symmetry of the electroweak force. It is not that I happened to add these groups in, rather they arose from the properties of quaternions themselves.

Now imagine two quaternions interacting like so:

J* J' = (J/|J| exp(J - J*))* J'/|J'| exp(J' - J'*)

For those folks paying close attention, this current-current interaction came up in post #1 where I tried to justify spotting a spin 2 particle in the current coupling term. The quaternion product J* J' does not have the same multiplication table as a standard quaternion product. I call this the Euclidean product, and it is not associative, since (a b)* c is not equal to a* (b c). The products point in different ways, although their norms are the same. There are 8 generators in this group which has a norm of 1. Sounds like a way to represent SU(3) to me, the symmetry of the strong force.

In the standard model, there are 12 generators for the symmetry U(1)xSU(2)xSU(3). What I am proposing is a smaller model, with only 8 generators, the norm of two sets of U(1)xSU(2). This is consistent with the observation that one can isolate photons, W and Z particles, but not the 8 gluons due to quark confinement. OK, now I am lost in the math, so I'll stop here.


To summarize:

If a quaternion is squared, there is an interval and a 3-rope. For a pair of observers, if the interval is invariant, then the observers are both inertial. If the 3-rope is invariant, the pair of observers are in a gravitational field.

Write out an interaction for two normalized quaternion currents, and it will contain the symmetries of EM, the weak, and the strong forces.

Working with quaternions appears to be worth the costs.

doug

And this should be even more evident when it comes to MBH's and 'initial conditions' for how the universe could be working!

I am going to assume that 2 things are correct.

1. SMBH's/MBH's Exist. (Not Big Bang theory Dependent)
2. "Extra Gravity"/Exotic Matter exists (Needed for galaxy rotation curves and cluster dynamics...also Not Big Bang theory dependent)

Then I am going to just straight to...
Which basically says that the maths for a quantum gravity application have NEVER been developed correctly to show with any accuracy what is "Really" going on in the universe, galaxy rotations, and even in solar system dynamics IMHO!

SO, here is why (of course IMHO) the correct maths have not been able to be shown/developed...

When Einstein was developing SR, he only had enough information to get half of the concept correct...that being that light travels at "c" in Vacua/Empty Space. And that part is absolutely true! At least in the way Einstein considered 'empty space'/Vacua...however...

There was/and still is if you are honest/real/brutally honest as Feynman would say, a 'real' question as to the possibility of an Aether/Medium being present that would/does 'carry photons' in one way or another.

I will automatically stipulate that mainstream has been correct to deny every 'Aether/Medium theory' that has ever been presented, wave or otherwise!

However, That and the MMX has NOT proven or even negated the realization that a Medium that carries photons does not exist!

The MMX ONLY negated/showed that a 'stationary Aether/Medium' or a "River/Wind" directional Aether/medium DOES NOT EXIST!!!

BUT, if that 'extra gravity'/Exotic Matter/Point Particle/Non-Baryonic DM, that is collisionless and goes right through all baryonic Matter, isn't really 'extra gravity' BUT ALL of space...THEN the ONLY reason it is being thought of like it currently is, IS because of "Interpretations" based on Big Bang Initial Conditions!!! Or more precisely the CDM model...which is a 'hypothesized' WIMParticle!

SO, 'if' that 'extra gravity' is Neutrino-like, with an infinitesimal mass, traveling a "c" in Every/All directions, and carries the photons, THEN the MMX would find a Null result automatically.

SO, sweetser, you correctly brought up 'dimesional analysis', and this brings us to the information that Einstein DIDN'T have when he developed SR...

That being that "SPACE" (His "Empty Space") is made up of "Non-Baryonic Point Particles" traveling at "c" in Every/All directions that IS a "Dimesionless Background Gravity Field" (I can show you where this "Dimesionless Background Gravity Field" concept has been developed, BUT numerous erroneous conclusions have been drawn from it, including the 'directional aether' concepts that I have already agreed are wrong!)

NOW, 'one' of the things that tells me this is correct is...

It is absolutely "Impossible" that an electron can "Accelerate" a massless photon "Instantaneously" to 186,000 mps!!!

