Re: The speed of gravity revisited

[This replies to "Koobee Wublee", Steve Carlip, and Tom Roberts.]


"Koobee Wublee" writes:

[Wublee]: Claiming the speed of gravity exceeding the speed of light in free space violates relative simultaneity as demanded by the Lorentz transform and thus SR. Since GR is built on top of SR, GR is falsified in the process.

Special relativity (SR) has now been falsified in favor of Lorentzian relativity (LR). See Ref. [1] at end for a primer on LR. The main reasons for this replacement were published in Ref. [2], and boil down to these two:

** the lack of any experiment showing that the same Lorentz transformation equations work both ways between any two inertial frames as in SR, as opposed to working just one way (from the local gravitational potential field to any other inertial frame) as in LR; and

** six experiments showing that the propagation speed of gravitational force is >> c, which contradicts SR, but is in accord with LR having no speed limit. See Ref. [3].

If your only concern is that the Lorentz transformations do not work for speeds above c, the references explain why this is not a problem for LR. Changes caused by motion occur only to clocks, not to time, in LR. If we built a clock bases on the propagation of sound waves in air, then tried to accelerate that clock past the speed of sound, its rate would obey the Lorentz transformations (with c = speed of sound) up to speed c. But the clock would simply cease to function at speeds at or above speed c.

GR is okay because it is actually based on LR, not SR. It uses Lorentz transformations only in one direction, from the local gravitational potential field to any other inertial frame. Substituting LR for SR and leaving the math of GR as is means no more paradoxes, to the relief of students of physics everywhere.


and Steve Carlip writes:

[Carlip]: There is a rigorous proof, using the full Einstein field equations (and not just a low-order approximation that can hide the underlying structure), that gravitational influence propagates at the speed of light

Playing with the definitions of words does no one trying to follow this discussion any good. You avoid defining "gravitational influences" and just cite a reference. However, no one is disputing that changes in gravitational potential (the subject of the field equations) propagate at the speed of light, c. I am always careful to state that "the speed of gravity" measured by the six available experiments always means the 3-space propagation speed of gravitational force, and has nothing to do with changes in gravitational potential.

Then in Ref. [3], Vigier and I carefully showed exactly where in GR the switch is made from the speed of changes in gravitational potential (c) to the propagation speed of gravitational force (infinity). Without that switch, "gravitational influences" of all kinds, including force, would propagate at speed c; but the theory would then fail to represent observations in a gross way (spiraling orbits).

However, you already know these statements are correct. So what did you hope to accomplish for physics by your misleading wording? What you said about "gravitational influence" is untrue of gravitational force, which as you well know cannot propagate as slowly as the speed of light.

[Carlip]: If you really "agree[d] with GR as a mathematical theory," the argument would be over.

Apparently, it would not, because I do agree with GR as a mathematical theory, but have taken great pains to show (as others before me have done) that the mathematical theory has more than one physical interpretation; and that one of those interpretations (the "geometric") has now been falsified in favor of another (the "field" interpretation). In short, GR as Einstein taught it is just fine; but much of the post-Einstein evolution of GR has been unproductive or outright wrong.

It appears that you are so locked into the geometric interpretation that you equate falsifying it with falsifying the mathematical theory. But that would mean you never learned GR as Einstein taught it, because he had little use for the geometric interpretation. He was familiar with celestial mechanics and how astronomers test GR using observations made in Euclidean 3-space. You could learn much about Einstein's thinking by becoming more familiar with the basics of celestial mechanics.

At the very least, that effort would also allow us to communicate with a common lexicon and common definitions. When GR co-opts words such as "force" and "velocity", and redefines them in 4-space, they preclude the possibility of communicating with real-world physicists who conduct the relevant observations and experiments in 3-space. Examples of such communication failures appear throughout Tom Roberts' messages, such as the one I reply to next. He seems not to know that the 3-space world still exists.


and Tom Roberts writes:

[Roberts]: Experiments can test theories. They cannot possibly test interpretations of those theories. This is so because the way an experiment and a theory are compared is to take the equations of the theory, apply the experimental setup to them (e.g. as boundary conditions), and use the equations of the theory to predict (compute) the values that the experimental detectors measure. Nowhere in that is any interpretation of the equations used.

You should try comparing theory and observations sometime. Your phrase "apply the experimental setup to them" is equivalent to adopting an interpretation of the theory, a particular physical meaning for the symbols in the equations.

For example, a = GM/r^2 is an equation connection the gravitational acceleration of a target body (a) to the gravitational mass (GM) of a source mass and the distance (r) between the two. Many observations confirm this relation to be correct and complete for most purposes, excepting certain critical applications. It is obvious to everyone that there is no propagation delay in this equation. That fact about the equation has at least two different physical interpretations:

** [field GR] the effect the source mass has on the target body is instantaneous to the accuracy of the observations; or

** [geometric GR]: The source mass anticipates the future relative position, velocity, and acceleration of the target body one light-time ahead, then sends out its influence as if it came from the retarded source instead of the true source.

There is no question that the first of these two interpretations is favored by logic and observations.

