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The question is-"Consider a 3-d surface on which normal Euclidean geometry is valid. Now assume that electromagnetic field is allowed to pervade the whole of the surface . Now what is the possibility that the geometry of the space will be non-euclidean, if the field is assumed to be quantized ?"

The answer being-"Consider a space with n dimension, and which is pervaded by quantized electromagnetic field. Now, initially, the space is assumed to be euclidean, so its curvature is zero. In this flat background space, the quantized electromagnetic field will behave as if normal classical field where the photons will travel in normal field line trajectories. Since the field lines are present, which geometrically speaking are normally parabolic in the vicinity of a charge, the metric of the space will then be defined by the field lines only. Since every point on the field line is a photon which in turn is occupying a point in space. This makes the space non-euclidean, since there cannot be defined any straight line on this space and surely in euclidean space straight lines do exist. "

Now, is the solution correct ? If it is not correct, then why? and else why?

If the solution is correct, what I feel it difficult to comprehend that an EM field can distort the geometry of a space. Plz someone explain it.

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# Can a field disturb the geometry of a space?

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