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We have tried to quantize gravity. We have theorized that gravitation as a field has also particle nature, namely graviton. But, till now, we have not been able to prove it. Maybe in future, when we have better instruments, we can detect it.
Now, I will problematize the question a little further. We have been able to quantify light, and we have experimental proofs that photons exist. But, I doubt if we have been able to quantize electrical field, or magnetic field. That is, do we have a particle that travels between two charged bodies to “communicate the force” between them. Same is true for gravitation. Here, another dimension adds: that of bending of the space around a mass or a charge. That, the attraction between two masses or between two charges is nothing but an illustration of that fact that space is not free of the mass or charge, and is warped ( Not wraped or wrapped as you might think ‘warp’ is a misspelled word, to the contrary, it is invented to express the kind of space we are talking about). Space is complex phenomena and a ‘warped space’ will lead to ‘attraction between the two charges or masses kept in it.
Futhermore, it can be seen that space is not anymore a quantity free from the mass or charge. What I mean is this: The mass or charge, before Einstein, were seen as a separate entity from space. we assumed that a charge or a mass is ‘situated’ or ‘kept’ in space, as if space existed outside the realm of mass or charge. But it seems space is much more complex than that. Quantizing gravity or electrical field will have these issues to grapple with.
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