Einstein created the General Theory by deliberately omitting force from the analysis and only using acceleration to express dynamic responses. This is not a proof that force doesn't exist. It is only the method Einstein used to create his theory. By eliminating force from the theory, he condemned his theory to require very complex equations. He did a brilliant job of producing a good result with this enormous handicap, but that doesn't mean physics has to suffer this burden indefinitely. When force was eliminated from the equations, it meant that the other variables had to take up the slack. This is a common result in dimensional analysis. Reducing the number of dimensions alters the way the other dimensions must react. When force was eliminated from General Relativity, space-time curvature was the only possible result.
This web site uses force often. I know that Special Relativity was developed to apply to inertial reference frames only, which implies that force and acceleration are not included. But current literature already contains extensive use of force and acceration within Special Relativity. This concept is not my invention. Using force and acceleration within Special Relativity is not difficult. Extending this reasoning to gravity is also easy to do. This solution technique gives the same answers as General Relativity but is much easier to use. And this web site is the only place in the world that you can get meaningful explanations of how magnetism behaves relativistically. And magnetism is compared to dynamic acceleration and gravity. Show me where General Relativity can do that.
The theory on this web site uses the Newtonian model for gravity, just as solutions to the General Theory do. Newton's theory of gravity uses the concept of 'force at a distance'. This makes some physicists uncomfortable, including Einstein (and Newton). But 'space-time curvature' is just as mysterious a concept as 'force at a distance'. It doesn't show how gravity works. People just say that it does. Then they say Black Holes exist.
For those who don't believe in 'force at a distance', try this experiment. Put your finger on your computer mouse and push it across your desk top. That's 'force at a distance'. Wait a minute. You have been told that pushing your mouse with your finger was a direct application of force. But it's not. Your finger is composed of atoms and those atoms are 99.999...% empty space. They are composed of particles held together by a web of attractive and repellant forces that are just as mysterious as gravity. As your hand pushes the mouse through your finger, fields surrounding these particles push against each other across the empty space between them and finally bear upon the atoms in your mouse. My point - all forces are 'at a distance'.
So, you're not convinced? Hold two magnets in your fingers at a close distance. No direct connection exists, yet you feel a force. If space-time curves due to gravitational fields, shouldn't it also curve due to magnetic fields? Yet, if you place a non-magnetic material between the two magnets, it's gravitational character does not change? There is only one space-time. Does it curve or not? If it is curved by fields, then gravity, magnetism, electrostatics, etc. should all interact with each other in dramatic ways. General Relativity curvature of space-time is an interesting mathematical byproduct of the elimination of force from the equations. But it does not explain what happens in the real universe. I can't explain how force works at a distance. But I can observe in many simple experiements that it does. This web site does not explain how force works. Nobody can do that (yet?). But I do document what happens to Newtonian Physics when the idea of constancy of the speed of light is added to it.
This discussion is not a condemnation of the General Theory, but it is a call to physicists to simplify their lives by adopting a strategy where force is restored to our equations. The proof of this can be found in my article Black Holes on this web site. By using the Special Relativity approach, I have reproduce the Schwarzschild Solution to the General Theory in only two simple pages.
If I do have a criticism of the General Theory, it is that Einstein gave it the wrong name. The General Theory is not very general. It only concerns problems of individual point masses in empty space. Even those problems have to be greatly simplified if a solution is to be achieved. There are an infinite number of problems other than that which the General Theroy cannot address. These limitations are the direct result of the complexity of the General Theory directly related to the omission of force from the equations. But, as shown on this web site, the Special Theory can do anything that the General Theory can do. Plus it can analyse all those problems that the General Theory can't. Einstein should have call the General Theory the 'Special Theory' and should have called the Special Theory the 'General Theory'.
We owe Einstein our gratitude for the advances of Relativity Theory. Now it is time to advance even further.