My OperaMy Problem with Non-Linearly Complex Divergences
Wednesday, January 20, 2010 2:59:16 AM
I've been struggling with something I read recently about mapping of gravity divergences using test particles and I'm wondering if any of you have any ideas how it works or even better, can explain why the way I'm understanding it is incomplete or incorrect. To wrap up the problem tersely, let's imagine for a moment we have two particles of mass > 0 in a simple reference frame, as shown:
Now what I read was that you can create a mapping of the gravitational divergences using these so-called "test" particles. You simply imagine them, they have zero mass, and you use them to determine the gravitational effect at that position, which is simply the sum of the gravitational vectors between the test particle and all gravitational objects in the frame. Using a series of these particles, you can map a gravitational field of a system. Take test particle I for example, and this follows:
My problem with this is that the resultant, -IAB, is a vector. Vectors have magnitude. This magnitude creates a resultant acceleration which is based on the mass of the object the vector is applied to. For example, when you jump off a tall building you rush toward the earth but it makes little effort to rush toward you, even though Newton's Laws tell us that the gravitational force on you from the earth is the same as the gravitational force on the earth from you. (They are equal and opposite.) Since this vector is divided by the mass of the object, and we are so very light in comparison to the mass of the earth, we rush toward the earth more than it rushes toward us.
Having said that, our test particle can't be applied to the resultant vector -IAB because it's mass is zero. As the test particle's mass approaches zero, it's velocity approaches infinity.(Note that velocities > c are not allowed!) Also, you can't simply give your test particle mass > 0 because then it will cause an acceleration on A and B which will move them at t = t + 1. This results in a mapped field which does not correctly represent the actual field you are attempting to investigate.
My gut feeling is that the notion of the test particle as a means of creating a gravitational map is flawed. In a minor way, sure (since you can give i an arbitrarily small m > 0 such that the acceleration on A and B is negligible) but flawed nonetheless. It seems to me this is similar to the uncertainty principle, in a way. You can know the masses of the particles in the system (I think?) but you cannot properly map their gravitational field without affecting it in some, however minor, way.
Someone correct me if I'm wrong?
Now what I read was that you can create a mapping of the gravitational divergences using these so-called "test" particles. You simply imagine them, they have zero mass, and you use them to determine the gravitational effect at that position, which is simply the sum of the gravitational vectors between the test particle and all gravitational objects in the frame. Using a series of these particles, you can map a gravitational field of a system. Take test particle I for example, and this follows:
My problem with this is that the resultant, -IAB, is a vector. Vectors have magnitude. This magnitude creates a resultant acceleration which is based on the mass of the object the vector is applied to. For example, when you jump off a tall building you rush toward the earth but it makes little effort to rush toward you, even though Newton's Laws tell us that the gravitational force on you from the earth is the same as the gravitational force on the earth from you. (They are equal and opposite.) Since this vector is divided by the mass of the object, and we are so very light in comparison to the mass of the earth, we rush toward the earth more than it rushes toward us.
Having said that, our test particle can't be applied to the resultant vector -IAB because it's mass is zero. As the test particle's mass approaches zero, it's velocity approaches infinity.(Note that velocities > c are not allowed!) Also, you can't simply give your test particle mass > 0 because then it will cause an acceleration on A and B which will move them at t = t + 1. This results in a mapped field which does not correctly represent the actual field you are attempting to investigate.
My gut feeling is that the notion of the test particle as a means of creating a gravitational map is flawed. In a minor way, sure (since you can give i an arbitrarily small m > 0 such that the acceleration on A and B is negligible) but flawed nonetheless. It seems to me this is similar to the uncertainty principle, in a way. You can know the masses of the particles in the system (I think?) but you cannot properly map their gravitational field without affecting it in some, however minor, way.
Someone correct me if I'm wrong?
