According to certain interpretations of quantum mechanics, particles can indeed appear to "pop into and out of existence" through a phenomenon known as particle creation and annihilation. This behavior is a consequence of the inherent uncertainty and fluctuation at the quantum level.
In quantum field theory, particles are treated as excitations of underlying quantum fields that permeate space. These fields can undergo fluctuations, resulting in the creation or annihilation of particle-antiparticle pairs. These pairs can be created spontaneously and then annihilate each other, effectively appearing and disappearing in a very short timescale.
This phenomenon is described by the Heisenberg uncertainty principle, which states that there is an inherent uncertainty in the measurements of certain pairs of physical quantities, such as energy and time. This uncertainty allows for temporary violations of energy conservation, as long as the violation is within the limits allowed by the uncertainty principle.
Experimental evidence supporting the existence of particle creation and annihilation comes from a variety of sources. One notable example is the observation of the Casimir effect. This effect occurs when two closely spaced parallel conducting plates create a region of reduced quantum fluctuations between them. As a result, there is a net force pushing the plates together, which can be attributed to the creation and annihilation of virtual particle-antiparticle pairs.
Another example is the phenomenon of Hawking radiation. According to Stephen Hawking's theoretical work, black holes can emit radiation due to the creation of particle-antiparticle pairs near the event horizon. One particle falls into the black hole while the other escapes, leading to the appearance of radiation. While this radiation has not been directly observed for astrophysical black holes, its existence is supported by various theoretical and mathematical considerations.
It's important to note that these particle fluctuations are inherent to the quantum nature of the universe and occur on extremely small scales. They do not violate the conservation of energy over longer timescales or macroscopic systems. These fluctuations and the associated creation and annihilation processes are an essential part of quantum field theory, providing a mathematical framework that successfully describes many phenomena in particle physics.