Also, believe it or not, this "Gravity Field" that 'space' is made of is exactly how SMBH's get created, with their millions to billions of sol masses of gravity~

__________________
RussT
________________________________
Everything is, as it should be, otherwise, it wouldn't be!

Hello Russ:

In a forum such as ATM, one observes that going against specific sets of belief for specific reasons seams to invite other ATMer's to join in with their different objections. I'll point out the number of places where we do not join hands in the struggle against the physics oligarchy.

I believe these are "Super Massive Black Holes" and "Massive Black Holes". My point was to say that the math we use to describe these is good up to the point were a new metric we don't have must take over. I agree that there are places with lots of mass in a small volume. I am arguing that they do not exist with the kinds of math we have today to characterize them.

Please scan post #50. I am doing research in this area, focused on a particular partial differential equation:

m d2 R/dt2 Rhat + c V d m/d |R| Vhat = - G M m/R2 (Vhat + Rhat)

Here gravity works in a new direction, Vhat, and does its change in momentum by changing the distribution of mass with respect to distance. This equation is classical gravity in the Rhat direction since that involves only the constant G. It is a relativistic gravity effect along the Vhat direction since there is both a G and c. There is no quantum relativistic gravity here.

One reason to have hope is that the Modification of Newtonian Dynamics (MOND) proposal had a new force law when acceleration got tiny (>10^-10g I believe). The factor of c in the Vhat direction may let it kick in for a similar small amount. MOND cannot save the day due to observations for one galaxy passing through another. The gravitational mass based on the star light is in a different location than the gravitational potential. By having 2 vector terms instead of one as in classical Newtonian gravity, it may be possible to get this kind of separation in the proposal. Still, this is an area of study, nothing more.

For very specific, technical reasons, when I look at my action, I deny the need for a Higgs particle, although the good folks working on the LHC hope to show me wrong. As soon as I apply the above gravity equation to the rotation profile of a galaxy, I will deny the need for dark matter, although good people are looking for it. Nothing in my work suggests a need for an Aether, so, to be consistent, I will also live happily without an Aether.

It is true Einstein did not know about the Higgs or dark matter, but I don't think either of them will stand the test of time.

This is not how things work in quantum field theory, a topic that is darn hard to understand. Two electrons can exchange virtual photons. Because they take this action, they are able to scatter away from each other. If you are referring to a electron meeting a positron and becoming 2 gamma rays, such a process is governed by the uncertainty principle. Folks working in quantum field theory do make sure nothing can happen instantaneously. You can often spot this by a simple d/dt in the equation, which shows there is a time dependence.

I am amused on my bicycle when I can through a bit of pedaling make a few photons head out far faster than I will ever go. I don't really understand the magic of generators, but I have seen it happen.

One of my hangups is never to talk about space, only spacetime. GEM is the simplest 4D wave equation in spacetime. The simplest solution is the no mass solution, flat, empty old Minkowski spacetime. Put it the smallest bit of mass, and you get a simple harmonic oscillator. That is what the Earth has been doing around the Sun for 4 billion years: oscillating once a year. I'd like to oscillate around the center of the Earth, and I would do so if all the other stuff in the room didn't have the exact same goal. I think GEM is physically reasonable, which makes it unusual in the landscape of theoretical physics today.

doug

Hello:

My education on GR has been spotty. I did read all the way through Sean Carroll's GR lecture notes, trying to take good notes of those notes so I would have a deeper understanding of the theory. I was unaware of one of the technical weaknesses in the proposal (which someone on physicsforums educated me about). You can read about the issue of spin angular momentum here: http://en.wikipedia.org/wiki/Einstei...3Cartan_theory

Einstein's theory is wonderfully symmetric: from the Ricci tensor to the metric, there is nothing but symmetric tensors. That makes sense since the goal is to describe how a dynamic metrics changes. This creates a problem: there will be forms of energy that cannot be described by a symmetric tensor, such as spin. The Christoffel symbol is also a symmetric animal. One way to deal with this issue is to allow the connection to have torsion. I cannot follow the details, but it is a way to let antisymmetric contributions into the action. This is known as Einstein–Cartan theory.

