Re: The speed of gravity revisited

Steve Carlip writes:

[Carlip]: a gravitating object -- call it A -- moving at a constant velocity suddenly stops. What happens to the motion of a test body B a distance R away from the point that A stops?

This has nothing to do with the issue on the table, the propagation speed of gravitational force. It concerns only the propagation speed of changes in the gravitational potential field, about which there is no dispute -- it is speed c. So let's stay on topic, please.

We don't need A to be moving, then stop, as in your example. The issue of relevance here is present even when A is permanently at rest and its field is completely static. The direction of the source mass as sensed by an orbiting target body is toward its true instantaneous position when the target body or field point is at rest. And it is toward the source mass's retarded position (retarded by the speed of gravitational force) when the target body is orbiting. That's elementary physics.

The exact same statement is equally true if the source mass is moving, then stops (your example). That "move, then stop" distraction just makes a simple problem more complicated. Address your attention back to the static field problem, a much simpler one, and we will start to make progress.

[Carlip]: In general relativity, you solve this problem as follows ...

Most of your message was about this irrelevancy. But we have no issues between us about the math. It is only the physics behind the math that has been corrupted in modern GR texts to avoid uncomfortable conclusions such as gravitational force having to propagate >> c. When we straighten out that physics for those who hide behind the math, we get a simpler, revealing picture of the origin and nature of gravity -- neatly, one lacking in paradoxes.

Indeed, many of the most significant paradoxes in modern physics disappear in a single stroke once the light-speed limit is lifted. No more quantum "great smoky dragons", no more questioning of deep reality, no more miracles required. It's really a very pleasing picture once anyone gets past the mental blocks put there by teachers who knew no better.

[Carlip]: There is no room for ambiguity here. Given the mass, composition, and motion of A, the stress-energy tensor is unique. Given the stress-energy tensor, the metric is unique (up to extraneous gravitational
waves coming in from infinity). Given the metric, the geodesic equation
is unique. Given the geodesic equation and the initial position and velocity of B, the motion of B is unique.

This again ignores the relevant point here, namely, the aberration of A relative to B when B has a transverse motion. Show me where you see the aberration of the source mass in the equations of motion for the target body. You can't, because it isn't there. Instead of straining all plausibility and your personal credibility by trying to invent some logical reason for the missing aberration, why not accept the obvious, classical physics reason: If the speed of (3-space) gravitational force propagation is >> c, aberration is driven to zero.

[Carlip]: GR is a very successful theory, and if you reject it, you'll have to come up with a different explanation of why, for example, the last term of line 2 of eqn. (39.64) in MTW -- the equation you like to cite -- has a coefficient of -3/2.)

How very ironic. I take it you have no idea what each of these terms means physically. You picked the only term that has no observable consequences for any known astrophysical system, and is only non-zero (although still negligible) when more than two massive bodies are involved.

That said, what cryptic point were you trying to make?

[TomVF]: I'm guessing you must have never understood what the Einstein-Infeld-Hoffmann or Robertson-Noonan or Damour-Deruelle papers, deriving 3-space equations of motion, are all about. Why do those papers exist if the geodesic equations contain all the information we need about orbits?

[Carlip]: Those papers show that one can *derive* the geodesic equation from the field equations of general relativity, rather than postulating it separately.

[TomVF]: But that "derivation" is not simply "turning the crank". One of the assumptions that must be made along the way is the direction of the gradient - instantaneous or retarded.

[Carlip]: Unlike you, I have actually done this derivation, starting from the Einstein field equations. No such assumption is needed. You are just making this up.

It was I who first pointed you to the original papers deriving the equations of motion, not vice versa. If you think I'm just "making this up", then show me where in any of these papers the aberration of the source mass from the moving body is taken into account. Remember, setting that aberration to zero, as is done in Newtonian gravity, means physically that you are setting the speed of gravity to infinity because aberration is simply the ratio of the transverse orbiting body speed to the force propagation speed, and the only logical way it can fail to appear in the foresaid equations for a non-zero orbit speed is by adopting an infinite speed of gravity, thereby driving gravitational aberration to zero.

Obviously, there is no legitimate way out of this dilemma. That seems to cause you to keep reverting to mathematical issues and ignoring the physics behind the math. You are wrong to do so. The field equations ultimately tell us only about the gravitational potential field. They can tell us nothing about gravitational force without making some assumption about the propagation speed of that force. Adopting zero aberration (as in GR) is making an assumption that the force speed of infinite. -|Tom|-


Tom Van Flandern - Sequim, WA - see our web site on frontier astronomy research at http://metaresearch.org

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