Hi All, The following is taken from the most interesting exchange which has been going on these last few days.
I will submit that exchange in two posts (to adhere to the 40K limit) after I send the below so that context can be established. Jack Smith --------------------------- Stephen A. Lawrence wrote: Here's another cute example: A spherical chamber cut out of a uniformly dense planet which was _offset_ from the center would have a _uniform_ (but non-zero) G-field inside it. If you work it out, it's a completely uniform field ... [Jack Smith writes: For me, the field concept is only a calculational convenience. I prefer to imagine transfer of forces by means of particles. Quoting from "Relational Mechanics" by Andre K. T. Assis, 1999 (This book can be purchased at Amazon.com.) p. 217 "... relational mechanics predicts the appearance of a real gravitational centrifugal force exerted by the distant universe spinning around the bucket." p. 261 "We have derived the fact that all inertial forces of Newtonian mechanics, like the centrifugal force or Coriolis forces, are real forces ... This also explains the concavity in Newton's bucket as due to a relative rotation between the water and the distant universe ..." Maybe the distant stars are emitting particles (gravitons) which we experience as gravity.] Horace Heffner wrote: Gravitons interact with photons and vice versa. [Jack Smith writes: I like to picture gravitational red shift, if there really is such a thing, as the result of gravitons interacting with photons.] Horace Heffner wrote: I think any object held in that chamber would experience a gravitational red shift proportional to the g at its location, not to the gravitational potential. Stephen A. Lawrence wrote: I don't know if I understand you. Light should be redshifted as it crosses the chamber, in proportion to the intensity of the field in the chamber, right? Horace Heffner wrote: If what you were saying were true then objects in the center of the universe (assuming here a big bang) should all be massively red shifted, instead of vice versa. Stephen A. Lawrence wrote: Only if there's a gravitational field filling the universe, pointing to the center. That's the only way you'll get a lower gravitional potential at the center of the universe. And if there is such a field, then there must be a redshift associated with it, too. [Jack Smith writes: Assuming there is a "center of the universe," then there could be "a gravitational field filling the universe, pointing to the center." Le Sage postulated gravity by a push of particles and came up with design equations that are identical (I guess) to those of Newton. If there is a large body beneath my feet absorbing gravitons coming from that direction, I will experience a net force toward the body from the unshielded gravitons impacting me. The greater the net flux of gravitons, the greater the force of gravity that I will experience, and the greater the acceleration from this force -- g -- if I should start falling toward the center of the body. Again, I like to picture gravitational red shift as the result of gravitons interacting with photons.] Horace Heffner wrote: No matter how you cut it, clock rate is a function of gravitational field. If the effects of the gravitational field differ from the effects of acceleration (this difference at any point) then Einstein's fundamental assumption for GR is violated, and GR disappears in a flash! Stephen A. Lawrence wrote: Clocks in GR are apparently affected by gravitational _potential_ but not by the local intensity of the gravitational _field_. Horace Heffner wrote: >From a QM point of view this is utter nonsense. Field potential is merely a calculation device. Stephen A. Lawrence wrote: Absolutely. I agree. It's not a "field" in relativity either, and the "gravitational potential" doesn't behave like a sensible "potential". It's just a convenient way to think of it, and it works pretty well in the low-curvature (Newtonian) limit. Stephen A. Lawrence wrote: [regarding that spherical hole cut in a larger uniform sphere:] I don't know if I understand you. Light should be redshifted as it crosses the chamber, in proportion to the intensity of the field in the chamber, right? Horace Heffner wrote: Since the amount of red shift is a function of g, the change in red shift is a function of the change in g as movement occurs. Stephen A. Lawrence wrote: It's a very cute example. [... cute example: A spherical chamber cut out of a uniformly dense planet ...] I ran across it here: http://www.geocities.com/physics_world/gr/grav_cavity.htm Unfortunately it looks like the article has suffered an editing error (or six!) since the last time I saw it. It's completely illegible, at least in my browser, and the main illustration's gotten roached. Luckily I had stashed a copy of the (undamaged) page, to which I just referred to refresh my weak memory of the proof. The way to work this one out is to look at the field from an "intact" sphere, and _subtract_ the field due to the sphere we cut out to make the chamber. By the principle of superposition this is legit in Newtonian gravitation (doesn't quite work in GR, of course). The field at any point inside a uniform sphere of density rho is F = -(4/3)*pi*G*rho*R where "R" is the _radius vector_ from the center of the sphere to the point where we're finding the field. For the big sphere, let the radius vector be R1. For the small (cut-out) sphere let the radius vector be R2. (Note that they point from different origins, but that's OK, all we care about are the direction and length.) Then the net field anywhere inside the small (cut-out) sphere will be F(total) = -(4/3)*pi*G*rho*(R1 - R2) But (R1 - R2) is a _constant_, and is just the vector from the center of the big sphere to the center of the small sphere. So the force is also a constant, proportional to the distance between the spheres' centers, pointing along the line which connects the small sphere's center to the big sphere's center. [Jack Smith writes: Actually, the idea that frequencies of matter change with time, not light wavelengths with distance, as advanced by Hoyle, Arp, Tomes, and others makes more sense to me than "gravitational red shift" or the "Doppler red shift of an expanding universe." But I'm not going to open that can of worms here. What I want to ask here is how does someone distinguish between the "gravitational red shift" and the "Doppler red shift"? Supposedly, conservation of energy requires that photon frequency change with the change in gravitational potential energy (i.e. the further out of a gravitational well the photon rises, the more energy it loses as it fights against the field, hence red shift). This in turn depends on distance from the center of gravity, and has nothing to do with the size of the object in question, only on its mass, and the change in distance to the center of that mass. Assuming the following is correct: If you know the Gravitational Potential, o* : o* = -GM/R^2 where G is the gravitational constant 6.67E-11, M is the mass of the "Star" and R is it's radius ... From this the change in local light speed c: c = c0(1 + o*/c^2) or since wavelength (lambda) equals c/f, f = f0(1 + o*/c^2), ... R in the formula is in fact the distance from the center of the body, and has nothing to do with its radius. This further implies that the red shift [of sunlight] "seen" by Jupiter is greater than that seen by Earth. So here is my question: Since f = f0(1 + o*/c^2), and R is the distance to a celestial object, how does one distinguish between the red shift due to the mass and distance of the celestial object -- the gravitational red shift -- and the Doppler red shift due to the velocity at which the object is supposedly moving away from the Earth?]
