Suppose two terrestrial objects B1 and B2 have concentrated a high quantity of mass while being reasonably separated by a distance. When a high speed rocket ship flies by in direction more less parallel to the line connecting these two objects, relativity must predict a drastic disturbance in the physical state between B1 and B2. Not only the mass of each of the two objects is seen increased as moving mass by someone in the rocket ship according to relativity, but also the distance between B1 and B2 found shortened by the observer. Gravitational force between them must be predicted by this theory to increase many folds. Indeed, if relativity is valid, the increase is by a factor of {1/[1-(v/c)2]1/2}4 (2, 1/2, and 4 are all in superscript)! Gravitational force thus escalated must force these two objects to collide, or at least to be predicted as having much higher potential of ultimately colliding by this observer. Does relativity reveal what kind of physical effect that a fly-by rocket ship can exert on these two objects? Or does relativity have paragraph rewriting Newton’s equation of universal gravitational force in a moving person’s observation?
You have misinterpreted what the theory of relativity says. It tells you what the observer in the rocket ship measures. An observer at rest next to the two masses would not observe any changes in either their mass or the distance separating them. Your observer in the rocket ship would only observe a contraction of the distance between the two masses. Without actually interacting with them, he would not be able to measure a change in their mass, but that is a different situation from what you describe.
I don't know where you learned relativity, but this is wrong. Gravitational effects are observer independent. That is why general relativity is written in terms of tensors or an equivalent formalism.
Tensor is a mathematical means, not any insight of physics of any kind. An equation of 1+1=2, no matter how correct, tells you nothing about any material state in a physical world. On the ohter hand, without any math, people can explain why on can see his image in a mirror. Besides, does relativity proposes that gravitational effects are observer independent and tell people why it should?
Wouldn't the moving length contraction influence the gravitational effect? If the contraction affects time measurement, why is it exempted from affecting gravitational measurement? Besides, special relativity has mathematical prediction on how moving mass changes, how has it become "Without actually interacting with them, he would not be able to measure a change in their mass"? In fact, it is this prediction leads to the E=mc^{2}
Once again- the moving observer would observe an increase in mass of the two objects and a decrease in the distance between them. An observer in the rest frame of the two masses- and the two masses themselves- would see no change in mass, distance, or gravitational force.
This is much more than a paragraph, it is the entire theory of General Relativity. Newton's equation is simply not compatible with relativistically moving bodies, although GR does reduce to Newtonian gravity for non-relativistically moving bodies in weak gravitational fields. I don't believe this is true. Don't forget that in GR mass is not the source of gravity; in GR the source of gravity is the stress-energy tensor. This means that gravity couples not only to mass, but also to momentum, pressure, stress, etc.
I don't understand where you're going here. You posted an equation that turned out to be wrong, and now you seem to be complaining that things get quantitative too soon.
Possibly I have to discontiue this thread because I seem not being able to have a full grasp on how to follow the publishsing mecahnism here. For example, you can quote clearly from what I say, but I am unable to do the same thing. It only creates difficulty between our communicaiton. Thank you for all your time and effort, anyway.
Ah, after I complain, I see I can quote you clearly. But it is ok. I will come back some other time. Thank you.
I am glad to hear it. In the meantime you may wish to learn more about the use of tensors in GR as was mentioned previously. The main point is that in GR the source of gravity is not simply mass (a scalar) but energy, and momentum, and pressure, and stress all together (a tensor). And for relativistically moving bodies the mass is not the only significant component of the stress-energy tensor.