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Gravity

Dr. Tom Van Flandern's Meta Model of gravity describes a Universe where masses are pushed toward one another by tiny particles, rather than being pulled toward one another by a miraculous force.
Here we are talking about this theory, how it compares to Newton's theory of gravitation, and also to Einstein's theory of general relativity.
we're also really confounded by the fact that gravity appears to have an effect on objects at a distance instantaneously.

BOOKS

George and I recommend these fine books relating to Gravity and General Relativity:

Dark Matter, Missing Planets, & New Comets
by Tom Van Flandern
Van Flandern begins this book by introducing you to a fundamentally different view of the universe, embodied in his Meta Model. He also touches on a number of his other pet theories, all of which are somewhat at odds with current thinking in Physics and Astronomy. Many of his ideas are quite thought-provoking, and his theories about comets seem to be supported by some of the latest cometary observations made by spacecraft.

Black Holes and Time Warps
by Kip Thorne
Thorne is the Feynman Professor of Theoretical Physics at the California Institute of Technology. The book is great! He begins with a 30-plus page science fiction story about a starship and crew investigating black holes. It turns out that Black Holes are really great ways to describe General Relativity, since near a black hole, everything is extreme. Dr. Thorne sets out to explain relativity, time warps, worm holes, implosion, and even examines the definition of reality.

Journey into Gravity and Spacetime
by John Wheeler
n describing the workings of gravity, Wheeler draws on everything from flying tennis balls, to hurling gravity waves from crashing stars, the motion of the planets, and the collapse of a star into a black hole. This is an imaginative account by a physicist who has participated in most of the important work in physics of the last 50 years.

Discussion

Meta Model: Gravity
I'm hoping to someday post a summary of Dr. Tom's Meta Model as it applies to gravity... it is contained in his book Dark Matter, Missing Planets, & New Comets. His web site has a Gravity Page, too.
The Speed of Gravity
Here's a paper written by Dr. Van Flandern which presents experimental data to support his theories about the propagation of gravity: The Speed of Gravity - What the Experiments Say.
October 4, 2001: Tides
Another item that's been on the agenda for several weeks... George read Feynman's chapter on the Theory of Gravitation in Six Easy Pieces, and encountered the best explanation of why there is a high tide on the side of the Earth which is opposite the Moon, as well as on the side facing the Moon. Let's see if I can accurately remember Georges' version of what Feynman was saying!
OK, the oceans facing the Moon are pulled that way by the Moon's gravity-- that's the easy part. To understand the watery bulge on the opposite side of the Earth, we have to think about the dance in which the Earth and Moon are engaging. Compared to most natural satellites in the solar system, the Moon is quite large-- it's mass makes up a much larger percentage of the mass of the planet around which it orbits. This means the Earth and Moon earch orbit around a point which is a significant distance from the Earth's center (although it is still within the Earth's radius).

The resulting motion of the Earth is similar to twirling a frisbee around on the tip of your finger with your finger hooked under the rim of the Frisbee. Visualizing this, one can easily imagine that centrifugal "force" would be pushing out toward the rim of the Frisbee opposite your finger. This is the same thing happening on Earth! the water (and, in fact, everything on the surface) of the Earth opposite the "pivot point" around which the Moon and Earth orbit will be pushed away from that point by the centrifugal "force." It just so happens that the high tide is the only obvious manifestation.
Whew! I probably could have been more clear if I actually went and read the Feynman chapter... I'll try to draw a diagram (or lift one from the book). 10/7/01 - I did!
November 1, 2001: Theory of Gravitation
Wow! We've had a lot of action on the gravity front this week. George discovered while reading Six Easy Pieces that Feynman actually discusses the Meta Model version of gravity:

