- #1
TurtleMeister
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Thought experiment:
You are sitting on a platform which is sitting on a frictionless surface. I am sitting on a similar platform on the same frictionless surface next to you. If I reach out and pull you toward me, we will meet at our center of mass. If you reach out and pull me toward you, we will still meet at our center of mass. If we both pull then we will still meet at our center of mass. So it makes no difference which one of us pulls, we will always meet at our center of mass.
Now for the next thought experiment the reader must be familiar with the meanings of inertial mass (Mi), passive mass (Mp), and active mass (Ma).
According to the equivalence principle and GR, Mi = Mp = Ma. But suppose we could have a mass that does not have a gravitational field. In other words, Mi = Mp but Ma = 0. In all the text that I have read it states that this would violate conservation of momentum. So, suppose we have this special mass (M1) sitting on a platform on a frictionless surface, and nearby we have a normal mass (M2) sitting on a platform on the same frictionless surface. According to all the text I have read they will NOT meet at the center of mass. M2 will pull M1 to it but M2 will remain fixed in position. Why? M1 still has inertial mass. Can anyone explain this? Or how I am viewing this in the wrong way?
Here is my original post. I edited in the above in an effort to better explain my question.
According to the equivalence principle and GR, inertial mass = passive mass = active mass. I have no problem with that. However, I have recently come across a text which claims that a difference between active and passive mass would also violate the conservation of momentum and energy.
The author claims that two bodies M1 and M2, having equal passive mass but unequal active mass would violate the conservation of momentum and that one should immediately see this from the weak field inverse square law.
He then goes on to say that because of the different distribution of iron and aluminum on the moon, causing the corresponding centers of mass to have a different location, that a different ratio of active to passive mass for these elements would cause the moon to self-accelerate.
I do not understand how he arrives at this conclusion. Is this correct? Would passive mass <> active mass violate the conservation of momentum? And if so, how does the inverse square law show it?
What the author is claiming seems to be analogous to saying that if I have two blocks of iron, one magnetized, the other not, that the magnetized iron will attract pull the non magnetized iron to it but not vis-versa. Or in other words, if I put two blocks of iron of the same mass (one magnetized the other not) on a frictionless surface, the non-magnetized iron would move to the magnetized iron, but the magnetized iron would not move. Of course we know that would not happen. I realize that the magnetic field does not follow the inverse square law. However, it seems to be a fair analogy for the case of conservation of momentum. In both cases (gravity and magnetism) it's the total combined field of both bodies that affects the motion of both bodies toward the center of mass. If the author is correct, why would the same not be true (conservation of momentum is conserved) for two masses with a differing ratio of active to passive mass?
You are sitting on a platform which is sitting on a frictionless surface. I am sitting on a similar platform on the same frictionless surface next to you. If I reach out and pull you toward me, we will meet at our center of mass. If you reach out and pull me toward you, we will still meet at our center of mass. If we both pull then we will still meet at our center of mass. So it makes no difference which one of us pulls, we will always meet at our center of mass.
Now for the next thought experiment the reader must be familiar with the meanings of inertial mass (Mi), passive mass (Mp), and active mass (Ma).
According to the equivalence principle and GR, Mi = Mp = Ma. But suppose we could have a mass that does not have a gravitational field. In other words, Mi = Mp but Ma = 0. In all the text that I have read it states that this would violate conservation of momentum. So, suppose we have this special mass (M1) sitting on a platform on a frictionless surface, and nearby we have a normal mass (M2) sitting on a platform on the same frictionless surface. According to all the text I have read they will NOT meet at the center of mass. M2 will pull M1 to it but M2 will remain fixed in position. Why? M1 still has inertial mass. Can anyone explain this? Or how I am viewing this in the wrong way?
Here is my original post. I edited in the above in an effort to better explain my question.
According to the equivalence principle and GR, inertial mass = passive mass = active mass. I have no problem with that. However, I have recently come across a text which claims that a difference between active and passive mass would also violate the conservation of momentum and energy.
The author claims that two bodies M1 and M2, having equal passive mass but unequal active mass would violate the conservation of momentum and that one should immediately see this from the weak field inverse square law.
He then goes on to say that because of the different distribution of iron and aluminum on the moon, causing the corresponding centers of mass to have a different location, that a different ratio of active to passive mass for these elements would cause the moon to self-accelerate.
I do not understand how he arrives at this conclusion. Is this correct? Would passive mass <> active mass violate the conservation of momentum? And if so, how does the inverse square law show it?
What the author is claiming seems to be analogous to saying that if I have two blocks of iron, one magnetized, the other not, that the magnetized iron will attract pull the non magnetized iron to it but not vis-versa. Or in other words, if I put two blocks of iron of the same mass (one magnetized the other not) on a frictionless surface, the non-magnetized iron would move to the magnetized iron, but the magnetized iron would not move. Of course we know that would not happen. I realize that the magnetic field does not follow the inverse square law. However, it seems to be a fair analogy for the case of conservation of momentum. In both cases (gravity and magnetism) it's the total combined field of both bodies that affects the motion of both bodies toward the center of mass. If the author is correct, why would the same not be true (conservation of momentum is conserved) for two masses with a differing ratio of active to passive mass?
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