Physics/Can isolated system move its own center of mass?
QUESTION: Let's consider case when light has attraction with massive object. Then if light emitted from massive object inside black hole, the massive object will take additional momentum in opposite direction of light path. The scalar value of this momentum will be equal to sum of momentums of photons.(Law of momentum conservation). However, when light will travel to the edge of black hole, the massive object will continue attracting light which will continue loose its own momentum. i.e. loose its own energy and frequency. At the end of this interaction, the light will loose momentum and completely "evaporated". The additional momentum of massive object will compensated by momentum of "evaporated" photons. Based on law of energy conservation, the energy cannot disappear to nowhere. This energy of "evaporated" photons will be equal to work of displacement of center of mass of massive object of black hole.
Can isolated system move its own center of mass?
ANSWER: No, an isolated system cannot move its own center of mass. The act of re-absorbing the photon will transfer all that momentum back to the black hole itself.
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QUESTION: Thank you for answer. This is correct. The momentum of absorbed photon will return to massive object of black hole. For instance, if take two linked objects and repulse them form each other, they will continue fly away from each other till they will cancel theirs momentums through the link. These objects will be displaced from original positions. However the center of mass of these objects will remain in same position. If objects will attracted to each other then they will return to original positions. This is working for objects with rest mass.
However, for absorbed photons this particle cannot be interact with massive object when it lost momentum. When momentum return back to massive object of black hole, this massive object will be displaced from original position. Photon was displaced from original position and was absorbed far away from it's own initial position. Nothing can return back to massive object to return it back to original position, because photon canceled it's own momentum with massive object. The photon was absorbed and photon's mass is zero at this time. Therefore, the massive object cannot return back to original position and center of mass of black hole will be displaced from original state. However it violates Newtons Law.
Can this explanation as proof by contradiction shows what that interaction of photon with gravitational field does not have exchange of momentum? In a black hole the path of photon distorts by graviational field and this photon starts orbiting around this black hole without loosing its own momentum?
ANSWER: The interaction of the photon with the gravitational field changes its frequency. This has been measured. Therefore gravitation does act to exchange the photon momentum with the black hole momentum by equal and opposite amounts. I don't see any solid reason to believe that there's something wrong with conservation of momentum in this case. Light has energy content, which is equivalent to rest mass when dealing with the gravitational interaction.
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QUESTION: Thank you for answer. The conservation of momentum won't be violated in this time. The absorbed photon will cancels its own momentum with massive object of black hole. However the center of mass of isolated system will displaced into new location and will stay in rest position when photon will be absorbed by black hole, because photon cannot be returned back. I.e. both masses were displaced from theirs own places and one of them(photon) was absorbed when momentum was canceled during theirs interaction.
Therefore, based on law of momentum conservation and interaction of gravitational field with photons the isolated system such as black hole can be displaced by itself without acceleration.
Is this violation of Newtons law when an isolated system move by itself or it's normal when black hole absorb photons?
Absorbing the photon via the gravitational field will move the center of mass of the black hole back to its original position. The conservation of momentum and non-displacement of the center of mass are implicit in one another. Newton's laws are not violated in this case. The energy of the photon becomes part of the black hole mass. Since that energy is displaced from the center, absorbing it back into the black hole will (by translating the energy of the photon back to the location of the black hole) move the black hole.