"Many mechanisms for gravitation have been suggested. It is interesting to consider one of these, which many people have thought of from time to time. At first, one is quite excited and happy when he "discovers" it, but soon finds that it is not correct. It was first discovered about 1750. Suppose there were many particles moving in space at a very high speed in all directions and being only slightly absorbed in going through matter. When they are absorbed, they give an impulse to the Earth. However, since there are as many going one way as another, the impulses all balance. But when the sun is nearby, the particles coming toward the Earth through the Sun are partially absorbed, so fewer of them are coming from the sun than are coming from the other side. Therefore, the Earth feels a net impulse toward the Sun and it does not take one long to see that it is inversely as the square of the distance because of the variation of the solid angle that the Sun subtends as we vary the distance.
What is wrong with that machinery? It involves some new consequences which are not true. This particular idea has the following trouble: the Earth, in moving around the Sun, would impinge on more particles which are coming from its forward side than from its hind side (when you run in the rain, the rain in your face is stronger than that on the back of your head!). Therefore there would be more impulse given the Earth from the front, and the Earth would feel a resistance to motion and would be slowing up in its orbit. One can calculate how long it would take for the Earth to stop as a result of this resistance, and it would not take long enough for the Earth to still be in its orbit, so this mechanism does not work.
No machinery has ever been invented that "explains" gravity without also predicting some other phenomenon that does not exist."
George pointed out earlier in the week that Dr. Van Flandern would probably have addressed this, and that he assumed it had something to do with the c-gravitons moving quite a bit faster than the speed of light. It turns out George was right-- we both read the gravitation section of Dark Matter, and Dr. Tom does indeed address this mathematically (he states that the drag is proportional the ratio of the masses' speed (i.e., Earth) to the speed of the graviton), and the drag becomes undetectable.
I pointed out that Feynman (in 1960) felt comfortable using drag as an argument because he naturally assumed that any particle responsible for gravity would be bound by Einstein's Theory of Relativity and could travel no faster than the speed of light.
Personally, I'm having a little more trouble with Van Flandern's model for gravitation, since it requires not only the current thinking on gravity to be dead wrong, but also that relativity is wrong!

Van Flandern: I believe gravity is the result of tiny particles pushing masses.
Feynman: Ah! But what about drag on the masses if they're moving through the gravitons?
Van Flandern: Uh... they're... FASTER than light. Yeah! That's the ticket! A LOT faster! Let's see... in order to make them undetectable, let's say 10¹⁰c.
It seems too convenient... but I'm too uninformed to actually judge. So I'll try to keep an open mind. Oh-- is this the wrong time to bring up the article in the Meta Research Bulletin which hypothesizes that the Great Pyramid at Giza was actually a Plutonium Processing Plant? I suppose it is indeed the wrong time.
This still reminds me about the item we've had under the category of "Things We Can't Figure Out Yet": How does the Meta Model describe electrical forces, and specifically, how would it describe like-charged particles repelling each other?
November 8, 2001: Gravitational Field Propagation & Moving Masses

Marty: "Whoa-- that's heavy!"
Doc: "Heavy... there's that word again... has something happened in the future to affect the Earth's gravitational field???"

So, we talked some more about how gravity appears to operate instantaneously at a distance. I was telling George that I kicked this subject around with Corey and Fred at work, and did not reach any real conclusions.
The problem we're discussing is how does gravity seem to act instantaneously at a distance? From the reading I've done and the discussions in which I've listened, it seems that the rubber sheet is the best analogy.
When an object is pulled by a large mass, it is not a magic power reaching out from the mass and affeecting it instantaneously... but it seems like it. Rather, the object is interacting with the gravitational field of the larger mass, which radiates outward from the larger mass in all directions, curving space.

