Cades (*):
- I have had a look at the link and it does say the field is zero but doesn't explain why the field is zero rather than simply being a result of opposing forces.
Well, I am a bit torn if I should try to answer this question since I feel i am being trolled to hell on this thread and everything I write will be given a negative spin, so I would like to start this post by saying this post is not meant to be water-proof to a hostile interpretation and is not intended for Viviane.
The first (important) caveat is the reply is NOT taking into account relativity/quantum theory at all; if we should take this into account the proper answer is the gravitational field (as discussed in the section of "Cosmology" and by me) does not exist at all except as an approximation of limited validity.
Secondly there is the issue of how physical concepts really "exists" (does e.g. "force" really exist? does "energy" really exist?). I will assume we can both agree that these questions have the common-sense answer that allow us to say these things exists.
There are now two ways to discuss gravity in classical mechanics:
- Using a description where forces (computing using newtons law of gravitation) pull in the object(s) and determine the dynamics (I will call this the ropes-and-pullies view on physics)*.
- For each configuration of matter, determine the gravitational field and use this to compute the dynamics*.
Both of these description raise a number of questions that has been important historically (what is the gravitational field really? does it really exist? vs. how do objects know which other objects pull them?) and are obviously in conflict with relativity*. The second approach (fields) is sometimes preferred to the first for a few reasons (this is in my oppinion why it is in a textbook like Cosmology*):
- it generalizes naturally to a description of electromagnetism in terms of the electric field of a static configuration of charges (compare to the gravitational field for a configuration of matter)*
- it blends more easily into more advanced physics like quantum-field theory or general relativity (with important and complicated differences)*
- especially in the case of electromagnetism the formulation in terms of fields is "nicer" to work with; for instance Maxwells equations describe the electric/magnetic field. It also allow one to describe gravity in terms of a (scalar) potential function and allow one to "solve" for the electric field.*
This is not to say that the gravitational field "exist, period": In terms of more advanced physics it certainly do not*, and even in terms of Newtonian physics it should also simply be considered a convenient formulation*. However the "ropes-and-pullies" description of newtons law of gravitation, where one compute the force on an object by imagining it is connected by ropes to other objects that "pull" do not "exist, period" either for the above mentioned reasons*. The "ropes-and-pullies" view of gravity is also often very convenient for some computations and, at any rate, one often end up doing nearly the same computation (as in my argument for the shell theorem)*.
Now to return to the question. Suppose we allow ourselves to describe the system in terms of a gravitational field (as the authors of "Cosmology" does)*. Then the gravitational field is something we associate with a particular configuration of matter (per definition*). There exist a principle* (the superposition principle) that allow us to compute the gravitational field by (1) dividing the configuration of matter into several parts (2) compute the gravitational field individually for each of these parts (3) then the complete gravitational field is the sum of the individual fields; in the derivation i posted a few pages this is actually what I did by the integration and a similar result holds for electromagnetism. This naturally agree with the fact forces can be superimposed as in your argument*.
However in this case there is still just a single gravitational field for the final configuration: the gravitational field.
Suppose we then say: no-no, this is the "net" gravitational field, the "total" gravitational field or somesuch, then we must define what the "net"/"total" gravitational field is formally if we really believe these are different from the gravitational field, i.e. as an actual numerical quantity. What should that numerical quantity be? How should it be different from the gravitational field? I can't think of any meaningful suggestions.
Ofcourse you are free to say that as the gravitational field is just one way of phrasing the physics, and do not exist in the same way atoms exist, then we should define "no gravity" in terms of relativity/quantum gravity/string theory and take the discussion from there. Or you can say we should prefer the ropes-and-pullies version of newtons law and in this case "no gravity" can only be defined as the situation where we are assymptotically far away from any matter (as opposed to not being subject to acceleration due to gravity). I don't want to say these views are wrong which is also why in my original response to Prologos I formulated myself in terms of acceleration and not gravity except as a clarifying remark.
* this statement like everything else is not troll-proof.