Physics/Deformation of time-space continuum and law of momentum conservation
QUESTION: diagram for this question:
Based on Einsteinís 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.
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.
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?
ANSWER: Interesting notion. The issue always gets confusing when you're dealing with bent spacetime. However, in this case the momentum change would be transferred to the object causing the gravitational field, which you have entirely ignored (and it's the biggest thing in the system). It would be quite the calculation to prove it solidly, though, and would be an interesting challenge for someone specializing in the field. Just so you know, the scalar value (magnitude) of the photon momentum would indeed change as it entered and exit the gravitational potential (gravitational blueshift followed by redshift changes the frequency of the light). But that's a minor detail here.
1) No, it shouldn't violate conservation of momentum, because of momentum transfer to the massive object causing the lensing.
2) The change in momentum would have nothing to do with the source, and any affect (since lensing is a very weak phenomenon) would be dwarfed by the simple emission of the light in the first place. So no, this is not the basis of some kind of deep space drive.
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QUESTION: Thank you for answer. How photons interact with gravitational field? In my humble opinion, photons don't have mass and they should not interact with gravitational field. Deformation of time-space continuum distorts linear dimensions and the light continues traveling on straight line without gravitational interaction. Otherwise, gravitational field should withdraw partial momentum from photons and return it back when they pass out of deformated location. In case when gravitational field interact with photons then the easiest way is absorb them completely rather than return momentum.
ANSWER: Photons have energy. They gain and lose energy by interacting with the gravitational field accordingly, it's been observed on space and in the laboratory. The gravitational field in this case will actually first give the photons momentum and then take it away...but in components since they are traveling transverse to its pull. It's an exceedingly weak effect, taking many light years of travel to alter their angles by microradians.
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QUESTION: Thank you for answer. As it was mentioned before the blue-shift and red-shift happens with light when it was entered and leave massive object. This effect known as time dilation. Based on reference system of massive object with the time dilation the light has higher frequency than light for reference system in empty space. Since than energy of photon depends on its own frequency therefore the energy of light is higher in place close to massive object's location. I would not call it as interaction of light with gravitational field, because this variation of energy of photon could be explained without momentum exchange in pair massive object and photon.
If consider the space dimension in place close to the massive object then it it has nonlinear characteristic in case of changes of time dilation. Therefore in perspective to the reference system without massive object this current place with nonlinear dimension will acting like a lens which changes light direction.
The good analogue is light refraction, where different mediums are a places with different time dilation parameters.
What could prove what electromagnetic wave as light can be attracted by gravitational field with interaction of momentum? Or it's a clue for uniting of gravitational and electromagnetic fields?
You may not want to call it interaction of light with gravitational field, but that's exactly what it is. The gravitational field increased the energy of the light. Yes, it's also consistent with time dilation in the gravitational field, but the energy increase is real and has been measured. Momentum of light also depends on its frequency, and therefore changes as well. The light interacted with the gravitational field, that's not in question. It is definitely not a clue for unifying anything, however, the gravitational force is not based on electromagnetism.