Figure 1. A rubber sheet with a ball on it

Try to imagine it in two-dimensional terms using a rubber sheet (see Figure 1) upon which you place a bowling ball and a marble. You can see that if you place the marble on the sheet close enough to the bowling ball, it will be in a place where the sheet is curved by the weight of th bowling ball. The marble will immediately begin to roll toward the bowling ball. When it does so, it is interacting with the curve of the rubber sheet right at the point where it is in contact with the sheet. It is NOT interacting directly with the bowling ball, but is instead interacting with the curvature created by the bowling ball.
So, to us the bowling ball appears to be acting on the marble at a distance, but instead the marble is being acted upon by the "field" created by the bowling ball when it curved the rubber sheet.
In my kindergarten understanding of general relativity, it seems that a large mass (say... a star) curves space in three dimensions much as the bowling ball curves the rubber sheet. If this is so, then an object which is within that curved part of space (the gravitational field of the star) will fall toward the star because it is interacting with the curved space at its own position.
OK... this keeps us from transferring information (gravity) faster than light. But how does the gravitational field, or curvature in space get there? Surely the field itself could not propagate from the mass itself out to great distances instantaneously-- that's what we've just been working to avoid! So the field itself must propagate at the speed of light.
Does the gravitational field propagate ath the speed of light? If so, George sees another problem. Here's my version of his idea:

Figure 2. Rogue Planet passes Earth

If there are two objects: let's call them "Earth" and "Rogue Planet" (see Figure 2). Okay, the Earth is minding its own business, orbiting around the Sun. Then along comes this Earth-sized Rogue Planet! It is speeding into the solar system at a speed of, oh let's say 1000 miles/sec, and it is going to travel within 0.5 AU of the Earth (that's 46.5 million miles).
If at time t₀ the Rogue Planet is at point A, Earth will not receive the light reflected off of the Rogue Planet (that is, "see it" at point A) until 4 minutes later (let's call that time t₁). But by time t₁, the Rogue Planet will have traveled 240,000 miles (coincidentally, almost exactly the mean distance between the Earth and Moon) to point B.
So... at time t₁, the Rogue Planet is at point B, Earth sees it at point A, and toward which point does the Earth feel drawn by the Rogue Planet's gravitation field?
If gravity acts instantaneously at a distance (observations say it does), then the Earth should feel pulled directly toward point B. But if that is so, how did Rogue Planet's gravitational field propagate to be centered around point B at time t₁, apparently instantaneously??? If this is true, then the gravitational force of the Rogue Planet can be felt somewhere before light could reach it. That's bad.
If the gravitational field of the Rogue Planet propagates at the speed of light, then the Earth would not feel pulled from point A until time t₁, when the Rogue Planet was already at Point B, 240,000 miles away. This does not agree with observations. Hmm. Clearly, I do not know enough about this stuff!
ANY HELP IS APPRECIATED!!!
November 14, 2001: Mail from Jim Kuzeja

Hi Guys,
You might want to check out this site: http://www.weburbia.com/physics/relativity.html. Among other things it attempts to explain why gravity appears to propagate instantaneously. It seems pretty hand-wavy to me though. Also, the math in other parts makes my head ache.
November 15, 2001: Mail from Tony

You use the man-made concepts of time and a precisely (non-infintesimal) defined point in space in your example. In reality, the effect on the earth of the rogue planet would be constant and changing in space. Therefore the effects of gravity can not be measured the way that you want to measure them. Think about it... the gravity effect from the Sun does not take 8 minutes to reach Earth. The warp in space from the sun simply exists because the matter exists, therefore, the earth responds to it. Likewise, the warp in space from the earth (and the sun, and the stars) affects the moon. When you add the concept of precise points in time, you start to screw these things up. There simply is no such thing. Man created increments of time in order to measure the entropy (rate of change) of the universe around him. Light simply electromagnetically changes the space in which it travels, therefore, we can measure it and assign it a 'speed' (a time-based derivative).
If you can figure out a way to spontaneously create matter in a point in space, then you might have something!
One of the problems I have with the 'Big Bang' theory is that it presumes that there must have been a t₀. While there may have been a Big Bang (as we know and measure it), I don't specifically think that it was the beginning of everything. Infinity exists! and so does the infintesimal.
November 29, 2001: Some Answers!
Here are some answers to the questions we've been asking:
- Gravity Propagates at the Speed of Light.
  According th GR, as a mass moves through space, the curvature which it imparts on spacetime moves outward at the speed of light. (see Does Gravity travel at the Speed of Light?). It is important to note, however, that no direct measurements of the speed of gravity have yet been made!
- General Relativity Answers the Propagational Latency Problem.
  The field equations which define GR account for the propagational latency of gravitational fields. It turns out that the relative velocity of a mass causes the apparent force vector of its gravity (when acting upon another body) points not at the mass, but in front of the moving mass. The delta cancels out the propagational latency almost exactly, and would only differ from the Newtonian concept of instantaneous action in systems involving extremely high masses and velocities (Observations of distant binary pulsars are consistent with this). See again Does Gravity travel at the Speed of Light?.
  Great Quote:
  
