We discuss the question of how physical statements can be proven over digital communication channels between two parties (a "prover" and a "verifier") residing in two separate local systems. Examples include: (i) "a certain object in the prover's system has temperature X°C", (ii) "two certain objects in the prover's system are positioned at distance X", or (iii) "a certain object in the prover's system has been irreversibly altered or destroyed". As illustrated by these examples, our treatment goes beyond classical security sensors in considering more general physical statements. Another distinctive aspect is the underlying security model: We neither assume secret keys in the prover's system, nor do we suppose classical sensor hardware in his system which is tamper-resistant and trusted by the verifier. Without an established name, we call this new type of security protocol a "virtual proof of reality" or simply a "virtual proof" (VP). In order to illustrate our novel concept, we give example VPs based on temperature sensitive integrated circuits, disordered optical scattering media, and quantum systems. The corresponding protocols prove the temperature, relative position, or destruction/modification of certain physical objects in the prover's system to the verifier. These objects (so-called "witness objects") are prepared by the verifier and handed over to the prover prior to the VP. Furthermore, we verify the practical validity of our method for all our optical and circuit-based VPs in detailed proof-of-concept experiments. Our work touches upon, and partly extends, several established concepts in cryptography and security, including physical unclonable functions, quantum cryptography, interactive proof systems, and, most recently, physical zero-knowledge proofs. We also discuss potential advancements of our method, for example "public virtual proofs" that function without exchanging witness objects between the verifier and the prover.