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Gravity can be neither classical nor quantized

I argue that it is possible for a theory to be neither quantized nor classical. We should therefore give up the assumption that the fundamental theory which describes gravity at shortest distances must either be quantized, or quantization must emerge from a fundamentally classical theory. To illustrate my point I will discuss an example for a theory that is neither classical nor quantized, and argue that it has the potential to resolve the tensions between the quantum field theories of the standard model and general relativity.