[Roberts]: The experiments have said NOTHING WHATSOEVER about whether or not the "geometrical interpretation" [#] of GR is valid. The experiments have said that the EQUATIONS of GR are valid (for their specific measurements).

The experiments have only said that what you call the "approximation" theory is valid. But the approximation theory has infinite force propagation speed. In fact, the approximation theory looks almost identical to the equation example I just gave, except for those higher-order terms that are of no consequence for the "speed of gravity" issue.

[Roberts]: in GR the geometry is DYNAMIC, and this is fundamental to the theory.

My dictionary says: "dynamics: the branch of mechanics that deals with motion and the way in which forces produce motion". In the geometric interpretation of GR, what force initiates 3-space motion for a target body at rest relative to a source mass?

This is an important question. Please do not evade it.

[TomVF]: "Force" is the time rate of change of (3-space) momentum. ... orbital motion represents a force by definition of the word.

[Roberts]: That is just plain wrong. Here is how you can see that it is wrong: try to describe how one could MEASURE the "gravitational force" on an orbiting satellite. If you cannot do that, you cannot define "force" this way. And you CLEARLY cannot do it (if anyone had ever done it, GR would have been unnecessary, irrelevant, and almost certainly wrong).

We observe the satellite's x,y,z coordinates in the Earth-centered-inertial frame at a succession of times. Two such measurements determine the satellite's momentum. Additional measurements yield the time rate of change of that momentum. This is the 3-space force by definition.

How can you argue with a definition? This is physics 101. Your understanding of real-world physics seems severely incomplete.

[Roberts]: Note you must measure the force itself, not any geometrical aspects of the physical situation -- that would be geometry, and you're claiming this is not geometry.

Now you are playing word games. The example I just gave used flat Euclidean space, normal proper time, and conventional 3-space forces. Geometric GR uses curved space-time, coordinate time, and the initiation of motion without forces. In real-world physics, propagating forces are carriers with momentum that originated from a source mass and can collide with a target body and transfer their momentum. In no sense does this use the notion that "gravity is just geometry". Geometric GR does.

I'm always careful to put in the caveat "3-space" to avoid confusions of this sort over definitions. You apparently ignored that distinction.

[Roberts]: To test GR, one must use the equations of GR, or a valid approximation to them, not some cobbled-together equations into which you put "delayed forces". The linearized GR approximation is well known to give equations in which propagation delays don't appear.

Again, you seem to be speaking with confidence about a subject where you have no knowledge. The conversion from solutions to the field equations into 3-space equations of motion (for the purpose of comparing the theory with observations made in a flat Euclidean 3-space) is accomplished by a lengthy mathematical process. There are several versions in the literature, the most famous being that in Ref. [4]. In this *conversion* process, instantaneous action at a distance is adopted. Propagation delays are never even considered, let alone entered and later cancelled. This is also evident in the end equations, which reduce to the Newtonian equations for ordinary orbital motion in the majority of cases (weak field, low velocity). As even you admit, the Newtonian equations (necessarily) have infinite gravity propagation speed. There are no propagation delays at any order in these 3-space relativistic equations of motion.

And these are the equations used to test GR. I had no hand in "cobbling-together" these equations. Yet they are just as "instantaneous action at a distance" as is a = GM/r^2. In the weak-field, low-velocity cases such as most solar system orbits, these equations reduce to a = GM/r^2, with gravity propagating at infinite speed. And this has nothing to do with "approximations". Speed of light propagation for gravity fails to work by a gross amount even in weak-field, low-velocity cases.

[Roberts]: Even standing on a bathroom scale does not measure "gravitational force": it CLEARLY measures an UPWARD force on your body and a downward force on the floor, neither of which can possibly be the attractive force of gravity.

The downward force is most definitely the force of gravity, as can readily be verified by raising the person slightly above the floor and releasing him. It is cancelled by the upward force of the floor.

We are now talking past one another. I am familiar with the "new-speak" way of redefining common terms in relativity so as to make certain claims true, such as "gravity is not a force". Again, I am clear in my writing about what definitions I am using. In order to compare theory to observations made in flat Euclidean 3-space, GR's predictions must likewise be converted to flat, Euclidean 3-space. Then we can describe and compare the two interpretations of GR entirely in this flat, Euclidean 3-space where forces are the time rate of change of 3-space momentum, velocity is the time rate of change of position, acceleration is the time rate of change of velocity, and classical definitions are in full force and effect.

Without doing that, you wouldn't have any clue what the equations of GR say about orbital motion in real-world physics. -|Tom|-


REFERENCES:

[1] http://metaresearch.org/cosmology/gravity/LR.asp#_ednref10

[2] "Experimental Repeal of the Speed Limit for Gravitational, Electrodynamic, and Quantum Field Interactions", T. Van Flandern and J.P. Vigier, Found.Phys. 32:1031-1068 (2002).

[3] "The speed of gravity - What the experiments say", T. Van Flandern, Phys.Lett.A 250, 1-11 (1998); also at http://metaresearch.org/cosmology/speed_of_gravity.asp.

[4] Einstein, A., Infeld, L., and Hoffmann, B., "The gravitational equations and the problem of motion", Ann.Math. 39:65-100 (1938).


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

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