  "In general relativity, there actually is no answer to the question, 'What would happen to the Earth's orbit if the Sun suddenly disappeared?' The equations of general relativity simply have no solution that corresponds to this situation. The reason is that the equations contain the law of (local) conservation of mass-energy built into them in a fundamental way.
  To give an analogy, asking the above question to a general relativist is a little bit like asking a number theorist a question like 'If there were an integer between 29 and 30, would it be prime or not?' There just isn't any answer, since the hypothesis is impossible."
  -- Emory F. Bunn, Cal Berkeley
- There are Good Not-too-technical Sources which Explain General Relativity.
  Steven Carlip, from the University of California at Davis, recommends the following books for the faint of calculus heart:
  - Black Holes and Time Warps, by Kip Thorne
  - The Riddle of Gravitation, by Peter G. Bergmann
  - Journey into Gravity and Spacetime, by John Wheeler
  By dumb luck, I already have a copy of Kip Thorne's book. George and I wondered aloud just who was Kip Thorne... but a glance at the inside title page gave us quite an answer: He is the Feynman Professor of Theoretical Physics at the California Institute of Technology. The book is great so far! I've read about 60 pages or so. He begins with a 30-plus page science fiction story about a starship and crew investigating black holes. It turns out that Black Holes are really great ways to describe General Relativity, since near a black hole, everything is extreme. The differences between Einstein's Theory of Gravity and Newton's theory become glaring (this is analogous to Special Relativity-- Newton's Laws of motion differ most from Einstein's when you approach the speed of light).
sci.physics.relativity
As I mentioned before, there's this great newsgroup that just contains discussions about relativity. Unfortunately, a quick read of the newsgroup reveals that there are three kinds of contributors: 1. curious lay people, 2. knowledgable experts who try to provide answers for the curious, and 3. cranks and wierdos who flood the newsgroup with their half-baked views of how the universe really ought to work (here's an example). The really frightening thing is that they all seem to be engineers and software developers!
I just read a post tonight by Allen C. Goodrich (username GRAVITYMECHANIC2), in which he declares that many of the current views and laws of physics are false. He has conveniently published a book, which can be purchased for only $55.00 plus tax and shipping. I clicked through to his website, and it seems that his posting to the newsgroup is the entire contents of the web page.
Oh, here are his credentials:
- Amateur Astronomer for 70 years
- Licensed Engineer
- Graduate of RPI (that's pretty good!)
- holder of several copyrights and patents
These people seem to have little or no actual background in physics, yet they have no problem with throwing around wild ideas using terminology they do not understand... some dedicate entire websites to their alternative theories. Many of them have authored self-published books to publicize their theories (it's the only way for them to get exposure since the "establishment" is conspiring to supress their ideas). Here's one: http://www.rlgerl.com/
Even though there is a lot of good info at sci.physics.relativity, you really have to wade through a lot of this stuff to find it.
Oh, I just found another interesting post from a David Orton. If you go to the web site, you can read his own Quantum Inertial Dynamics theories.
Being a fan of the Absolute Frame of Reference myself (even though I know its not true-- I just like it!), I was drawn to the theories of Gerald L. O'Barr... at least for a second or two. He likes aether, too! His theories can be viewed on his lengthy website. His posts are very entertaining, and always include lots of exclamation marks!!!!

