Can deformations of time-space continuum violates law of momentum conservation?

· Physics

Based on Einstein’s theory of relativity a mass as property of physical objects creates deformation of time-space continuum. Therefore the light path bends in gravitational fields of massive objects. However, for reference system of light this bent path looks like straight path. This effect called as gravitational lens.

fileblack_hole_lensing_web

Based on this effect, the light changes angle of original path in reference systems of observer of source of light. Therefore photon momentum of source and receiver of light will not be equivalent for reference system of source, because angles of light for source and receiver will be different.

light_gravilens

Therefore, thee scalar value of photons won’t change (Law of momentum conservation). However the angle of photon relative to parallel planes of source-target will be different for start and end events. The vector of momentum of photon will be changed, but not scalar value.

Here could be a few interesting questions.
1. Can deformations of time-space continuum violates law of momentum conservation?
2. Following to law of momentum conservation and difference of vectors direction of photon for source and target positions could isolated system get unbalanced acceleration into one direction?

To keep law of momentum conservation for isolated system in proper condition, the massive object will interact with light and attracts it with exchange of their momentum.

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 momentum 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 it will completely absorbed. The additional momentum of massive object will be completely canceled with momentum of absorbed photons . Based on law of energy conservation, the energy cannot disappear to nowhere. This energy of absorbed photons will be equal to work of displacement of center of mass of massive object of black hole.

Blackhole1

Therefore, based on this assumption when massive object can attract photons the center of mass of isolated system such as black hole can move in space. This violates Newtons law. Also, if light has angular momentum then it should disappear to nowhere. This  disappearance of angular momentum is violating law of momentum conservation.

So, in terms of minimum violations of laws, using Occam’s razor method better assumption is when photons are not absorbed inside black hole. Mostly the common hypothesis about what the photon’s trajectory is distorted by gravitational field and they are orbiting around of black hole on distance of photon’s sphere radius. Also,  they may return back by spiral trajectory. In this case, the photon itself should not experience gravity attraction as an object with mass rest and should not lost its own momentum. Red/blue shift effects are showing time dilation only, because photon will have a different frequency measurement by this time difference. Gravitational lens effect is showing trajectory distortion which could be better explained as refraction in two different mediums with different time and constant speed of light. Since distance is a product of velocity with time and gravitational field is changing as a gradient vector from center of object with rest mass then two different points of photon with different distance from center of object with rest mass will travel with different value and it will create a curved trajectory around massive object. Again photon will not experience a gravitational attraction as an object with rest mass. This hypotheses does not violate any laws except one thing. If trajectory of photons bends around massive object then total momentum of isotropic continuum of space-time  will not be equal zero.

 

Law of momentum conservation for curved time-space dimension.

If massive object with rest mass bends a time-space dimension around itself then path of photons close to this object is already curled without any transfer of momentum with it. Therefore, the law of momentum conservation must have additional component of curved time-space dimension for correct equation into curved dimension.

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