Can someone give me an example of a conflict between Einstein's relativity and quantum theory?

I've read that relativity explains the workings of the larger universe while quantum theory explains the workings of the very small, such as atoms. I always hear that the two theories conflict but I've never been told anything specific. So, where is it that they disagree?|||The simplest example: instantaneous propagation of information. Special and general relativity postulates that information cannot propagate faster than the speed of light. Mathematically, this says that all field equations must be strictly hyperbolic. However, the Schroedinger equations that governs quantum mechanics is not hyperbolic: mathematically it allows the "probability amplitude" (if you accept the Copenhagen interpretation) of finding a particle at two extremely different parts of space to be related. To illustrate better: consider the photon diffraction experiment. Quantum theory says that the photon can be considered both as a particle and a wave. Now, let's send the photon through a narrow slit. It's wave nature means that it will be diffracted, which can be thought of as the wave becoming a spherical wave propagating from the slit (not unlike the water wave that forms after you toss a pebble into a placid lake). So the radiation can, by the wave nature, reach basically any point on a screen set up on the other side of the slit. On the other hand, the particle nature means that the photon can only shine on a single point of the screen at a time. But the instant you observe the photon hitting a particular point on the screen, you immediately know that the photon cannot have hit any other point on the screen: this indicates an instantaneous transfer of information.





Another common example used for this illustration is the quantum entanglement. By quantum theory, it is possible to send out two particles such that their quantum states are not known before hand, but are guaranteed to be the same: the act of observing one of them serves to tell the state of the other. If you send two such particles in opposite directions a wait a long while, they will be reallly far away from each other. But since observing one changes the state of the other immediately, you have faster than light information transfer.





Much of the above are fixed somewhat in quantum field theory, which reconciles quantum mechanics with special relativity.





With general relativity, however, there is still a problem. A good illustration is the nature of the particle. The particle, an electron for example, are often considered as point masses in quantum theory. But a point mass has no spatial extent, and thus has infinite density, which means that they should create singularities in space-time (mini blackholes) according to general relativity, a notion that is rather absurd as considered by many.|||Thanks!

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