I was just pointing out that the gravitational field is not completely comparable to the EM field, as it lacks a repulsive component and is not made up of two fields.
Once again, you demonstrate that you simply have no idea what you're talking about. The electromagnetic field is a single rank-2 tensor field. Because it's antisymmetric, we can express it as two separate vector fields, but that's not what it really is. How about gravity? By golly, we get the
same thing. The gravitomagnetic field is usually too weak to notice, but it's there.
It's true that gravity and E&M are different because gravity has only one charge type, and like charges attract. But IIRC you're still in denial about what the consequences of that are (
negative potential energy). Feel free to correct me if you've figure that part out.
This is where the difference comes in, and why the Biot Savart force law does not need infinitely long filaments, as would be required by gravity.
Wrong. So wrong. The 1/r form of the Biot-Savart force law does indeed need infinitely long filaments, or else it's only an approximation. In fact, if you look it up in Griffiths Intro to Electrodynamics, you'll find that the 1/r form of the law isn't even what he gives as the Biot-Savart law, but rather an integral over your current element with each term contributing 1/r
2. From which it's rather obvious (to anyone who knows any vector calculus, anyways) that the 1/r form for straight wire currents MUST be an approximation if the wire is finite length.
No, you obviously don't get it: it only gives 1/r if your integral is over an infinite source line. If it's finite, then it will be
approximately 1/r if your distance from the source is much less than the length of the source. But this is true for ANY integral of a 1/r
2 force, including (you guessed it) gravity AND magnetism.
Ah. Heres the crux of the issue. This is where the inherant properties of plasmas to form into filaments come in. And where the exclusively attractive field of gravity can not compare, as it can not create linearities.
You keep saying gravity can't create filaments, but you've got nothing other than your intuition to demonstrate that. Actual many-body simulations demonstrate that your intuition is as wrong as the rest of your thinking on this topic.
Yes, you can integrate over the current line to get a 1/r. And yes, you can also integrate gravity over a mass line and get 1/r. BUT there will never be a line mass big enough in nature due to the exclusively attractive nature of the gravitational field.
You just don't get it. A line mass only needs to be "big enough" relative to the separation distance. And that applies to both electromagnetic forces AND gravity. If a line source is long enough to produce approximately 1/r forces from magnetism, then it will obviously
and necessarily be long enough to produce approximately 1/r forces from gravity
as well, in the
same bloody place. You can't get charge or current without mass. If the universe is filamentary with 1/r electromagnetic forces operating on cosmic scales, then there will
necessarily be 1/r gravitational forces as well.
Plus you need infinitely long straight infinitely fine filaments for it to work perfectly, which is patently obserd.
That's the
exact same thing in the case of the Biot-Savart law. Talking about 1/r scaling is rather
obviously (well, obvious to everyone else) talking about approximate scaling. Oh, and they don't need to be infinitely fine either, only cylindrically symmetric. That applies to both gravity and currents.
Well, this is where the **** hits the pan. I'm still waiting for you to produce a paper where a 1/r law is used for gravity. There are hundreds that show that the 1/r force holds over a huge range scale for amperes law (or its equivalent Biot Savart version)
Line sources are of little interest to most gravity situations. And like I said, 1/r scaling for a line source is a
necessary result of three things:
1) linearity of the field with respect to sources
2) 1/r
2 scaling for a point source
3) the universe being logically consistent
So which one of those do you want to challenge, Zeuzzz? Because otherwise, there simply
is no alternative. None. Playing journal hunt games won't change any of that.