Steve Carlip and Tom Van Flandern
Tom Van Flandern has been posting to sci.physics.relativity since at least 1995 (that's as far back as I've been able to look). throughout that time, he and others have been debating many issues. Steven Carlip has been willing to engage Tom and try to explain General Relativity to him.
Steve characterizes Tom's general approach as taking Newtonian mechanics and trying to directly apply light-speed propagation delays (this doesn't compute-- Tom says (and Steve has agreed) that the orbits of planets under such conditions would spiral out of control).
John Baez (at UC Riverside) has a great webpage which addresses misconceptions in physics. He dedicates a specific section to the Speed of gravity issue, and it features Dr. Tom Van Flandern. He has also collected numerous posts from sci.physics.relativity over the years made by Steve Carlip, himself, and other leading gravitation physicists. They make for really good reading, but there is a LOT of material. It is broken up into two large pages:
- The Debate from 1995 to 2000
- The Debate from 2000 onward
Dr. Tom published a paper in a refereed journal entitled The Speed of Gravity - What the Experiments Say.
Steve Carlip published a rebuttal paper in the same journal entitled Aberration and the Speed of Gravity.
Not swayed, Tom has responded with The Speed of Gravity - Repeal of the Speed Limit.
In 1997, Steve wrote a well-reasoned response to Tom in a so-called final attempt to help him understand GR (their discussions continued well past this time!). He does a good job of relating the curvature of spacetime and the propagation of gravitational field changes to similar phenomena in electromagnetism. I've added this post verbatim to the gravity page.

Experimental Idea
Ever since reading these explanations, I've been continuing to think about the "rubber sheet" analogy for curved space and gravity. Please indulge this flashback to the November 8 lunch:

Figure 1.

Try to imagine it in two-dimensional terms using a rubber sheet (see Figure 1) upon which you place a bowling ball and a marble. You can see that if you place the marble on the sheet close enough to the bowling ball, it will be in a place where the sheet is curved by the weight of th bowling ball. The marble will immediately begin to roll toward the bowling ball. When it does so, it is interacting with the curve of the rubber sheet right at the point where it is in contact with the sheet. It is NOT interacting directly with the bowling ball, but is instead interacting with the curvature created by the bowling ball.
So, to us the bowling ball appears to be acting on the marble [instantaneously] at a distance, but instead the marble is being acted upon by the "field" created by the bowling ball when it curved the rubber sheet.

Okay... so what about the propagation issue? It seems to me you could expand the analogy by rolling the bowling ball across the sheet. If the ball is rolling, I can easily imagine that the shape of the indentation in the sheet is NOT circular, but rather is compressed on the leading edge (this is the result of the indentation propagating forward ahead of the bowling ball).
Not only is the indentation not circular when viewed from above-- the actual curvature is probably deformed in 3 dimensions when compared to the indentation occurring when the ball is at rest. So while a marble placed in the indentation created by a ball at rest would begin to accelerate directly toward the ball, I would expect that a marble under the influence of an indentation created by a rolling bowling ball would accelerate along the deformed curve and it might NOT be directly toward the bowling ball.
It would be very interesting to create such a physical experiment. One could:
1. suspend a flexible rubber sheet in a frame
2. paint grid lines on the sheet
3. position several time-synchronized digital video cameras to capture the action from a variety of angles
4. roll a bowling ball across the rubber sheetwith the cameras running
5. Use the synchronized digital video to create a 3-dimensional model of the shape of the bowling ball's indentation while it is moving
6. Mathematically determine the vector which a marble would follow along the deformed indentation.
I predict that a marble placed on a point whose direction from the bowling ball is perpendicular to the balls movement would roll in a direction which would point in front of the moving ball. I'm assuming that this would compensate for any delays in propagation of the "field."
December 4, 2001: A post by Steve Carlip in response to Tom Van Flandern

------------------------------------------------------------------------
Re: speed of gravity
Author: Steve Carlip (carlip@dirac.ucdavis.edu)
Date: 1997/05/29
Forum: sci.physics
------------------------------------------------------------------------

Tom Van Flandern (metares@well.com) wrote:
: But even now, I'd be very happy with a clear explanation, whichever way
: it went. In fact, I've looked forward to each response from Steve
: Carlip, thinking that surely mutual understanding must be just around
: the next corner. Steve is knowledgeable enough about relativity and a
: good enough teacher to be able to understand the dilemma and pinpoint
: the solution if one exists. I am as frustrated as he must be that no
: solution to the dilemma seems to be forthcoming.