GEM theory does not have to altered one bit. There is already an antisymmetric tensor as part of the action. It would appear like spin orbit coupling is more "naturally" handled by GEM.

doug

In general relativity, the gravitational field is characterized by a symmetric rank-2 tensor, the metric tensor. The possibility of generalizing the metric tensor has been considered by many, including Einstein and others. A general (nonsymmetric) tensor can always be decomposed into a symmetric and an antisymmetric part. As the electromagnetic field is characterized by an antisymmetric rank-2 tensor, there is an obvious possibility for a unified theory: a nonsymmetric tensor composed of a symmetric part representing gravity, and an antisymmetric part that represents electromagnetism. Research in this direction ultimately proved fruitless; the desired classical unified field theory was not found. http://en.wikipedia.org/wiki/Nonsymm...ational_theory

in 1995, Moffat noted that the field corresponding with the antisymmetric part need not be massless, like the electromagnetic (or gravitational) fields.

The antisymmetric tensor field is found to satisfy the equations of a Maxwell-Proca massive antisymmetric tensor field. Furthermore, the theory permits one or more "running constants": it allows the mass of the antisymmetric field, the coupling constant between the antisymmetric field and matter, and the gravitational constant to vary as functions of space and time coordinates. In other words, NGT can be described as a theory that involves a symmetric tensor field (gravity), an antisymmetric tensor field, and one or more scalar fields. In this, the theory bears superficial similarity to the tensor-vector-scalar gravity theory (TeVeS) of gravity proposed by Bekenstein. To distinguish his work from Bekenstein's, Moffat calls this version of his theory Metric-Skew-Tensor Gravity (MSTG).
http://arxiv.org/PS_cache/gr-qc/pdf/9910/9910112v2.pdf

Do you think , Sweetser, the antisimmetric tensor field has a possibility to explain the gravity ?
Czeslaw

This is probably an oversimplification of things (and perhaps has/have already been explored and or discarded), but two ideas suggest themselves in considering some things from a 50,000 foot-level here w/regards to the discussion.

Has anyone ever considered that when the qualities/properties of space (or space time) and the elementary particles emerged as things got more and more 'organized' after the big bang that there was some 'co-dependent order' in how, when, and why they emerged as they did and approach things from that direction? Perhaps that would give some general clues?

Also, as it's apparently the interaction with the Higgs Field via the (hypothetical) Higgs boson that 'imparts' the quality of mass to matter, isn't that a likely place to search for some angle to unify gravity and SM w/QM)? It would seem naiively obvious to me that another hint could be that we've not been able to detect gravity 'waves' in space nor have we been able to detect the Higgs boson as of yet is that perhaps the reasons for both are related...?

Given that mass is the determining factor for the intensity of a gravitational field, well...it just seems reasonable that the suspected "guilty particle" should be able shed some light as to how/why gravitation arises and propagates as it does (and perhaps complementarily, those things could give hints themselves as to where to look). One problem is, as I understand it, the energies needed to probe those levels are not trivially achieved (115 GeV and higher, IIRC), but may soon be possible.

Anyway, just a late-night thought I'm tossing out...wondering if there's any relevance to it. or is it just high in nuisance value?

__________________
"...wait for the ricochet."

With the way they are treating "Time freezing at the event horizon" (For a distant observer) and the "flipping" of Time and Space on the interior, I can certainly sympathize with the bolded view.

However, this treatment goes directly to the T=0 and 'inside' solution of an expanding singularity with an 'horizon' that cannot possibly exist.

So, to get the maths you are looking for, for the Quantum Gravity, the SMBH's are 100% necessary. That IS where the 'Point Particles'/Strings/Gravity...the so called "Extra Gravity" is coming from.

But, I can see that we are not going to be joining hands in the struggle, so I will leave you to your search.

__________________
RussT
________________________________
Everything is, as it should be, otherwise, it wouldn't be!

Hello czeslaw:

There is a divide between GR to handle gravity, and EM, the weak force, and the strong force. I believe EM, the weak, and the strong force all use exterior