OK, Tom, let's try this one more time. (After this, I quit.) For simplicity, look at the case of electromagnetism rather than gravity---the basic phenomenon is the same, and the math is easier.
Start with Maxwell's equations, written in terms of the potential, and suppose the source of the electromagnetic field is a point charge. The general retarded solution for the potential is then given by equations (21.133)-(21.34) of volume II of the Feynman lectures. I'll return to this point below. You can check this by, for instance, simple Greens function techniques.
Now compute the electric field and magnetic fields from these potentials. It's not that hard a calculation; the result is given by equation (21.1) of the same chapter.
Now using these fields, work out the direction of the force exerted by a moving charge. If the charge is moving at a constant velocity, you will find that the force points to its "instantaneous" position. (Do the computation!) If the charge is accelerating, the force no longer points toward the "instantaneous" position, but it points to a position that is obtained by linear extrapolation from the retarded position.
If you are interested in gravity rather than electromagnetism, the corresponding calculation is considerably harder. But as you know, Tom, it has been done by Damour et al. The outline is the same as in the electromagnetic case: one starts with a set of field equations in the presence of a source, computes the retarded "potentials" (in this case, variations of the metric), and calculates the resulting force. In general relativity, as you know, the cancellation of the retardation is somewhat more precise than in the electromagnetic case, but the principle is the same.
As far as I can tell, you have put forward three basic objections to this answer:
1. "Damour's calculations are wrong (or involve extra ad hoc assumptions beyond the Einstein field equations)." While you have occasionally claimed this, you have not demonstrated any such errors or assumptions. Recently, for example, you asserted that conservation of angular momentum was an "extra" assumption, apparently failing to realize that it was a consequence of the field equations rather than an additional input. Let me suggest, Tom, that you don't know enough general relativity to make a claim of this sort.
2. "The potentials being used---the Lieard-Wiechert potentials in electromagnetism, for instance---are not "really" retarded." This is also incorrect, and seems to be based on your preconception of what a retarded potential "ought to" look like. The Lieard-Wiechert potentials are retarded in the following senses:

a) The potentials at time t are determined entirely by the properties of the source at time t-r/c. This is clear if you look at the integral expressions (21.15)-(21.16) in Feynman. The potentials *do* depend on the (retarded) velocity as well as the retarded position, of course, and the force is not merely a retarded Coulomb interaction. (Feynman's notation in (21.34) is ambiguous, by the way; the velocity v in this expression is the retarded velocity.)
b) The interaction is causal: if the source is suddenly disturbed by an external force, the changes in the field propagate at the speed of light. This is true in general relativity as well, though it is more subtle, since there is no such thing as an "external force" any more---there is no such thing as a "gravitationally neutral" object, and the gravitational field of the source of any disturbance must be taken into account.

3. "The result is too unintuitive." While you haven't said this explicitly, it seems to be a thread running through your posts. I'm not sure how to respond, except to say that your intuition is perhaps too limited. In particular, you seem to be convinced that forces in nature ought to be central and velocity-independent. Why?
: I do not know how to say this more plainly: I do not wish to change the
: field equations. At all. (At least not in connection with this speed of
: gravity issue.) The field equations do an excellent job of describing
: nature.

: My point is that the field equations use instantaneous interactions to
: accomplish this success. But relativists claim that gravity propagates
: at the speed of light.

For simplicity, let's talk about electromagnetism again rather than gravity. Do you think Maxwell's equations "use instantaneous interactions"? If so, consider a charge initially at rest at the origin, which is suddenly accelerated at time t. Do you believe that Maxwell's equations predict an instantaneous, universal change in the electromagnetic field of the particle? (If you do, you're wrong.)
Steve Carlip
carlip@dirac.ucdavis.edu

Last modified 11/29/2003.

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Steve Carlip and Tom Van Flandern

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